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Problem 65001

2) A 0.3 kg ball is tied to a 1 m piece of string and spun so that it is moving in a horizontal circle as shown below. The angle measured between the vertical dashed line and the string is $20^{\circ}$ . Determine angular speed of the ball and tension in the string. $\left[\omega=3.2 \mathrm{rad} \mathrm{~s}^{-1} \text { and } T=3.1 \mathrm{~N}\right]$

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Problem 65002

For the rotation $-\frac{71 \pi}{8}$ , find the coterminal angle from $0 \leq \theta<2 \pi$ , the quadrant, and the reference angle.

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Problem 65003

Fill in all necessary information from the given function. 1.

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Problem 65004

18. Solve the following inequality algebraically $|2 x-6|<7$

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Problem 65005

$3(x+2)=21$

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Problem 65006

Jack orders a pizza with a 20-inch diameter for a party.
8. What is the length of each slice?
9. What is the area of the whole pizza?

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Problem 65007

10. Iodine is a non-polar diatomic molecule, yet its molecules have enough attraction for each other that the element exists as a solid at room temperature. Identify the attractive force and explain why it is strong enough to keep the molecules of $\mathrm{I}_{2}$ attached to each other even at room temperature.

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Problem 65008

The box plot represents the number of minutes customers spend on hold when calling a company. Number of Minutes Spent on Hold
What is the upper quartile of the data? 3 5 6 8 Mark this and return Save and Exit Next Submit

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Problem 65009

The data set represents the number of miles Mary jogged each day for the past nine days. $6,7,5,0,6,12,8,6,9$
What is the outlier of the data? 0 6 7 12

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Problem 65010

The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your onswer. How could you correctly rewrite the equation $4(5+3)=2(22-6)$ using the distributive property? $20+12=44-12$

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Problem 65011

Solve for $a$ . Express your answer in simplest radical form if necessary. $a^{3}=78$
Answer Attempt 1 out of 2

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Problem 65012

2 (2) Calculate the perimeter and area of the polygon below. Show all work. $\begin{array}{l} 8^{2}=64 \\ 5^{2}=-16 \\ \sqrt{3} a=6 \end{array}$ $4+6=$

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Problem 65013

The data set below has a lower quartile of 13 and an upper quartile of 37 . $1,12,13,15,18,20,35,37,40,78$
Which statement is true about any outliers of the data set? The data set does not have any outliers. The lowest value, 1 , is the only outlier. The greatest value, 78 , is the only outlier. Both 1 and 78 are outliers.

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Problem 65014

Find the value of $y$ . Round your answer to the nearest tenth.

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Problem 65015

Find the missing side length. Round to the nearest tenth.

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Problem 65016

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

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Problem 65017

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. Previous

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Problem 65018

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

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Problem 65019

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. Previous

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Problem 65020

Given: $\overline{A F} \cong \overline{F C}, \angle A B E \cong \angle E B C$ Which line is the angle bisector?

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Problem 65021

(4) What is $x$ ?
$x^{2}=169$ $\square$ $\begin{array}{l} x=-84.5 \\ x=-16 \end{array}$ $\qquad$ $\begin{array}{l} \hat{x}=-16 \\ x=-13 \end{array}$ $\square$ $x=13$
$x=16$ $\qquad$ $x=84.5$

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Problem 65022

$\text { [6 } 3348663186 \text { 8] }$
How many comparisons will be performed in this array using sequential search for the searchltem 6? 7 2 1 4 3 6 5 0

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Problem 65023

The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
Answer Attempt 1 out of 20

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Problem 65024

78. If $f(x)=\ln (x)$ and $g$ is a differentiable function with domain $x>0$ such that $\lim _{x \rightarrow \infty} g(x)=\infty$ and $g^{\prime}$ has a horizontal asymptote at $y=4$ then $\lim _{x \rightarrow \infty} \frac{f(x)}{g(x)}$ is A. 0 B. -4 C. 4 D. nonexistent

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Problem 65025

2. How many ways can the letters of ALOHA be arranged if: a) the A's must be together? (2 marks)
AA $\qquad$ - $4!=24$ b) the A's cannot be together? (1 mark) $\qquad$ A $\qquad$ A $\qquad$ $3!=$ $\square$ 6 c) each arrangement must begin with a vowel and the consonants cannot be together? (2 marks) A.A. 0 L. H $\qquad$ $L H$

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Problem 65026

Find the horizontal asymptote, if any, of the graph of the rational function. $h(x)=\frac{11 x^{3}}{5 x^{2}+8}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choi A. The horizontal asymptote is $\square$ . (Type an equation.) B. There is no horizontal asymptote.

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Problem 65027

Find the horizontal asymptote, if any, of the graph of the rational function. $f(x)=\frac{-6 x+7}{5 x+4}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is $\square$ . (Type an equation. Simplify your answer. Use integers or fractions for any numbers in the equation.) B. There is no horizontal asymptote.

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Problem 65028

$\begin{array}{l}6(w+1)-3 w=3(w+4 \\ 2(3 a-1)=4 a+10 \\ 7 b-3(b+2)=4 b-11 \\ 5(c-2)+3 c=4(2 c+1\end{array}$

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Problem 65029

Essay 10 points Let $f(x)=\frac{1}{x+5}-4$ - Enter the equation of the vertical asymptote of $f(x)$ . - Enter the equation of the horizontal asymptote of $f(x)$ . - Enter the domain of $f(x)$ in interval notation. - Enter the range of $f(x)$ in interval notation. - State the vertical and/or horizontal transformation(s). - Graph $f(x)$ , by hand. - Include: - Asymptotes as dotted lines - x-intercepts as precise points - Open dot where there is a hole in the graph (if applicable) (1 point) each correct answer (5 points) correct labeled graph Remember, you can type in your answer and work or you can take a picture of it and upload the image. Edit View Insert Format Tools Table

