Model

Problem 2701

The half-life of caffeine in the human body is about 6.4 hours. A cup of coffee has about 100 mg of caffeine. a. Write an equation for the amount of caffeine in a person's body after drinking a cup of coffee? Let $C$ be the milligrams of caffeine in the body after $t$ hours. $\square$ b. How much caffeine will remain after 10 hours? $\square$ mg c. How long until there are only 20 mg remaining? $\square$ hours

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Problem 2702

Carla Vista Corporation was organized on January 1,2027. It is authorized to issue 23,000 shares of $5 \%, \$ 50$ par value preferred stock and 458,000 shares of no-par common stock with a stated value of $\$ 2$ per share, The following stock transactions were completed during the frist year.
Jan. 10 Issued 69,000 shares of common stock for cash at $\$ 5$ per share. Mar. 1 Issued 11,400 shares of preferred stock for cash at $\$ 57$ per share. May 1 Issued 114,000 shares of common stock for cash at $\$ 8$ per share. Sept. 1 Issued 4,800 shares of common stock for cashat $\$ 4$ per share. Nov. 1 Issued 2,800 shares of preferred stock for cash at $\$ 55$ per share. (a)
Your Answer Correct Answer
Your answer is correct.
Prepare a tabular summary to record the transactions. (If a transoction couses a decrease In Assets, Liabivilies or Stochholders' Equity. place a negative sign (or parentheses) in front of the amount entered for the particular Asset, Uability or Equity item that was neduced.). eTextbook and Media Solution Attempts: 3 of 3 used (b)
Prepare the paid-tic capital portion of the stockholders equity section at December 31, 2027. CARLA vista corporation Partial Balance Sheet December 31, 2027 $\square$ $\square$ $\square$ $\square$ 3 $\square$ $\square$ $\square$ $\square$ $\square$

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Problem 2703

Write the sentence as an equation. the product of 189 and $h$ equals $m$
Type a slash ( / ) if you want to use a division sign. $\square$ Submit

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Problem 2704

WS: $30-2$ A6 Sem
7. The table below shows Canmore's population from 2010 to 2017. The data is taken from Alberta.ca Regional Dashboard. \begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline Year & 2010 & 2011 & 2012 & 2013 & 2014 & 2015 & 2016 & 2017 \\ \hline Population & 12841 & 12796 & 13177 & 13604 & 14037 & 14193 & 14646 & 14936 \\ \hline \end{tabular} a. Assuming the population of a Canmore has been growing exponentially, find the regression equation in the form $P(t)=a b^{t}$ , where $P(t)$ is the population and $t$ is the number of years since 2010 ( 2010 is year 0 in your calculator). Express the values of $a$ to the nearest whole number and $b$ to the nearest thousandth. (1 mark) b. Using your regression equation, calculate what the population of Canmore should have been, to the nearest whole number, in 2020. (1 mark) c. If the actual population of Canmore in 2020 was 14798 people, why might the predicted population be different than the actual population? ( 1 mark) d. Assuming that the growth rate of Canmore follows your regression equation, during what year will the population reach 18000 ? ( 1 mark)

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Problem 2705

Soncept Questions
The diagram to the right is a Lorenz curve. Using the 3-point curved line drawing tool, sketch a Lorenz curve that illustrates a more (but not perfectly) equal distribution of income than the Lorenz curve depicted to the right. Label this curve ' $\mathrm{LC}_{2}$ '. Note: Carefully follow the instructions above and only draw the required object.

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Problem 2706

Question 6 (a) Form a quadratic equation whose roots are $3 \frac{1}{2}$ and $-2 \frac{1}{3}$ . Express your answer in the form $a x^{2}+b x+c=0$ , where $a, b, c$ are integers. (b) Form an equation whose roots are twice those in previous part.

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Problem 2707

42. До гіперболи належить $M_{0}(-5,3)$ , а ексцентриситет гіперболи дорівнює $\sqrt{2}$ . Скласти канонічне рівняння гіперболи та побудувати ії.
43. Скласти рівняння і побудувати гіперболу, якщо вона має асимптоти $y= \pm \frac{2}{3} x$ і їй належить точка $M_{1}(9 / 2,-1)$ .

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Problem 2708

إليك المعلومـات التالية عن منشـاة محمد التجاريـة: 10000 دينار، في حينّ كان رصيد البنك طبقا لدفاتر منشـاة محمد التجاريـة
مبلغ 8000 دينار. 1-تبين أن الشيكات الصـادرة التالية لم تصرف بعد من قبل البك، الشيك رقم 101 بمبلغ 1500 دينار، والشيك ديك رقم 151 بمبلغ 2000 دينار، والشيك رقم 201 بمبلغ 500 دينار. 2- أرفق البك بكشغ الحساب إشعارا يغيد بـان البنك قد قام بتحصيل كمبيالة قيمتها 500 دينار بتاريخ 29/12 إلا أن المنشاة لم تسجلها بدفاترهـا. 3- قامت المنشاة بإيداع مبلغ 500 دينار نقدا بحسابها في البنك بتاريخ يظهر بكثف حسـاب البنك الوارد من البنك. 5- أعاد البنك شيكا بقيمة 2000 دينار لعدم وجود رصيد للعيد العميل احمد 6- قام البنك بتسجيل عمولات بن المينة بقيمة 100 دينار على المنشأة إلا أن
المبلغ لم يسجل بدفاتر المنشنأة بعد. المطلوب:
1. عمل مذكرة تسوية البنك في 12/12/2012.31 (15 علامـات) علامـات).

