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Problem 25301

PROBLEMS Show your work for partial credit
1. What is the dollar amount that a Home Insurance policy would pay in each of the following situations?
a. Wind damage of $3,683; the insured has a $1,000 deductible.
b. Theft of a TV worth $2,200; the insured has a $500 deductible.
c. Vandalism that does $945 of damage to a home; the insured has a $1,000 deductible.

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Problem 25302

A cat runs due east 120 feet to a corne After turning through an angle of $67.8^{\circ}$ the cat walks 362 feet to the second corner. Then the cat walks back to the starting point. What is the area of the triangle formed by his path? $\text { [?] } \mathrm{ft}^{2}$
Round to the nearest hundredth.

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Problem 25303

2. Cathy's house burned down, losing household items worth a total of $\$68{,}000$ . Her house was insured for $\$200{,}000$ and her homeowners' policy provided coverage for personal belongings up to $70$ percent of the insured value of the house.
a. Calculate how much personal property insurance coverage Cathy's policy will provide.
b. Will Cathy receive payment for all the items destroyed in the fire?

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Problem 25304

Daily Caloric Intake According to one source, people eat on average 3630 calories per day. If the standard deviation is 325 calories, find the $z$ score for each raw score. Round $z$ scores to at least two decimal places.
Part: $\mathbf{0} / \mathbf{3}$ $\square$
Part 1 of 3
The $z$ score corresponding to 2890 calories is $\square$ .

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Problem 25305

Let $y$ denote the number of broken eggs in a randomly selected carton of one dozen eggs. \begin{tabular}{|c|c|c|c|c|c|} \hline $y$ & 0 & 1 & 2 & 3 & 4 \\ \hline $p(y)$ & 0.60 & 0.25 & 0.10 & 0.03 & 0.02 \\ \hline \end{tabular} (a) Calculate and interpret $\mu_{y}$ . $\mu_{y}=$ $\square$ (b) Consider the following questions. (i) In the long run, for what percentage of cartons is the number of broken eggs less than $\mu_{y}$ ? $\qquad$ \% (ii) Does this surprise you? Yes No (c) Explain why $\mu_{y}$ is not equal to $\frac{0+1+2+3+4}{5}=2.0$ . This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally likely. This computation of the mean is incorrect because the value in the denominator should equal the maximum $y$ value. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when calculating the mean. This computation of the mean is incorrect because it does not take into account the probabilities with which the number of broken eggs need to be weighted.

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Problem 25306

Finding the interest and future value of a simple interest loan or...
To be able to buy a new computer, Kira decides to save for 4 years. She opens a savings account with $\$ 800$ . The account pays simple interest at an annual rate of $5 \%$ . She doesn't make any more deposits. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Kira earn? \ $而 (b) What will the total amount in the account be (including interest)?$ $\$ \square$ $

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Problem 25307

$\begin{aligned} -6.8+2.4 & =-6+(-0.8)+2+0.4 \\ & =?+(-0.8)+0.4 \end{aligned}$ $\qquad$ Break apart the $\qquad$ Add the integ

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Problem 25308

3. Sam Kern has 50/100/25 auto insurance coverage. One day he lost control of his vehicle hitting an Escalade and the Escalade was shoved into a Corvette. Damage to the Escalade was $\$17,864$ , and damage to the Corvette was $\$21,520$ .
a. What dollar amount of damages will the insurance company pay?
b. What dollar amount of damages will Sam have to pay?

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Problem 25309

()) What is the perimeter of the shape? 4)） $\square$ centimeters

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Problem 25310

$x+y=1$
Use the graphing tool to graph the equation. Click to enlarge graph

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Problem 25311

) : The parallelogram $D^{\prime} E^{\prime} F^{\prime} G^{\prime}$ is a dilation of the parallelogram $D E F G$ . What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number. $\square$

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Problem 25312

A gun has muzzle speed $146$ m/s. Find two angles of elevation (in degrees) that can be used to hit a target $830$ m away. (Enter your answers as a comma-separated list. Round your answers to one decimal place. Use $g = 9.8$ m/s².) $\alpha =$

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Problem 25313

Keisha made \$144 for 8 hours of work. At the same rate, how much would she make for 13 hours of work?

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Problem 25314

Find the phase shift, amplitude, and period of the function. $y=-1+\sin (2 \pi x-\pi)$ Give the exact values, not decimal approximations

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Problem 25315

Find the length s of the are of a circle of ractus 10 miles subterided by the centrat angle $t 9^{\circ}$ . s (arc length) $=$ $\square$ miles (Type an integer or decimal rounded to three decimal places as needed.)

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Problem 25316

Suppose an element is undergoing radioactive decay Determine the decay constant $\lambda$ if a 10 mg sample decays to 8 mg after 5 years.

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Problem 25317

*6. A bungee jumper of mass 54.5 kg (including safety gear) is standing on a platform 85.0 m above a river. The length of the unstretched bungee cord is 10.1 m . The force constant of the cord is $58.5 \mathrm{~N} / \mathrm{m}$ . The jumper falls from rest. The cord acts like an ideal spring. Use conservation of energy to determine the jumper's height above the river when he is travelling at $9.47 \mathrm{~m} / \mathrm{s}$ [down] on the first fall (when the string is actually stretched). Assume air resistance is negligible. Number 6 is tough, you'll need to use the quadratic formula

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Problem 25318

$\int 2x \cdot 1(x^2 - 3)^5 dx$ by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant. Answer:

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Problem 25319

$\text{Using Table 8.1 from Section 8.1 of the OpenStax textbook entitled Chemistry 2E by Flowers, Leopold et al., mark the following bond lengths from shortest to longest, with 1 being the shortest:}$
\begin{align} \text{C-H} & \quad \square \\ \text{C-C} & \quad \square \\ \text{C=C} & \quad \square \\ \text{H-H} & \quad \square \\ \text{C} \equiv \text{C} & \quad \square \\ \end{align}
\text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.}
\text{Dialogue Transcript:}
\text{assistant:} \text{Hello! It looks like you're trying to order the bond lengths from shortest to longest using information from Table 8.1 in the Chemistry 2E textbook. However, I don't have access to the table itself, so I need a bit more information to help you.}
\text{Could you please provide the bond lengths from Table 8.1 for the following bonds: C-H, C-C, C=C, H-H, and C≡C?}
\text{Once you share that information, I can help you arrange the bond lengths in the order you're looking for!}
\text{user:} \text{I uploaded an image and extracted the following:} \text{* Text: $\mathrm{CH}_{2} \mathrm{C}_{6} \mathrm{H}_{5}$ (a common paint thinner) requires $3 / 5.5 \mathrm{KJ} / \mathrm{mol}$ .} \text{Representative Bond Energies and Lengths} \begin{tabular}{|c|c|c|c|c|c|} \hline \text{Bond} & \text{Length (pm)} & \text{Energy (kJ/mol)} & \text{Bond} & \text{Length (pm)} & \text{Energy (kJ/mol)} \\ \hline \text{H-H} & 74 & 436 & \text{C-O} & 140.1 & 358 \\ \hline \text{H-C} & 106.8 & 413 & \text{C=O} & 119.7 & 745 \\ \hline \text{H-N} & 101.5 & 391 & \text{C} \equiv \text{O} & 113.7 & 1072 \\ \hline \text{H-O} & 97.5 & 467 & \text{H-Cl} & 127.5 & 431 \\ \hline \text{C-C} & 150.6 & 347 & \text{H-Br} & 141.4 & 366 \\ \hline \text{C=C} & 133.5 & 614 & \text{H-I} & 160.9 & 298 \\ \hline \text{C} \equiv \text{C} & 120.8 & 839 & \text{O-O} & 148 & 146 \\ \hline \text{C-N} & 142.1 & 305 & \text{O=O} & 120.8 & 498 \\ \hline \text{C=N} & 130.0 & 615 & \text{F-F} & 141.2 & 159 \\ \hline \text{C} \equiv \text{N} & 116.1 & 891 & \text{Cl-Cl} & 198.8 & 243 \\ \hline \end{tabular} \text{Table 8.1}$

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Problem 25320

The students in Jayce's grade voted to select a guest speaker. $20\%$ of the students voted for a famous athlete. If there are 65 students in Jayce's grade, how many students voted for the athlete? students

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Problem 25321

16. (14 pts) What is the $H_3O^+$ ion concentration of a dimethylamine, $(CH_3)_2NH$ , solution prepared by dissolving 0.0425 mol of base in a glass of water to give 135 mL solution? pK $_{b}$ for dimethylamine is 3.27.
a. Write the chemical equation for the $(CH_3)_2NH$ dissociation in water.
$M = \frac{mol}{L} = \frac{0.0425 \text{ mol}}{0.135 \text{ L}} = 0.315 \text{ M}$
$(CH_3)_2NH + H_2O \rightleftharpoons (CH_3)_2NH_2^+ + OH^-$
b. Calculate the $H_3O^+$ ion concentration for
$K_b = 10^{-3.27}$
00310

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Problem 25322

Which two substances are covalent compounds?
1. $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})$ and $\mathrm{KI}(\mathrm{s})$
2. $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})$ and $\mathrm{HCl}(\mathrm{g})$
3. $\mathrm{KI}(\mathrm{s})$ and $\mathrm{NaCl}(\mathrm{s})$
4. $\mathrm{NaCl}(\mathrm{s})$ and $\mathrm{HCl}(\mathrm{g})$

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Problem 25323

Question 68
Find all zeros of $f(x)=x^{3}-7 x^{2}+9 x+$ not decimal approximations.

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Problem 25324

Which type of substance can conduct electricity in the liquid phase but not in the solid phase?
1. ionic compound
2. molecular compound
3. metallic element
4. nonmetallic element Submit Answer

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Problem 25325

Find the sum. $\frac{1}{5} + \frac{4}{5} + \frac{4^2}{5} + \frac{4^3}{5} + \dots + \frac{4^{n-1}}{5}$ Complete the sum of the sequence. $S_n = \Box(\Box^n - 1)$ (Type an integer or a simplified fraction.)

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Problem 25326

$\frac{(f_o - f_e)^2}{f_e} = \frac{(\text{Observed cell frequency} - \text{Expected cell frequency})^2}{\text{Expected cell frequency}}$

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Problem 25327

Find the unit rate that helps you solve the problem. How many inches are in $10$ feet?
$10$ feet $\times$ ______ $=$ $?$ inches
$\frac{1 \text{ inch}}{12 \text{ feet}}$
$\frac{1 \text{ foot}}{12 \text{ inches}}$
$\frac{12 \text{ inches}}{1 \text{ foot}}$
$\frac{12 \text{ feet}}{1 \text{ inch}}$

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Problem 25328

Match each polynomial expression to its additive inverse. $6x^2 + x - 2$ $-6x^2 - x - 2$ $6x^2 - x + 2$ $-6x^2 + x - 2$ $-6x^2 + x - 2$ $6x^2 - x + 2$ $-6x^2 - x + 2$ $6x^2 + x + 2$

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Problem 25329

1 2 $=3$ $\checkmark 4$ 6 7 5 8 9 10
High Blood Pressure Twenty-one percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probability. Round your answers to at least 3 decimal places.
Part 1 of 3 (a) None will have high blood pressure. $P($ none have high blood pressure $)=0.025$
Part 2 of 3 (b) One-half will have high blood pressure. $P$ (one-half have high blood pressure) $=0.007$
Part: $2 / 3$
Part 3 of 3 (c) Exactly 7 will have high blood pressure. $P($ exactly 7 have high blood pressure $)=$ $\square$