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Problem 65030

The mass of a colony of bacteria, in grams, is modeled by the function $P$ given by $P(t)=2+5 \tan ^{-1}\left(\frac{t}{2}\right)$ , where $t$ is measured in days. What is the instantaneous rate of change of the mass of the colony, in grams per day, at the moment the colony reaches a mass of 6 grams? (A) -0.606 (B) 0.250 (C) 1.214 (D) 1.942

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Problem 65031

$\text{Find the slope of the line that passes through each set of points: } (4, 4) \text{ and } (6, 6). \text{ Find the answer below and decorate the stocking with the features listed.}$

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Problem 65032

This model shows a unit square divided into smaller square tiles. $1 \text { unit }$
Find the area of the shaded rectangle by multiplying its length and width. Fill in the equation. $\square$ $\square$ $\square$

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Problem 65033

As a town gets smaller, the population of its high school decreases by $7 \%$ each year. The senior class has 320 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation.
Write an equation to represent this situation. Let $t$ be the number of years before the class will have 100 students. $\square$ (Type an equation using $t$ as the variable. Use integers or decimals for any numbers in the equation.) Solve the equation. $\ln t=$ $\square$ years the senior class will have about 100 students. (Type an integer or decimal rounded to the nearest hundredth as needed.)

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Problem 65034

Given $x>0$ and $y>0$ , select the expression that is equivalent to $\sqrt[4]{256 x^{16} y^{6}}$

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Problem 65035

1. Order: 500 mg
Supply on Hand: $250 \mathrm{mg} / \mathrm{tab}$

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Problem 65036

6. Two masses are tied to a rope on a pulley, as shown below. a. When the system is released from this position, what is the acceleration of the 2.0-kg mass? b. How long does it take for the $2.0-\mathrm{kg}$ mass to fall to the floor?

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Problem 65037

$\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}$

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Problem 65038

Graph the function. $f(x)=\sqrt{x}-7$

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Problem 65039

Problem 6 Sothy plans to walk 10000 steps.
He starts his walk at 8:00 AM.
At 8:23 AM, his phone tells him that he has taken 2000 steps.
If he continues at this rate, when will he reach 10000 steps? Submit

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Problem 65040

Solve the right triangle.

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Problem 65041

A b=1.49, c 7.42 b B וה U

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Problem 65042

The table below shows the amount of rainfall and the temperature at noon in each of 8 cities. Create a scatter plot for the data. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Amount of rainfall \\ (in millimeters) \end{tabular} & \begin{tabular}{c} Temperature \\ (in ${ }^{\circ} \mathrm{C}$ ) \end{tabular} \\ \hline 3 & 13 \\ \hline 5 & 9 \\ \hline 7 & 10 \\ \hline 8 & 8 \\ \hline 10 & 5 \\ \hline 11 & 6 \\ \hline 12 & 2 \\ \hline 14 & 3 \\ \hline \end{tabular}

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Problem 65043

90. What is the absolute minimum value of $y=\frac{4}{3} x^{3}-8 x^{2}+15 x$ on $1 \leq x \leq 3$ ? A. 0 $f(x)^{1}=4 x^{2}-16 x+15$ B. $\frac{25}{3}$ C. 9 $\begin{array}{ll} f(1)=\frac{25}{3} & 4 x^{2}-10 x-6 x+15 \\ 1(3)=9 & 2 x(2 x-5)-3(2 x-5) \end{array}$ D. $\frac{52}{3}$ $\begin{array}{ll} f(3)=9 & 2 x(2 x-5)-3(2 x-5 \\ f \mid 5)=\frac{25}{3} & (2 x-3)(2 x-5) \end{array}$

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Problem 65044

Simplify each expression $(9 x+7)\left(-5 x^{4}-x^{3}\right)$

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Problem 65045

A bug has fallen into a whirlpool, and it's distance from the center is given by: $r=\theta$ , where $0 \leq \theta \leq 4 \pi$ It is being sucked from the outside towards the center of the swirl in the whirlpool.
What is the horizontal component of the bug's location, after it has spun through an angle of $\frac{11 \pi}{6}$ radians? $x=-4.68$ $x=5.89$ $x=4.99$ $x=9.56$