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Problem 2709

2. (MP) Use Tools Marcela gets to school later than her friend Kim about half the time. Describe a way to simulate this event for 10 school days. Then perform the simulation. How many times does it show Marcela arriving later than Kim? What is the experimental probability of this event?

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Problem 2710

Express the function graphed on the axes below as a piecewise function.
Answer Altempt 1 put of 3 $f(x)=\left\{\begin{array}{ll}\square & \text { for } \square \\ \square & \text { for } \square\end{array}\right.$ $\square$ $\square$ $\square$ $\square$ $\square$ Adi Rule Remowe Rule Submit Answer

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Problem 2711

An electron microscope can magnify an object from 3000 times to 100,000 times. Assuming these values are exact, express these magnifications $M$ as an inequality and graph them. $\qquad$
Express M as a single inequality.

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Problem 2712

Question 1 of 10, Step 1 of 2 0/14 Correct 3
A company makes two grades of paint, grade I, guaranteed for 5 years, and grade II, guaranteed for 10 years. A gallon of grade I costs $\$ 3.50$ to make, while a gallon of grade II costs $\$ 3.70$ to make. The weekly fixed costs are $\$ 3450$ .
Step 1 of 2 : Find the cost function $C(x, y)$ for making $x$ gallons of grade I and $y$ gallons of grade II. Answer Tables Keypad Keyboard Shortcuts $C(x, y)=\square$ Submit Answer

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Problem 2713

1- Write a Python program that requests five integer values from the user. It then prints the maximum and minimum values entered. If the user enters the values $3,2,5,0$ , and 1 , the program would indicate that 5 is the maximum and 0 is the minimum. Your program should handle ties properly; for example, if the user enters 2, 42, 3 and 3, the program should report 2 as the minimum and 4 as maximum.

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Problem 2714

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 410 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled? Assume the population is normally distributed.
State the null and alternative hypotheses for the above scenario.

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Problem 2715

$14{ }^{F}$ is inversely proportional to the square of $v$ . Given that $F=6.5$ when $\nu=4$ find a formula for $F_{\text {in }}$ terms of $v$ .

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Problem 2716

Question 2 (1 point) A car starts from rest and continues at a rate of $v=\frac{1}{8} t^{2} \mathrm{ft} / \mathrm{s}$ . Find the function that relates the distance $s$ the car has traveled to the time $t$ in seconds.

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Problem 2717

Noor wants to spend less than $\$ 20$ on condiments. Each kilogram of salt costs $\$ 1.50$ , and each kilogram of pepper costs \$2.50.
Write an inequality that represents the number of kilograms of salt $(S)$ and pepper $(P)$ Noor can buy on her budget.

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Problem 2718

Question Show Examples
The rate of change $\frac{d P}{d t}$ of the number of bacteria in a tank is modeled by a logistic differential equation. The maximum capacity of the tank is 914 bacteria. At 8 AM , the number of bacteria in the tank is 228 and is increasing at a rate of 37 bacteria per minute. Write a differential equation to describe the situation.
Answer Attempt 1 out of 2 $\frac{d P}{d t}=$ $\square$ Submit Answer

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Problem 2719

The fox population in a certain region has an annual growth rate of 5 percent per year. (Note: Foxes mate once per year.)
It is estimated that the fox population in the year 2020 was 14000. (a) Find an exponential function that models the fox population $t$ years after 2020 (Note: $t=0$ for 2020). The function is $P(t)=$ $\square$ (b) Use the function from part (a) to estimate the fox population in the year 2028. (The answer should be an integer.) There will be $\square$ foxes in the year 2028.

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Problem 2720

Find an equation for the graph shown to the right.
Type the equation in the form $y=A \sin (\omega x)$ or $y=A \cos (\omega x)$ . $\mathrm{y}=\square$ (Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 2721

Find an equation for the graph shown to the right.
Type the equation in the form $y=A \sin (\omega x)$ or $y=A \cos (\omega x)$ . $y=\square$ (Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 2722

Find an equation for the graph shown to the right.
Type the equation in the form $y=A \sin (\omega x)$ or $y=A \cos (\omega x)$ . $y=\square$ (Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 2723

A fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides is to be made of material that costs : dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Dimensions: $\square$ x $\square$
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Problem 2724

Which equation represents the same line as the points in the table? \begin{tabular}{|c|c|} \hline Input (x) & Output $(y)$ \\ \hline-4 & 5 \\ \hline 0 & 2 \\ \hline $\frac{8}{3}$ & 0 \\ \hline \end{tabular} $y=-\frac{3}{4} x+\frac{8}{3}$ $y=-\frac{3}{4} x+2$ $y=2 x-\frac{3}{4}$ $y=-3 x+2$

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Problem 2725

The table below shows the amount of time each of the 15 students in an introductory biology class spent studying for the first exam, and the student's score on the exam out of 100. \begin{tabular}{|c|c|} \hline $x$ (minutes spent studying) & $y$ (score on exam in points) \\ \hline 150 & 98 \\ \hline 70 & 65 \\ \hline 100 & 74 \\ \hline 120 & 46 \\ \hline 60 & 72 \\ \hline 0 & 52 \\ \hline 10 & 35 \\ \hline 75 & 79 \\ \hline 120 & 80 \\ \hline 45 & 72 \\ \hline 50 & 80 \\ \hline 0 & 30 \\ \hline 10 & 56 \\ \hline 40 & 64 \\ \hline 30 & 81 \\ \hline \end{tabular}
To check this is entered correctly on your calculator, press [stat], go to CALC, and select "2:2-Var Stats". Run this on your two lists. When you scroll down the list, you should see $\Sigma x y=65155$
Enter the data into your calculator and obtain a linear equation of best fit using the linear regression feature. Type the equation here, in the form $y=m x+b$ . If necessary, round the values of $m$ and $b$ to three decimal places. $\square$ Based on your regression equation, what score would you predict for a student who has studied for 1 hour and 10 minutes? Round your answer to a whole number of points. $\square$ points Based on your regression equation, how much time should a "typical" student spend studying if they wanted to score at least 75 points on the exam? Round your answer up to the next full minute. $\square$ minutes