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Problem 25330

Complete the following truth table. Use T for true and F for false. You may add more colymon put those added columns will not be graded. \begin{tabular}{|c|c|c|c|} \hline $p$ & $q$ & $\sim q \rightarrow \sim p$ & $\sim p \rightarrow \sim q$ \\ \hline T & T & $\square$ & $\square$ \\ \hline T & F & $\square$ & $\square$ \\ \hline F & T & $\square$ & $\square$ \\ \hline F & F & $\square$ & $\square$ \\ \hline \end{tabular} $\left\{\begin{array}{ccc}p & q & \\ \sim \square & \square \wedge \square & \square \vee \square \\ \square \rightarrow \square & \square \mapsto \square & \\ x & 5\end{array}\right.$

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Problem 25331

Use curl to determine whether the vector field $\mathbf{F} = \langle 3x^6 y, x^7 + 3y^8 z, y^9 \rangle$ is conservative.
(a) Find curl $\mathbf{F}$ .
curl $\mathbf{F}$ = $\langle \hphantom{a}, \hphantom{a}, \hphantom{a} \rangle$ .
Question Help: Video Message instructor Submit Part

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Problem 25332

Find all values of x in the interval $[0, 2\pi]$ that satisfy the equation. (Enter your answers as a comma-separated list.)
$2 \sin(x) = 2 \tan(x)$
x =

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Problem 25333

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$

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Problem 25334

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$ b) $g(x) = x^3 + 3x^2 - 4x - 12$

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Problem 25335

[-/5.43 Points] DETAILS LARPCALC11 7.3.026.MI.
Solve the system of linear equations and check any solution algebraically. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express $x$ , $y$ , and $z$ in terms of the real number $a$ .) $\begin{cases} 2x + 4y + z = 5 \\ x - 2y - 3z = 1 \\ x + y - z = -1 \end{cases}$ $(x, y, z) = ($

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Problem 25336

Find the inverse of the one-to-one function. $f(x)=(x+5)^{3}$ $f^{-1}(x)=$ $\square$ (Type an exact answer, using radicals as needec

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Problem 25337

Evaluate the integral. $\int \frac{\sin(2t+7)}{\cos^2(2t+7)}dt$ $\int \frac{\sin(2t+7)}{\cos^2(2t+7)}dt =$

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Problem 25338

If $PQ = 37$ , $QO = 32$ , $PO = 42$ , $TR = 16$ , and $SR = 21$ , find the perimeter of $\triangle RST$ . Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

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Problem 25339

Question 8 Complete the following, based off of Video #5: Compare the following decimals: $0.50 ? 0.5$ 2 pts

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Problem 25340

Question 4
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a $z$ -score of 0.3571 (to 4 decimal places) $\square$

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Problem 25341

What is the meaning of this expression? $6^3$
$6^3 = \square$ (Type your answer as a product. Do not simplify.)

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Problem 25342

A race is $\frac{7}{10}$ kilometers long. Aldo ran 9 of these races. How far did he run altogether?
Write your answer in simplest form.

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Problem 25343

Question 5
A survey of athletes at a high school is conducted, and the following facts are discovered: $40 \%$ of the athletes are football players, $22 \%$ are basketball players, and $15 \%$ of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?
Probability = $\square$ \% (Please enter your answer as a percent)

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Problem 25344

Convert. When necessary, express your answer as a decimal.
1) 36 feet = \_\_\_\_\_ yards 2) 264 inches = \_\_\_\_\_ feet 3) 6 miles = \_\_\_\_\_ yards 4) 15,480 yards = \_\_\_\_\_ miles 5) 3 miles = \_\_\_\_\_ feet 6) 400 ounces = \_\_\_\_\_ pounds 7) 32 pounds = \_\_\_\_\_ ounces 8) 7.25 tons = \_\_\_\_\_ pounds 9) 11,000 pounds = \_\_\_\_\_ tons 10) 15 minutes = \_\_\_\_\_ seconds 11) $8\frac{1}{2}$ hours = \_\_\_\_\_ minutes 12) 49 weeks = \_\_\_\_\_ days 13) 8 pints = \_\_\_\_\_ cups 14) 14 quarts = \_\_\_\_\_ gallons

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Problem 25345

Question 6
In a large population, $55 \%$ of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal to 4 places.

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Problem 25346

Giving a test to a group of students, the grades and gender are summarized below Grades and Gender \begin{tabular}{|c|r|r|r|r|} \hline & \multicolumn{1}{|c|}{ A } & B & C & Total \\ \hline Male & 19 & 10 & 18 & $\mathbf{4 7}$ \\ \hline Female & 2 & 3 & 9 & $\mathbf{1 4}$ \\ \hline Total & $\mathbf{2 1}$ & $\mathbf{1 3}$ & $\mathbf{2 7}$ & $\mathbf{6 1}$ \\ \hline \end{tabular}
If one student is chosen at random, find the probability that the student was female AND got a "C". Round your answer to 4 decimal places. $\square$

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Problem 25347

(5) $78 \text{ ounces} = \frac{\phantom{00}}{} \text{ cups}$ (6) $200 \text{ cups} = \frac{\phantom{00}}{} \text{ gallons}$

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Problem 25348

1) 36 centimeters = millimeters 2) 890 millimeters = centimeters 3) 3800 meters = kilometers 4) 11.5 kilometers = meters 5) 1.5 meters = millimeters 6) 0.0815 meters = centimeters 7) 65,000 mm = km 8) 75 mm = meters 9) 14 centimeters = meters 10) 70 meters = centimeters 11) 1200 meters = kilometers 12) 3.2 kilometers = meters 13) 80 meters = millimeters 14) 0.5 kilometers = meters 15) 137 centimeters = meters 16) 10.2 centimeters = millimeters 17) 43,000 millimeters = meters 18) 71 meters = millimeters

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Problem 25349

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b). Click the icon to view some finance formulas. Principal: $\$8500$ Rate: $3.5\%$ Compounded: monthly Time: 5 years
a. Find how much money there will be in the account after the given number of years. The amount of money in the account after 5 years is $\$$ _____. (Round to the nearest hundredth as needed.)

