Equation

Problem 1501

Solve the equation. Give all solution in 0θ<2π0 \leq \theta<2 \pi 2cos(θ)=12 \cos (\theta)=1
Select all that apply 0 π2\frac{\pi}{2} π\pi 3π2\frac{3 \pi}{2} π6-\frac{\pi}{6} π6\frac{\pi}{6} 2π3\frac{2 \pi}{3} 7π6\frac{7 \pi}{6} 5π3\frac{5 \pi}{3} π4-\frac{\pi}{4} π4\frac{\pi}{4} 3π4\frac{3 \pi}{4} 5π4\frac{5 \pi}{4} 7π4\frac{7 \pi}{4} π3-\frac{\pi}{3} π3\frac{\pi}{3} 5π6\frac{5 \pi}{6} 4π3\frac{4 \pi}{3} 11π6\frac{11 \pi}{6} π2-\frac{\pi}{2}

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Problem 1502

 o|e్1 A| \begin{array}{l} \text { o|e్1 A| } \end{array} \begin{array}{l} \Rightarrow \end{array} \square\square \square \square \square \square \square 0 0 \vdots \vdots Δ\Delta

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Problem 1503

19. 4y=3x4-y=3 x \begin{tabular}{c|c} X & Y \\ \hline 2 & \\ 1 & \\ -2 & \end{tabular}

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Problem 1504

Solve 8+9x=538+9 x=53

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Problem 1505

Evaluate. (6x24x+4)dx(6x24x+4)dx=\begin{array}{l} \int\left(6 x^{2} \cdot-4 x+4\right) d x \\ \int\left(6 x^{2}-4 x+4\right) d x=\square \end{array} \square (Type an exact answer.)

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Problem 1506

43+47=\frac{4}{3}+\frac{4}{7}=

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Problem 1507

Question Show Examples
Find the slope of a line perpendicular to the line whose equation is 3x+y=83 x+y=8. Fully simplify your answer.
Answer Attempt 1 out of 2

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Problem 1508

Question Show Examples
Find the slope of a line perpendicular to the line whose equation is x2y=8x-2 y=-8. Fully simplify your answer.
Answer Attempt 1 out of 2

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Problem 1509

8. The mean age of students at a certain college was 26.6 years old in 2005. An administrator thinks the mean age for online students differs from this value. She randomly surveys 56 online students and finds that the sample mean is 29.4 years with a standard deviation of 2.1 years. At the 1%1 \% level of significance (α=0.01)(\alpha=0.01), what can be concluded about the administrator's claim? Include the following steps in your test. - State the null and alternative hypotheses - Calculate the test statistic - Find the p-value - Make a decision whether to reject H0\mathrm{H}_{0} - Write an interpretation of the results

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Problem 1510

Question Show Examples
What is the equation of the line that passes through the point (3,6)(-3,-6) and has a slope of 23-\frac{2}{3} ?
Answer Attempt 1 out of 2

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Problem 1511

Question Show Examples
What is the equation of the line that passes through the point (3,6)(-3,-6) and has a slope of 23-\frac{2}{3} ?
Answer Attempt 2 out of 2

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Problem 1512

Show Examples
Question What is the equation of the line that passes through the point (6,3)(-6,-3) and has a slope of 16-\frac{1}{6} ?
Answer Attempt 1 out of 2

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Problem 1513

Show Examples
Question What is the equation of the line that passes through the point (6,2)(6,2) and has a slope of 13\frac{1}{3} ?

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Problem 1514

Question Watch Video Show Examples
What is an equation of the line that passes through the point (5,3)(5,-3) and is parallel to the line 4x+5y=154 x+5 y=15 ?

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Problem 1515

Which equation represents a line which is parallel to the line y=2x5y=2 x-5 ?
Answer 2x+y=82 x+y=8 y2x=8y-2 x=-8 x+2y=4x+2 y=-4 x2y=6x-2 y=6

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Problem 1516

Determine the molarity of a solution formed by dissolving 188.2 g LiBr in enough water to yield 574.7 mL of solution.