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Problem 65046

6. $a^{5}\left(-9 a^{4}-9 a^{3}+4 a^{2}\right)$

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Problem 65047

```latex \begin{tabular}{|l|c|c|c|c|} \hline \multicolumn{1}{|c|}{ Artikelbez. } & Artikelnr. & Einzelpreis & Anzahl & Gesamtpreis \\ \hline Drucker IP 236 & 120478 & 235,70\,€ & 2 & 471,42\,€ \\ \hline Monitor 17 Zoll & 524712 & 365,80\,€ & 3 & 1097,90\,€ \\ \hline CD-Rohling & 258413 & 0,75\,€ & 200 & 150\,€ \\ \hline Infrarot-Maus & 569322 & 10,75\,€ & 5 & 53,75\,€ \\ \hline Toner-Kartusche IC 23 & 442523 & 99,85\,€ & 4 & 395,40\,€ \\ \hline \end{tabular}
Netto
19 \% MwSt.
Brutto
The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.
Dialogue Transcript:
assistant: Hallo! Es sieht so aus, als ob du eine Tabelle mit Artikeldetails und Preisen vor dir hast. Kannst du mir bitte genauer sagen, welche Berechnung oder Information du benötigst? Möchtest du vielleicht den Gesamtbetrag inklusive Mehrwertsteuer berechnen oder gibt es eine andere spezifische Aufgabe, bei der ich dir helfen kann? Lass es mich wissen!
user: Ja
assistant: Super! Um dir besser helfen zu können, brauche ich eine klarere Vorstellung davon, was genau du berechnen möchtest. Geht es darum, den Gesamtbetrag inklusive Mehrwertsteuer zu ermitteln, oder gibt es etwas anderes, das du bearbeitet haben möchtest? Bitte teile mir mit, worauf du hinaus willst.
user: I uploaded an image and extracted the following: * Text: \begin{tabular}{|l|r|r|c|c|} \hline \multicolumn{1}{|c|}{ Artikelbez. } & Artikelnr. & Einzelpreis & Anzahl & \multicolumn{1}{c|}{ Gesamtpreis } \\ \hline Drucker IP 236 & 120478 & 235,70\,€ & 2 & 471,42\,€ \\ \hline Monitor 17 Zoll & 524712 & 365,80\,€ & 3 & 1097,40\,€ \\ \hline CD-Rohling & 258413 & 0,75\,€ & 200 & 1,50\,€ \\ \hline Infrarot-Maus & 569322 & 10,75\,€ & 5 & 53,75\,€ \\ \hline Toner-Kartusche IC 23 & 442523 & 99,85\,€ & 4 & 395,40\,€ \\ \hline \end{tabular}
Netto 19 \% MwSt. Brutto $\square$ $\square$ $\square$ ```

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Problem 65048

Plot the point $(5,-1)$ and identify the quadrant.
Click on the graph to plot a point. Click a point to delete it.

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Problem 65049

9. $6 x+8=50$

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Problem 65050

11. $13=-4 k+9$

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Problem 65051

Question Watch V
Find the median and mean of the data set below: $47,15,6,49,45,30$
Answer Attempt 1 out of 2
Median = $\square$ Mean = $\square$ Submit Answer

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Problem 65052

For time $0 \leq t \leq 10$ , water is flowing into a small tub at a rate given by the function $F$ defined by $F(t)=\arctan \left(\frac{\pi}{2}-\frac{t}{10}\right)$ . For time $5 \leq t \leq 10$ , water is leaking from the tub at a rate given by the function $L$ defined by $L(t)=0.03\left(20 t-t^{2}-75\right)$ . Both $F(t)$ and $L(t)$ are measured in cubic feet per minute, and $t$ is measured in minutes. The volume of water in the tub, in cubic feet, at time $t$ minutes is given by $W(t)$ . (a) At time $t=3$ , there are 2.5 cubic feet of water in the tub. Write an equation for the locally linear approximation of $W$ at $t=3$ , and use it to approximate the volume of water in the tub at time $t=3.5$ .
No response entered (b) Find $W^{\prime \prime}(8)$ . Using correct units, interpret the meaning of $W^{\prime \prime}(8)$ in the context of the problem.
No response entered (c) Is there a time $t$ , for $5<t<10$ , at which the rate of change of the volume of water in the tub changes from positive to negative? Give a reason for your answer.

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Problem 65053

Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function? $y=9 x^{2}-9 x+20$ A. both a relation and a function B. function only C. relation only D. neither a relation nor a function

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Problem 65054

4. $x^{2}-16=0$

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Problem 65055

The perimeter of a triangle is 107 m . The second side is three times as long as the first side. The third side is 5 m shorter than than the second side. How long is each side.
Determine the length of each side of the triangle. The first side is $\square$ m
The second side is $\square$ m.
The third side is $\square$ m

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Problem 65056

Identifying an Error Deepak plotted these points on the number line. Point A: -0.3 Point B: $-\frac{3}{4}$ Point C: $-1 \frac{1}{4}$ Point D: -0.7 Which point did he plot incorrectly? Point a Intro Done

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Problem 65057

Find the vector of stable probabilities for the Markov chain whose transition matrix is $\begin{array}{c} {\left[\begin{array}{ccc} 0.1 & 0.8 & 0.1 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right]} \\ W= \end{array}$ $\square$ $\square$

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Problem 65058

Find an equation for a sinusoidal function that has period $2 \pi$ , amplitude 2 , and contains the point ( $2 \pi, 0$ ).
Write your answer in the form $\mathrm{f}(\mathrm{x})=\mathrm{A} \sin (\mathrm{Bx}+\mathrm{C})+\mathrm{D}$ , where $\mathrm{A}, \mathrm{B}, \mathrm{C}$ , and D are real numbers. $f(x)=$ $\square$