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Problem 25350

Find B-A
$A = \begin{bmatrix} 9 & 2 \\ 9 & 1 \end{bmatrix}$ $B = \begin{bmatrix} -8 & 2 \\ 9 & -9 \end{bmatrix}$
B-A=☐

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Problem 25351

A newsgroup is interested in constructing a 90\% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 546 randomly selected Americans surveyed, 403 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With $90 \%$ confidence the proportion of all Americans who favor the new Green initiative is between $\square$ and $\square$ b. If many groups of 546 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About $\square$ percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about $\square$ percent will not contain the true population proportion.

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Problem 25352

Question 13
In a recent poll, 580 people were asked if they liked dogs, and 68\% said they did. Find the Margin of Error for this poll, at the $99 \%$ confidence level. Give your answer to four decimal places if possible. $\square$

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Problem 25353

12) 732 mg = \_\_\_\_\_ g 13) 76 t = \_\_\_\_\_ kg 14) 0.054 t = \_\_\_\_\_ kg 15) 43,000 mg = \_\_\_\_\_ kg 16) Add: 320 g + 8 kg + 870 mg = \_\_\_\_\_\_\_

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Problem 25354

Question 8 Complete the following, based off of Video #5: Compare the following decimals: $0.50 ? 0.5$
Question 9 Which video was your favorite out of the 5? Why was it your favorite? 2 pts

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Problem 25355

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a black 2.
The probability is $\boxed{}$ . (Simplify your answer. Type an integer or a fraction.)

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Problem 25356

Aisha wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 77 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.1 and a standard deviation of 1.7. What is the $80 \%$ confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Assume the data is from a normally distributed population. Round answers to 3 decimal places where possible. $\square$ $<\mu<$ $\square$

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Problem 25357

$\int_0^{16} \sin(\sqrt{x}) \, dx, \quad n = 4$

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Problem 25358

Step 1
The angle whose tangent is $\sqrt{3}$ is the angle whose sine and cosine functions have the same sign the same sign.
Step 2 So, one such angle in Quadrant I is $\begin{aligned} \tan (\theta) & =\sqrt{3} \\ & =\frac{\pi}{3} \frac{\pi 3}{3} \end{aligned}$
Step 3
But the sine and cosine functions have the same sign if $\theta$ is in Quadrant $\begin{aligned} \tan (\theta) & =\sqrt{3} \\ & =\frac{(\sqrt{2} \pi}{3} \end{aligned}$ Submit Skip (you cannot come back) Need Help? Read It Submit Answer

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Problem 25359

Question Select the statement that is the contrapositive of the following statement: If it's good weather, then we can go to the beach.
Answer
If it's good weather, then we can't go If we can't go to the beach, then it's to the beach. not good weather.
If we can go to the beach, then it's If it's not good weather, then we can't good weather. go to the beach.

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Problem 25360

Find the limit of the sequence $a_n = \frac{(2n-1)!}{(2n+1)!}$

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Problem 25361

$2 \sin \left(x+\frac{\pi}{6}\right)-1=0$

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Problem 25362

Find $g$ .
$30^\circ$ E G $133^\circ$ $f$ $g$ $9$ F Write your answer as an integer or as a decimal rounded to the nearest tenth. $g =$

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Problem 25363

Perimeter, Area, and Volume Area of a piecewise rectangular figure Find the area of the figure. (Sides meet at right angles.) 8 cm 3 cm 5 cm 5 cm 5 cm $2$ cm²

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Problem 25364

22 Solve the following quadratic equations by square roots. Write all answers in simplest form.
$3x^2 - 108 = 0$
$x^2 = 36$
Solution(s):

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Problem 25365

$9x^2 - 16 = 0$ $x^2 =$ Solution(s):

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Problem 25366

Déterminez l'abscisse à l'origine de la fonction affine suivante

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Problem 25367

\begin{tabular}{cccc} & Bachelor's & Master's & Doctorate \\ Men & 653,037 & 313,838 & 25,771 \\ Women & 687,564 & 315,906 & 25,253 \end{tabular}
Send data to Excel
Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.
Part 1 of 4 (a) What is the probability that the degree is a bachelor's degree? $P(\text { bachelor's degree })=0.663$
Part 2 of 4 (b) What is the probability that the degree was a master's degree or a degree awarded to a women? $P(\text { master's degree or awarded to woman })=0.664$
Part: 2 / 4
Part 3 of 4 (c) What is the probability that the degree was a bachelor's degree awarded to a men. $P(\text { bachelor's degree awarded to men })=$ $\square$ Skip Part Check Save For Later Submit Assianm

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Problem 25368

An acceptance speech gives thanks for a gift, an award, or some other form of public recognition. True or False True False

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Problem 25369

Part 1 of 3 Points: 0 of 1 Save
Question list A sample of blood pressure measurements is taken for a group of adults, and those values ( mm Hg ) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two samples; then compare the variation. \begin{tabular}{rrrrrrrrrrr} Systolic & 120 & 128 & 159 & 95 & 155 & 121 & 115 & 137 & 126 & 119 \\ Dᄆ 5 \\ Diastolic & 82 & 78 & 76 & 52 & 91 & 87 & 57 & 65 & 70 & 80 \end{tabular}
Question 19
Question 20 The coefficient of variation for the systolic measurements is $\square$ \%. (Type an integer or decimal rounded to one decimal place as needed.) Question 21
Question 22
Question 23
Question 24 Clear all Check answer Dec 8 10:43 US

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Problem 25370

3. Вычислить интеграл: a) $\int \frac{d x}{2 x+4}$ b) b) $\int_{0}^{2}\left(x^{2}+\sin x\right) d x$ c) $\int_{-1}^{3} \frac{d x}{1+9 x^{2}}$

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Problem 25371

1. Найти предел функции: a) $\lim _{x \rightarrow 5} \frac{x+1}{x-5}$ b) $\lim _{x \rightarrow \infty} \frac{2-x+3 x^{3}}{-4 x^{2}+9 x^{6}}$ $v_{c} \lim _{x \rightarrow 0} \frac{\sqrt{1+3 x}-\sqrt{1-2 x}}{x^{2}+5 x}$ d) $\lim _{x \rightarrow 1} \frac{x^{4}-1}{2 x^{4}-x^{2}-1}$

