Math

Problem 4401

4 markers cost $7.04\$ 7.04.
Which equation would help determine the cost of 7 markers? Choose 1 answer: (A) 47=$7.04x\frac{4}{7}=\frac{\$ 7.04}{x} (B) x7=4$7.04\frac{x}{7}=\frac{4}{\$ 7.04} (C) 7x=$7.044\frac{7}{x}=\frac{\$ 7.04}{4} (D) 47=x$7.04\frac{4}{7}=\frac{x}{\$ 7.04} (E) None of the above

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Problem 4402

```latex \documentclass{article} \usepackage{amsmath} \usepackage{amssymb}
\begin{document}
\section*{Problem 12.83}
Assume that the particles are released from rest at r=r0r = r_{0}.
\begin{enumerate} \item[(a)] Determine the expression relating their relative position rr and time. Hint: \int \sqrt{x(1-x)} \, dx = \sin^{-1}(\sqrt{x}) - \sqrt{x(1-x)} \] \item[(b)] Determine the time it takes for the objects to come into contact if r_{0} = 3 \, \text{m},, Aand and Bhavemassesof have masses of 1.1 \, \text{kg}and and 2.3 \, \text{kg}, respectively, and \begin{enumerate} \item[(i)] The diameters of Aand and Bare are d_{A} = 22 \, \text{cm}and and d_{B} = 15 \, \text{cm}, respectively. \item[(ii)] The diameters of Aand and B$ are infinitesimally small. \end{enumerate} \end{enumerate}
\textbf{Figure P12.82 and P12.83}
\end{document} ```

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Problem 4403

A culture contains 15,000 bacteria, with the population increasing exponentially the culture contains 25,000 bacteria after 12 hours. a. Write a function in the form y=y0ekt y=y_{0} e^{\text {kt }} giving the number of bacteria after thours b. Write the function from part a in the form y=y0aty=y_{0} a^{t} c. How long will it be until there are 50,000 bacteria? a. The exponential equation is \square \square (Round to three decimal places as needed.)

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Problem 4404

Use the graph of the function ff shown to answer parts (a)-( n ). (a) Find f(21)f(-21) and f(6)f(-6). f(21)=f(6)=\begin{array}{r} f(-21)=\square \\ f(-6)=\square \end{array}

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Problem 4405

Use the Distance Formula to tind the distance between each pair of points. 1 point 29\sqrt{29} 61\sqrt{61} Option 3 Option 1 5.5 5

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Problem 4406

Problems 12.82 and 12.83 Two masses mAm_{A} and mBm_{B} are placed at a distance r0r_{0} from one another. Because of their mutual gravitational attraction, the acceleration of sphere BB as seen from sphere AA is given by r¨=G(mA+mBr2)\ddot{r}=-G\left(\frac{m_{A}+m_{B}}{r^{2}}\right) where G=6.674×1011 m3/(kgs2)=3.439×108ft3/(G=6.674 \times 10^{-11} \mathrm{~m}^{3} /\left(\mathrm{kg} \cdot \mathrm{s}^{2}\right)=3.439 \times 10^{-8} \mathrm{ft}^{3} /\left(\right. slug s2)\left.\cdot \mathrm{s}^{2}\right) is the universal gravitational constant. Problem 12.82 If the spheres are released from rest, determine (a) The velocity of BB (as seen by AA ) as a function of the distance rr. (b) The velocity of BB (as seen by AA ) at impact if r0=7ftr_{0}=7 \mathrm{ft}, the weight of AA is 2.1 lb , the weight of BB is 0.7 lb , and (i) The diameters of AA and BB are dA=1.5ftd_{A}=1.5 \mathrm{ft} and dB=1.2ftd_{B}=1.2 \mathrm{ft}, respectively. (ii) The diameters of AA and BB are infinitesimally small. Answer (a) r˙=2G(mA+mB)r0rr0\dot{r}=-\sqrt{2 G\left(m_{A}+m_{B}\right)} \sqrt{\frac{r_{0}-r}{r_{0}}}; (b) (i) r˙=5.98.0×105ft/s\dot{r}=-5.98 .0 \times 10^{-5} \mathrm{ft} / \mathrm{s}, (ii) r˙\dot{r} \rightarrow-\infty
Problem 12.83 Assume that the particles are released from rest at r=r0r=r_{0}. (a) Determine the expression relating their relative position rr and time. Hint: x/(1x)dx=sin1(x)x(1x)\int \sqrt{x /(1-x)} d x=\sin ^{-1}(\sqrt{x})-\sqrt{x(1-x)} (b) Determine the time it takes for the objects to come into contact if r0=3 m,Ar_{0}=3 \mathrm{~m}, A and BB have masses of 1.1 and 2.3 kg , respectively, and (i) The diameters of AA and BB are dA=22 cmd_{A}=22 \mathrm{~cm} and dB=15 cmd_{B}=15 \mathrm{~cm}, respectively. (ii) The diameters of AA and BB are infinitesimally small.