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Problem 65059

Solve the Inequality. $y+7<-6$
The inequality is $\square$

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Problem 65060

Find the unknown angle measures.

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Problem 65061

Find the derivative of the function $f(x)=\frac{e^{x}+1}{9(x) e^{x}-1}$ . Simplify your answer.

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Problem 65062

$\left(\frac{1-\sqrt{5}}{2}\right)^{12}$

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Problem 65063

Let $f$ be a twice-differentiable function such that $f^{\prime}(1)=0$ . The second derivative of $f$ is given by $f^{\prime \prime}(x)=x^{2} \cos \left(x^{2}+\pi\right)$ for $-1 \leq x \leq 3$ . (a) On what open intervals contained in $-1<x<3$ is the graph of $f$ concave up? Give a reason for your answer.
No response entered (b) Does $f$ have a relative minimum, a relative maximum, or neither at $x=1$ ? Justify your answer.
No response entered (c) Use the Mean Value Theorem on the closed interval $[-1,1]$ to show that $f^{\prime}(-1)$ cannot equal 2.5.
No response entered (d) Does the graph of $f$ have a point of inflection at $x=0$ ? Give a reason for your answer.

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Problem 65064

A particle moves along the $x$ -axis so that its position at time $t>0$ is given by $x(t)=\frac{t^{2}-9}{3 t^{2}+8}$ . (a) Show that the velocity of the particle at time $t$ is given by $v(t)=\frac{70 t}{\left(3 t^{2}+8\right)^{2}}$ .
No response entered (b) Is the particle moving toward the origin or away from the origin at time $t=2$ ? Give a reason for your answer.
No response entered (c) The acceleration of the particle is given by $a(t)$ . Write an expression for $a(t)$ , and find the value of $a(2)$ .
No response entered (d) What position does the particle approach as $t$ approaches infinity?

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Problem 65065

Unless otherwise specified, the domain of a function $f$ is assumed to be the set of all real numbers $x$ for which $f(x)$ is a real number. $W(t)=\left\{\begin{array}{cl} \frac{17}{2}-\frac{3}{2} \cos \left(\frac{\pi t}{6}\right) & \text { for } 0 \leq t \leq 6 \\ 10-\frac{1}{5}(t-6)^{2} & \text { for } 6<t \leq 10 \end{array}\right.$
The depth of a river at a certain point is modeled by the function $W$ defined above, where $W(t)$ is measured in feet and time $t$ is measured in hours. (a) Find $W^{\prime}(8)$ . Using correct units, explain the meaning of $W^{\prime}(8)$ in the context of the problem.
No response entered (b) The graph of $W$ is concave down for $3 \leq t \leq 3.5$ . Use the line tangent to the graph of $W$ at $t=3$ to show that $W(3.5) \leq 9$ .
No response entered (c) Find $\lim _{t \rightarrow 2} \frac{w(t)-t^{3}+\frac{1}{4}}{t-2}$ .

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Problem 65066

\begin{tabular}{|c||c|c|c|c|} \hline $x$ & -3 & -2 & -1 & 1 \\ \hline $f(x)$ & $-\frac{5}{2}$ & -3 & -2 & $\frac{2}{3}$ \\ \hline $f^{\prime}(x)$ & -1 & $\frac{1}{3}$ & $\frac{6}{5}$ & $\frac{4}{3}$ \\ \hline \end{tabular}
The table above gives values of the differentiable function $f$ and its derivative for selected values of $x$ . (a) Let $g$ be the function defined by $g(x)=\frac{f\left(x^{2}\right)}{e^{x}}$ . Find $g^{\prime}(-1)$ .
No response entered (b) Let $h$ be the function defined by $h(x)=f(f(-2 x))$ . Find $h^{\prime}(1)$ .
No response entered (c) Let $k$ be the function defined by $k(x)=f(x) \cdot \arcsin \left(\frac{x}{2}\right)$ . Find $k^{\prime}(-1)$ .

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Problem 65067

Consider the curve given by the equation $(2 y+1)^{3}-24 x=-3$ . (a) Show that $\frac{d y}{d x}=\frac{4}{(2 y+1)^{2}}$ .
No response entered (b) Write an equation for the line tangent to the curve at the point $(-1,-2)$ .
No response entered (c) Evaluate $\frac{d^{2} y}{d x^{2}}$ at the point $(-1,-2)$ .
No response entered (d) The point $\left(\frac{1}{6}, 0\right)$ is on the curve. Find the value of $\left(y^{-1}\right)^{\prime}(0)$ . (3) $55^{\circ} \mathrm{F}$

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Problem 65068

$\left(2 g^{3}+g^{2}\right)\left(4 g^{3}-7 g^{2}-3 g\right)$

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Problem 65069

Use logarithmic differentiation to differentiate each function with respect to $x$ . You do not need to simplify or substitute for $y$ . $y=\frac{\left(x^{2}+4\right)^{3}}{\left(2 x^{4}-1\right)^{5} \cdot\left(4 x^{9}+5\right)^{6}}$ A) $\frac{d y}{d x}=y\left(\frac{6 x}{x^{2}+4}-\frac{160 x^{3}}{2 x^{4}-1}-\frac{864 x^{8}}{4 x^{9}+5}\right)$ B) $\frac{d y}{d x}=y\left(\frac{18 x}{x^{2}+4}-\frac{80 x^{3}}{2 x^{4}-1}+\frac{432 x^{8}}{4 x^{9}+5}\right)$ C) $\frac{d y}{d x}=y\left(\frac{6 x}{x^{2}+4}-\frac{40 x^{3}}{2 x^{4}-1}+\frac{864 x^{8}}{4 x^{9}+5}\right)$ D) $\frac{d y}{d x}=y\left(\frac{6 x}{x^{2}+4}-\frac{40 x^{3}}{2 x^{4}-1}-\frac{216 x^{8}}{4 x^{9}+5}\right)$

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Problem 65070

6. Найдите точки, в которых компоненты градиента функции $z=x^{2}+y^{2}+5 x y+x-4 y+1$ равны нулю.

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Problem 65071

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through $(8,-1)$ and perpendicular to the line whose equation is $x-7 y-9=0$

