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Problem 10701

4 Two Squares are shown. Find the area and perimeter of each. $\begin{array}{c} P=\ldots \text { units } \\ A=\quad \text { square units } \end{array}$ a) The perimeter increased by a factor of $\qquad$ . b) The area increased by a factor of $\qquad$

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Problem 10702

Analyze the polynomial function $f(x)=-4(x+4)(x-3)^{3}$ using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function.
The graph of $f$ behaves like $y=$ $\square$ for large values of $|x|$ . (b) Find the $x$ -and $y$ -intercepts of the graph of the function.
The $x$ -intercept(s) is/are $\square$ . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The $y$ -intercept(s) is/are $\square$ 1. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) (c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.
The real zero(s) of $f$ is/are $\square$ (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The lesser zero is a zero of multiplicity $\square$ , so the graph of $f(1)$ $\qquad$ the $x$ -axis at $x=$ $\qquad$ . The greater zero is a zero of multiplicity $\square$ so the graph off (2) $\qquad$ the $x$ -axis at $x=$ $\square$ . (d) Use a graphing utility to graph the function. The graphs are shown in the viewing window $X_{\min }=-10, X_{\max }=10, X_{s d l}=1$ , $Y_{\min }=-2100, Y_{\max }=2100 Y_{\text {scl }}=210$ . Choose the correct graph below. A. B. c. D.

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Problem 10703

Suppose a $7 \times 11$ matrix $A$ has seven pivot columns. Is $\operatorname{Col} A=\mathbb{R}^{7} ?$ Is $N u l=\mathbb{R}^{4}$ ? Explain your answers.
Is $\operatorname{Col} A=\mathbb{R}^{7}$ ? A: No, $\operatorname{Col} A$ is not $\mathbb{R}^{7}$ . Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Col} A=4$ . Thus, $\operatorname{Col} A$ is equal to $\mathbb{R}^{4}$ . B. No. Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Col} A=7$ . Thus, $\operatorname{Col} A$ is a seven-dimensional subspace of $\mathbb{R}^{7}$ , so $\mathrm{Col} A$ is not equal to $\mathbb{R}^{7}$ . C. Yes. Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Col} A=7$ . Thus, $\operatorname{Col} A$ is a seven-dimensional subspace of $\mathbb{R}^{7}$ , so $\operatorname{Col} A$ is equal to $\mathbb{R}^{7}$ . D. No, the column space of $A$ is not $\mathbb{R}^{7}$ . Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Col} A=0$ . Thus, $\operatorname{Col} A$ is equal to 0 .
Is $\operatorname{Nul} A=\mathbb{R}^{4}$ ? A. No, Nul $A$ is not equal to $\mathbb{R}^{4}$ . It is true that $\operatorname{dim} \operatorname{Nul} A=4$ , but Nul $A$ is a subspace of $\mathbb{R}^{11}$ . B. No, Nul $A$ is not equal to $\mathbb{R}^{4}$ . Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Nul} A=7$ . Thus, Nul $A$ is equal to $\mathbb{R}^{7}$ . C. No, Nul $A$ is equal to $\mathbb{R}^{4}$ . Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Nul} A=0$ . Thus, Nul $A$ is equal to 0 . D. Yes, Nul $A$ is equal to $\mathbb{R}^{4}$ . Since $A$ has seven pivot columns, $\operatorname{dim} \operatorname{Nul} A=4$ . Thus, Nul $A$ is equal to $\mathbb{R}^{4}$ .

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Problem 10704

2 The coordinate grid shows triangle $P Q R$ . 8.10ABD. 3
Triangle $P Q R$ is rotated $270^{\circ}$ clockwise about the origin to create triangle $P^{\prime} Q^{\prime} R^{\prime}$ . Choose the correct answer from each drop-down menu to complete the statements.
The side lengths of triangle $P^{\prime} Q^{\prime} R^{\prime}$ are $\square$ to the corresponding side lengths of triangle $P Q R$ . $\checkmark$ equal not equal
The angle measures of triangle $P^{\prime} Q^{\prime} R^{\prime}$ are $\square$ to the corresponding angle measures of triangle $P Q R$ . congruent not congruent 03034 N 至

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Problem 10705

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

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Problem 10706

Narese $\qquad$ Oate
8. 10ABD Module Assessment 1
1 Thangle Efis strown on the coordinate grid. The quadrilateral is rellectel across the $y$ -axis to crate triangle EfG: Q.10480. 2
Which statement is true? A Triangle E'F G' is congruent to triangle EFG. 8 The area of triangle E'FG is greater than the area of triangle EFG. C The permeter of triangle $E^{\prime} F^{\prime} G^{\prime}$ is less than the perimeter of triangle EFG. D The angle measures of triangle E'F'G' are not congruent to the angle measures of triangle EFG.

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Problem 10707

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

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Problem 10708

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$
Range: $\square$ $(-2,2)$ 6

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Problem 10709

Question Watch Video Show Examples
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\begin{aligned} 9 x-8 y & =-8 \\ -8 x+8 y & =0 \end{aligned}$
Answer Subtract to eliminate $\mathbf{y}$ . Submit Answer Subtract to eliminate $\mathbf{x}$ . Add to eliminate $\mathbf{y}$ . Add to eliminate $\mathbf{x .}$

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Problem 10710

Suppose that $F^{\prime}(x)=f(x)$ and $F(0)=3, F(2)=7$ . a. What is the area under $y=f(x)$ over $[0,2]$ if $f(x) \geq 0$ ? b. What is the graphical interpretation of $F(2)-F(0)$ if $f(x)$ takes on both positive and negative values?

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Problem 10711

3 fentagan JKLMN was transtated 8 unlits to the left and 7 units up to creatre pentagon Jok M'N: Which rule describes this transformation? A The perimeter of pentagon JKL'M"N" is grater than the perimeter of pentagon JKLMN. (3) The area of pentagon J'K' 'MN' is less than the area of pentagon JKLMN.
C The angle measures of pentagon J'K'L M'N' are not congruent to the corresponding angle measures of pentagon JKLMN.
D The orientation of the vertices of pentagon $J^{\prime} K L^{\prime} M^{\prime} N^{\prime}$ Is the same as the orientation of the vertices of pentagon JKLMN.