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Problem 2726

Fifth National bank offers four different certificates of deposit (CD). The first CD (A) offers a $4 \%$ interest rate for amount greater than $\$ 10,000$ . The second CD (B) offers a $4.2 \%$ interest rate for amount greater than $\$ 25,000$ . The third CD (C) offers a $4.5 \%$ interest rate for amount greater than $\$ 30,000$ . Finally, the fourth CD (D) offers a $5 \%$ interest rate for amount greater than $\$ 35,000$ . A customer has $\$ 150,000$ to deposit. She wishes to deposit not more than $1 / 3$ of her money in any of the CDs. She likes to deposit exactly three times of her money in CD\#2 than CD\#1. She wishes the sum of the first and the second CDs to be less than or equal to the third CD.
Question 1 Which of the constraints needs to be adjusted if interest rate for the third CD is increased after running the problem through Excel's Solver? None

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Problem 2727

Set up the problem shown below and use Solver to verify that you will get $\$ 5,266.67$ in interest per year.
You have $\$ 120,000$ to invest in 4 CDs. The rates are shown in the following table: \begin{tabular}{|l|l|l|} \hline CDs & Amount Invested & Interest Rate \\ \hline A & $\$$ - & $3 \%$ \\ \hline B & $\$-$ & $4 \%$ \\ \hline C & $\$-$ & $4.50 \%$ \\ \hline D & $\$-$ & $5 \%$ \\ \hline \end{tabular}
There is a constraint that the money invested in CD B be exactly twice the amount of money invested in CD A. This means that you can dispense with one of the decision variables.

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Problem 2728

$\text{Given the following data points:}$ \begin{align} &\text{Shoe size (pointure de Soulier): 6, Foot length (longueur du pied): 20, Height (hauteur): 146.5} \\ &\text{Shoe size (pointure de Soulier): 6.5, Foot length (longueur du pied): 24, Height (hauteur): 162} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): 22.5, Height (hauteur): 163} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): 23, Height (hauteur): 166} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): 18, Height (hauteur): 169} \\ &\text{Shoe size (pointure de Soulier): 7, Foot length (longueur du pied): \text{unknown}, Height (hauteur): \text{unknown}} \end{align}
$\text{Using a linear model, predict the height for the last data point with a shoe size of 7.}$
$\text{Determine whether interpolation or extrapolation is used in this prediction.}$

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Problem 2729

Write the standard form of the equation of the circle with the given center and radius. Center $(-4,-5), r=\sqrt{2}$
The equation of the circle in standard form is $\square$ (Simplify your answer.)

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Problem 2730

Select the correct sequence to convert days to seconds:
1. days $\rightarrow$ seconds
2. days $\rightarrow$ minutes $\rightarrow$ hours $\rightarrow$ seconds
3. days $\rightarrow$ hours $\rightarrow$ minutes $\rightarrow$ seconds
4. days $\rightarrow$ hours $\rightarrow$ seconds

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Problem 2731

Write the electron configuration for a sodium ion (Na $^+$ ).

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Problem 2732

Create a grouped frequency distribution for these IQ scores: 85-89 for the first class, with equal widths for others.

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Problem 2733

Explain how to represent division with 2-digit divisors in math problems.

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Problem 2734

Given the fraction $\frac{3}{5}$ :
1. Model it on a 10x10 grid.
2. Create a table of 5 equivalent ratios to 100.
3. Identify decimal and percent equivalents; explain errors in options A, B, D.
4. Find the number where $\frac{3}{5}$ of it equals 18.
5. Draw a number line for question 4.

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Problem 2735

Find the position of the missing score (orange box) on a graph where total distance below the mean is 5 and above is 7.

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Problem 2736

Write a system of equations for the vector equation $x_{1}\begin{bmatrix} 3 \\ -3 \\ 7 \end{bmatrix} + x_{2}\begin{bmatrix} 6 \\ 0 \\ -6 \end{bmatrix} = \begin{bmatrix} 4 \\ -2 \\ 8 \end{bmatrix}$ . Choose the correct option.

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Problem 2737

Express the system as a vector and matrix equation:
$\begin{array}{r} 9 x_{1}+x_{2}-3 x_{3}=8 \\ 10 x_{2}+4 x_{3}=0 \end{array}$

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Problem 2738

Solve the inequality $|3p - 4| < p + 8$ and graph the solution set.

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Problem 2739

Create the augmented matrix from $A$ and $b$ for $A \mathbf{x}=\mathbf{b}$ , then solve for $\mathbf{x}$ .

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Problem 2740

Create the augmented matrix for $A \mathbf{x} = \mathbf{b}$ , then solve for $\mathbf{x}$ as a vector. Given:
$A=\begin{bmatrix} 1 & 2 & -4 \\ -3 & -3 & 3 \\ 3 & 2 & 2 \end{bmatrix}, \; b=\begin{bmatrix} 4 \\ 3 \\ -8 \end{bmatrix}$

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Problem 2741

Draw a line to model Chicago's population growth from 1880 (500,000) to 1930 (3,400,000) and find its equation.