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Problem 65072

[4] If $A^{-1}=\left[\begin{array}{cc}3 & 2 \\ -1 & 1\end{array}\right]$ and $B^{-1}=\left[\begin{array}{cc}1 & -1 \\ -3 & 4\end{array}\right]$ , and $(A B)^{-1}=\left[\begin{array}{ll}x & z \\ y & h\end{array}\right]$ , then $x+y+z+h$ a) -10 b) 3 c) 8 d) 20 [5] If $\left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right|=-3$ , then $\operatorname{det}\left(2\left[\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right]\right)=$ a) -6 b) -48 c) -12 d) -32 [6] The linear system given by $A X=B$ where $A$ is $2 \times 2$ square matrix, $A_{x}=\left[\begin{array}{cc}2 & -1 \\ 6 & 1\end{array}\right]$ and $A_{y}=\left[\begin{array}{ll}3 & 2 \\ 1 & 6\end{array}\right]$ , then $X=$ a) $\left[\begin{array}{l}2 \\ 4\end{array}\right]$ b) $\left[\begin{array}{c}-2 \\ 4\end{array}\right]$ c) $\left[\begin{array}{l}4 \\ 2\end{array}\right]$ d) $\left[\begin{array}{l}-4 \\ -2\end{array}\right]$
Q2: Write (T) for the correct statement and (F) for the false one [1] $\qquad$ If $|A|=\left|A^{-1}\right|$ then $|A|$ must equal to 1. [2] $\qquad$ If $A=[-\sqrt{2}]$ then $A^{-1}=\left[-\frac{\sqrt{2}}{2}\right]$ [3] $\qquad$ $3 A^{\mathrm{T}} A$ is a symmetric matrix. [4] $\qquad$ The matrix $A=\left[\begin{array}{cccc}1 & 5 & -3 & 0 \\ 0 & -2 & 0 & 8 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 2\end{array}\right]$ is singular.

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Problem 65073

7. The circular pool in a park is undergoing improvement work. Workers build a fence in the shape of a square outside the pool, as shown in Figure 1.
Figure 1
Figure 2 $\begin{array}{l} \begin{array}{r} 3.14 \\ \times 18 \\ 3.140 \end{array} 314 \\ + \times 138 \\ \hline \\ \hline 565.20 \end{array}$ (a) The length of the fence is 180 m . What is the circumference of the circular pool? (Show your steps) (Take $\pi=3.14$ ) (b) The workers build a path of width 3 m around the fence, as shown in Figure 2. What is the of this path? $\int m^{2}$
Answer: The area of this path is $2196 \mathrm{~m}^{2}$ $\qquad$ . (Give the answer with a unit) Page 11 of 11

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Problem 65074

The input voltage $\mathrm{X}_{(t)}$ ), and output voltage $\mathrm{Y}_{(t)}$ of an electrical system are sampled simultaneously at regular intervals with the following results. $\begin{array}{r} n=0,1,2, \quad 3, \quad 4,5,6,7,8,9, \ldots \\ X(n T)=15,10,6,2, \quad 1,0,0,0,0,0, \ldots \\ Y(n T)=15,15,7.5,-2.75,-2.5, \cdots, \cdots,-,-\ldots \end{array}$
Calculate the missing values of the output voltage $\mathrm{Y}(\mathrm{nT})$ above. Mint: Assume that $\mathrm{X}(\mathrm{t})=0$ for $\mathrm{t}<0$ , and that only nonzero imputse response samples are $\mathrm{h}(\mathrm{n})$ , for $0 \leq \mathrm{n} \leq 4$ .

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Problem 65075

Let $g$ be the function defined by $g(x)=\left(x^{2}-x+1\right) e^{x}$ . What is the absolute maximum value of $g$ on the interval $[-4,1] ?$ (A) 1 (B) $e$ (C) $\frac{3}{e}$ (D) $\frac{21}{e^{1}}$ https://apclassroom.collegeboard.org/25/assessments/results/62905152/performance/591...

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Problem 65076

The graph of $f^{\prime \prime}$ , the second derivative of the continuous function $f$ , is shown above on the interval $[0,9]$ . On this interval $f$ has only one critical point, which occurs at $x=6$ . Which of the following statements is true about the function $f$ on the interval $[0,9]$ ? (A) $f$ has a relative minimum at $x=6$ but not an absolute minimum. (B) The absolute minimum of $f$ is at $x=6$ .
C $f$ has a relative maximum at $x=6$ but not an absolute maximum. (D) The absolute maximum of $f$ is at $x=6$ .

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Problem 65077

tentukan $\frac{\partial w}{\partial t}$ dengan aturan rantai dan ungkapkan Jawaban akhir dalam bentuk $s$ dan $t$ .
12. $w=e^{x y+z} ; x=s+t, y=s-t, z=t^{2}$ .

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Problem 65078

8.1 .00 9.1 .00 10.1 .00 11.1 .00 12.1 .00 13.1 .00 14.1 .00

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Problem 65079

Given $\triangle K L M \sim \triangle N O M$ . Enter segments in the blanks provided that would result in a true equation.
Answer $\frac{\mathrm{KL}}{\mathrm{LM}}=$ Submit Answer

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Problem 65080

KEA CY PA-Common Core Mat 122.core.learn.edgenuity.com/player/ pookmarks Edgenuity Scanlon PLC HR 6-74 Downloads HMH Central Login s) (s) WIP Home - William Pen Cool Math Games - TIME REMAINING 59:39
1 28 (4) A: 茔 6 \% 8 9 (1)
The band leader is recording the number of students in the seventh and eighth grades who play flute and clarinet. Which describes the variables in the two-way table? \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{ Band Assignments } \\ \hline & Flute & Clarinet & Total \\ \hline $7^{\text {th }}$ Grade & 19 & 24 & 43 \\ \hline $8^{\text {th }}$ Grade & 22 & 18 & 40 \\ \hline Total & & & \\ \hline \hline \end{tabular} type of instrument and total number of seventh and eighth graders type of instrument and total number of seventh graders grade number and number of clarinet players grade number and type of instrument Mark this and retum Save and Exit Nex: Submit

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Problem 65081