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Problem 4407

The following table shows a proportional relationship between ww and zz. \begin{tabular}{ll} ww & zz \\ \hline 18 & 2 \\ 45 & 5 \\ 81 & 9 \end{tabular}
Write an equation to describe the relationship between ww and zz. Equations may include exact decimals, proper fractions, or improper fractions. Please do NOT round or use mixed numbers. \square

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Problem 4408

Solve the inequality involving absolute value. x44<4\left|\frac{x-4}{4}\right|<4
Enter the exact answer in interval notation.
To enter \infty, type infinity. To enter UU, type UU.

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Problem 4409

A total of 560 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold? adult tickets

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Problem 4410

Alexandra paid $7\$ 7 to park her car for 3 hours at the parking garage. The garage charges a constant hourly parking rate.
Write an equation that shows the relationship between pp, the number of hours parked, and cc, the cost in dollars. Do NOT use a mixed number. \square

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Problem 4411

18251825=\begin{array}{l}\frac{18}{25} \\ \frac{18}{25}=\end{array}

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Problem 4412

Justin runs at a constant rate, traveling 17 km in 2 hours. Write an equation that shows the relationship between dd, the distance he runs in kilometers, and hh, the time he spends running in hours. Do NOT ise a mixed number. \square

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Problem 4413

Find the xx - and yy-intercepts for the function. f(x)=x+1x2+9f(x)=\frac{x+1}{x^{2}+9}
Enter your answers as points, (a,b)(a, b).
The xx-intercept is \square 田.
The yy-intercept is \square
Show your work and explain, in your own words, how you arrived at your answers.

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Problem 4414

7. Ellen's dad spends $5\$ 5 a week on newspapers. a) How much less newspaper money will he have 8 weeks from now?

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Problem 4415

Wangari plants trees at a constant rate of 12 trees every 3 hours. Write an equation that relates pp, the number of trees Wangari plants, and hh, the time she spends planting them in hours. \square

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Problem 4416

Solve for vv. v6=48\frac{v}{6}=\frac{4}{8}
Simplify your answer as much as possible. v=v=

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Problem 4417

Use the graph of the function f shown to answer parts (a)-( n ). Negative Positive (e) For what value(s) of xx is f(x)=0f(x)=0 ? x=18,3,12x=-18,-3,12 (Use a comma to separate answers as needed.) (f) For what values of xx is f(x)>0f(x)>0 ? 18<x<3,12<x18-18<x<-3,12<x \leq 18 (Type a compound inequality. Use a comma to separate answers as needed.) (g) What is the domain of ff ?
The domain of f is {x21x18}\{x \mid-21 \leq x \leq 18\}. (Type a compound inequality.) (h) What is the range of ff ?
The range of ff is {y\{y \mid \square (Type a compound inequality.)

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Problem 4418

a1/lnaa^{1 / \ln a} using base ee, for a>0a1a>0 \notin a \neq 1

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Problem 4419

(27)6=\left(\frac{2}{7}\right)^{6}=

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Problem 4420

鸾, What is the surface area? \square square meters submit

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Problem 4421

Alice can wash and wax her car in 3 hour and 30 minutes. If Bernice helped her, Alice could do the job in 2 hours. How long would it take Bernice working alone?

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Problem 4422

1. The equation of a demand function is given by Q=855PQ=85-5 P where QQ is the number of buses demand to travel to Monze daily. PP is the price per Bus fare in K. a) What is the change in demand QQ when the PP increases by 1 unit? b) What is the demand when P=0P=0 ? c) What is the price P when Q=0Q=0 ?

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Problem 4423

6. 256a34\sqrt[4]{256 a^{3}}

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Problem 4424

It takes 338. kJ/mol\mathrm{kJ} / \mathrm{mol} to break an carbon-chlorine single bond. Calculate the maximum wavelength of light for which an carbon-chlorine single bond could be broken by absorbing a single photon.
Be sure your answer has the correct number of significant digits. \square nm

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Problem 4425

(21)1=(21)^{1}=

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Problem 4426

Tell whether the order pair is a solution to the given equation
38. y=3x;(4,13)y=-3 x ;(4,-13)
39. y=3x2;(1,5)y=3 x-2 ;(-1,-5)

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Problem 4427

If mJNP=2x+3,mKNL=3x17m \angle J N P=2 x+3, m \angle K N L=3 x-17, and mKNJ=3x+34m \angle K N J=3 x+34, find the measure of each angle. mJNP=mKNL=mKNJ=\begin{array}{l} m \angle J N P= \\ m \angle K N L= \\ m \angle K N J=\square \end{array}

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Problem 4428

If mJNP=2x+3,mKNL=3x17m \angle J N P=2 x+3, m \angle K N L=3 x-17, and mKNJ=3x+34m \angle K N J=3 x+34, find the measure of each angle.