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Problem 10712

The total revenue and total cost functions for the production and sale of $x$ TV s are given as $\left(x(x)=160 x-0.5 x^{2}\right.$ and $C(x)=3240+14 x$ (A) Find the value of $x$ where the graph of $R(x)$ has a horizontal tangent line. $x$ values is 160 (B) Find the profit function in terms of $x$ . $P(x)=-0.5 x^{2}+146 x-3240$ (c) Find the value of $x$ where the graph of $P(x)$ has a horizontal tangent line. x vallues $=146$ (1) ist all the $x$ values of the break-even point(s).
If there are no break-even points, enter NONE List of $x$ values =

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Problem 10713

When randomly selecting an adult, $A$ denotes the event of selecting someone with blue eyes. What do $P(A)$ and $P(\bar{A})$ represent? $P(A)$ represents the $\square$ $P(\bar{A})$ represents the

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Problem 10714

Let $\mathbf{v}_{1}=\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{l}4 \\ 1 \\ 5\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}7 \\ 2 \\ 11\end{array}\right]$ , and $\mathbf{w}=\left[\begin{array}{l}5 \\ 1 \\ 4\end{array}\right]$ . a. Is $\mathbf{w}$ in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? How many vectors are in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? b. How many vectors are in $\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? c. Is $\mathbf{w}$ in the subspace spanned by $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? Why? a. Is $\mathbf{w}$ in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? A. Vector $\mathbf{w}$ is not in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because it is not a linear combination of $\mathbf{v}_{1}, \mathbf{v}_{2}$ , and $\mathbf{v}_{3}$ . B. Vector $\mathbf{w}$ is in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because the subspace generated by $\mathbf{v}_{1}, \mathbf{v}_{2}$ , and $\mathbf{v}_{3}$ is $\mathbb{R}^{3}$ . C. Vector $\mathbf{w}$ is not in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because it is not $\mathbf{v}_{1}, \mathbf{v}_{2}$ , or $\mathbf{v}_{3}$ . D. Vector $\mathbf{w}$ is in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because it is a linear combination of $\mathbf{v}_{1}, \mathbf{v}_{2}$ , and $\mathbf{v}_{3}$ .
How many vectors are in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The number of vectors in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ is $\square$ . B. There are infinitely many vectors in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ . b. How many vectors are in $\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The number of vectors in $\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ is $\square$ $\square$ . B. There are infinitely many vectors in Span $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ .

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Problem 10715

Consider the graph shown below. y 200 150 100 8. 4 2 50 50 100 150 -200 2 X 6 8 -250 If the complete graph of the function is shown, estimate the absolute maximum and absolute minimum. absolute maximum (x, y) = absolute minimum (x, y) =

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Problem 10716

The points $(-3,-4)$ and $(-5,-9)$ are a maximum and minimum, respectively, of a periodic function $f(x)$ , which has period 9 . What is the amplitude of the function? The amplitude is $\square$ 2.5 $\square$ What is an equation for the midline? The midline is $y=$ $\square$ $-6.5$
Which of the following points must lie on the graph of the function $y=f(x)$ ? Select all that are correct. $(31,-12)$ $(-50,-9)$ $(22,-4)$ $(31,-9)$ $(24,-4)$ $(-48,-1)$ None of the above

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Problem 10717

Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) $f(x)=-3(x+2)^{2}-6$ domain $\square$ range $\square$

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Problem 10718

From a random sample of 51 adults who earned an associate's degree from a community college (but no education beyond), the mean lifetime earnings was $\$ 1.6$ million. The sample standard deviation was $\$ 0.5$ million. Construct a $95 \%$ confidence interval for the mean lifetime income of adults who earned an associate's degree and no formal education beyond.
A What type of inference problem is this? (iii) Confidence interval for a population mean (ii) Confidence interval for the population mean of paired differences (iii) Confidence interval for a population proportion (iv) Confidence interval for the difference in two population proportions
B Are the criteria for approximate normality met? Explain. Random sample C Compute the margin of error. Round to three decimal places. $140,627$
D Compute the lower limit and upper limit of the $95 \%$ confidence interval. Round to three decimal places. $\text { Lower Limit }=1,459,373 \quad \text { Upper Limit }=1,740,627$
E Interpret the confidence interval in the context of this situation.

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Problem 10719

Function $A$ and Function $B$ are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

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Problem 10720

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The amount of snowfall in December in City A b. The number of fish caught during a fishing tournament c. The eye color of people on commercial aircraft flights d. The number of statistics students now reading a book e. The number of bald eagles in a country f. The amount of rain in City B during April a. Is the amount of snowfall in December in City A a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable. C. It is not a random variable. b. Is the number of fish caught during a fishing tournament a discrete random variable, a continuous random variable, or not a random variable? A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable c. Is the eye color of people on commercial aircraft flights a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable. C. It is not a randirm variable. d. Is the number of statistics students now reading a book a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable. C. It is not a random variable.

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Problem 10721

Question 9, 5.1.6 Part 1 of 6 HW Score: 50\%, O Points: 0 of 1
Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The number of pigeons in a country b. The hair color of adults in the United States c. The time it takes for a light bulb to burn out d. The number of statistics students now doing their homework e. The square footage of a pool f. The number of light bulbs that burn out in the next year in a room with 16 bulbs a. Is the number of pigeons in a country a discrete random variable, continuous random variable, or not a random variable? A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.

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Problem 10722

\begin{tabular}{|l|l|l|} \hline Unit of Labor & Total Product & Product Price \\ \hline 0 & 0 & $\$ 2.20$ \\ \hline 1 & 15 & 2.00 \\ \hline 2 & 28 & 1.80 \\ \hline 3 & 39 & 1.60 \\ \hline 5 & 58 & 1.40 \\ \hline 6 & 65 & 1.20 \\ \hline \end{tabular}
The data in the table reveal that (A) the firm is selling its product in a purely competitive market.
B the firm is hiring labor in an imperfectly competitive market. (C) there is no level of output at which this firm can operate at a profit.
D the firm is selling its product in an imperfectly competitive market.

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Problem 10723

9. Explain why rewriting $\sqrt{50}$ as $\sqrt{25} \cdot \sqrt{2}$ helps you simplify $\sqrt{50}$ , but rewriting $\sqrt{50}$ as $\sqrt{10} \cdot \sqrt{5}$ does not.

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Problem 10724

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. $-2 x^{2}+6 x-9=0$
Discriminant:
Number of real solutions:

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Problem 10725

If $f(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing. Answer (in interval notation): $\square$

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Problem 10726

Section 9.2 Follow-up Exercises Determine the dimension of each of the following matrices and find the transpose. $1\left(\begin{array}{lll}8 & -8 & 5\end{array}\right.$ 3) $3\left(\begin{array}{rr}0 & 1 \\ 5 & 2 \\ -6 & 8 \\ -2 & 4\end{array}\right)$ $\begin{array}{l} \mathbf{2}\left(\begin{array}{rr} 2 & 6 \\ -3 & 8 \end{array}\right) \\ \mathbf{4}\left(\begin{array}{rrr} 2 & 10 & -1 \\ -3 & -5 & 0 \\ 4 & -8 & 2 \end{array}\right) \\ \mathbf{6}\left(\begin{array}{rrrr} -6 & 3 & 2 & 4 \\ 2 & 3 & 3 & 4 \\ 2 & -1 & 5 & 8 \end{array}\right) \\ \mathbf{8}\left(\begin{array}{rrrrr} 1 & 3 & 5 & 7 & 9 \\ 2 & 4 & 6 & 8 & 10 \end{array}\right) \\ \mathbf{1 0}\left(\begin{array}{rrrrr} 6 & 1 & 2 & 3 & 5 \\ 2 & 0 & 4 & 6 & 1 \\ 3 & 1 & -2 & 3 & 5 \\ 4 & 3 & 2 & 1 & 0 \end{array}\right) \end{array}$ $\begin{array}{l} \mathbf{5}\left(\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right) \\ \mathbf{7}\left(\begin{array}{l} 1 \\ 2 \\ 3 \\ 4 \end{array}\right) \\ \mathbf{9}\left(\begin{array}{lll} 1 & 3 & 5 \\ 6 & 4 & 2 \\ 0 & 1 & 2 \\ 4 & 6 & 3 \\ 5 & 1 & 2 \end{array}\right) \end{array}$