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Problem 1517

Evaluate. e8xdxe8xdx=\begin{array}{c} \int e^{8 x} d x \\ \int e^{8 x} d x= \end{array} \square

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Problem 1518

It is believed that 11%11 \% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 250 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem. a) The symbol for the random variable involved in this problem is ? \square The wording for the random variable in context is as follows: Select an answer b) The symbol for the parameter involved in this problem is \square ?
The wording for the parameter in context is as follows: Select an answer c) Fill in the correct null and alternative hypotheses: H0: ? 0 ?  HA:? ? ?  \begin{array}{l} H_{0}: \text { ? } 0 \text { ? } \cdot \text { } \square \\ H_{A}: ? \text { ? ? } \cdot \text { } \square \end{array} d) A Type I error in the context of this problem would be:
Select an answer \square e) A Type II error in the context of this problem would be: Select an answer

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Problem 1519

b)
Find the two solutions of z2=25jz^{2}=2-5 j in the form z1=r1eθ1jz_{1}=r_{1} e^{\theta_{1} j}, (the principal solution), and z2=r2eθ2jz_{2}=r_{2} e^{\theta_{2} j}.
For z1=r1eθ1z_{1}=r_{1} e^{\theta_{1}}, where r1=r_{1}= \qquad and θ1=\theta_{1}= \qquad radians
For z2=r2eθ2jz_{2}=r_{2} e^{\theta_{2} j}, where r2=r_{2}= \qquad and θ2=\theta_{2}= \qquad radians

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Problem 1520

QUESTION 3 \cdot 1 POINT
What value of xx makes the equation 3(x5)=27(x+4)3^{(x-5)}=27^{(x+4)} true? Do not include " x=x= " in your answer. (Express your answer as a decimal, if necessary.)

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Problem 1521

What is the surface area of the cone? SA=πrs+πr2S A=\pi r s+\pi r^{2}
Surface Area:

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Problem 1522

In the figures below EFGHJK\triangle E F G \sim \triangle H J K, and EX and HY are medians.
2. What is the length of HY?

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Problem 1523

In the state of New York, there are 232 eight year olds diagnosed with ASD out of 18,555 eight year olds evaluated. In the state of Maryland, there are 43 eight year olds diagnosed with ASD out of 2,464 eight year olds evaluated. Is there enough evidence to show that the proportion of children diagnosed with ASD in New York is more than the proportion in Maryland? Test at the 1%1 \% level.
State the hypotheses. H0:p1?p2Ha:p1?p2\begin{array}{l} H_{0}: p_{1} ? \otimes p_{2} \\ H_{a}: p_{1} ? \otimes p_{2} \end{array}
Calculate the test statistics. Round to four decimal places. p^1=\hat{p}_{1}= \square p^2=\hat{p}_{2}= \square Calculate the standardized test statistic. Round three decimal places. z=z= \square Find the pp-value. Round to four decimal places. pp-value == \square State your decision. Since the p -value is less than .01 , reject H0H_{0}. Since the pp-value is greater than .01 , fail to reject H0H_{0}. Since the pp-value is less than .01 , fail to reject H0H_{0}. Since the pp-value is greater than .01 , reject H0H_{0}.
Interpret the results. At the 1%1 \% level of significance, there is enough evidence to show that the proportion of children diagnosed with ASD in New York is less than the proportion in Maryland. At the 1%1 \% level of significance, there is enough evidence to show that the proportion of children diagnosed with ASD in New York is not equal to the proportion in Maryland. At the 1%1 \% level of significance, there is not enough evidence to show that the proportion of children diagnosed with ASD in New York is not equal to the proportion in Maryland. At the 1%1 \% level of significance, there is not enough evidence to show that the proportion of children diagnosed with ASD in New York is more than the proportion in Maryland. At the 1%1 \% level of significance, there is enough evidence to show that the proportion of children diagnosed with ASD in New York is more than the proportion in Maryland.

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Problem 1524

Crown molding is a decorative trim installed over the joint between the walls of a room and the ceiling. (If you are not sure that you understand the idea, do an Internet search to find an example picture of crown molding). Andy intends to install crown molding around the four sides of the dining room. There will be no gaps. The dining room ceiling is a rectangle with dimensions 11 feet 11 inches by 10 feet. The crown molding is sold in 4 -foot lengths that cost $17\$ 17 each. He decides to purchase enough pieces to allow for 10%10 \% waste due to possible mistakes.
Question 17/2517 / 25
If sales tax is 8.25%8.25 \%, what is the total cost? \ \square$