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Problem 4429

Solve for xx. 8x=59x=\begin{array}{l} \frac{8}{x}=\frac{5}{9} \\ x= \end{array}

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Problem 4430

Adjacent Angles that are not a Linear Pair
Obtuse Vertical Angles
Complementary Nonadjacent Angles
Linear Pair
Acute Vertical Angles [ Choose ] Angles DFB and CFE Angles ADC and EDH Angles DGE and BGH Angles EDG and BGD Angles BCF and CAE Angles CDH and HDE Angles CFE and EFD [Choose ]

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Problem 4431

2. The equation of the demand function is given by P=170P=170 where PP is the price of 10 kg bag of sugar in kwacha. a) What is the slope of this demand function? Describe what this means. b) Plot the graph of this demand function.

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Problem 4432

Points: 0 of 1 Save
Calculate the limit in the following exercise, using a table. Verify your answer by using a graphing calculator. limx10x2100x+10\lim _{x \rightarrow-10} \frac{x^{2}-100}{x+10}
Let f(x)=x2100x+10f(x)=\frac{x^{2}-100}{x+10}. Complete the table below. x10.110.0110.0019.9999.999.9f(x)\begin{array}{lllllll} \mathbf{x} & -10.1 & -10.01 & -10.001 & -9.999 & -9.99 & -9.9 \\ \mathbf{f}(\mathrm{x}) & \square & \square & \square & \square & \square & \square \end{array} (Round to three decimal places as needed.)

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Problem 4433

3) Find the area of the region bounded by f(x)=2e2x,g(x)=e2x+1f(x)=2 e^{2 x}, g(x)=e^{2 x}+1 and [1,2][-1,2]. (a) Find points of intersection/s. (b) In the interval [1,2][-1,2] find which integral is above and which is below. (c) Write the integral to find the area inside [1,2],f(x)=2e2x[-1,2], f(x)=2 e^{2 x} and g(x)=e2x+1g(x)=e^{2 x}+1. No need to integrate.

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Problem 4434

3. Maggie spent $4.05\$ 4.05 on cheese and fruit at the farmer's market. She bought 18\frac{1}{8} pound of apples, 14\frac{1}{4} pound of pears, and 1.25 pounds of bananas. If fruit cost $0.80\$ 0.80 per pound, how much did Maggie spend on cheese?

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Problem 4435

100. limx1x31x21\lim _{x \rightarrow 1} \frac{x^{3}-1}{x^{2}-1}

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Problem 4436

Part A
Rolls of foil are 308 mm wide and 0.013 mm thick. (The density of foil is 2.7 g/cm32.7 \mathrm{~g} / \mathrm{cm}^{3}.) What maximum length of foil can be made from 1.26 kg of foil? Express the length to two significant figures and include the appropriate units.

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Problem 4437

Use the figure below, which gives a graph of the function f(x)f(x), to give values for the indicated limits. If a limit does not exist, enter DNE.
Note: You can click on the graph to enlarge the image. (a) limx0f(x)=\lim _{x \rightarrow 0^{-}} f(x)= \square help (limits). (b) limx0+f(x)=\lim _{x \rightarrow 0^{+}} f(x)= \square

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Problem 4438

Decide whether each proposed multiplication or division of measurements is possible. If it is possible, write the result in the last column of the table. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} proposed \\ multiplication or \\ division \end{tabular} & \begin{tabular}{c} Is this \\ possible? \end{tabular} & result \\ \hline(2.0 g)(0.026 kg)=?(2.0 \mathrm{~g}) \cdot(0.026 \mathrm{~kg})=? & \begin{tabular}{c} yes \\ no \end{tabular} & \square \\ \hline(8.0 kg)(3.0 m)=?(8.0 \mathrm{~kg}) \cdot(3.0 \mathrm{~m})=? & \begin{tabular}{l} yes \\ yo \end{tabular} & \square \\ \hline(7.0 kg)(1.0 kg)=?(7.0 \mathrm{~kg}) \cdot(1.0 \mathrm{~kg})=? & \square yes \\ & \\ \hline \end{tabular}

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Problem 4439

16×16\frac{1}{6} \times \frac{1}{6}

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Problem 4440

Simplify the expression. 2783\sqrt[3]{\frac{-27}{8}}
Enter the exact answer. Hint: You can write roots as fractional exponents, for example 2783\sqrt[3]{\frac{-27}{8}} as (27/8)(1/3)(-27 / 8)^{\wedge}(1 / 3). However, the answer to this question is a fraction without needing a rowt symbol.