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Problem 10727

107 Assignment 11: Problem 6 (1 point)
Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by $C=70000+40 x, \quad R=400-\frac{x^{2}}{20}$ where the production output in one week is $x$ calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:
Rate of change in cost $=$ 20000 $\square$ Rate of change in revenue $=-20000$ $\square$ Rate of change in profit $=-24000$ $\square$

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Problem 10728

The function $f(x)=\frac{1}{x+4}-3$ is a rational function. a. Use transformations of $y=\frac{1}{x}$ or $y=\frac{1}{x^{2}}$ to sketch the graph. b. Find all $x$ -intercepts or state that the function has no $x$ -intercepts. c. Find the $y$ -intercept or state that the function does not have a $y$ -intercept. d. Find the equation(s) of all vertical asymptotes. e. Find the equation(s) of all horizontal asymptotes.

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Problem 10729

107 Assignment 11: Problem 6 (1 point)
Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by $C=70000+40 x, \quad R=400-\frac{x^{2}}{20}$ where the production output in one week is $x$ calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:
Rate of change in cost $=$ 20000 $\square$ Rate of change in revenue $=-20000$ $\square$ Rate of change in profit $=-24000$ $\square$

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Problem 10730

On veut déterminer la relation entre la spécialisation d'un diplômé en aḋministration et le secteur d'emploi où il travaille. L'étude porte sur un échantillon aléatoire de 200 sujets et le tableau suivant représente les données observées. \begin{tabular}{lcccc} & \multicolumn{4}{c}{ Spécialisation } \\ Secteur \\ D'emploi & Comptabilité & Finance & Marketing & Gestion \\ \cline { 2 - 5 } & 10 & 4 & 12 & 14 \\ Fabrication & 11 & 8 & 14 & 17 \\ Service & 2 & 3 & 44 & 21 \\ Vente au détall & 7 & 15 & 10 & 8 \\ Autre & & & & \end{tabular}
Est-ce que la spécialisation d'un diplômé en administration influence significativement son secteur d'emploi?
1. Écrivez vos hypothèses HO et H 1
2. Calculez les effectifs théoriques.
3. Calculez le khi-carré et comparez à la valeur dans la table pour un niveau de test de $5 \%$ .
4. Concluez de façon précise et complête.
Note: Une conclusion de type H0 doit rester neutre, une conclusion de type H1 doit être affirmative et suivie d'une analyse de la dépendance entre les deux variables.

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Problem 10731

and after the diesel exhaust exposure. The resulting data are given in the accompanying table. For purposes of this exercise, assume that the sample of 10 men is representative of healthy adult males. \begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{ Subject } & \multicolumn{4}{|c|}{ MPF (in Hz) } \\ \cline { 2 - 5 } & Location 1 before & Location 1 after & Location 2 before & Location 2 after \\ \hline 1 & 6.4 & 8.0 & 6.8 & 9.4 \\ \hline 2 & 8.6 & 12.7 & 9.5 & 11.2 \\ \hline 3 & 7.4 & 8.4 & 6.6 & 10.2 \\ \hline 4 & 8.6 & 9.0 & 9.0 & 9.7 \\ \hline 5 & 9.9 & 8.4 & 9.6 & 9.2 \\ \hline 6 & 7.8 & 11.0 & 9.0 & 11.8 \\ \hline 7 & 7.4 & 14.4 & 7.8 & 9.3 \\ \hline 8 & 6.7 & 7.3 & 7.1 & 8.0 \\ \hline 10 & 8.8 & 11.2 & 7.4 & 9.3 \\ \hline \end{tabular}
Use a table or technology. Round your answers to two decimal places.) ( 081 , 315 ) Hz

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Problem 10732

Hide 4 ■ Mark for Review
A ball of mass $m$ is loaded into a launcher with a spring of spring constant $k$ . The ball is pushed down until it is at a vertical position $y=0$ , and the spring is compressed a distance $\Delta L$ , as shown. The ball is then released from rest. Immediately after leaving the launcher, the $x$ - and $y$ -components of the ball's velocity are $v_{x}$ and $v_{y}$ , respectively. The ball reaches a maximum height of $y_{\text {max }}$ and lands a horizontal distance $\Delta x$ away from its initial position. Energy losses due to friction are negligible. Which of the following is a correct conservation of energy equation that compares the total mechanical energy of the ball-spring-Earth system immediately before the ball is launched to the total mechanical energy of the ball-spring-Earth system the moment the ball reaches its maximum height?

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Problem 10733

(Note if any boxes seem not applicable, leave blank.) A random sample of 130 business executives was classified according to age and the degree of risk aversion as measured by a psychological test.
Degree of Risk Aversion \begin{tabular}{|c|c|c|c|c|} \hline Age & \multicolumn{3}{|c|}{ Low } & Medium \\ High & Total \\ \hline Below 45 & 14 & 22 & 7 & 43 \\ \hline $45-55$ & 16 & 33 & 12 & 61 \\ \hline Over 55 & 4 & 15 & 7 & 26 \\ \hline Total & & & & 130 \\ \hline \end{tabular}
Do these data demonstrate an association between risk aversion and age?
Test Statistic: $\square$ According to your table, the P -value is bounded by: .50 $\square$ Is there sufficient evidence to demonstrate an association between

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Problem 10734

Consider the function.(If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\square$ concave down $\square$ (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=$ $\square$

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Problem 10735

$\text{Note: Figure not drawn to scale.}$
A fan is attached to the top of a block, as shown. The block is released from rest at the top of a ramp and the fan exerts a constant force on the block opposite the block's direction of motion. The block slides a distance $D_{1}$ along the ramp and then transitions to a horizontal surface, eventually coming to rest momentarily after traveling a distance $D_{2}$ . Frictional forces are negligible. Which of the following correctly describes the relationship between $D_{2}$ and $D_{1}$ ?
(A) $D_{2}$ must be less than $D_{1}$ .

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Problem 10736

Without graphing, find the vertex, the axis of symmetry, and $f(x)=-\frac{2}{3}(x+8)^{2}+4$
What is the vertex? $(-8,4)$ (Type an ordered pair.) What is the equation of the axis of symmetry? $\square$

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Problem 10737

Use the expression below to complete the table. The first column lists parts of the expression. Identify the parts of the expression that correspond to the descriptions to complete the table. $x+2(8+1)-4.8$
Fill in the entries in the table. \begin{tabular}{|l|c|c|} \hline \multicolumn{1}{|c|}{ Description of Part } & \multicolumn{2}{|c|}{ Part } \\ \hline Variable & & \\ \hline Sum & & \\ \hline Product & & \\ \hline Constant numencal value term & & \\ \hline \end{tabular} (Use the operation symbols in the math palette as needed. Do not simplify.)