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Problem 25372

2. Вычислить производную функции: a) $y=10 x^{3}+\frac{3}{x \sqrt{x}}-\frac{4}{5} x^{-\frac{1}{4}}$ b) $y=\sin x \cdot \ln x$

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Problem 25373

4. Решить дифферениальнее ураввение: a) $\sin ^{2} x d y+(2 y+1) d x=0$ b) $y+x y^{\prime}=0$

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Problem 25374

The velocity function (in meters per second) is given for a particle moving along a line. $v(t)=5 t-9, \quad 0 \leq t \leq 3$ (a) Find the displacement. $\qquad$ m (b) Find the distance traveled by the particle during the given time interval. $\qquad$ m Need Help? Road It Watch It

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Problem 25375

Question 14 of 25 (1 point) | Question Attempt: 1 or I
College Degrees Awarded The table below represents the college degrees awarded in a recent academic year by Español gender. \begin{tabular}{cccc} & Bachelor's & Master's & Doctorate \\ \hline Men & 548,254 & 251,468 & 23,728 \\ Women & 609,872 & 270,538 & 23,320 \end{tabular} Send data to Excel
Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.
Part: $0 / 4$ $\square$
Part 1 of 4 (a) What is the probability that the degree is a doctorate? $P(\text { doctorate })=0.027$ $\square$
Part: $1 / 4$ $\square$
Part 2 of 4 (b) What is the probability that the degree was a bachelor's degree or a degree awarded to a men? $P(\text { bachelor's degree or awarded to men })=$ $\square$ Next Part

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Problem 25376

Q2)(3Pts) When two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass ( $m_1$ =3kg, $m_2$ =9kg) as in Figure 1, the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to determine the value of $g=9.8 m/s^2$ . The magnitude of the acceleration ( $m/s^2$ ) of the two objects is around: A) 1.6 B) 7.0 C) 4.9 D) 5.9 E) 4.2

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Problem 25377

Identify the transformation based on the coordinates below. Figure 1: $E$ (-9, 3), $F$ (-8, 5), $G$ (-5, 5), $H$ (-4, 3) Figure 1': $E'$ (9, -3), $F'$ (8, -5), $G'$ (5, -5), $H'$ (4, -3) $90^\circ$ rotation (clockwise) $180^\circ$ rotation dilation

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Problem 25378

The opposite figure represents a part of an electric circuit, then the potential of the point (y) is ........... a) + 3.6 V b) - 3.6 V c) + 8.4 V $V_x = 2.4$ V $R = 5$ Ω $I = 1.2$ A d) - 8.4 V

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Problem 25379

Triangle $ABC$ will be rotated $90^\circ$ counter-clockwise about the origin. What will be the resulting coordinate of Point $A'$ ?

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Problem 25380

Your teacher has $\frac{1}{5}$ of a bag of candy to give to 5 students. What fraction of the bag of candy will each student get?

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Problem 25381

The fraction $\frac{1}{2}$ is shaded in the diagram below. Divide $\frac{1}{2}$ into 3 equal parts. What is the size of each part? 0 $\frac{1}{4}$ $\frac{1}{2}$ $\frac{3}{4}$ 1

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Problem 25382

Distinguishing between the area and perimeter of a rectangle
$67 \text{ yd}$ $87 \text{ yd}$
(a) Use the calculator to find the area and perimeter of the parking lot. Make sure to include the correct units. Area: $5829 \text{ yd}^2$ Perimeter: $308 \text{ yd}$
(b) The lot will be paved. Which measure would be used in finding the amount of pavement needed? Perimeter Area
(c) A chain will surround the lot. Which measure would be used in finding the amount of chain needed? Perimeter Area
$\text{yd}$ $\text{yd}^2$ $\text{yd}^3$ $\times$

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Problem 25383

4. A bath tub is in the shape of a rectangular prism 1.6 m long, 90 cm wide and 35 cm high. The depth of water in the tub is 20 cm. A child begins throwing cylindrical solids of radius 5 cm and height 15 cm into the tub. Find to two decimal places:
a the volume of the water in the tub initially $50400 \text{cm}^3$
b the volume of one cylindrical solid $235.5 \text{cm}^3$
c the volume of water displaced by 8 solids
d the sum of the volume of water and the volume of 8 solids
e the depth of water in the pool after 8 solids have been thrown in

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Problem 25384

Q3 $AB$ is a uniform rod of length 5m and weight 20N. In these diagrams $AB$ is resting in a horizontal position on supports at $C$ and $D$ . In each case, find the magnitudes of the reactions at $C$ and $D$ . 1m $C$ 3m $D$ 1m $B$ $A$
1. Find eq of resultant force
2. Find eq

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Problem 25385

Question 5
The cost of a ticket to the circus is $\$23.00$ for children and $\$39.00$ for adults. On a certain day, attendance at the circus was 1,000 and the total gate revenue was $\$32,600$ . How many children and how many adults bought tickets?
The number of children was $(\qquad)$ and the number of adult was $(\qquad)$ Submit Question

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Problem 25386

In the opposite figure : $x + y + z = \dots$ (a) 15 (b) 18.2 (c) 22 (d) 22.2 9cm. 7cm. 12cm. $x$ cm. $y$ cm.