KEA CY PA-Common Core Mat 122.core.learn.edgenuity.com/player/ et bookmarks Edgenuity Scanlon PLC HR 6-74 Downloads HMH Central Login Is Is $\overline{W P}$ Home - William Pen Cool Math Games - Common Core Math 8 Q2 1 2 8 4 ( 8 6 7 8 9 10 TIMEREMAINING 58:47
The lunch coordinator is recording the drink choices of the students in her school. She has partially completed the table. Which describes the variables in the two-way table? \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{ Lunch Drinks } \\ \hline & Milk & Water & Total \\ \hline Girls & & 52 & 85 \\ \hline Boys & 41 & & 93 \\ \hline Total & & & \\ \hline \hline \end{tabular} gender and number who chose milk gender and drink choice number who chose milk and number of boys number who chose milk and total students

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Problem 65082

KEA CY PA-Common Core MaL
122. core learn edgenuity com/player/ Cool Math Games - bookmarks Edgenuity Scanlon PLC HR 6-74 Downloads HMH Central Login Home - William Pen English Common Core Math 8 Q2 TIMEREMANING 58:19 1 2 3 8 8 5 5 8 9 18 s] Is] WP Home-William Pen
Mr. Hanai recorded the outfit choices of the students for picture day from two periods. Which describes the variables in the two-way table? \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{ Outfits for School Pictures } \\ \hline & Pants & Skirt & Total \\ \hline $3^{\text {rd }}$ Period & 31 & 23 & 54 \\ \hline $4^{\text {th }}$ Period & 23 & 35 & 58 \\ \hline Total & 54 & 58 & 112 \\ \hline \hline \end{tabular} type of outfit and total students type of outfit and total students in third period period number and type of outfit period number and total students who wore pants

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Problem 65083

Find the derivative. $y=\frac{\ln (6 x+7)}{e^{6 x+7}}$
Select one: A. $\frac{1-6[\ln (6 x+7)]^{2}}{\ln [6 x+7] e^{(6 x+7)}}$ B. $\frac{1}{(6 x+7) e^{(6 x+7)}}$ C. $\frac{6-(36 x+42) \ln (6 x+7)}{(6 x+7) e^{(6 x+7)}}$ D. $\frac{1-(6 x+7) \ln (6 x+7)}{(6 x+7) e^{(6 x+7)}}$

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Problem 65084

23-28 True-False Determine whether tr - statement is true or false. Explain your answer.
23. If $f(x)$ is continuous at $x=c$ , then so is $|f(x)|$ .
24. If $|f(x)|$ is continuous at $x=c$ , then so is $f(x)$ .
25. If $f$ and $g$ are discontinuous at $x=c$ , then so is $f+g$ .
26. If $f$ and $g$ are discontinuous at $x=c$ , then so is $f g$ .

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Problem 65085

10) The improper integral $\int_{0}^{\infty} \frac{16 \tan ^{-1} x}{1+x^{2}} d x$ A) diverges B) converges to $2 \pi^{2}$ C) converges to $\frac{1}{2} \pi^{2}$ D) converges to $\frac{3}{2} \pi^{2}$ E) NOTA

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Problem 65086

Condense each expression to a single logarithm. 19) $\log _{3} x-\log _{3} y$ 20) $\log _{8} a+\log _{8} b$ 21) $\frac{\log _{2} u}{3}$ 22) $2 \log _{3} 12$ 23) $\log _{5} 8+\log _{5} 7$ 24) $\log _{2} 10-\log _{2} 3$ 25) $4 \log x$ 26) $\frac{\log _{5} x}{2}$

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Problem 65087

Joanna has a total of 50 coins in her purse. • The coins are either nickels or quarters. ■ The total value of the coins is $7.10. Which system of equations can be used to determine the number of nickels, n, and quarters, q, that Joanna has in her purse? O n+q= 50 0.05n+ 0.25q = 7.10 n+q=7.10 50n+50q = 7.10 0.05n+ 0.25q = 50 n+q= 7.10 0.05n+ 0.25q = 7.10 50n+ 50q = 7.10

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Problem 65088

Rational Functions, Equations, and Inequalities
NAME $\qquad$ Williams 0.
DATE : 181 1212024 $\qquad$ K $1 / 16$ T 15 c 14 A 112 1) For each function, identify the location of the hole (if applicable), the equation(s) of the vertical asymptote(s) and the equation of the horizontal asymptote. (a) $f(x)=\frac{x+1}{x^{2}+x}$ (b) $g(x)=\frac{x^{2}+4 x+4}{x^{2}-4}$ [K-6]

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Problem 65089

Provious Noxt Sample Space and Venn Diagrams: Mastery Submit Test Tools Into 3
Select the correct answer. Two events, $E_{1}$ and $E_{2}$ , are defined for a random experiment. What is the probability that at least one of the two events occurs in any trial of the experiment? A. $P\left(E_{1}\right)-P\left(E_{2}\right)-P\left(E_{1} \cap E_{2}\right)$ B. $P\left(E_{1}\right)+P\left(E_{2}\right)-2 P\left(E_{1} \cap E_{2}\right)$ C. $P\left(E_{1}\right)+P\left(E_{2}\right)-P\left(E_{1} \cap E_{2}\right)$ D. $P\left(E_{1}\right)+P\left(E_{2}\right)+P\left(E_{1} \cap E_{2}\right)$

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Problem 65090

The acceleration, in meters per second per second, of a race car is modeled by $A(t)=t^{3}-\frac{15}{2} t^{2}+12 t+10$ , where $t$ is measured in seconds. What is the car's maximum acceleration on the time interval $0 \leq t \leq 6$ ? (A) The maximum acceleration of the race car is 2 meters per second per second and occurs at $t=4$ seconds.
B The maximum acceleration of the race car is 6 meters per second per second and occurs at $t=28$ seconds. C. The maximum acceleration of the race car is 15.5 meters per second per second and occurs at $t=1$ second. (D) The maximum acceleration of the race car is 28 meters per second per second and occurs at $t=6$ seconds.

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Problem 65091