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Problem 10738

Classify each pair of angles. $\measuredangle 2$ and $\measuredangle 7$ $\measuredangle 1$ and $\measuredangle 5$ $\measuredangle 6$ and $\measuredangle 7$ $\measuredangle 3$ and $\measuredangle 5$ $\measuredangle 1$ and $\measuredangle 2$ $\measuredangle 4$ and $\measuredangle 5$
Consecutive Interior angles Vertical angles Adjacent angles Alternate Interior angles Corresponding angles
Alternate Exterior angles

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Problem 10739

4. Given the following sequence, which statement below is true? (1 Point) $-18,-9,0,9,18, \ldots \ldots \ldots 648$ The ratio of the sequence is 9 The common difference of the sequence is 9 The sequence above has 70 terms The sum of the sequence is 23620

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Problem 10740

Describe the graph using both set-builder notation and interval notation.
The solution set is $\{x \mid$ $\square$ B. (Type an inequality. Use integers or fractions for any numbers in the inequality.)

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Problem 10741

Find the center, the vertices, the foci, and the asymptotes. Then draw the graph. $\frac{(x-2)^{2}}{9}-\frac{(y+5)^{2}}{16}=1$

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Problem 10742

Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A system of two equations in two variables whose graphs are a circle and a line can have four real ordered-pair solutions.
Choose the correct answer below. A. The statement is false. The correct statement is "A system of two equations in two variables whose graphs are a circle and a line can have two or one real ordered-pair solutions." B. The statement is false. The correct statement is "A system of two equations in two variables whose graphs are a circle and a line can have only three real ordered-pair solutions." C. The statement is false. The correct statement is "A system of two equations in two variables whose graphs are a circle and a line can have only one real ordered-pair solution." D. The statement is true.

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Problem 10743

Elasticity of Demand The demand function for a certain brand of backpacks is $p=53 \ln \left(\frac{53}{x}\right) \quad(0<x \leq 53)$ where $p$ is the unit price in dollars and $x$ is the quantity (in hundreds) demanded per month. (a) Find the elasticity of demand $E(p)$ . $E(p)=$ $\square$
Determine the range of prices corresponding to inelastic, unitary, and elastic demand. Demand is inelastic if $\square$ , unitary if $\square$ --Select-, and elastic if $\square$ -Select--. (b) If the unit price is increased slightly from $\$ 53$ , will the revenue increase or decrease? The revenue will increase. The revenue will decrease. The revenue will remain constant.

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Problem 10744

Sketch the graph of the solution set of the system of inequalities. $\left\{\begin{array}{l} x-y^{2}>0 \\ x-2 y>3 \end{array}\right.$

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Problem 10745

Let $A$ be an $n \times n$ matrix and suppose that $\vec{v}$ is a $\lambda$ -eigenvector for $A$ .
Select all of the following statements which are true.
From the 5 options, select all that apply $A \vec{v}=\lambda \vec{v}$ $(\lambda I-A) \vec{v}=\overrightarrow{0}$ $\lambda \neq 0$ $\vec{v} \neq 0$ $\vec{v}$ is a solution to the system with augmented matrix $(A \mid 0)$
3

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Problem 10746

3. State the domain and range of each function. Explain your thinking. a. $f(x)=-3 \sqrt{2 x+8}-1$ [4 marks] b. $g(x)=-5 \cos (9[x-80 \pi])+3[3$ marks] c. $-2 \log _{3}\left(x^{2}-5\right)+1$ [4 marks]

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Problem 10747

Find the local minimum value of the function $f(x) = x \ln(2x)$ .

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Problem 10748

The equations of three lines are given below. Line 1: $y=\frac{2}{3} x+7$ Line 2: $3 y=2 x+5$ Line 3: $4 x-6 y=8$
For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

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Problem 10749

The equations of three lines are given below. Line 1: $y=-2 x-8$ Line 2: $3 x-6 y=-6$ Line 3: $y=-2 x+1$
For each pair of lines, determine whether they are parallel, perpendicular, or neith
Line 1 and Line 2 : Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3 : Parallel Perpendicular Neither

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Problem 10750

Consider the function $m(x)=24 x^{5}-360 x^{4}+1400 x^{3}-5 .$
Differentiate $m$ and use the derivative to determine each of the following.
The intervals on which $m$ is increasing. $m$ increases on: $\square$ The intervals on which $m$ is decreasing. $m$ decreases on: $\square$ The value(s) of $x$ at which $m$ has a relative maximum. If there are more than one solutions, separate them by a comma. Use exact values. $m$ has local maximum(s) at $x=$ $\square$ The value(s) of $x$ at which $m$ has a relative minimum. If there are more than one solutions, separate them by a comma. Use exact values. $m$ has local minimum(s) at $x=$ $\square$

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Problem 10751

Which of the following illustrates the commutative property of multiplication?
Enter a, b, c, d, or e. a. $z y=y z$ b. $a+(c+d)=(a+c)+d$ c. $y+a=a+y$ d. $(d b)(e+f)=d[b(e+f)]$ e. $(a c+d e)(e f)=(d e+a c)(e f)$

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Problem 10752

15 The graph below shows the distance, in miles, that a group of campers hiked from a camp over time.
Part A: During which one-hour interval were the campers hiking the fastest? Explain your reasoning. $\qquad$

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Problem 10753

Consider the function.(If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\square$ concave down $\square$ (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=$ $\square$

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Problem 10754

Consider the function.(If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\square$ concave down $\square$ (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=\square$

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Problem 10755

Consider the function. (If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\quad(4,6) \cup(8, \infty)$ decreasing $\quad(-\infty, 4) \cup(6,8)$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\quad(-\infty, 4.84) \cup(7.16, \infty)$ concave down (4.84,7.16) (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=4.84,7.16$

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Problem 10756

Consider the function. (If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\quad(4,6) \cup(8, \infty)$ decreasing $\quad(-\infty, 4) \cup(6,8)$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\quad(-\infty, 4.84) \cup(7.16, \infty)$ concave down (4.84,7.16) (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=4.84,7.16$

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Problem 10757

Consider the function. (If an answer does not exist, enter DNE.) $f(x)=\sin (x)+\sin ^{3}(x) \text { over }-\pi<x<\pi$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$

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Problem 10758

Analyze the graph of $f^{\prime}$ , then list all inflection points and intervals where $f$ is concave up and concave down. (Enter your answer for inflection points as a comma-separated list. Enter your answers for concavity using interval notation. If an answer does not exist, enter DNE.) locations of inflection points $\quad x=$ $\square$ concave up $\square$ concave down $\square$

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Problem 10759

Analyze the graph of $f^{\prime}$ , then list all intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing $-2,0$ U 2,3 decreasing $-2,2$