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Problem 25387

12) $\operatorname{sech} x$ is equal to $4 \frac{2}{e^{x}-e^{-x}}$ B. $\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$ c. $\frac{2}{e^{x}+e^{-x}}$ D. $\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}$ 13.) To evaluate the $\int \sin ^{2} \theta d \theta$ , we use the identity/formula A. $\sin ^{2} \theta=\frac{1}{\csc ^{2} \theta}$ C. $\sin ^{2} \theta=\frac{1}{2}(1+\csc 2 \theta)$ B. $\sin ^{2} \theta=1-\cos ^{2} \theta$ D. $\sin ^{2} \theta=\frac{1}{2}(1-\cos 2 \theta)$ 14) Evaluate: $\int \frac{\sec 20 \text { ton } 20 d s}{\sec 2 \theta+4}$ A. $\frac{1}{2} \ln |\sec 20+4| r 0$ C. $\ln |\sec 2 \theta+4|+c$
B $2 \ln |\sec 2 \theta+4|+C$ D. $\frac{1}{2} \tan ^{-1} \frac{\sec \theta}{2}+C$ 15.) $\int x^{2} \ln (x+1) d x$ can best be evahated by
4. Logarithmic Formula B. Gesenal pewer formula C. Algebraic substitution D. Integration by Ponts 16.) To evaluate $\int \tan \sqrt{x+1} d x$ A. let $u=\sqrt{x+1}$ and $d u=d x$ a lit $u=\sqrt{x+1}$ and $2 u d u=d x$ c. let $u=\sqrt{x+1}$ and $d u=\frac{d x}{2 \sqrt{x+1}}$
0. use $\int \tan u d n$ formulo right autay

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Problem 25388

Homework Progress ations $\begin{array}{l} 2 x-5 y=9 \\ 3 x+4 y=2 \end{array}$
Optional working

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Problem 25389

$\int_{0}^{\pi} \frac{\sin ^{3}(x)}{1+\cos ^{2}(x)} d x$

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Problem 25390

Find the equations to the tangents from the origin to the circle $x^{2}+y^{2}-6 x-3 y+9=0$ the coordinates of their points of contacts.

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Problem 25391

Compound Probability Score: 3/4 Penalty: none
Question Watch Video Show Examples A bag contains 6 red marbles, 7 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10ooth, that both marbles drawn will be green?

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Problem 25392

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $\$ 21,714$ The variable costs will be $\$ 10.75$ per book. The publisher will sell the finished product to bookstores at a price of $\$ 21.25$ per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

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Problem 25393

Math 142-8111 (FA'24) in Canvas andres salazar 12/09/24 3:54 AM Homework: HW \#12: Sections 9.1-9.3 Question 38, 9.3.6-T HW Score: $64.3 \%, 32.15$ of 50 points Part 1 of 6 Points: 0 of 1 Save
Question list Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below. \begin{tabular}{lllcccccc} \hline Male & 15,710 & 27,243 & 1359 & 7676 & 19,266 & 15,734 & 13,532 & 25,101 \\ \hline Female & 24,464 & 13,027 & 18,834 & 17,762 & 12,841 & 16,316 & 15,904 & 19,201 \\ \hline \end{tabular} Question 37 Question 38 Question 39 Question 40 a. Use a 0.01 significance level to test the claim that among couples, males speak fewer words in a day than females.
In this example, $\mu_{d}$ is the mean value of the differences $d$ for the population of all pairs of data, where each individual difference $d$ is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test? $\mathrm{H}_{0}=\mu_{\mathrm{d}}$ $\square$ word(s) $\mathrm{H}_{1}=\mu_{\mathrm{d}}$ $\square$ $\square$ word(s) (Type integers or decimals. Do not round.) Question 41 Question 42

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Problem 25394

問 78 次の球面の方程式を求めよ。 (1) 中心が点 $\mathrm{A}(1,-\sqrt{2}, \sqrt{5})$ で，原点を通る球面。 (2) 2 点 $\mathrm{B}(1,3,5), \mathrm{C}(7,9,11)$ が直径の両端である球面. (3) 4 点 $\mathrm{D}(0,0,0), \mathrm{E}(2,0,0), \mathrm{F}(0,4,0), \mathrm{G}(0,0,-6)$ を通る球面.

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Problem 25395

Homework: HW \#12: Sections 9.1-9.3 Question 40, 9.3.11-T HW Score: $71.53 \%, 35.76$ of 50 points Part 1 of 6 Points: 0 of 1 Save
Question list Question 40 Question 41 */, Question 42 x/s Question 43 Question 44 Question 45
The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below. \begin{tabular}{lllllllllll} \hline Actress (years) & 25 & 25 & 33 & 26 & 39 & 28 & 24 & 41 & 33 & 37 \\ \hline Actor (years) & 60 & 40 & 33 & 38 & 31 & 33 & 49 & 42 & 34 & 43 \\ \hline \end{tabular} a. Use the sample data with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors). In this example, $\mu_{\mathrm{d}}$ is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress's age minus the actor's age. What are the null and altermative hypotheses for the hypothesis test? $\mathrm{H}_{0}: \mu_{\mathrm{d}}$ $\square$ year(s) $\mathrm{H}_{1}: \mu_{\mathrm{d}}$ $\square$ years) (Type integers or decimals. Do not round.)
Help me solve this View an example Get more help - Clear all check answer

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Problem 25396

$\begin{array}{l}\cdot \ln \left(e^{9}\right)=9 \\ \cdot e^{\ln (8)}=8 \\ \cdot e^{\ln (\sqrt{13})}=\sqrt{13} 0^{6} \\ \cdot \ln \left(\sqrt[3]{e^{5}}\right)=\square \\ \cdot \ln \left(\frac{1}{e^{5}}\right)=\square\end{array}$

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Problem 25397

Which sign makes the statement true? $\frac{2}{3} ? \frac{8}{12}$

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Problem 25398

Suppose $X \sim N(2, 6)$ . What value of $x$ has a $z$ -score of three?