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Problem 2742

Create an equation for this: 19 minus $\frac{5}{3}$ of a number equals 4. Solve for $x$ . Options: A. $19-\frac{5}{3} x=4$ B. $\frac{5}{3}-19 x=4$ C. $19-\frac{5}{3}=4$ D. $5 \frac{5}{3} x-19=4$ . Find $x$ .

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Problem 2743

Write a compound inequality for: A quantity $x$ is less than 8 or greater than 21.

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Problem 2744

List the sample space for choosing 2 marbles at random from a bag with green, red, and blue marbles.

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Problem 2745

1. List the months of the birthdays: {January, April, May}.
2. List multiples of 3 from 0 to 21: {0, 3, 6, 9, 12, 15, 18, 21}.
3. Represent quantities in interval notation.
4. Kelly can work hours in the interval [60, 120].

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Problem 2746

Find a formula for $a_{n}$ using the sequence $3, 8, 13, 18, 23, \ldots$ .

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Problem 2747

Determine the formula for $a_{n}$ using the sequence $a_{0}, a_{1}, a_{2}, \ldots$ given as $-2, 3, -4, 5, -6, \ldots$ .

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Problem 2748

Find a formula for $a_{n}$ based on the sequence: -4, 9, -14, 19, -24. What is $a_{n}=$ ?

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Problem 2749

Bert made 3 batches of sauce using 24 ounces total, reducing hot sauce by 2 ounces per batch. Find $u$ : usual amount per batch.
Which equation to use? $3(u-2)=24$ $3 u-2=24$ $2 u-3=24$ $2(u-3)=24$
What is $u$ ? Answer in ounces.

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Problem 2750

Find a formula for $a_{n}$ based on the sequence $0, 3, -6, 9, -12, \ldots$ . What is $a_{n}=$ ?

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Problem 2751

Ms. Garza ordered 9 cases of caramel apples, sold 685, and had 35 left. What equation finds apples per case? $9c - 685 = 35$

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Problem 2752

Find the formula for the sequence $a_{n}=\{3,6,9,12, \ldots\}$ . Options: $a_{n}=3 n$ , $a_{3}=3_{a}$ , $a_{n}=9 n$ , $a_{n}=6_{n}$ .

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Problem 2753

Find the equation of a line parallel to the one with slope $1/2$ that passes through $(0,-3)$ .

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Problem 2754

Find a linear equation for the line through $(1,4)$ with slope 6.

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Problem 2755

Find the linear equation of the line through the points $(1,-6)$ and $(-1,-1)$ . $y(x) =$

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Problem 2756

Find functions $f$ and $g$ such that $h(x)=(x+8)^{3}=f(g(x))$ . Use $f(x)=x^{3}$ or $g(x)=x+8$

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Problem 2757

Find a linear equation for the line passing through the points $(0.5,-0.75)$ and $(1,-5.75)$ . $y(x)=$

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Problem 2758

Find the price per bushel of corn using $p(x)=6+0.08 x+0.09 x^{2}$ for $x=0$ to $5$ .

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Problem 2759

Next week, you charged \$9 per guest with 39 guests on average. Find:
(a) The linear demand equation $q(p)=$ (b) The revenue function $R(p)=$ (c) The cost function $C(p)=-25.5p+488$

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Problem 2760

Next week, you charge \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find revenue $R(p)=$ . (c) Given costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Determine break-even entrance fees $p=$ (two values, rounded to two decimals).

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Problem 2761

Given sales and prices for Q1 2009 and 2010, find the linear demand function $q(p)$ and predict sales at \$75. For each \$1 price increase, how many units decrease?

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Problem 2762

Find the linear demand function for cell phones using the 2009 and 2010 data. Predict sales at \$156 and state the decrease per \$1 increase.
$q(p)=$

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Problem 2763

RideEm Bicycles can make 170 bikes for \$10,300 and 190 bikes for \$10,900.
(a) Find the cost function $C(x)=$ . (b) What are the fixed costs in dollars? (c) What are the variable costs in dollars?

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Problem 2764

Worldwide cell phone sales data for 2009 and 2010 shows prices at \$163 (2009) and \$153 (2010).
(a) Demand equation: $q(p)=-39p+6,472$ . Predict sales at \$156. Round to nearest million.
(b) Sales decrease by 39 million units for each \$1 price increase.

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Problem 2765

Given \$7,500:
(a) Create a linear function for development fee $p$ based on contracts $q$ :
p(q)=
(b) Find total revenue $R$ from $q$ contracts:
R(q)=
(c) Monthly costs: Fixed: \ $150,000, Variable: \$1,500q. Cost function$ C(q)=
(d) Profit function $P(q)=
(e) Find break-even contracts signed: ISeeYou breaks even at contracts.

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Problem 2766

Charge \ $9 per guest, average 39 guests. Find demand$ q(p) $, revenue$ R(p) $, profit$ P(p)$, and break-even fees.

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Problem 2767

ISeeYou charges \$7,500.
(a) Create a linear function for the fee $p$ for $q$ contracts: $p(q)=$ . (b) Determine total revenue $R$ from $q$ contracts: $R(q)=$ . (c) Monthly costs: Fixed \ $150,000, Variable \$1,500 per contract. Find cost function:$ C(q)=$.