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Problem 4441

3. Given the supply function, P=500+2QP=500+2 Q, where PP is the price of a bottle of a perfume, QQ is the number of litres supplied. a) What is the value of QQ when P=K750P=K 750 ? b) What is the value of P when Q=35Q=35 ?

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Problem 4442

Write an equation for a rational function with the given characteristics.
Vertical asymptotes at x=3x=-3 and x=6,xx=6, x-intercepts at (5,0)(-5,0) and (3,0)(3,0), horizontal asymptote at y=6y=-6
Enclose numerators and denominators in parentheses. For example, (ab)/(1+n)(a-b) /(1+n).
Include a multiplication sign between symbols. For example, axa^{*} x.

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Problem 4443

whyt is the velke of, 25 .

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Problem 4444

Simplify the expression. 2783\sqrt[3]{\frac{-27}{8}}
Enter the exact answer. Hint: You can write roots as fractional exponents, for example 2783\sqrt[3]{\frac{-27}{8}} as (27/8)(1/3)(-27 / 8)^{\wedge}(1 / 3). However, the answer to this question is a fraction without needing a root symbol.

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Problem 4445

Consider the arithmetic series 2+5+8+2+5+8+\ldots. Determine the number of terms of the series required to give a sum of 222 by developing and solving a quadratic equation,

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Problem 4446

4. Suppose a manufacturer of shoes will place on the market 50 pairs when the price is K35 and 35 pairs when the price is K2O. a) Find the supply function in the form P=f(Q)P=f(Q) and sketch its graph. b) What will be P when Q=85Q=85 ?

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Problem 4447

Figure II is a translation image of Figure I. Write a rule to describe the translation.
The translation rule is (x,y)h+(),y+()(x, y) \rightarrow h+(\square), y+(\square). w an example Get more help - Clear all Check answer

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Problem 4448

What is the percent increase of a rise in temperature from 8080^{\circ} to 100100^{\circ} ?

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Problem 4449

Use the figure below, which gives a graph of the function f(x)f(x), to give values for the indicated limits. If a limit does not exist, enter DNE.
Note: You can click on the graph to enlarge the image. (a) limx2f(x)=\lim _{x \rightarrow-2^{-}} f(x)= \square help (limits) (b) limx2+f(x)=\lim _{x \rightarrow-2^{+}} f(x)= \square (c) limx2f(x)=\lim _{x \rightarrow-2} f(x)= \square (d) limx1f(x)=\lim _{x \rightarrow-1} f(x)= \square

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Problem 4450

Given the equations: x=2 x = -2 y=9x y = 9 - x
Determine the slope of the line represented by each equation.

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Problem 4451

(4) Find the area of the region bounded by f(x)=x4/3f(x)=x^{4 / 3} and g(x)=2x1/3g(x)=2 x^{1 / 3}

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Problem 4452

Use division method to Find all zeros of the function f(x)=2x39x2f(x)=2 x^{3}-9 x^{2} intergers and fractions for answers, not decimals. Show your work on paper to receive full credits.
The zeros are: \square The fully factor form is f(x)=f(x)= \square
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Problem 4453

A 60° 750 lbs. 30° B <

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Problem 4454

Following the idea in Example 1.25, what is the value of the summation j=25(j21)?\sum_{j=2}^{5}\left(j^{2}-1\right) ?

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Problem 4455

Each of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100 . \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{ Sample of Size 5 data set } \\ \hline 108 & 119 & 95 & 92 & 93 & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{ Sample of Size 12} \\ \hline 108 & 119 & 95 & 92 & 93 & 96 \\ \hline 93 & 98 & 106 & 112 & 112 & 103 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{7}{|c|}{ Sample of Size 30 } \\ \hline 108 & 119 & 95 & 92 & 93 & 96 \\ \hline 93 & 98 & 106 & 112 & 112 & 103 \\ \hline 100 & 102 & 105 & 109 & 91 & 94 \\ \hline 98 & 98 & 112 & 104 & 100 & 91 \\ \hline 101 & 100 & 95 & 95 & 101 & 109 \\ \hline \end{tabular}
What is the median of the new sample of size 30 ? 100.5 (Type an integer or decimal rounded to one decimal place as needed.)
For each sample size, state what happens to the mean and median.
For each sample size, the mean remains constant, and the median substantially increases
Comment on the role that the number of observations plays in resistance. A. As the sample size increases, the impact of the misrecorded data on the mean decreases. B. As the sample size increases, the impact of the misrecorded data on the mean remains the same.

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Problem 4456

Find the slope and y-intercept of the equation y=35x7.\text{Find the slope and } y\text{-intercept of the equation } y = \frac{3}{5} x - 7.