Use the square root property to solve the Quadratic Equation. $2(x-4)^{2}=200$

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Problem 65092

6) Explain how a quadratic function and its reciprocal function are related with regards to positive and negative intervals. Use an example with your explanation.

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Problem 65093

7) A biologist predicted that the population of tadpoles in a pond could be modelled by the function $f(x)=\frac{40 x}{x+7}$ , where x is given in days and $0 \leq x \leq 10$ . The function that actually models the tadpole population is $g(x)=\frac{80}{(x+7)(x+1)}$ for $0 \leq x \leq 10$ . Determine when $\mathrm{f}(\mathrm{x}) \geq \mathrm{g}(\mathrm{x})$ .

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Problem 65094

Use the Box Method to Simplify the following: $(x+3)(x-2)$

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Problem 65095

2 correct factorization of $x^{2}-2 x-15 z$ a $(x+5)(x-3)$ b $(x+5) \quad(x+3)$ $c(x-5)(x-3)$ $d(x-5)(x+3)$

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Problem 65096

4. Determine the value of missing side length for the following right triangle.

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Problem 65097

Given two points, $(3,3)$ and $(1,-3)$ , write the equation of the line passing through these points.

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Problem 65098

$\sqrt{3} \cdot \sqrt{5}$

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Problem 65099

5. $\begin{aligned} y & =-2 x+2 \\ & y=7 x+11\end{aligned}$

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Problem 65100

Mitosis is a process of cell reproduction in which one cell divides into two identical cells. $E$ , coli is a fast-growing bacterium that is often responsible for food poisoning in uncooked meat. It can reproduce itself in 15 minutes. If you begir with 100 E. coli bacteria, how many will there be in 1 hour? a. 1200 bacteria c. 1500 bacteriá b. 1400 bacteria d. 1600 bacteria
Please select the best answer from the choices provided A B C D

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Math

Problem 65001

Problem 65002

For the rotation −71π8-\frac{71 \pi}{8}−871π​, find the coterminal angle from 0≤θ<2π0 \leq \theta<2 \pi0≤θ<2π, the quadrant, and the reference angle.

Problem 65003

Fill in all necessary information from the given function. 1.

Problem 65004

18. Solve the following inequality algebraically ∣2x−6∣<7|2 x-6|<7∣2x−6∣<7

Problem 65005

3(x+2)=213(x+2)=213(x+2)=21

Problem 65006

Jack orders a pizza with a 20-inch diameter for a party.8. What is the length of each slice?9. What is the area of the whole pizza?

Problem 65007

Problem 65008

The box plot represents the number of minutes customers spend on hold when calling a company. Number of Minutes Spent on HoldWhat is the upper quartile of the data? 3 5 6 8 Mark this and return Save and Exit Next Submit

Problem 65009

The data set represents the number of miles Mary jogged each day for the past nine days. 6,7,5,0,6,12,8,6,96,7,5,0,6,12,8,6,96,7,5,0,6,12,8,6,9What is the outlier of the data? 0 6 7 12

Problem 65010

The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your onswer. How could you correctly rewrite the equation 4(5+3)=2(22−6)4(5+3)=2(22-6)4(5+3)=2(22−6) using the distributive property? 20+12=44−1220+12=44-1220+12=44−12

Problem 65011

Solve for aaa. Express your answer in simplest radical form if necessary. a3=78a^{3}=78a3=78Answer Attempt 1 out of 2

Problem 65012

2 (2) Calculate the perimeter and area of the polygon below. Show all work. 82=6452=−163a=6\begin{array}{l} 8^{2}=64 \\ 5^{2}=-16 \\ \sqrt{3} a=6 \end{array}82=6452=−163​a=6​ 4+6=4+6=4+6=

Problem 65013

Problem 65014

Find the value of yyy. Round your answer to the nearest tenth.

Problem 65015

Find the missing side length. Round to the nearest tenth.

Problem 65016

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

Problem 65017

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. Previous

Problem 65018

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

Problem 65019

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. Previous

Problem 65020

Given: AF‾≅FC‾,∠ABE≅∠EBC\overline{A F} \cong \overline{F C}, \angle A B E \cong \angle E B CAF≅FC,∠ABE≅∠EBC Which line is the angle bisector?

Problem 65021

(4) What is xxx ?x2=169x^{2}=169x2=169 □\square□ x=−84.5x=−16\begin{array}{l} x=-84.5 \\ x=-16 \end{array}x=−84.5x=−16​ \qquad x^=−16x=−13\begin{array}{l} \hat{x}=-16 \\ x=-13 \end{array}x^=−16x=−13​ □\square□ x=13x=13x=13x=16x=16x=16 \qquad x=84.5x=84.5x=84.5

Problem 65022

[6 3348663186 8] \text { [6 } 3348663186 \text { 8] } [6 3348663186 8] How many comparisons will be performed in this array using sequential search for the searchltem 6? 7 2 1 4 3 6 5 0

Problem 65023

The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.Answer Attempt 1 out of 20

Problem 65024

Problem 65025

Problem 65026

Problem 65027

Problem 65028

6(w+1)−3w=3(w+42(3a−1)=4a+107b−3(b+2)=4b−115(c−2)+3c=4(2c+1\begin{array}{l}6(w+1)-3 w=3(w+4 \\ 2(3 a-1)=4 a+10 \\ 7 b-3(b+2)=4 b-11 \\ 5(c-2)+3 c=4(2 c+1\end{array}6(w+1)−3w=3(w+42(3a−1)=4a+107b−3(b+2)=4b−115(c−2)+3c=4(2c+1​

Problem 65029

Problem 65030

Problem 65031

Problem 65032

This model shows a unit square divided into smaller square tiles. 1 unit 1 \text { unit }1 unit Find the area of the shaded rectangle by multiplying its length and width. Fill in the equation. □\square□ □\square□ □\square□