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Problem 2768

Next week, you charged \$9 per guest with an average of 39 guests.
(a) Find the demand equation $q(p)=$ . (b) Find revenue $R(p)=$ . (c) Given $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Determine break-even entrance fees, rounded to two decimal places.

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Problem 2769

Given cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

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Problem 2770

Next week, you charged \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find the revenue function $R(p)=$ . (c) Given costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Find break-even entrance fees, rounding to two decimal places.

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Problem 2771

Next week, you charge \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find revenue $R(p)=$ . (c) Costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Determine break-even entrance fees $p=$ .

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Problem 2772

RideEm Bicycles produces 170 bikes for \ $10,300 and 190 bikes for \$10,900. Find the cost function$ C(x)$ and fixed/variable costs.

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Problem 2773

Show how a rainy season affects the supply of tomatoes by shifting the supply curve right on the graph.

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Problem 2774

Mark earns \$1,650/month. New job pays \$9.80/hour + overtime. Find overtime hours to match weekly earnings.

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Problem 2775

How much do 11 toy parts cost if 2 parts are \$0.90, 7 parts are \$3.15, 12 parts are \$5.40, and 15 parts are \$6.75?

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Problem 2776

Solve for the number in the equation: 9 - $\frac{x}{7} = -5$ .

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Problem 2777

Si cuentas tus latidos desde la medianoche del 1 de enero de 2000, ¿cuándo alcanzarías el latido número $1,000,000$ y el $1,000,000,000$ ?

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Problem 2778

A car worth \ $22,500 decreases by \$3200 per year for 6 years. Define$ V(x) $for$ 0 \leq x \leq 6 $and find$ V(3)$.

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Problem 2779

Graph the pool emptying rate function to find the time to empty it. Transform $f(x) = |x - 1| + 3$ with a horizontal shrink by $\frac{1}{3}$ .

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Problem 2780

The pool drains at 3 inches/hour. After 5 hours, the depth is 32 inches. Find the point-slope equation.

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Problem 2781

Create a 3x3 magic square using 9 of the numbers: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Explain your solution and strategies.

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Problem 2782

Create a bar chart for the college choice survey data: Definitely yes (0.447), Probably yes (0.373), Probably no (0.134), Definitely no (0.046). Suggest a headline for your article.

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Problem 2783

Find the cost of a Toronto car in USD using dimensional analysis. Choose the right fractions to cross-cancel units. Use $25000 \mathrm{CAD}$ and $1 \mathrm{USD} / 1.329 \mathrm{CAD}$ . Round to the nearest dollar.

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Problem 2784

A mug contains 220 grams of water. How many moles is this? Use the fractions 220 g/1 and 1 mole/18 g for your calculation. Round to one decimal place.

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Problem 2785

Select two fractions that, when multiplied, yield the cost per mile to drive, rounding to the nearest cent:
1 gallon / 2.30 dollars 2.30 dollars / 1 gallon 24 miles / 1 gallon 1 gallon / 24 miles
Find the cost in \$ per mile.

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Problem 2786

Determine the line equation that goes through points $P=(1,4)$ and $Q=(-1,-4)$ .

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Problem 2787

Your answer is incorrect. The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of $5.6 \mathrm{~mm}^{2}$ and an observed doubling time of 5 minutes. (a) Let $t$ be the time (in minutes) passed, and let $y$ be the area of the sample at time $t$ . Write a formula relating $y$ to $t$ . Use exact expressions to fill in the missing parts of the formula. Do not use approximations. $y=5.6 e^{\left(\frac{\ln 2}{5}\right) t}$ (b) What will the area of the sample be in 22 minutes?
Do not round any intermediate computations, and round your answer to the nearest tenth. $179.2 \mathrm{~mm}^{2}$

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Problem 2788

e) . $1, .1, .1$
4. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation? a) Assign " $0,1,2$ " as watching the shopping channel at least once a week and " $3,4,5,6,7,8$ , and 9 " as not watching. b) Assign " $0,1,2,3$ " as watching the shopping channel at least once a week and " $4,5,6,7,8$ , and 9 " as not watching. c) Assign " $1,2,3,4,5$ " as watching the shopping channel at least once a week and " $6,7,8,9$ , and 0 " as not watching. d) Assign " 0 " as watching the shopping channel at least once a week and " $1,2,3,4$ , and 5 " as not watching; ignore digits "6, 7, 8, and 9." e) Assign " 3 " as watching the shopping channel at least once a week and " $0,1,2,4,5,6,7,8$ , and 9" as not watching.

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Problem 2789

Write an equation in slope-intercept form for the line with slope $\frac{1}{4}$ and $y$ -intercept 3 .

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Problem 2790

21. John wants to get a gym membership. He is deciding between two gyms. Gym A charges a monthly flat rate of $\$ 20$ , plus $\$ 2$ per visit. Gym B charges a monthly flat rate of $\$ 15$ , plus $\$ 3$ per visit. a) Create the two equations -
Gym A: Gym B: b) Find the POI. What does this represent?

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Problem 2791

ixl.com
Graph this line using the slope and $y$ -intercept: $y=-\frac{1}{3} x-8$
Click to select points on the graph. Submit Work it out

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Problem 2792

Dom dic 1 ixl.com
Graph this line using the slope and $y$ -intercept: $y=-\frac{3}{4} x-2$
Click to select points on the graph. Submit Work it out

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Problem 2793

8:21 p.m. Dom dic 1 ixl.com
Graph this line using the slope and $y$ -intercept: $y=\frac{8}{3} x-1$
Click to select points on the graph. Submit Work it out

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Problem 2794

Graph this line using the slope and $y$ -intercept: $y=\frac{2}{3} x-10$
Click to select points on the graph. Submit

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Problem 2795

ng and reasoning. MEDIUM O Write a sinusoidal equation that has the following characteristics: The midline is at y = 5 The length of one period is 60° y= 4 sin ②x-60°).