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Problem 4457

Using Theorem 1.28 , what is the value of the sum k=083k\sum_{k=0}^{8} 3^{k} ? 3912\frac{3^{9}-1}{2} 3812\frac{3^{8}-1}{2} 393^{9} 3(3812)3 \cdot\left(\frac{3^{8}-1}{2}\right)

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Problem 4458

In Marissa's calculus course, attendance counts for 15%15 \% of the grade, quizzes count for 15%15 \% of the grade, exams count for 50%50 \% of the grade, and the final exam counts for 20%20 \% of the grade. Marissa had a 100%100 \% average for attendance, 93%93 \% for quizzes, 86%86 \% for exams, and 85%85 \% on the final. Determine Marissa's course average.
Marissa's course average is \square %\%. (Type an integer or a decimal. Do not round.)

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Problem 4459

terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither. a. a(1)=7,a(n)=a(n1)3\quad a(1)=7, a(n)=a(n-1)-3 for n2n \geq 2. b. b(1)=2,b(n)=2b(n1)1\quad b(1)=2, b(n)=2 \cdot b(n-1)-1 for n2n \geq 2. c. c(1)=3,c(n)=10c(n1)\quad c(1)=3, c(n)=10 \cdot c(n-1) for n2n \geq 2. d. d(1)=1,d(n)=nd(n1)d(1)=1, d(n)=n \cdot d(n-1) for n2n \geq 2.

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Problem 4460

The table shows projections for the female population of a country (in millions). \begin{tabular}{l|c|c|c} Year & 2020 & 2045 & 2050 \\ \hline Female Population & 181 & 227 & 236 \end{tabular} (a) Find a quadratic function f(x)=ax2+bx+c\mathrm{f}(\mathrm{x})=\mathrm{ax}{ }^{2}+\mathrm{bx}+\mathrm{c} that gives the female population (in millions) in year x , where x=0\mathrm{x}=0 corresponds to the year 2000 . (b) Estimate the female population in the year 2030 . (a) The coefficient of x2x^{2} in the equation is a=a= \square (Do not round until the final answer. Then round to three decimal places as needed.)

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Problem 4461

Simplify the expression. 2783\sqrt[3]{\frac{-27}{8}}
Enter the exact answer. Hint: You can write roots as fractional exponents, for example 2783\sqrt[3]{\frac{-27}{8}} as (27/8)(1/3)(-27 / 8)^{\wedge}(1 / 3). However, the answer to this question is a fraction without needing a root symbol.

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Problem 4462

Find the inverse of the function on the given domain. f(x)=(x4)2,[4,)f1(x)=\begin{array}{l} f(x)=(x-4)^{2},[4, \infty) \\ f^{-1}(x)= \end{array}

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Problem 4463

Check My Work Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ( $2,354,67\$ 2,354,67 ). All percentage values in the answers need to include a percentage sign (\%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).
The Vetrone family members are all Cincinnati Reds baseball fans. They went to five games last season. The cost of each game, including parking, tickets, and food, is listed below. \266,$201,$197,$188,$162Roundyouranswerstothenearestcent.a.Whatisthemeancostpergameattended?b.Whatistherange?266, \$201, \$197, \$188, \$162 Round your answers to the nearest cent. a. What is the mean cost per game attended? b. What is the range? \squarec.Whatisthevariance? c. What is the variance? \squared.Whatisthestandarddeviation? d. What is the standard deviation? \squaree.IfallfivemembersoftheVetronefamilywenttoeachgame,whatwasthemeancostperpersontoattendeachgame? e. If all five members of the Vetrone family went to each game, what was the mean cost per person to attend each game? \square$

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Problem 4464

What is the slope of a line that passes through the points (1,3)(1,3) and (7,5)(7,5) in the xyx y-plane?

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Problem 4465

The circumference CC of a circle is a function of its radius given by C(r)=2πrC(r)=2 \pi r. a. Express the radius of a circle as a function of its circumference. Call this function r(C)r(C).
Enter the exact answer.