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Problem 25399

```latex Gegeben sei die Funktion $f(x) = x^2 \cdot e^{-x}$ . Verwenden Sie den Formansatz $F(x) = (ax^2 + bx + c) \cdot e^{-x}$ , um die Stammfunktion von $f(x)$ zu bestimmen. Erläutern Sie in einem kurzen Text, wie man durch diesen Formansatz an die Stammfunktion gelangt.

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Problem 25400

題 59. 次の球面の方程式を求めよ. (1) 2 点 $\mathrm{A}(1,-1,3), \mathrm{B}(-3,5,3)$ が直径の両端である球面。 2) 4 点 $C(0,1,0), D(2,1,2), E(4,1,0), F(2,-1,0)$ を通る球面.

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Solve

Problem 25301

Problem 25302

Problem 25303

Problem 25304

Problem 25305

Problem 25306

Problem 25307

−6.8+2.4=−6+(−0.8)+2+0.4=?+(−0.8)+0.4\begin{aligned} -6.8+2.4 & =-6+(-0.8)+2+0.4 \\ & =?+(-0.8)+0.4 \end{aligned}−6.8+2.4​=−6+(−0.8)+2+0.4=?+(−0.8)+0.4​ \qquad Break apart the \qquad Add the integ

Problem 25308

Problem 25309

()) What is the perimeter of the shape? 4)） □\square□ centimeters

Problem 25310

x+y=1x+y=1x+y=1Use the graphing tool to graph the equation. Click to enlarge graph

Problem 25311

Problem 25312

A gun has muzzle speed 146146146 m/s. Find two angles of elevation (in degrees) that can be used to hit a target 830830830 m away. (Enter your answers as a comma-separated list. Round your answers to one decimal place. Use g=9.8g = 9.8g=9.8 m/s².) α=\alpha =α=

Problem 25313

Keisha made \$144 for 8 hours of work. At the same rate, how much would she make for 13 hours of work?

Problem 25314

Find the phase shift, amplitude, and period of the function. y=−1+sin⁡(2πx−π)y=-1+\sin (2 \pi x-\pi)y=−1+sin(2πx−π) Give the exact values, not decimal approximations

Problem 25315

Find the length s of the are of a circle of ractus 10 miles subterided by the centrat angle t9∘t 9^{\circ}t9∘. s (arc length) === □\square□ miles (Type an integer or decimal rounded to three decimal places as needed.)

Problem 25316

Suppose an element is undergoing radioactive decay Determine the decay constant λ \lambda λ if a 10 mg sample decays to 8 mg after 5 years.

Problem 25317

Problem 25318

∫2x⋅1(x2−3)5dx\int 2x \cdot 1(x^2 - 3)^5 dx∫2x⋅1(x2−3)5dx by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant. Answer:

Problem 25319

Problem 25320

The students in Jayce's grade voted to select a guest speaker. 20%20\%20% of the students voted for a famous athlete. If there are 65 students in Jayce's grade, how many students voted for the athlete? students

Problem 25321

Problem 25322

Problem 25323

Question 68Find all zeros of f(x)=x3−7x2+9x+f(x)=x^{3}-7 x^{2}+9 x+f(x)=x3−7x2+9x+ not decimal approximations.

Problem 25324

Which type of substance can conduct electricity in the liquid phase but not in the solid phase?1. ionic compound2. molecular compound3. metallic element4. nonmetallic element Submit Answer

Problem 25325

Problem 25326

Problem 25327

Problem 25328

Problem 25329

Problem 25330

Problem 25331

Problem 25332

Find all values of x in the interval [0,2π] [0, 2\pi] [0,2π] that satisfy the equation. (Enter your answers as a comma-separated list.)2sin⁡(x)=2tan⁡(x) 2 \sin(x) = 2 \tan(x) 2sin(x)=2tan(x)x =

Problem 25333

5. List all real solutions for each polynomial function. a) f(x)=x3−4x2−7x+10f(x) = x^3 - 4x^2 - 7x + 10f(x)=x3−4x2−7x+10

Problem 25334

5. List all real solutions for each polynomial function. a) f(x)=x3−4x2−7x+10f(x) = x^3 - 4x^2 - 7x + 10f(x)=x3−4x2−7x+10 b) g(x)=x3+3x2−4x−12g(x) = x^3 + 3x^2 - 4x - 12g(x)=x3+3x2−4x−12

Problem 25335

Problem 25336

Find the inverse of the one-to-one function. f(x)=(x+5)3f(x)=(x+5)^{3}f(x)=(x+5)3 f−1(x)=f^{-1}(x)=f−1(x)= □\square□ (Type an exact answer, using radicals as needec

Problem 25337

Evaluate the integral. ∫sin⁡(2t+7)cos⁡2(2t+7)dt\int \frac{\sin(2t+7)}{\cos^2(2t+7)}dt∫cos2(2t+7)sin(2t+7)​dt ∫sin⁡(2t+7)cos⁡2(2t+7)dt=\int \frac{\sin(2t+7)}{\cos^2(2t+7)}dt = ∫cos2(2t+7)sin(2t+7)​dt=

Problem 25338

If PQ=37PQ = 37PQ=37, QO=32QO = 32QO=32, PO=42PO = 42PO=42, TR=16TR = 16TR=16, and SR=21SR = 21SR=21, find the perimeter of △RST\triangle RST△RST. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Problem 25339

Question 8 Complete the following, based off of Video #5: Compare the following decimals: 0.50?0.50.50 ? 0.50.50?0.5 2 pts

Problem 25340

Question 4Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a zzz-score of 0.3571 (to 4 decimal places) □\square□

Problem 25341

What is the meaning of this expression? 636^36363=□6^3 = \square63=□ (Type your answer as a product. Do not simplify.)

Problem 25342

A race is 710\frac{7}{10}107​ kilometers long. Aldo ran 9 of these races. How far did he run altogether?Write your answer in simplest form.

Problem 25343

Problem 25344

Problem 25345

Question 6In a large population, 55%55 \%55% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?Give your answer as a decimal to 4 places.

Problem 25346

Problem 25347

(5) 78 ounces=00 cups78 \text{ ounces} = \frac{\phantom{00}}{} \text{ cups}78 ounces=00​ cups (6) 200 cups=00 gallons200 \text{ cups} = \frac{\phantom{00}}{} \text{ gallons}200 cups=00​ gallons

Problem 25348