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Problem 10760

```latex \text{Flüssigkeiten bei einem Produktionsprozess} \\ \text{In einem Produktionsprozess werden Flüssigkeiten erhitzt und anschließend abgekühlt. Der Temperaturverlauf kann gezielt gesteuert werden, sodass er sich für den gesamten Erhitzungs- bzw. Abkühlungsvorgang für } t \geq 0 \text{ durch eine der in } \mathbb{R} \text{ definierten Funktionen } f_{k} \text{ mit } f_{k}(t)=23+20 \cdot t \cdot e^{-\frac{1}{10} \cdot k \cdot t}, \text{ wobei } k \text{ eine positive, reelle Zahl sein soll, beschreiben lässt. Dabei ist } t \text{ die seit Beginn des Vorgangs vergangene Zeit in Minuten und } f_{k}(t) \text{ die Temperatur in } { }^{\circ} C. \\ \text{a) Die in Abbildung 1 dargestellten Graphen } A, B \text{ und } C \text{ gehören jeweils zu einem der Werte } k=0,5 ; k=2 \text{ und } k=5. \text{ Ordnen Sie jedem dieser Werte den zugehörigen Graphen zu.} \\ \text{b) Begründen Sie, dass der in Abbildung 1 dargestellte Graph } D \text{ nicht zu einer der Funktionen } f_{k} \text{ gehören kann.} \\ \text{c) Zeigen Sie, dass gilt} \\ f_{k}^{\prime}(t)=20 \cdot e^{-\frac{1}{10} \cdot k \cdot t} \cdot\left(1-\frac{1}{10} \cdot k \cdot t\right) \\ \text{d) Ermitteln Sie denjenigen Wert von } k, \text{ für den die Flüssigkeit im Modell eine Höchsttemperatur von } 123^{\circ} \mathrm{C} \text{ erreicht.} \\ \text{e) Ermitteln Sie die Koordinaten des Wendepunktes des Graphen von } f_{10}. \text{ Interpretieren Sie anschließend die Bedeutung der x-Koordinate dieses Wendepunkts des Graphen von } f_{10} \text{ im Sachzusammenhang.} ```

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Problem 10761

Examine the input-output table, which contains some of the ordered pairs of a linear function. \begin{tabular}{|c|c|} \hline Input $(x)$ & Output $(y)$ \\ \hline-4 & 4 \\ \hline-2 & 1 \\ \hline 0 & -2 \\ \hline 4 & -5 \\ \hline \end{tabular}
What is the initial value of the function? $-4$ $-2$ 0 4

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Problem 10762

1. Find the minimum value of $2 x^{2}+12 x+4$ and the value/values of $x$ where the minimum is attained.

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Problem 10763

6.0 Sulla base delle informazioni che puoi dedurre dal grafico, completa le uguaglianze seguenti. a. $\lim _{x \rightarrow-\infty} f(x)=$ $\qquad$ f. $\lim _{x \rightarrow-\infty} \frac{1}{f(x)}=$ . $\qquad$ b. $\lim _{x \rightarrow-1^{-}} f(x)=$ $\qquad$ g. $\lim _{x \rightarrow-2^{+}} \frac{1}{f(x)}=$ $\qquad$ D] $-\infty$ c. $\lim _{x \rightarrow 1^{+}} f(x)=$ $\qquad$ d. $\lim _{x \rightarrow+\infty} f(x)=$ $\qquad$ h. $\lim _{x \rightarrow 1^{-}} e^{f(x)}=$ $\qquad$ e. $\lim _{x \rightarrow 0}[f(x)+3]=$ $\qquad$ i. $\lim _{x \rightarrow 1^{+}} e^{f(x)}=$ $\qquad$

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Problem 10764

To find the intervals of increase and decrease, as well as the points of extrema for the function $F(x) = x + \frac{6}{(-8x+4)^{1/2}}$ , we need to:
1. Determine the first derivative $F'(x)$ .
2. Find the critical points by setting $F'(x) = 0$ and solving for $x$ .
3. Use the first derivative test to determine the intervals of increase and decrease.
4. Identify the points of local maxima and minima based on the sign changes of $F'(x)$ .
Given the second derivative $f^{\prime\prime}(x) = \frac{20-x}{2 \sqrt{-2x+1}(-2x+1)^2}$ , we can also analyze the concavity and possible inflection points.

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Problem 10765

2 Ein Betrieb stellt ein Produkt mit den Inputfaktoren $x$ (in ME) und $y$ ( Output soll 1000 ME betragen. Die Faktormengenkombinationen, die zu diesem Output führen, lassen sich mit der Isoquantengleichung $y(x)=\frac{40}{x-2}+3$ beschreiben. Bei einem Kostenbudget in Höhe von 730 GE lautet die Gleichung der Isokostengeraden $y(x)=-10 x+73$ , bei einem Kostenbudget von 550 GE lautet sie $y(x)=-10 x+55$ . a) Untersuchen Sie, ob sich mit diesen Kostenbudgets der angestrebte Output erzielen lässt. Geben Sie ggf. die Kombinationsmengen der Inputfaktoren an. b) Berechnen Sie die Minimalkostenkombination. c) Bestimmen Sie die Gleichung der kostenminimalen Isokostengeraden. d) Berechnen Sie, wie hoch das Kostenbudget mindestens sein muss, wenn ein Output von 1000 ME produziert werden soll. e) Erstellen Sie eine Grafik, die Ihre Ergebnisse veranschaulicht. Geben Sie für die Isoquante die Gleichung der Polgeraden und der Asymptote an.

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Problem 10766

Graph the solution set of the system of inequalities. $\left\{\begin{array}{l} y<\frac{1}{4} x+6 \\ y \geq 2 x-1 \end{array}\right.$ Webassign.
Find the coordinates of the vertex. (If there is no solution, enter NO SC $(x, y)=(\square)$

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Problem 10767

Consider the equation $f(x, y, z)=\frac{1}{x y}+\frac{1}{y z}+\frac{1}{z x}=1$ , where $x \neq 0, y \neq 0, z \neq 0$ . (a) (3 points) Express $z$ as a function of $x$ and $y$ . (b) (4 points) Compute the directional derivative of $z$ along direction $\vec{u}=\cos \theta \hat{i}+\sin \theta \hat{j}$ at $(x, y)$ . (c) (3 points) Compute $\vec{\nabla} z$ and find the direction of minimum rate of change at the point $(2,1)$ . (d) (6 points) Let $p=\left(2,1, z_{0}\right)$ be a point on the level surface $f(x, y, z)=1$ . Using the result obtained in parts (a) and (c), find the value of $z_{0}$ and the equation of the tangent plane of the level surface at the point $p$ .

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Problem 10768

Exercises - at which point on $y=a x^{2}+b x+c$ is the curvature maximized? - at which points on the ellipse $\left\{\begin{array}{l}x=a \cos t \\ y=b \sin t\end{array}\right.$ are curvatures maximized/minimized?

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Problem 10769

10.1 Given $f(x)=3-x^{2}$ (with domain $\left.(-\infty, \infty)\right)$ , $g(x)=2-x($ with domain $(-\infty, \infty))$ , $h(x)=\frac{1}{x}$ (with domain $\left.(0, \infty)\right)$ , find the following compositions (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ h$ (d) $g \circ h$ (+) hof; What is the domain this function? $(+)$ hog; What is the domain this function? 10.2 Determine the inverses of the following functions (a) $f(x)=4-5 x$ , (with domain $(-\infty, \infty)$ ) (b) $h(x)=x^{2}-3 x+2$ , (with domain $\left.\left.(2, \infty)\right)\right]$ $(+) f(x)=\frac{2 x+1}{3-x}$ , (also find the domain and range of $\ell$ and of $f^{-1}$ )