Enclose numerators and denominators in parentheses. For example, (ab)/(1+n)(a-b) /(1+n). r(C)=r(C)= b. Find r(34π)r(34 \pi) and interpret its meaning. r(34π)=r(34 \pi)= \square Number

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Problem 4466

Find the inverse of the function on the given domain. f(x)=(x4)2,[4,)f(x)=(x-4)^{2},[4, \infty)

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Problem 4467

Which sets of ordered pairs represent functions from AA to BB ? (Select all that app A={a,b,c} and B={1,2,3,4}A=\{a, b, c\} \text { and } B=\{1,2,3,4\} {(a,2),(c,3),(c,4),(b,4)}\{(a, 2),(c, 3),(c, 4),(b, 4)\} {(a,2),(b,3),(c,4)}\{(a, 2),(b, 3),(c, 4)\} {(2,a),(1,a),(3,c),(4,b)}\{(2, a),(1, a),(3, c),(4, b)\} Need Help? Read it Watch it Submit Answer 3. [-/1 Points] DETAILS MY NOTES
Determine whether the equation represents yy as a function of xx. y=x+3y=\sqrt{x+3} Yes No Need Help? Read It Watch it 4. [-/1 Points] DETAILS MY NOTES
Determine whether the equation represents yy as a function of xx. y=4x|y|=4-x Yes No

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Problem 4468

Pित्त Pिovian fina (fimentany and Supplementany Angles in Exercises 17, 18, 19, and 20 , 17. 80. a 3 b. 1.5

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Problem 4469

For the function f(x)=x29xf(x)=x^{2}-9 x, simplify each expression as much as possible
1. f(x+h)f(x)h,h0\frac{f(x+h)-f(x)}{h}, h \neq 0 : \square
2. f(w)f(x)wx,xw\frac{f(w)-f(x)}{w-x}, x \neq w : \square

Note: You can earn partial credit on this problem.

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Problem 4470

Find the inverse of the function. f(x)=95x3f(x)=9-5 x^{3}
Hint: The cube root is the same as an exponent of 1/31 / 3, so for 19x3\sqrt[3]{19 x}, you could type in (19x)(1/3)\left(19^{*} x\right)^{\wedge}(1 / 3). Remember your parentheses!

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Problem 4471

ons \& Modeling with Quadratic Equat Question 11, "Bus Econ 3.2.51
The profit for a product is given by P(x)=14x2+1540x42,000P(x)=-14 x^{2}+1540 x-42,000, where xx is the number of units produced and sold. How many units give break even (that is, give zero profit) for this product?

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Problem 4472

limxa+x2ax+x2a2xa\lim _{x \rightarrow a^{+}} \frac{\sqrt{x^{2}-a x}+\sqrt{x^{2}-a^{2}}}{\sqrt{x-a}} ail (aR)(a \in \mathbb{R})

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Problem 4473

Perform the operation. (9x+9)+(9x28x+6)(9 x+9)+\left(-9 x^{2}-8 x+6\right)

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Problem 4474

6. At the corner's pasta restaurant it is expected that 350 dishes will be sold at a price of K200 each. For each k 4 reduction in price, 20 more dishes will be sold. The restaurant is willing to supply 325 pasta dishes at K100 each, and 475 dishes at K220 each. a) Find the linear demand equation of the pasta dish. b) Find the linear supply equation of the pasta dish. c) Find the equilibrium price and the quantity of the pasta dish.

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Problem 4475

3. 求下列函数的微分: (1) y=1x+2xy=\frac{1}{x}+2 \sqrt{x} (2) y=xsin2xy=x \sin 2 x (3) y=xx2+1y=\frac{x}{\sqrt{x^{2}+1}}; (4) y=ln2(1x)y=\ln ^{2}(1-x) ; (5) y=x2e2xy=x^{2} \mathrm{e}^{2 x}; (6) y=excos(3x)y=\mathrm{e}^{-x} \cos (3-x); (7) y=arcsin1x2y=\arcsin \sqrt{1-x^{2}}; (8) y=tan2(1+2x2)y=\tan ^{2}\left(1+2 x^{2}\right); (9) y=arctan1x21+x2y=\arctan \frac{1-x^{2}}{1+x^{2}} (10) s=Asin(ωt+φ)(A,ω,φs=A \sin (\omega t+\varphi)(A, \omega, \varphi 是常数 )).
4. 将适当的函数填人下列括号内,使等式成立: (1) d()=2 dx\mathrm{d}(\quad)=2 \mathrm{~d} x; (2) d()=3xdxd(\quad)=3 x d x (3) d()=cost dt\mathrm{d}(\quad)=\cos t \mathrm{~d} t (4) d()=sinωxdx(ω0)d(\quad)=\sin \omega x d x \quad(\omega \neq 0); (5) d()=11+x dx\mathrm{d}(\quad)=\frac{1}{1+x} \mathrm{~d} x (6) d()=e2xdxd(\quad)=e^{-2 x} d x (7) d()=1x dxd(\quad)=\frac{1}{\sqrt{x}} \mathrm{~d} x (8) d()=sec23x dxd(\quad)=\sec ^{2} 3 x \mathrm{~d} x.

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Problem 4476

Gustaf wants to earn $3,000\$ 3,000 simple interest on a $9,000\$ 9,000 investment with an annual simple interest rate of 2.5%2.5 \%. How long should Gustaf plan to invest his money?

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Problem 4477

Thinking of density curve shapes, if an instructor gave a test and most students did well, the distribution of grades should be \qquad -skewed.

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Problem 4478

E.7. You can click on the Review link to access the section in your e Text.