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Problem 2796

Let $x$ represent the number of hours that Trenton spends studying algebra, and let $y$ represent the number of hours he spent studying history. For parts (a)-(e), write an inequality to represent the given statement.
Part 1 of 6 (a) Trenton has a total of at most 7 hr to study for both algebra and history combined.
An inequality that represents this statement is $x+y \leq 7$ .
Part: $1 / 6$
Part 2 of 6 (b) Trenton will spend at least 1 hr studying algebra.
An inequality that represents this statement is $\square$

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Problem 2797

\begin{tabular}{|c||c|c|c|c|c|c|c|} \hline \begin{tabular}{c} $t$ \\ (in seconds) \end{tabular} & 0.1 & 0.5 & 0.9 & 1.5 & 1.9 & 2.3 & 2.6 \\ \hline \begin{tabular}{c} $H(t)$ \\ (in meters) \end{tabular} & 1.4 & 5.7 & 8.4 & 9.6 & 8.4 & 5.6 & 2.5 \\ \hline \end{tabular}
1. Justin Tucker, the kicker for the Baltimore Ravens, is considered one of the greatest kickers in NFL history. On a recent kickoff, the height of the ball, in meters, was measured for selected times. This data is shown in the table above. a) Based on this situation and the data presented in the table, would a linear, quadratic, or cubic function be most appropriate to model this data? Give a reason for your answer. b) Find the appropriate regression function to model these data. c) Using the model found in part $b$ , what is the predicted height of the football, in meters, at tine $t=1.3$ seconds?

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Problem 2798

A cleaning company charges $\$ 120$ for each office it cleans. The fixed monthly cost of $\$ 490$ for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $\$ 50$ per office and includes labor, gasoline, and cleaning supplies. (a) Write a linear cost function representing the cost $C(x)$ (in $\$$ ) to clean $x$ offices per month. (b) Write a linear revenue function representing the revenue $R(x)$ (in $\$$ ) for cleaning $x$ offices per month. (c) Determine the number of offices to be cleaned per month for the company to break even. (d) If 10 offices are cleaned, will the company make money or lose money?
Part 1 of 4 (a) The linear cost function representing the cost is $C(x)=490+50 x$ .
Part: $1 / 4$
Part 2 of 4 (b) The linear revenue function representing the revenue is $R(x)=\square$ . Skip Part Check Save For Later Submit earch

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Problem 2799

the simple statements p: There is a fire in the fireplace. $q$ : The house is cold. ch each compound statement to its symbolic form. There is a fire in the fireplace if and only if the house is not cold. If there is a fire in the fireplace then the house is not cold. There is no fire in the fireplace and the house is cold. a. $\sim p \vee q$ There is a fire in the fireplace or the house is not cold. b. $\sim p \wedge q$ There is no fire in the fireplace or the house is cold. c. $\sim p \leftrightarrow q$
d. $q \rightarrow \sim p$ e. $p \wedge \sim q$
There is no fire in the fireplace if and only if the house is cold. f. $p \leftrightarrow \sim q$
There is a fire in the fireplace and the house is not cold. g. $p \rightarrow \sim q$ If the house is cold then there is no fire in the fireplace. h. $p \vee \sim q$

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Problem 2800

2. Estimate the affordable monthly mortgage payment, the affordable mortgage amount, and the affordable home purchase price for the following situation (Figure 9.1.4 Mortgage Affordability Calculation).
Monthly gross income, \$4,167 Down payment to be made-15 percent of purchase price
Other debt (monthly payment), \$500 Monthly Property Taxes and Home Insurance, \$200 30-year loan at 8 percent a. Affordable monthly mortgage payment b. Affordable mortgage amount c. Affordable home purchase

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Model

Problem 2701

Problem 2702

Problem 2703

Write the sentence as an equation. the product of 189 and hhh equals mmmType a slash ( / ) if you want to use a division sign. □\square□ Submit

Problem 2704

Problem 2705

Problem 2706

Question 6 (a) Form a quadratic equation whose roots are 3123 \frac{1}{2}321​ and −213-2 \frac{1}{3}−231​. Express your answer in the form ax2+bx+c=0a x^{2}+b x+c=0ax2+bx+c=0, where a,b,ca, b, ca,b,c are integers. (b) Form an equation whose roots are twice those in previous part.

Problem 2707

Problem 2708

Problem 2709

2. (MP) Use Tools Marcela gets to school later than her friend Kim about half the time. Describe a way to simulate this event for 10 school days. Then perform the simulation. How many times does it show Marcela arriving later than Kim? What is the experimental probability of this event?

Problem 2710

Problem 2711

An electron microscope can magnify an object from 3000 times to 100,000 times. Assuming these values are exact, express these magnifications MMM as an inequality and graph them. \qquadExpress M as a single inequality.

Problem 2712

Problem 2713

Problem 2714

Problem 2715

14F14{ }^{F}14F is inversely proportional to the square of vvv. Given that F=6.5F=6.5F=6.5 when ν=4\nu=4ν=4 find a formula for Fin F_{\text {in }}Fin ​ terms of vvv.