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Problem 1525

A recent study questioned students in Fresno City College to see if they felt stress in their math and psychology classes. Out of 78 math students, 46 said they felt stress, while out of 48 psychology students, 26 said they felt stress. Is this enough evidence to show that the stress experienced by math students (Population 1) are significantly different from psychology students (Population 2) at a significance level of α=0.01\alpha=0.01 ?
1. For this study, we should use Select an answer
2. The null and alternative hypotheses would be:
3. The test statistic == \square (please show your answer to 3 decimal places.)
4. The pp-value == \square (Please show your answer to 4 decimal places.)
5. The pp-value is Select an answer \square α\alpha
6. Based on this, we should Select an answer \square the null hypothesis.
7. As such, the final conclusion is that ... The sample data suggests that the first populaton proportion is significantly different from the second population proportion at α=0.01\alpha=0.01, so there is sufficient evidence to conclude that the stress experienced by math students are different from psychology students. The sample data suggests that the first population proportion is not significantly different from the second population proportion at α=0.01\alpha=0.01, so there is not sufficient evidence to conclude that the stress experienced by math students are different from psychology students.

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Problem 1526

P=2L+2WP=2 L+2 W with P=P= perimeter, L=L= length, W=W= width
Question 18/2518 / 25
Andy's house is on a large lot. He bought 90 yards of chain-link fence on sale. He wants to use all of the material to fence in an area in his backyard. He can only make the fenced area 70 feet wide and he wants it to be as long as possible. What is the longest length possible for the sides? \square ft

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Problem 1527

Find the xx - and yy-intercepts of the graph of the linear equation 3x+6y=243 x+6 y=24.
The xx-intercept is \square \square.
The yy-intercept is \square \square.

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Problem 1528

Account Dashboard Courses Calendar Inbox History 10 Multiple Choice 3.5 points
A $30,000\$ 30,000 corporate bond is convertible to 120 shares of the corporation's common stock. What price per share must the corporation's stock be before bondholders would consider converting a bond to the company's common stock? \$50 \$250 \$300 \$30 Next Help

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Problem 1529

Question 5 (2 points) Apply the One to One Property of Exponents to solve the following exponential equation. Enter either an integer (no decimal) or a fraction in the form a/b. For example, if your answer is 14-\frac{1}{4}, type 1/4-1 / 4. x=38x=9x+1x=\quad 3^{8-x}=9^{x+1} \square A)

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Problem 1531

Sulue fie fillowing equations tors 2x5= ar 2x5=12x=6 ar 2x=4z=3 ar x=2\begin{array}{rrr} 2 x-5=- & \text { ar } & 2 x-5=-1 \\ 2 x=6 & \text { ar } & 2 x=4 \\ z=3 & \text { ar } & x=2 \end{array}
Thice integess ar simplifed tactions) What ss the rext sten?
1. Euature 2x5>12 x-5 \mid>1 fir the zalues found in the previcus step

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Problem 1532

8.) Given PQundefinedRSundefined\overleftrightarrow{P Q} \| \overleftrightarrow{R S}, write a mathematical sentence (an equation) to show the relationship between QBC\angle Q B C and SCB\angle S C B. 9.) Solve your equation from \#8 to find the value of aa.

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Problem 1533

c. 2(y+2)=3y2-(y+2)=3 y

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Problem 1534

The pulse rates of 176 randomly selected adult males vary from a low of 39 bpm to a high of 111 bpm . Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 95%95 \% confidence that the sample mean is within 4 bpm of the population mean. Complete parts (a) through (c) below. a. Find the sample size using the range rule of thumb to estimate σ\sigma. n=n= \square (Round up to the nearest whole number as needed.)

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Problem 1535

A factory machine was purchased for $379000\$ 379000 on January 1, 2021. It was estimated that it would have a $80000\$ 80000 salvage value at the end of its 5 -year useful life. It was also estimated that the machine would be run 35000 hours in the 5 years. The company ran the machine for 3500 actual hours in 2021. If the company uses the units-of-activity method of depreciation, the amount of depreciation expense for 2021 would be

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Problem 1536

Jack's car used 11 gallons to travel 264 miles. How many gallons of gas would he need to travel 48 miles?
Answer Attempt 1 out of 2 \square gallons Submit Answer