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Problem 10770

0 Write the letter of the correct match next to each problem. equiangular tri. Created on TheTeachersCorner.net Match-up Maker $\qquad$ a. original geometric figure $\qquad$ equilateral tri. b. extra line drawn to help analyze geometric relationships $\qquad$ isosceles triangle c. turn around a fixed point through a specific angle $\qquad$ scalene triangle d. at least 2 congruent sides $\qquad$ auxiliary line e. polygon(s) with all congruent corresponding parts $\qquad$ congruent $\qquad$ congruent polygons f. operation that maps an original geometric figure onto a new figure $\qquad$ corresponding g. 3 congruent sides $\qquad$ included angle h. 3 congruent acute angles $\qquad$ included side $\qquad$ base angle $\qquad$ transformation $\qquad$ preimage m. no congruent sides $\qquad$ image n. new geometric figure $\qquad$ reflection o. slide that moves all points the same distance $\qquad$ translation p. side located between 2 consecutive angles $\qquad$ rotation q. angle formed by two adjacent sides of a polygon

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Problem 10771

6. What is the coefficient of $x^{13}$ in the expression $\left(\sqrt{x}-\frac{1}{x^{4}}\right)^{89}$ .

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Problem 10772

البطة نات الفاصلة 0 انظر الميكل المقبل . - $f^{\prime}(-2)$ ） $f(0)$ ( 0 $\lim _{h^{\prime} \rightarrow 0} \frac{f(-1+h)-f(-1)}{h}$ . $f(x)=-x^{3}-3 x^{2}+2$

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Problem 10773

Which expression is equivalent to $\left(2^{\frac{1}{2}}-2^{\frac{3}{4}}\right)^{2}$ ? $\sqrt[4]{2^{3}}$ $\sqrt{2^{5}}$ $\sqrt[4]{4^{3}}$ $\sqrt{4^{5}}$

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Problem 10774

Which statement is true about the solution of $\sqrt[3]{x^{2}-12}=\sqrt[3]{4 x}$ ? $x=-2$ is an extraneous solution, and $x=6$ is a true solution. $x=6$ is an extraneous solution, and $x=-2$ is a true solution. Both $x=-2$ and $x=6$ are extraneous solutions. Both $x=-2$ and $x=6$ are true solutions.

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Problem 10775

Given that $\sqrt[3]{\frac{904}{3051}}=\sqrt[3]{\frac{b \cdot d}{c \cdot d}}$ , where $b$ and $d$ ; and $c$ and $d$ are the factors of $904 \& 3051$ , respectively. If $b$ and $c$ are perfect cubes, find the value of $d$ .
Q (Enter a number/value)

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Problem 10776

Which equation shows a valid step in solving $\sqrt[3]{2 x-6}+\sqrt[3]{2 x+6}=0$ ? $(\sqrt[3]{2 x-6})^{2}=(\sqrt[3]{2 x+6})^{2}$ $(\sqrt[3]{2 x-6})^{2}=(-\sqrt[3]{2 x+6})^{2}$ $(\sqrt[3]{2 x-6})^{3}=(\sqrt[3]{2 x+6})^{3}$ $(\sqrt[3]{2 x-6})^{3}=(-\sqrt[3]{2 x+6})^{3}$ Mark this and return sessmentViewer/Activit...

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Problem 10777

13) Ends of a diameter: $(-17,-9)$ and $(-19,-9)$ 14) Ends of a diameter: $(-3,11)$ and $(3,-13)$ 15) Center: $(-15,3 \sqrt{7})$ 16) Center: $(-11,-14)$
Area: $2 \pi$ Area: $16 \pi$ 17) Center: $(-5,12)$ 18) Center: $(15,14)$
Circumference: $8 \pi$ Circumference: $2 \pi \sqrt{15}$ 19) Center: $(2,-5)$
Point on Circle: $(-7,-1)$ 20) Center: $(14,17)$
Point on Circle: $(15,17)$ 21) Center: $(-15,9)$ 22) Center: $(-2,12)$
Tangent to $x=-17$ Tangent to $x=-5$

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Problem 10778

Which equation shows a valid, practical step in solving $\sqrt[4]{2 x-8}+\sqrt[4]{2 x+8}=0$ ? $(\sqrt[4]{2 x-8})^{3}=-(\sqrt[4]{2 x+8})^{3}$ $(\sqrt[4]{2 x-8})^{3}=(-\sqrt[4]{2 x+8})^{3}$ $(\sqrt[4]{2 x-8})^{4}=-(\sqrt[4]{2 x+8})^{4}$ $(\sqrt[4]{2 x-8})^{4}=(-\sqrt[4]{2 x+8})^{4}$

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Problem 10779

Which equation can be rewritten as $x+4=x^{2}$ ? Assume $x>0$
$\sqrt{x}+2=x$
$\sqrt{x+2}=x$ $\sqrt{x+4}=x$ $\sqrt{x^{2}+16}=x$

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Problem 10780

20. $x=\frac{1}{3} y+2$ , $-2 x-y=1$

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Problem 10781

For the system of equations below, graph each line to determine the solution. Write the solution as an ordered pair.
Each line must be drawn correctly and the solution must be correct in order to receive all points. $\left\{\begin{array}{l} y=\frac{2}{3} x+4 \\ y=-2 x-4 \end{array}\right.$
Clear All Draw:

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Problem 10782

Practice Problems: Use the table to answer questions 1 -9. The table below shows the number of employees that were hired each month at Canyons and Gameday during 2023. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline & Jan & Feb & Mar & Apr & May & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\ \hline Canyons & 15 & 4 & 0 & 3 & 4 & 1 & 1 & 3 & 4 & 5 & 7 & 7 \\ \hline Gameday & 1 & 3 & 3 & 4 & 4 & 5 & 2 & 0 & 3 & 2 & 5 & 3 \\ \hline \end{tabular} 1) Determine the measures of center for each data set. \begin{tabular}{|l|l|l|l|} \hline & Mean & Median & Mode \\ \hline Canyons & 4,5 & 4 & \\ \hline Gameday & & & \\ \hline \end{tabular} 2) Determine the measures of spread for each data set. \begin{tabular}{|l|l|l|l|} \hline & Range & IQR & Standard Deviation \\ \hline Canyons & & & \\ \hline Gameday & & & \\ \hline \end{tabular} 3) Determine the 5-number summary for each data set. \begin{tabular}{|l|l|l|l|l|l|} \hline & $Q_{0}$ Min. & $Q_{1}$ & $Q_{2}$ med. & $Q_{3}$ & $Q_{4}$ Mar \\ \hline Canyons & & & & & \\ \hline Gameday & & & & & \\ \hline \end{tabular} 4) Create box plots for each data set. LABEL!

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Problem 10783

For the system of equations below, graph each line to determine the solution. Write the solution as an ordered pair.
Each line must be drawn correctly and the solution must be correct in order to receive all points. $\left\{\begin{array}{l} y=\frac{2}{3} x+4 \\ y=-2 x-4 \end{array}\right.$
Clear All Draw:

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Problem 10784

10. What is the imaginary part of the complex number $7-5 i$ ? a. 7 b. -5 c. 5 d. 0 a b C d not given

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Problem 10785

20. Which complex number lies on the imaginary axis? a. $4+0 i$ b. $0+3 i$ c. $-2+2 i$ d. $1-i$ a b C d not given

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Problem 10786

Find the $x$ - and $y$ -intercepts of the following lines.
1. $2 x+3 y=24$
2. $3 x-5 y=30$