Problem 2716

Question 2 (1 point) A car starts from rest and continues at a rate of v=18t2ft/sv=\frac{1}{8} t^{2} \mathrm{ft} / \mathrm{s}v=81​t2ft/s. Find the function that relates the distance sss the car has traveled to the time ttt in seconds.

Problem 2717

Noor wants to spend less than $20\$ 20$20 on condiments. Each kilogram of salt costs $1.50\$ 1.50$1.50, and each kilogram of pepper costs \$2.50.Write an inequality that represents the number of kilograms of salt (S)(S)(S) and pepper (P)(P)(P) Noor can buy on her budget.

Problem 2718

Problem 2719

Problem 2720

Problem 2721

Problem 2722

Problem 2723

Problem 2724

Problem 2725

Problem 2726

Problem 2727

Problem 2728

Problem 2729

Write the standard form of the equation of the circle with the given center and radius. Center (−4,−5),r=2(-4,-5), r=\sqrt{2}(−4,−5),r=2​The equation of the circle in standard form is □\square□ (Simplify your answer.)

Problem 2730

Problem 2731

Write the electron configuration for a sodium ion (Na+^++).

Problem 2732

Create a grouped frequency distribution for these IQ scores: 85-89 for the first class, with equal widths for others.

Problem 2733

Explain how to represent division with 2-digit divisors in math problems.

Problem 2734

Given the fraction 35\frac{3}{5}53​:1. Model it on a 10x10 grid.2. Create a table of 5 equivalent ratios to 100.3. Identify decimal and percent equivalents; explain errors in options A, B, D.4. Find the number where 35\frac{3}{5}53​ of it equals 18.5. Draw a number line for question 4.

Problem 2735

Find the position of the missing score (orange box) on a graph where total distance below the mean is 5 and above is 7.

Problem 2736

Problem 2737

Express the system as a vector and matrix equation:9x1+x2−3x3=810x2+4x3=0 \begin{array}{r} 9 x_{1}+x_{2}-3 x_{3}=8 \\ 10 x_{2}+4 x_{3}=0 \end{array} 9x1​+x2​−3x3​=810x2​+4x3​=0​

Problem 2738

Solve the inequality ∣3p−4∣<p+8|3p - 4| < p + 8∣3p−4∣<p+8 and graph the solution set.

Problem 2739

Create the augmented matrix from AAA and bbb for Ax=bA \mathbf{x}=\mathbf{b}Ax=b, then solve for x\mathbf{x}x.

Problem 2740

Problem 2741

Draw a line to model Chicago's population growth from 1880 (500,000) to 1930 (3,400,000) and find its equation.

Problem 2742

Create an equation for this: 19 minus 53\frac{5}{3}35​ of a number equals 4. Solve for xxx. Options: A. 19−53x=419-\frac{5}{3} x=419−35​x=4 B. 53−19x=4\frac{5}{3}-19 x=435​−19x=4 C. 19−53=419-\frac{5}{3}=419−35​=4 D. 553x−19=45 \frac{5}{3} x-19=4535​x−19=4. Find xxx.

Problem 2743

Write a compound inequality for: A quantity xxx is less than 8 or greater than 21.

Problem 2744

List the sample space for choosing 2 marbles at random from a bag with green, red, and blue marbles.

Problem 2745

1. List the months of the birthdays: {January, April, May}.2. List multiples of 3 from 0 to 21: {0, 3, 6, 9, 12, 15, 18, 21}.3. Represent quantities in interval notation.4. Kelly can work hours in the interval [60, 120].

Problem 2746

Find a formula for ana_{n}an​ using the sequence 3,8,13,18,23,…3, 8, 13, 18, 23, \ldots3,8,13,18,23,….

Problem 2747

Determine the formula for ana_{n}an​ using the sequence a0,a1,a2,…a_{0}, a_{1}, a_{2}, \ldotsa0​,a1​,a2​,… given as −2,3,−4,5,−6,…-2, 3, -4, 5, -6, \ldots−2,3,−4,5,−6,….

Problem 2748

Find a formula for ana_{n}an​ based on the sequence: -4, 9, -14, 19, -24. What is an=a_{n}=an​=?

Problem 2749

Problem 2750

Find a formula for ana_{n}an​ based on the sequence 0,3,−6,9,−12,…0, 3, -6, 9, -12, \ldots0,3,−6,9,−12,…. What is an=a_{n}=an​=?

Problem 2751

Ms. Garza ordered 9 cases of caramel apples, sold 685, and had 35 left. What equation finds apples per case? 9c−685=359c - 685 = 359c−685=35

Problem 2752

Find the formula for the sequence an={3,6,9,12,…}a_{n}=\{3,6,9,12, \ldots\}an​={3,6,9,12,…}. Options: an=3na_{n}=3 nan​=3n, a3=3aa_{3}=3_{a}a3​=3a​, an=9na_{n}=9 nan​=9n, an=6na_{n}=6_{n}an​=6n​.

Write the sentence as an equation. the product of 189 and $h$ equals $m$
Type a slash ( / ) if you want to use a division sign. $\square$ Submit

Question 6 (a) Form a quadratic equation whose roots are $3 \frac{1}{2}$ and $-2 \frac{1}{3}$ . Express your answer in the form $a x^{2}+b x+c=0$ , where $a, b, c$ are integers. (b) Form an equation whose roots are twice those in previous part.

An electron microscope can magnify an object from 3000 times to 100,000 times. Assuming these values are exact, express these magnifications $M$ as an inequality and graph them. $\qquad$
Express M as a single inequality.