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Problem 1537

2. a. x3+x8x2+37x+4=x212x+49159x+4\frac{x^{3}+x-8 x^{2}+37}{x+4}=x^{2}-12 x+49-\frac{159}{x+4} b. 10x39x28x+115x2=2x2x2+75x2\frac{10 x^{3}-9 x^{2}-8 x+11}{5 x-2}=2 x^{2}-x-2+\frac{7}{5 x-2} c. 3x+2x3x2=x22x1\frac{3 x+2-x^{3}}{x-2}=-x^{2}-2 x-1 d. x42x2+12x4=x3+4x2+14x+56+236x4\frac{x^{4}-2 x^{2}+12}{x-4}=x^{3}+4 x^{2}+14 x+56+\frac{236}{x-4} e. x52x47x3+13x2+2x18x22x3=x34x+53x22x3\frac{x^{5}-2 x^{4}-7 x^{3}+13 x^{2}+2 x-18}{x^{2}-2 x-3}=x^{3}-4 x+5-\frac{3}{x^{2}-2 x-3}

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Problem 1538

Question Write the equation of the line that passes through the points (4,7)(4,7) and (5,7)(5,-7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

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Problem 1539

3 If RU\overline{R U} is an altitude for RST\triangle R S T, find xx. x=x=

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Problem 1540

Which equation represents a line which is perpendicular to x=0x=0 ?
Answer Attempt 1 out of 3 y=x3y=x-3 x=4yx=-4 y Submit Answer x=5x=5 y=6y=-6

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Problem 1541

m cm×100m \rightarrow \mathrm{~cm} \times 100
Solve.
1. Tia cut a 4 -meter 8 -centimeter wire into 10 equal pieces. Marta cut a 540 -centimeter wire into 9 equa pieces. How much longer is one of Marta's wires than one of Tia's?

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Problem 1542

2. Error Analysis Raul has 32.4 milliliters of solution. He uses 0.1 milliliter of solution for each experiment. Paul states that he can complete 3.24 trials using all of his solution. How do you respond to him?

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Problem 1543

The number of bats in a cave decreased by 75%75 \% between last year and this year. Last year there were 60 bats in the cave. What is the population this year?
The number of alligators in a swamp increased by 25\% between last year and this year. Last year there were 50\mathbf{5 0} alligators in the swamp. What is the population this year?

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Problem 1544

0t40 \leq t \leq 4 \text {. }
2. Find the corresponding rectangular equation of the following parametric equations: a. x=2t3,y=3t+1x=2 t-3, y=3 t+1 b. x=t3,y=t22x=t^{3}, y=\frac{t^{2}}{2} c. x=secθ,y=cosθx=\sec \theta, y=\cos \theta

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Problem 1545

 P(hsuccesses )=nCpn(1ρ)nhnB=n!(nh)h\begin{array}{c} \text { P(hsuccesses })=n^{C} p^{n}(1-\rho)^{n-h} \\ n^{B}=\frac{n!}{(n-h)|h|} \end{array} 7C5(16)2(16)5{ }_{7} C_{5}\left(\frac{1}{6}\right)^{2}\left(\frac{1}{6}\right)^{5} 7C5(16)5(56)2{ }_{7} C_{5}\left(\frac{1}{6}\right)^{5}\left(\frac{5}{6}\right)^{2} 7C2(16)2(56)5{ }_{7} \mathrm{C}_{2}\left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{5} 7C2(26)2(46)5{ }_{7} C_{2}\left(\frac{2}{6}\right)^{2}\left(\frac{4}{6}\right)^{5}

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Problem 1546

Listen
Find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle.
The smaller acute angles measures \square { }^{\circ} and the larger acute angle measures \square { }^{\circ}.

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Problem 1547

shley wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 4.8%4.8 \% interest, compounded monthly. Payments will be made at ie end of each month. ow much money will she need to pay into the annuity each month for the annuity to have a total value of $7000\$ 7000 after 5 years? ot nound intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

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Problem 1548

Consider the following monthly amortization schedule: \begin{tabular}{|c|c|c|c|c|} \hline Payment \# & Payment & Interest & Debt Payment & Balance \\ \hline 1 & 996.45 & 750.00 & 216.45 & 149,783.55149,783.55 \\ \hline 2 & 996.45 & 748.92 & 217.53 & 149,566.02149,566.02 \\ \hline 3 & 996.45 & & & \\ \hline \end{tabular}
With the exception of column one, all amounts are in dollars. Calculate the annual interest rate on this loan.