Total U.S. National Park System land occupies 84.4 million acres. How many square miles is this? (Note that 1 acre =43,560ft2=43,560 \mathrm{ft}^{2} and 1 mile =5280ft=5280 \mathrm{ft}.) Express your answer in square miles to three significant figures.
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Part B
Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is National Park System land ? Express your answer in percent to three significant figures.

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Problem 4479

Find the Distance

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Problem 4480

Write 116\frac{1}{16} as a decimal number. Submit

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Problem 4481

 (5) y=x25xy21012\begin{array}{l} \text { (5) } y=x^{2}-5 \\ \begin{array}{c|c} x & y \\ \hline-2 \\ -1 & \\ 0 & \\ 1 & \\ 2 & \end{array} \end{array}

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Problem 4482

Three Normal distributions all have mean 20. Distribution A has standard deviation 1, distribution B has standard deviation 5, and distribution CC has standard deviation 10. The distribution with the flattest peak is \qquad Distribution A Distribution C Distribution B They will all have the same shape.

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Problem 4483

3. 求下列函数的微分: (1) y=1x+2xy=\frac{1}{x}+2 \sqrt{x}; (2) y=xsin2xy=x \sin 2 x (3) y=xx2+1y=\frac{x}{\sqrt{x^{2}+1}}; (4) y=ln2(1x)y=\ln ^{2}(1-x) ; (5) y=x2e2xy=x^{2} e^{2 x}; (6) y=excos(3x)y=\mathrm{e}^{-x} \cos (3-x) (7) y=arcsin1x2y=\arcsin \sqrt{1-x^{2}}; (8) y=tan2(1+2x2)y=\tan ^{2}\left(1+2 x^{2}\right); (9) y=arctan1x21+x2y=\arctan \frac{1-x^{2}}{1+x^{2}}; (10) s=Asin(ωt+φ)(A,ω,φs=A \sin (\omega t+\varphi)(A, \omega, \varphi 是常数 )).
4. 将适当的函数填人下列括号内,使等式成立: (1) d()=2 dx\mathrm{d}(\quad)=2 \mathrm{~d} x (2) d()=3xdxd(\quad)=3 x d x (3) d()=cost dt\mathrm{d}(\quad)=\cos t \mathrm{~d} t; (4) d()=sinωxdx(ω0)d(\quad)=\sin \omega x d x \quad(\omega \neq 0); (5) d()=11+x dx\mathrm{d}(\quad)=\frac{1}{1+x} \mathrm{~d} x; (6) d()=e2xdxd(\quad)=e^{-2 x} d x; (7) d()=1x dx\mathrm{d}(\quad)=\frac{1}{\sqrt{x}} \mathrm{~d} x; (8) d()=sec23x dx\mathrm{d}(\quad)=\sec ^{2} 3 x \mathrm{~d} x.

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Problem 4484

Suppose the lengths of sport-utility vehicles (SUV) are Normally distributed with mean μ=190\mu=190 inches and standard deviation σ=5\sigma=5 inches. Marshall just bought a brand-new SUV that is 194.5 inches long and he is interested in knowing what percentage of SUVs is longer than his. Using his statistical knowledge, he drew a normal curve and labeled the appropriate area of interest. Because his value is above the mean, it can be said that his zz-score will be \qquad Plot B zero negative 194.5 positive

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Problem 4485

3x2+2x5=03 x^{2}+2 x-5=0

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Problem 4486

Most computer random number generators (at least initially-we can build others based on this) give random numbers uniformly distributed between 0 and 1 . That is, any number between 0 and 1 is equally likely to occur. Because the area under the curve is equal to 1 , each tenth occurs 10%10 \% of the time, or 0.1 . What proportion of the time should our random number generator give us a value less than 0.3 or larger than 0.8 ? 30%30 \% 50\% 20\% 80%80 \%

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Problem 4487

x˙A]\left.\dot{x}_{A}\right] Which sign makes the statement true? 0.8?45-0.8 ? \frac{-4}{5} \square \square \square Submit

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Problem 4488

Find the inverse of the function on the given domain. f(x)=(x4)2,[4,)f(x)=(x-4)^{2},[4, \infty) aba^{b} sin(a)\sin (a) \infty α\alpha f1(x)=f^{-1}(x)=

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Problem 4489

4. It is possible to use the Squeeze Theorem to prove that limx0(xsin(1x))=0\lim _{x \rightarrow 0}\left(x \cdot \sin \left(\frac{1}{x}\right)\right)=0. Why couldn't we obtain the same result by writing limx0(xsin(1x))=limx0xlimx0(sin(1x))=0limx0(sin(1x))=0?\begin{aligned} \lim _{x \rightarrow 0}\left(x \cdot \sin \left(\frac{1}{x}\right)\right) & =\lim _{x \rightarrow 0} x \cdot \lim _{x \rightarrow 0}\left(\sin \left(\frac{1}{x}\right)\right) \\ & =0 \cdot \lim _{x \rightarrow 0}\left(\sin \left(\frac{1}{x}\right)\right)=0 ? \end{aligned}

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Problem 4490

1 point A $27,000\$ 27,000 car has a resale value of $18,000\$ 18,000 five years after it was purchased. Assuming the value of this car depreciates linearly, estimate the value of the car 8 years after it was purchased. Enter your answer rounded to the nearest whole number. Do not enter the $\$ symbol. Type your answer...