Problem 25349

Problem 25350

Find B-AA=[9291]A = \begin{bmatrix} 9 & 2 \\ 9 & 1 \end{bmatrix}A=[99​21​] B=[−829−9]B = \begin{bmatrix} -8 & 2 \\ 9 & -9 \end{bmatrix}B=[−89​2−9​]B-A=☐

Problem 25351

Problem 25352

Question 13In a recent poll, 580 people were asked if they liked dogs, and 68\% said they did. Find the Margin of Error for this poll, at the 99%99 \%99% confidence level. Give your answer to four decimal places if possible. □\square□

Problem 25353

$\begin{aligned} -6.8+2.4 & =-6+(-0.8)+2+0.4 \\ & =?+(-0.8)+0.4 \end{aligned}$ $\qquad$ Break apart the $\qquad$ Add the integ

()) What is the perimeter of the shape? 4)） $\square$ centimeters

$x+y=1$
Use the graphing tool to graph the equation. Click to enlarge graph

A gun has muzzle speed $146$ m/s. Find two angles of elevation (in degrees) that can be used to hit a target $830$ m away. (Enter your answers as a comma-separated list. Round your answers to one decimal place. Use $g = 9.8$ m/s².) $\alpha =$

Find the phase shift, amplitude, and period of the function. $y=-1+\sin (2 \pi x-\pi)$ Give the exact values, not decimal approximations

Find the length s of the are of a circle of ractus 10 miles subterided by the centrat angle $t 9^{\circ}$ . s (arc length) $=$ $\square$ miles (Type an integer or decimal rounded to three decimal places as needed.)

Suppose an element is undergoing radioactive decay Determine the decay constant $\lambda$ if a 10 mg sample decays to 8 mg after 5 years.

$\int 2x \cdot 1(x^2 - 3)^5 dx$ by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant. Answer:

The students in Jayce's grade voted to select a guest speaker. $20\%$ of the students voted for a famous athlete. If there are 65 students in Jayce's grade, how many students voted for the athlete? students

Question 68
Find all zeros of $f(x)=x^{3}-7 x^{2}+9 x+$ not decimal approximations.

Which type of substance can conduct electricity in the liquid phase but not in the solid phase?
1. ionic compound
2. molecular compound
3. metallic element
4. nonmetallic element Submit Answer

Find all values of x in the interval $[0, 2\pi]$ that satisfy the equation. (Enter your answers as a comma-separated list.)
$2 \sin(x) = 2 \tan(x)$
x =

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$ b) $g(x) = x^3 + 3x^2 - 4x - 12$

Find the inverse of the one-to-one function. $f(x)=(x+5)^{3}$ $f^{-1}(x)=$ $\square$ (Type an exact answer, using radicals as needec

Evaluate the integral. $\int \frac{\sin(2t+7)}{\cos^2(2t+7)}dt$ $\int \frac{\sin(2t+7)}{\cos^2(2t+7)}dt =$

If $PQ = 37$ , $QO = 32$ , $PO = 42$ , $TR = 16$ , and $SR = 21$ , find the perimeter of $\triangle RST$ . Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Question 8 Complete the following, based off of Video #5: Compare the following decimals: $0.50 ? 0.5$ 2 pts

Question 4
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a $z$ -score of 0.3571 (to 4 decimal places) $\square$

What is the meaning of this expression? $6^3$
$6^3 = \square$ (Type your answer as a product. Do not simplify.)

A race is $\frac{7}{10}$ kilometers long. Aldo ran 9 of these races. How far did he run altogether?
Write your answer in simplest form.

Question 6
In a large population, $55 \%$ of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal to 4 places.

(5) $78 \text{ ounces} = \frac{\phantom{00}}{} \text{ cups}$ (6) $200 \text{ cups} = \frac{\phantom{00}}{} \text{ gallons}$

Find B-A
$A = \begin{bmatrix} 9 & 2 \\ 9 & 1 \end{bmatrix}$ $B = \begin{bmatrix} -8 & 2 \\ 9 & -9 \end{bmatrix}$
B-A=☐

Question 13
In a recent poll, 580 people were asked if they liked dogs, and 68\% said they did. Find the Margin of Error for this poll, at the $99 \%$ confidence level. Give your answer to four decimal places if possible. $\square$

Question 8 Complete the following, based off of Video #5: Compare the following decimals: $0.50 ? 0.5$
Question 9 Which video was your favorite out of the 5? Why was it your favorite? 2 pts

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a black 2.
The probability is $\boxed{}$ . (Simplify your answer. Type an integer or a fraction.)

$\int_0^{16} \sin(\sqrt{x}) \, dx, \quad n = 4$

Find the limit of the sequence $a_n = \frac{(2n-1)!}{(2n+1)!}$

$2 \sin \left(x+\frac{\pi}{6}\right)-1=0$

Find $g$ .
$30^\circ$ E G $133^\circ$ $f$ $g$ $9$ F Write your answer as an integer or as a decimal rounded to the nearest tenth. $g =$

Perimeter, Area, and Volume Area of a piecewise rectangular figure Find the area of the figure. (Sides meet at right angles.) 8 cm 3 cm 5 cm 5 cm 5 cm $2$ cm²

22 Solve the following quadratic equations by square roots. Write all answers in simplest form.
$3x^2 - 108 = 0$
$x^2 = 36$
Solution(s):

$9x^2 - 16 = 0$ $x^2 =$ Solution(s):

3. Вычислить интеграл: a) $\int \frac{d x}{2 x+4}$ b) b) $\int_{0}^{2}\left(x^{2}+\sin x\right) d x$ c) $\int_{-1}^{3} \frac{d x}{1+9 x^{2}}$

2. Вычислить производную функции: a) $y=10 x^{3}+\frac{3}{x \sqrt{x}}-\frac{4}{5} x^{-\frac{1}{4}}$ b) $y=\sin x \cdot \ln x$

4. Решить дифферениальнее ураввение: a) $\sin ^{2} x d y+(2 y+1) d x=0$ b) $y+x y^{\prime}=0$