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Problem 1549

Solve using the quadratic formula. 7d2+4d=07 d^{2}+4 d=0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

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Problem 1550

Solve using the quadratic formula. 3h2+7h2=03 h^{2}+7 h-2=0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

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Problem 1551

ERROR ANALYSIS Describe the error in finding m1m \angle 1. The sum of 360360^{\circ} and 154154^{\circ} should be 514514^{\circ}. The sum of the measures of the angles should be 180180^{\circ}. The sum of 115115^{\circ} and 3939^{\circ} should be 144144^{\circ}. The sum of the measures of the angles should be 9090^{\circ}. Correct the error in finding m1\mathrm{m} \angle 1. 115+39+m1=115^{\circ}+39^{\circ}+m \angle 1= \square \square +m1=+m \angle 1= \square m1=m \angle 1= \square : 514514^{\circ} 360360^{\circ} 216216^{\circ} 206 180180^{\circ} 154154^{\circ} 144144^{\circ} 9090^{\circ} 6464^{\circ} 3636^{\circ} 2626^{\circ}

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Problem 1552

3 Intil initheresment continued Date Form
3 Sean has 10 books. He has 6 more books than Kali has. How many books does Kali have? PartaA\mathrm{Parta}_{A} Draw a picture to show the problem.
Part BB Write an equation to solve the problem. How many books does Kali have?
Solution \qquad 4 Maria makes a picture graph to Bookshelf Items show all the things on her bookshelf. Which statements about her bookshelf are true? Choose all the correct answers. (A) Maria has 5 more dolls than lamps. (B) Maria has 2 fewer books than dolls. (C) Maria has the same number of dolls as books. (D) Maria has 12 things on her bookshelf. (E) Maria has more books than dolls. Grade 2 Unit 1 Unit Assessment-Form A 2 - Curriculum Associates, LLC copying permitted for classoom use. bowntoaded by G. Finley at UNION SPRINES E.EM SCHOOL. This resource explies on 6/30/2025.

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Problem 1553

Write two mixed numbers that have a sum of 3 .

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Problem 1554

48÷..=648 \div \ldots .-.=6

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Problem 1555

b) (10 marks) Consider the following IVP problem: 14yy+10y=(2x3)2;y(0)=1;y(0)=0\frac{1}{4} y^{\prime \prime}-y^{\prime}+10 y=(2 x-3)^{2} ; y(0)=1 ; y^{\prime}(0)=0 i. Write the complementary equation for the given equation. ii. Write the auxiliary equation for the equation in part (i), solve it and hence obtain the general solution of the complementary equation. iii. Find a particular solution for the given equation. iv. Write the general solution for the given equation. v. Hence find the solution for the given IVP problem.

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Problem 1556

5x2(x2)=19+5x+75 x-2(x-2)=1-9+5 x+7

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Problem 1557

4) Prove Trigonometric Identities tanθ+cotθ=secθcscθ\tan \theta+\cot \theta=\sec \theta \csc \theta

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Problem 1558

4. In the United States, it is well-known that for the population of males, the mean height is 69.1 inches with standard deviation 4 inches. A researcher believes that a certain group is significantly taller than other males, due to genetic factors. For a sample of 25 such men, the mean is 71.2 inches with standard deviation 3.5 inches. a. Can it be reasonably assumed that the population is normally distributed? Are the criteria met to perform a z-test for the mean? Explain. b. Set up the null and alternative hypothesis to test if this population is taller than average. c. Calculate the value of the test statistic. d. Find the p-value. e. At the 5%5 \% level of significance (α=0.05)(\alpha=0.05), make a decision whether to reject H0H_{0}. f. What can we conclude?

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Problem 1559

Given the balanced chemical reaction:\text{Given the balanced chemical reaction:} N2H4+2H2O2N2+4H2O\text{N}_2\text{H}_4 + 2\text{H}_2\text{O}_2 \rightarrow \text{N}_2 + 4\text{H}_2\text{O} \text{If 11.1 \text{ mol } \text{N}_2\text{H}_4 is mixed with 1.4 \text{ mol } \text{H}_2\text{O}_2, calculate the following:} Part 3 of 4: How much N2 is formed? Answer in units of mol.\text{Part 3 of 4: How much } \text{N}_2 \text{ is formed? Answer in units of mol.} Part 4 of 4: How much H2O is formed? Answer in units of mol.\text{Part 4 of 4: How much } \text{H}_2\text{O} \text{ is formed? Answer in units of mol.}

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Problem 1560

for a manturing company wishes to reduce the mean time needed serer visit to a customer location in his region. Nationally, this company sets a standard that a customer service visit should last at most four hours, on average. He is concerned that the service technicians in his region may be violating that standard, so he samples 41 customer service visits. In this sample, the mean time needed for a service visit is 4.2 hours with standard deviation 1.6 hours. In a previous example, we determined that the tt-test for the mean should be conducted. a. Set up the null and alternative hypothesis to test the regional manager's claim that the standard set by the company is being violated. b. Calculate the value of the test statistic. c. Find the p-value. d. At the α=0.05\alpha=0.05 level of significance, make a decision whether to reject H0\mathrm{H}_{0}. e. Interpret this conclusion.