Problem 65033

Problem 65034

Given x>0x>0x>0 and y>0y>0y>0, select the expression that is equivalent to 256x16y64\sqrt[4]{256 x^{16} y^{6}}4256x16y6​

Problem 65035

1. Order: 500 mgSupply on Hand: 250mg/tab250 \mathrm{mg} / \mathrm{tab}250mg/tab

Problem 65036

6. Two masses are tied to a rope on a pulley, as shown below. a. When the system is released from this position, what is the acceleration of the 2.0-kg mass? b. How long does it take for the 2.0−kg2.0-\mathrm{kg}2.0−kg mass to fall to the floor?

Problem 65037

c=17B=29∘\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}c=17B=29∘​

Problem 65038

Graph the function. f(x)=x−7f(x)=\sqrt{x}-7f(x)=x​−7

Problem 65039

Problem 6 Sothy plans to walk 10000 steps.He starts his walk at 8:00 AM.At 8:23 AM, his phone tells him that he has taken 2000 steps.If he continues at this rate, when will he reach 10000 steps? Submit

Problem 65040

Solve the right triangle.

Problem 65041

A b=1.49, c 7.42 b B וה U

Problem 65042

Problem 65043

Problem 65044

Simplify each expression (9x+7)(−5x4−x3)(9 x+7)\left(-5 x^{4}-x^{3}\right)(9x+7)(−5x4−x3)

Problem 65045

Problem 65046

6. a5(−9a4−9a3+4a2)a^{5}\left(-9 a^{4}-9 a^{3}+4 a^{2}\right)a5(−9a4−9a3+4a2)

Problem 65047

For the rotation $-\frac{71 \pi}{8}$ , find the coterminal angle from $0 \leq \theta<2 \pi$ , the quadrant, and the reference angle.

18. Solve the following inequality algebraically $|2 x-6|<7$

$3(x+2)=21$

Jack orders a pizza with a 20-inch diameter for a party.
8. What is the length of each slice?
9. What is the area of the whole pizza?

The box plot represents the number of minutes customers spend on hold when calling a company. Number of Minutes Spent on Hold
What is the upper quartile of the data? 3 5 6 8 Mark this and return Save and Exit Next Submit

The data set represents the number of miles Mary jogged each day for the past nine days. $6,7,5,0,6,12,8,6,9$
What is the outlier of the data? 0 6 7 12

The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your onswer. How could you correctly rewrite the equation $4(5+3)=2(22-6)$ using the distributive property? $20+12=44-12$

Solve for $a$ . Express your answer in simplest radical form if necessary. $a^{3}=78$
Answer Attempt 1 out of 2

2 (2) Calculate the perimeter and area of the polygon below. Show all work. $\begin{array}{l} 8^{2}=64 \\ 5^{2}=-16 \\ \sqrt{3} a=6 \end{array}$ $4+6=$

Find the value of $y$ . Round your answer to the nearest tenth.

Given: $\overline{A F} \cong \overline{F C}, \angle A B E \cong \angle E B C$ Which line is the angle bisector?

(4) What is $x$ ?
$x^{2}=169$ $\square$ $\begin{array}{l} x=-84.5 \\ x=-16 \end{array}$ $\qquad$ $\begin{array}{l} \hat{x}=-16 \\ x=-13 \end{array}$ $\square$ $x=13$
$x=16$ $\qquad$ $x=84.5$

$\text { [6 } 3348663186 \text { 8] }$
How many comparisons will be performed in this array using sequential search for the searchltem 6? 7 2 1 4 3 6 5 0

The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
Answer Attempt 1 out of 20

$\begin{array}{l}6(w+1)-3 w=3(w+4 \\ 2(3 a-1)=4 a+10 \\ 7 b-3(b+2)=4 b-11 \\ 5(c-2)+3 c=4(2 c+1\end{array}$

This model shows a unit square divided into smaller square tiles. $1 \text { unit }$
Find the area of the shaded rectangle by multiplying its length and width. Fill in the equation. $\square$ $\square$ $\square$

Given $x>0$ and $y>0$ , select the expression that is equivalent to $\sqrt[4]{256 x^{16} y^{6}}$

1. Order: 500 mg
Supply on Hand: $250 \mathrm{mg} / \mathrm{tab}$

6. Two masses are tied to a rope on a pulley, as shown below. a. When the system is released from this position, what is the acceleration of the 2.0-kg mass? b. How long does it take for the $2.0-\mathrm{kg}$ mass to fall to the floor?

$\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}$

Graph the function. $f(x)=\sqrt{x}-7$

Problem 6 Sothy plans to walk 10000 steps.
He starts his walk at 8:00 AM.
At 8:23 AM, his phone tells him that he has taken 2000 steps.
If he continues at this rate, when will he reach 10000 steps? Submit

Simplify each expression $(9 x+7)\left(-5 x^{4}-x^{3}\right)$

6. $a^{5}\left(-9 a^{4}-9 a^{3}+4 a^{2}\right)$

Plot the point $(5,-1)$ and identify the quadrant.
Click on the graph to plot a point. Click a point to delete it.

9. $6 x+8=50$

11. $13=-4 k+9$

Question Watch V
Find the median and mean of the data set below: $47,15,6,49,45,30$
Answer Attempt 1 out of 2
Median = $\square$ Mean = $\square$ Submit Answer

Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function? $y=9 x^{2}-9 x+20$ A. both a relation and a function B. function only C. relation only D. neither a relation nor a function

4. $x^{2}-16=0$

Identifying an Error Deepak plotted these points on the number line. Point A: -0.3 Point B: $-\frac{3}{4}$ Point C: $-1 \frac{1}{4}$ Point D: -0.7 Which point did he plot incorrectly? Point a Intro Done

Solve the Inequality. $y+7<-6$
The inequality is $\square$

Find the derivative of the function $f(x)=\frac{e^{x}+1}{9(x) e^{x}-1}$ . Simplify your answer.

$\left(\frac{1-\sqrt{5}}{2}\right)^{12}$

$\left(2 g^{3}+g^{2}\right)\left(4 g^{3}-7 g^{2}-3 g\right)$

6. Найдите точки, в которых компоненты градиента функции $z=x^{2}+y^{2}+5 x y+x-4 y+1$ равны нулю.

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through $(8,-1)$ and perpendicular to the line whose equation is $x-7 y-9=0$