3. $7 x-4 y=84$
4. $x+y=8$ $5, x=5$
6. $3 y=66$

See Solution

Problem 10787

Find the domain of the function $f(x)$ . $f(x)=\frac{4}{5 x-9}$
Select the correct choice below and, if necessary, fill in the answer box to complete you A. The domain is $\{x \mid$ $\square$ \}. (Simplify your answer. Type an inequality or a compound inequality.) B. The domain is $\square$ 3. (Simplify your answer. Use a comma to separate answers as needed.) C. The domain is $\{x \mid x$ is a real number and $x \neq$ $\square$ \}. (Simplify your answer. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers.

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Problem 10788

13 Finde den Fehler! a) Zeige durch Einsetzen eines Werts für x oder mithilfe einer Probe, dass die Rechnungen falsch sein müssen. b) Erkläre, was falsch gemacht wurde, und korrigiere im Heft. $\text { (1) } \begin{aligned} & 4 x-(x+2) \\ = & 4 x-x+2 \\ = & 3 x+2 \end{aligned}$ (2) $5 x+3=0 \quad \mid-2$ $7 x=0 \quad 1: 7$ (3) $\begin{array}{c} 4 x+2=2 x-2 \\ 2 x=-4 \quad \mid-2 \\ x=-6 \end{array}$ $\text { (4) } \begin{aligned} \frac{2}{5} x+\frac{1}{5} & =0,3 \quad \mid \cdot 5 \\ 2 x+\frac{1}{5} & =0,15 \quad \left\lvert\,-\frac{1}{5}\right. \\ 2 x & =-0,05 \quad \mid: 2 \\ x & =-0,25 \end{aligned}$

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Problem 10789

43 $\frac{(x+2)(x-2)-x^{2}}{5 x-5} \geq 0$ $\frac{(x+3)(x-2)-x^{2}}{(x-3)(x+2)-x^{2}}<0$

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Problem 10790

Based on the data shown below, calculate the correlation coefficient (rounded to three decimal places) \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 27.61 \\ \hline 4 & 29.88 \\ \hline 5 & 29.95 \\ \hline 6 & 31.32 \\ \hline 7 & 34.89 \\ \hline 8 & 35.06 \\ \hline \end{tabular}

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Problem 10791

8.. Two years ago, Print Co, acquired $30 \%$ of Stamp Co, common stock for $\$ 750,000$ . Today, Print acquired the remaining $70 \%$ shares of Stamp for $\$ 2,100,000$ cash. Print's total investment would a mount to A. $\$ 3,200,000$ , B. $\$ 2,500,000$ , C. $\$ 3,000,000$ , D. $\$ 2,850,000$ .

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Problem 10792

Green plants need light in order to survive. Structures in the leaves absorb light, which in turn, helps plants make their own food.
Under which color of light will plants be least likely to make food? red blue orange green

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Problem 10793

16 \text{ Verschiedene Grundstücke unterscheiden sich nur durch die Länge einer Strecke } x. \text{ Judith, Pia, Cem und Lukas haben Terme für den Flächeninhalt der Grundstücke in } \mathrm{m}^{2} \text{ notiert.}
\text{Judith: } 11,4 \cdot x-4,3 \cdot(x-9,9)
\text{Cem: } 9,9 \cdot 11,4+(x-9,9) \cdot 7,1
\text{Pia: } 9,9 \cdot 4,3+9,9 \cdot 7,1+7,1 \cdot(x-9,9)
\text{Lukas: } 9,9 \cdot 4,3+x \cdot 7,1
\text{a) Gib an, welcher Term zu welcher Zeichnung gehört. Begründe deine Entscheidung.}
\text{b) Gib einen Term für den Umfang des Grundstücks an und berechne, für welchen Wert von } x \text{ der Umfang 52 m beträgt.}

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Problem 10794

Determine whether descriptive or inferential statistics were used. Fifty-seven percent of Hispanics in the United States have type O blood.
This is an example of (Choose one) $\nabla$ statistics.

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Problem 10795

27. Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses, and adjust their diet. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted, and an astronaut's acceleration is measured to be $0.893 \mathrm{~m} / \mathrm{s}^{2}$ . (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer. (c) Discuss how this would affect the measurement of the astronaut's acceleration. Propose a method by which recoil of the vehicle is avoided.

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Problem 10796

1. a. Express $\cos (x)$ in terms of $\cot (x)$ and $\csc (x)$ . b. Express $\csc (x)$ in terms of $\cos (x)$ and $\tan (x)$ .

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Problem 10797

astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer. (c) Discuss how this would affect the measurement of the astronaut's acceleration. Propose a method by which recoil of the vehicle is avoided.
28. In Figure 5.4.3, the net external force on the $24-\mathrm{kg}$ mower is given as 51 N . If the force of friction opposing the motion is 24 N , what force F '(in newtons is the person exerting on the mower? Suppose the mower is moving at $1.5 \mathrm{~m} / \mathrm{s}$ when the force $F$ is removed. How far will the mower go before stopping?

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Problem 10798

. If the rocket sled shown in the previous problem starts with only one rocket burning, what is the magnitude of this acceleration? Assume that the mass of the system is $2.10 \times 10^{3} \mathrm{~kg}$ , the thrust T is $2.40 \times 10^{4} \mathrm{~N}$ , and the force of friction opposing the motion is 650.0 N . (b) Why is the acceleration not onefourth of what it is with all rockets burning?

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Problem 10799

the system is $2.10 \times 10^{3} \mathrm{~kg}$ , the thrust T is $2.40 \times 10^{4} \mathrm{~N}$ , and the force of friction opposing the motion is 650.0 N . (b) Why is the acceleration not onefourth of what it is with all rockets burning? What is the deceleration of the rocket sled if it comes to rest in 1.10 s from a speed of $1000.0 \mathrm{~km} / \mathrm{h}$ ? (Such deceleration caused one test subject to black out and have temporary blindness.)

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Problem 10800

nomework11.4: Problem 1 (1 point)
Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as $x \rightarrow \pm \infty$ : $f(x)=\frac{x^{4}-7}{x^{3}-6}, g(x)=\frac{x^{3}-7}{x^{3}-6}$ , and $h(x)=\frac{x^{2}-7}{x^{3}-6}$ $f(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas) $g(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas) $h(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas)
Note: You can earn partial credit on this problem.

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Problem 10701

Problem 10702

Problem 10703

Problem 10704

Problem 10705

Given the function shown in the graph below, state the domain and range of the function using interval notation:Domain: □\square□ Range: □\square□