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Problem 1561

A certain game involves tossing 3 fair coins, and it pays 99 \notin for 3 heads, 44 \notin for 2 heads, fand 22 \notin for 1 head. Is 44 \notin a fair price to pay to play this game? That is, does the 4ϕ4 \phi cost to play make the game fair?
The 4c4 c cost to play \square is not a fair price to pay because the expected winnings are \square 4. (Type an integer or a fraction. Simplify your answer.)

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Problem 1562

Given secA=857\sec A=-\frac{\sqrt{85}}{7} and that angle AA is in Quadrant II, find the exact value of cscA\csc A in simplest radical form using a rational denominator.

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Problem 1563

Sec 9.4 Rare Events, the
1. At significance level α=0.10\alpha=0.10, determine if the null hypothesis should be rejected given the test statistic and p -value. 1 A manufacturer of automobile batteries claims that the average life of its best battery is 54 months. A consumer advocacy group believes that this might be incorrect. The test statistic is found to be -7.07 and the p -value is 0\approx 0.

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Problem 1564

Ten thousand raffle tickets are sold. One first prize of $1000\$ 1000, two second prizes of $750\$ 750, and three third prizes of $200\$ 200 each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings?
The expected gross winnings are \square cents. (Round your answer to the nearest whole cent.)

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Problem 1565

3. Psychologists were interested in the physiological changes that occur when a person laughed. The subjects in the study watched videos to encourage laughter. While the subjects were laughing, the researchers measured the subject's pulse. In a sample of 90 subjects, the mean heart rate was 73.5 beats per minute (bpm) with standard deviation 6 bpm . The mean resting heart rate of the population of all adults is known to be 71 bpm with standard deviation 7.5 bpm . The researchers wish to determine if the mean heart rate is elevated during laughter. In a previous example, we determined that the z -test for the mean should be conducted. a. Set up the null and alternative hypothesis for this test. b. Calculate the value of the test statistic. c. Find the p-value. d. At the α=0.05\alpha=0.05 level of significance, make a decision whether to reject H0\mathrm{H}_{0}. e. Can it be determined that the mean heart rate is elevated during laughter?

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Problem 1566

can2α1+can2α=sin2α\frac{\operatorname{can}^{2} \alpha}{1+\operatorname{can}^{2} \alpha}=\sin ^{2} \alpha

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Problem 1567

A turtle travels 512\frac{5}{12} mile in 13\frac{1}{3} hour and a snail travels 18\frac{1}{8} mile in 34\frac{3}{4} hour. Which animal is faster? The turtle's rate is greater than 1 mile per hour.
The snail's rate is less than 1 mile per hour.
Find the turtle's speed in miles per hour.
The turtle's speed is mile(s) per hour.

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Problem 1568

5. At a certain government agency, all employees must undergo a training course and take an online quiz to assess their knowledge. The completion time for the population of all government employees who take the quiz is normally distributed with mean 32 minutes and standard deviation 13 minutes. It is suspected that one group of employees cheated on the quiz, since their completion time was shorter than average. In this sample of 34 employees, the mean completion time was 29 minutes with standard deviation 4 minutes. At the α=0.05\alpha=0.05 level of significance, what can be concluded? Include the following steps in your test. - State the null and alternative hypotheses - Calculate the test statistic - Find the p-value - Make a decision whether to reject H0\mathrm{H}_{0} - Write an interpretation of the results

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Problem 1569

4) Prove Trigonometric Identities (10 marks, 5 each) tanθ+cotθ=secθcscθcan2α1+can2α=sin2α\tan \theta+\cot \theta=\sec \theta \csc \theta \quad \frac{\operatorname{can}^{2} \alpha}{1+\operatorname{can}^{2} \alpha}=\sin ^{2} \alpha

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Problem 1570

DIO DEEPER You can read 12 pages of a book in 15 minutes. How many hours will it take you to read a 312 -page book?