$14{ }^{F}$ is inversely proportional to the square of $v$ . Given that $F=6.5$ when $\nu=4$ find a formula for $F_{\text {in }}$ terms of $v$ .

Question 2 (1 point) A car starts from rest and continues at a rate of $v=\frac{1}{8} t^{2} \mathrm{ft} / \mathrm{s}$ . Find the function that relates the distance $s$ the car has traveled to the time $t$ in seconds.

Noor wants to spend less than $\$ 20$ on condiments. Each kilogram of salt costs $\$ 1.50$ , and each kilogram of pepper costs \$2.50.
Write an inequality that represents the number of kilograms of salt $(S)$ and pepper $(P)$ Noor can buy on her budget.

Write the standard form of the equation of the circle with the given center and radius. Center $(-4,-5), r=\sqrt{2}$
The equation of the circle in standard form is $\square$ (Simplify your answer.)

Write the electron configuration for a sodium ion (Na $^+$ ).

Given the fraction $\frac{3}{5}$ :
1. Model it on a 10x10 grid.
2. Create a table of 5 equivalent ratios to 100.
3. Identify decimal and percent equivalents; explain errors in options A, B, D.
4. Find the number where $\frac{3}{5}$ of it equals 18.
5. Draw a number line for question 4.

Express the system as a vector and matrix equation:
$\begin{array}{r} 9 x_{1}+x_{2}-3 x_{3}=8 \\ 10 x_{2}+4 x_{3}=0 \end{array}$

Solve the inequality $|3p - 4| < p + 8$ and graph the solution set.

Create the augmented matrix from $A$ and $b$ for $A \mathbf{x}=\mathbf{b}$ , then solve for $\mathbf{x}$ .

Create an equation for this: 19 minus $\frac{5}{3}$ of a number equals 4. Solve for $x$ . Options: A. $19-\frac{5}{3} x=4$ B. $\frac{5}{3}-19 x=4$ C. $19-\frac{5}{3}=4$ D. $5 \frac{5}{3} x-19=4$ . Find $x$ .

Write a compound inequality for: A quantity $x$ is less than 8 or greater than 21.

1. List the months of the birthdays: {January, April, May}.
2. List multiples of 3 from 0 to 21: {0, 3, 6, 9, 12, 15, 18, 21}.
3. Represent quantities in interval notation.
4. Kelly can work hours in the interval [60, 120].

Find a formula for $a_{n}$ using the sequence $3, 8, 13, 18, 23, \ldots$ .

Determine the formula for $a_{n}$ using the sequence $a_{0}, a_{1}, a_{2}, \ldots$ given as $-2, 3, -4, 5, -6, \ldots$ .

Find a formula for $a_{n}$ based on the sequence: -4, 9, -14, 19, -24. What is $a_{n}=$ ?

Find a formula for $a_{n}$ based on the sequence $0, 3, -6, 9, -12, \ldots$ . What is $a_{n}=$ ?

Ms. Garza ordered 9 cases of caramel apples, sold 685, and had 35 left. What equation finds apples per case? $9c - 685 = 35$

Find the formula for the sequence $a_{n}=\{3,6,9,12, \ldots\}$ . Options: $a_{n}=3 n$ , $a_{3}=3_{a}$ , $a_{n}=9 n$ , $a_{n}=6_{n}$ .

Find the equation of a line parallel to the one with slope $1/2$ that passes through $(0,-3)$ .

Find a linear equation for the line through $(1,4)$ with slope 6.

Find the linear equation of the line through the points $(1,-6)$ and $(-1,-1)$ . $y(x) =$

Find functions $f$ and $g$ such that $h(x)=(x+8)^{3}=f(g(x))$ . Use $f(x)=x^{3}$ or $g(x)=x+8$

Find a linear equation for the line passing through the points $(0.5,-0.75)$ and $(1,-5.75)$ . $y(x)=$

Find the price per bushel of corn using $p(x)=6+0.08 x+0.09 x^{2}$ for $x=0$ to $5$ .

Next week, you charged \$9 per guest with 39 guests on average. Find:
(a) The linear demand equation $q(p)=$ (b) The revenue function $R(p)=$ (c) The cost function $C(p)=-25.5p+488$

Given sales and prices for Q1 2009 and 2010, find the linear demand function $q(p)$ and predict sales at \$75. For each \$1 price increase, how many units decrease?

Find the linear demand function for cell phones using the 2009 and 2010 data. Predict sales at \$156 and state the decrease per \$1 increase.
$q(p)=$

RideEm Bicycles can make 170 bikes for \$10,300 and 190 bikes for \$10,900.
(a) Find the cost function $C(x)=$ . (b) What are the fixed costs in dollars? (c) What are the variable costs in dollars?

Worldwide cell phone sales data for 2009 and 2010 shows prices at \$163 (2009) and \$153 (2010).
(a) Demand equation: $q(p)=-39p+6,472$ . Predict sales at \$156. Round to nearest million.
(b) Sales decrease by 39 million units for each \$1 price increase.

Charge \ $9 per guest, average 39 guests. Find demand$ q(p) $, revenue$ R(p) $, profit$ P(p)$, and break-even fees.

Given cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

Next week, you charge \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find revenue $R(p)=$ . (c) Costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Determine break-even entrance fees $p=$ .

RideEm Bicycles produces 170 bikes for \ $10,300 and 190 bikes for \$10,900. Find the cost function$ C(x)$ and fixed/variable costs.