Problem 10706

Problem 10707

Given the function shown in the graph below, state the domain and range of the function using interval notation:Domain: □\square□ Range: □\square□

Problem 10708

Given the function shown in the graph below, state the domain and range of the function using interval notation:Domain: □\square□Range: □\square□ (−2,2)(-2,2)(−2,2) 6

Problem 10709

Problem 10710

Problem 10711

Problem 10712

Problem 10713

When randomly selecting an adult, AAA denotes the event of selecting someone with blue eyes. What do P(A)P(A)P(A) and P(Aˉ)P(\bar{A})P(Aˉ) represent? P(A)P(A)P(A) represents the □\square□ P(Aˉ)P(\bar{A})P(Aˉ) represents the

Problem 10714

Problem 10715

Consider the graph shown below. y 200 150 100 8. 4 2 50 50 100 150 -200 2 X 6 8 -250 If the complete graph of the function is shown, estimate the absolute maximum and absolute minimum. absolute maximum (x, y) = absolute minimum (x, y) =

Problem 10716

Problem 10717

Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) f(x)=−3(x+2)2−6f(x)=-3(x+2)^{2}-6f(x)=−3(x+2)2−6 domain □\square□ range □\square□

Problem 10718

Problem 10719

Function AAA and Function BBB are linear functions.Function AFunction B \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

Problem 10720

Problem 10721

Problem 10722

Problem 10723

9. Explain why rewriting 50\sqrt{50}50​ as 25⋅2\sqrt{25} \cdot \sqrt{2}25​⋅2​ helps you simplify 50\sqrt{50}50​, but rewriting 50\sqrt{50}50​ as 10⋅5\sqrt{10} \cdot \sqrt{5}10​⋅5​ does not.

Problem 10724

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. −2x2+6x−9=0-2 x^{2}+6 x-9=0−2x2+6x−9=0Discriminant: Number of real solutions:

Problem 10725

If f(x)=∫0x(16−t2)et3dtf(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d tf(x)=∫0x​(16−t2)et3dt for all xxx, then find the largest open interval on which fff is increasing. Answer (in interval notation): □\square□

Problem 10726

Problem 10727

Problem 10728

Problem 10729

Problem 10730

Problem 10731

Problem 10732

Problem 10733

Problem 10734

Problem 10735

Problem 10736

Without graphing, find the vertex, the axis of symmetry, and f(x)=−23(x+8)2+4f(x)=-\frac{2}{3}(x+8)^{2}+4f(x)=−32​(x+8)2+4What is the vertex? (−8,4)(-8,4)(−8,4) (Type an ordered pair.) What is the equation of the axis of symmetry? □\square□

Problem 10737

Problem 10738

Problem 10739

Problem 10740

Describe the graph using both set-builder notation and interval notation.The solution set is {x∣\{x \mid{x∣ □\square□ B. (Type an inequality. Use integers or fractions for any numbers in the inequality.)

Problem 10741

Find the center, the vertices, the foci, and the asymptotes. Then draw the graph. (x−2)29−(y+5)216=1\frac{(x-2)^{2}}{9}-\frac{(y+5)^{2}}{16}=19(x−2)2​−16(y+5)2​=1

Problem 10742

Problem 10743

Problem 10744

Sketch the graph of the solution set of the system of inequalities. {x−y2>0x−2y>3\left\{\begin{array}{l} x-y^{2}>0 \\ x-2 y>3 \end{array}\right.{x−y2>0x−2y>3​

Problem 10745

Problem 10746

Problem 10747

Find the local minimum value of the function f(x)=xln⁡(2x) f(x) = x \ln(2x) f(x)=xln(2x).

Problem 10748

Problem 10749

Problem 10750

Problem 10751

Problem 10752

15 The graph below shows the distance, in miles, that a group of campers hiked from a camp over time.Part A: During which one-hour interval were the campers hiking the fastest? Explain your reasoning. \qquad

Problem 10753

Problem 10754

Problem 10755

Problem 10756

Problem 10757

Problem 10758

Problem 10759

Analyze the graph of f′f^{\prime}f′, then list all intervals where fff is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing −2,0-2,0−2,0 U 2,3 decreasing −2,2-2,2−2,2

Problem 10760

Problem 10761

Problem 10762

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$
Range: $\square$ $(-2,2)$ 6

When randomly selecting an adult, $A$ denotes the event of selecting someone with blue eyes. What do $P(A)$ and $P(\bar{A})$ represent? $P(A)$ represents the $\square$ $P(\bar{A})$ represents the

Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) $f(x)=-3(x+2)^{2}-6$ domain $\square$ range $\square$

Function $A$ and Function $B$ are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

9. Explain why rewriting $\sqrt{50}$ as $\sqrt{25} \cdot \sqrt{2}$ helps you simplify $\sqrt{50}$ , but rewriting $\sqrt{50}$ as $\sqrt{10} \cdot \sqrt{5}$ does not.

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. $-2 x^{2}+6 x-9=0$
Discriminant:
Number of real solutions:

If $f(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing. Answer (in interval notation): $\square$

Without graphing, find the vertex, the axis of symmetry, and $f(x)=-\frac{2}{3}(x+8)^{2}+4$
What is the vertex? $(-8,4)$ (Type an ordered pair.) What is the equation of the axis of symmetry? $\square$

Describe the graph using both set-builder notation and interval notation.
The solution set is $\{x \mid$ $\square$ B. (Type an inequality. Use integers or fractions for any numbers in the inequality.)

Find the center, the vertices, the foci, and the asymptotes. Then draw the graph. $\frac{(x-2)^{2}}{9}-\frac{(y+5)^{2}}{16}=1$

Sketch the graph of the solution set of the system of inequalities. $\left\{\begin{array}{l} x-y^{2}>0 \\ x-2 y>3 \end{array}\right.$

Find the local minimum value of the function $f(x) = x \ln(2x)$ .

15 The graph below shows the distance, in miles, that a group of campers hiked from a camp over time.
Part A: During which one-hour interval were the campers hiking the fastest? Explain your reasoning. $\qquad$

Analyze the graph of $f^{\prime}$ , then list all intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing $-2,0$ U 2,3 decreasing $-2,2$

1. Find the minimum value of $2 x^{2}+12 x+4$ and the value/values of $x$ where the minimum is attained.

Graph the solution set of the system of inequalities. $\left\{\begin{array}{l} y<\frac{1}{4} x+6 \\ y \geq 2 x-1 \end{array}\right.$ Webassign.
Find the coordinates of the vertex. (If there is no solution, enter NO SC $(x, y)=(\square)$

Exercises - at which point on $y=a x^{2}+b x+c$ is the curvature maximized? - at which points on the ellipse $\left\{\begin{array}{l}x=a \cos t \\ y=b \sin t\end{array}\right.$ are curvatures maximized/minimized?

6. What is the coefficient of $x^{13}$ in the expression $\left(\sqrt{x}-\frac{1}{x^{4}}\right)^{89}$ .

Which expression is equivalent to $\left(2^{\frac{1}{2}}-2^{\frac{3}{4}}\right)^{2}$ ? $\sqrt[4]{2^{3}}$ $\sqrt{2^{5}}$ $\sqrt[4]{4^{3}}$ $\sqrt{4^{5}}$