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Problem 1571

5) Albert and Belle are part of a scientific team studying thunderclouds. The team is about to launch a weather balloon into an active part of a cloud. Albert's rope is 7.8 m long and makes an angle of 36 degrees with the ground. Belle's rope is 5.9 m long. Draw a sketch and determine the angle that Belle makes with the ground. (6 marks)

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Problem 1572

(22) Solve the following linear Diophantine equations: (i) 56x+72y=4056 x+72 y=40. (ii) 221x+91y=117221 x+91 y=117. (iii) 2378x+1769y=2142378 x+1769 y=214. (iv) 242x+338y=18242 x+338 y=18.

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Problem 1573

Which equation is correctly rewritten to solve for yy ? 12y+d=19y+t12 y+d=-19 y+t A. y=31(td)y=31(t-d) B. y=td31y=\frac{t-d}{31} C. y=t+d7y=\frac{t+d}{-7} D. y=7(t+d)y=-7(t+d)

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Problem 1574

(vii) 84x438y=15084 x-438 y=150.
Having that gcd(a,b)=1\operatorname{gcd}(a, b)=1, prove the following: (i) gcd(2a+b,a+2b)=1\operatorname{gcd}(2 a+b, a+2 b)=1 or 3 . (ii) god(a+b,a2+b2)=1\operatorname{god}\left(a+b, a^{2}+b^{2}\right)=1 or 2 .
For a,bZ+a, b \in \mathbf{Z}^{+}, and n1n \geq 1, prove that if anbna^{n} \mid b^{n}, then aba \mid b

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Problem 1575

6. Select all the points which are relativA function. a. Point AA b. Point BB c. Point CC d. Point DD e. Point EE f. Point FF g. Point GG
7. What are the xx-intercepts of the graph of y=(3x+8)(5x3)(x1)y=(3 x+8)(5 x-3)(x-1) ?

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Problem 1576

For babysitting, Nicole charges a flat fee of $3\$ 3, plus $5\$ 5 per hour. Write an equation for the cost, C , after hh hours of babysitting.

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Problem 1577

3. Carpet costs $16\$ 16 a square foot. A rectangular floor is 16 feet long by 14 feet wide. How much would it cost to carpet the floor?

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Problem 1578

b. (3x2+2x7)(7x2+x1)=\left(3 x^{2}+2 x-7\right)-\left(7 x^{2}+x-1\right)= \square (Simplify your answer. Do not factor.)

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Problem 1579

The city of Raleigh has 10,500 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 130 said they'd vote for Brown, 199 said they'd vote for Feliz, and 21 were undecided.
Use this information from the sample to complete the following statements about the population of all registered voters in Raleigh. Round your answers to the nearest person.
Based on this sample, we could expect 3,900 0839000^{8} 3900 of the 10,500 registered voters to vote for Brown.
Based on this sample, we could expect \square of the 10,500 registered voters to vote for Feliz. Based on this sample, \square of the 10,500 registered voters are still undecided.
Question Help: Video Message instructor Submit Question

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Problem 1580

A rectangle has its base on the xx-axis and its upper two vertices on the parabola y=49x2y=49-x^{2}. What is the largest possible area (in squared units) of the rectangle? \square squared units

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Problem 1581

A slide is 7 feet long and 4 feet high. How long is its base, from the bottom of the ladder to the end of the slide? If necessary, round to the nearest tenth. \square feet

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Problem 1582

Philip bicycles 5 miles west to get from his house to school. After school, he bicycles 8 miles north to his friend Dan's house. How far is Philip's house from Dan's house, measured in a straight line? If necessary, round to the nearest tenth. \qquad miles

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Problem 1583

Question 4 (2 points) Apply the One to One Property of Logarithms to solve each of the following exponential equations for x . \square 2x=32^{x}=3 \square 2x+1=32^{x+1}=3
1. log2(3)\log _{2}(3) \square 3x+2=23^{x+2}=2
2. log2(3)1\log _{2}(3)-1
3. log3(2)2\log _{3}(2)-2

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Problem 1584

Find the locus of P(x,y)P(x, y) which moves such that a) Its distance from (4,5)(-4,5) is 5 . b) Its distance form xx-axis is always 5 units. c) Its distance from yy-axis is always -3 . d) Its distance from (5,2)(-5,-2) is always 6 units. e) Its distance from origin is 3 . f) Its distance from (1,6)(1,6) is 7