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Problem 4491

5. Colour in the base ten blocks you would use to make the number: 1,485 \square \square \square \square \square \square III \square \square \square WWmm \square \square \#\#\#\#\# \square \square \square \square (1) 0

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Problem 4492

Evaluate the following expression, or state that the root is not a real number. 16+9\sqrt{16+9}

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Problem 4493

Find the function value, if possible. q(t)=5t2+6t2q(t)=\frac{5 t^{2}+6}{t^{2}} (a) q(2)q(2) (b) q(0)q(0) (c) q(x)q(-x)

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Problem 4494

70. How many numbers between 50 and 100 are evenly divisible by 3 ? A. 16 B. 17 C. 18 D. 33

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Problem 4495

Suppose f(x)=x1xf(x)=\frac{x-1}{x} and g(x)=11xg(x)=\frac{1}{1-x}
Then (fg)(x)=(f \circ g)(x)= \square , and (gf)(x)=(g \circ f)(x)= \square . Remarkable!

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Problem 4496

10. 74=v47\frac{7}{4}=v-\frac{4}{7}

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Problem 4497

4. [2.945.88[2.945 .88 Points]
DETAILS MY NOTES SCALCET9 6.XP.1.UOZ. Sketch the region endosed by the given curves. Decide whether to integrate with respect to xx or yy. Draw a typical approximating rectangle. y=x23x,y=2x+6y=x^{2}-3 x, y=2 x+6 fod the wee ef the regian. \square Aned Heip? thanes

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Problem 4498

Saved Help Save \& Exit Submit
Answer the following questions. Hint. Use the accounting equation. a. At the beginning of the year, Addison Company's assets are $300,000\$ 300,000 and its equity is $100,000\$ 100,000. During the year, assets increase $80,000\$ 80,000 and liabilities increase $50,000\$ 50,000. What is the equity at year-end? b. Office Store Company has assets equal to $123,000\$ 123,000 and liabilities equal to $47,000\$ 47,000 at year-end. What is the equity for Office Store Company at year-end? c. At the beginning of the year, Quaker Company's liabilities equal $70,000\$ 70,000. During the year, assets increase by $60,000\$ 60,000, and at year-end assets equal $190,000\$ 190,000. Liabilities decrease $5,000\$ 5,000 during the year. What are the beginning and ending amounts of equity?
Complete this question by entering your answers in the tabs below. Required A Required B Required C
At the beginning of the year, Addison Company's assets are $300,000\$ 300,000 and its equity is $10\$ 10 I increase $80,000\$ 80,000 and liabilities increase $50,000\$ 50,000. What is the equity at year-end? \begin{tabular}{|c|c|c|c|c|c|c|} \hline & Assets & == & Liabilities + & + & \multicolumn{2}{|l|}{ Equity } \\ \hline Beginning & $300,000=\$ 300,000= & == & & + & \ & 100,000 \\ \hline Change & 80,000= & = & 50,000+ & + & & \\ \hline Ending & & =$ & + & + & & \\ \hline \end{tabular} Bequired A Required B

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Problem 4499

omplete the table. f(x)={36x2,x<6x6,x6f(x)=\left\{\begin{array}{ll} 36-x^{2}, & x<6 \\ x-6, & x \geq 6 \end{array}\right. \begin{tabular}{|l|l|l|l|l|l|} \hlinexx & 4 & 5 & 6 & 7 & 8 \\ \hlinef(x)f(x) & & & & & \\ \hline \end{tabular}

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Problem 4500

Use the currency exchange rates in the table for the following question.
Your dinner in Mexico City cost 2680 Mexican pesos. How much was it in U.S. dollars? \begin{tabular}{lll} \multicolumn{1}{c}{ Currency } & \begin{tabular}{c} Dollars per \\ Foreign \end{tabular} & \begin{tabular}{c} Foreign per \\ Dollar \end{tabular} \\ British pound & 1.356 & 0.7376 \\ Canadian dollar & 0.7828 & 1.277 \\ European euro & 1.225 & 0.8165 \\ Japanese yen & 0.009694 & 103.2 \\ Mexican peso & 0.05035 & 19.86 \end{tabular}
Your dinner cost \ \square$ in U.S. dollars. (Round to two decimal places as needed.)

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