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Problem 1585

1H2+1I221 \quad \mathrm{H}_{2}+1 \quad \mathrm{I}_{2} \rightarrow 2
If 5.7×10235.7 \times 10^{23} particles of I2\mathrm{I}_{2} are reacted, how many grams of HI (molar mass 127.91 g/mol)\left.127.91 \mathrm{~g} / \mathrm{mol}\right) will be produced? \square grams of HI

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Problem 1586

3-101.
Write an equation for each situation below showing that the area as a product is equal to the area as a sum. Homework Help i  Prosuct: (12x+1)(x5)=(2x259x5)12x+1 sum 2m24m16m6m20m5\begin{array}{l} \text { Prosuct: }(12 x+1)(x-5)=\left(2 x^{2}-59 x-5\right) \\ 12 \mathrm{x} \quad+1 \\ \text { sum } \\ 2 m^{2} \quad-4 m \quad-1 \\ \begin{array}{l|l|l|l|} \hline 6 m & 6 m & -20 m & \\ \hline & -5 & & \\ \hline \end{array} \end{array}

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Problem 1587

H2+CO2H2O+CO\mathrm{H}_{2}+\mathrm{CO}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}
If 48.87 liters of H2\mathrm{H}_{2} are reacted, how many liters of CO2\mathrm{CO}_{2} will also be reacted at STP? \square liters of CO2\mathrm{CO}_{2}

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Problem 1588

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the domain and range of the function. f(x)=6xx218f(x)=6 x-x^{2}-18
Use the graphing tool to graph the equation. Use the vertex and one of the intercepts when drawing the graph.
Click to enlargitin graph

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Problem 1589

7. Write and solve an equation for the model shown below.
Equation: \qquad Solution: \qquad

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Problem 1590

If there is a 0.8%0.8 \% chance that none of the books you would like to check out of the library are available, what is the probability that at least one of the books you want is available? Round to 1 decimal place as needed. Be sure to convert to \% and include your \% in the answer.
Your Answer: \square Answer \square units

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Problem 1591

14. If o(E)=9:11o\left(E^{\prime}\right)=9: 11, find p(E)p(E).
15. Find the probability of choosing 7 winning spots in nine-spot keno.

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Problem 1592

Use the following information to answer the next question The power rating of a particular dynamic electronic circuit is given by the equation P=1w0.246tP=1-w^{-0.246 t} where PP is the power rating, tt is the amount of time since the circuit is switched on and ww is a constant.
2. After the circuit has been operational for 43 seconds, the power rating is 0.83 . The value of ww, to the nearest hundredth, is A. 0.09 B. 0.25 C. 1.18 D. 10.58

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Problem 1593

Find the measure of angle CC.
The measure of angle CC is \square

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Problem 1594

b+3e=f2\frac{b+3}{e} = \frac{f}{2} solve for ee

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Problem 1595

yc=53y+23\frac{y}{c}=\frac{-5}{3 y+23}

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Problem 1596

Consider the following two lines: Line 3: y=23x3y=-\frac{2}{3} x-3 Line 4: x=32y10x=-\frac{3}{2} y-10 The slope of Line 3 is: m=m= \square The slope of Line 4 is: m=m= \square Finally, which of the following is true? Select an answer

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Problem 1597

14÷112=\frac{1}{4} \div 1 \frac{1}{2}=

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Problem 1598

During a clearance sale at a sporting goods store, skateboards were marked down 30\%. On Saturday, an additional 25\% was taken off already reduced prices of skateboards. If a skateboard originally cost \$119.50, what was the final price after all discounts had been taken? Round to the nearest cent. (Example 2)

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Problem 1599

Which multiplication equation can you use to find 5÷135 \div \frac{1}{3} ? 5×3=155 \times 3=15 1×3=31 \times 3=3 5×13=535 \times \frac{1}{3}=\frac{5}{3} 3×15=353 \times \frac{1}{5}=\frac{3}{5}

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Problem 1600

Points: 0 of 1
Assume the carrying copacity of the Earth is 27 billion, Use the 1960 annual growth rate of 2.1%2.1 \% and population of 3 billion to predict the base growth rate and current growth rate with a logistio model, Assume a current world population of 7.8 billion. How does the prodictod growth rate compare to the actual growth rate of about 1,1%1,1 \% per year?
What is the base growth rate? \square \% (Round to four docimal places as needed.)

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