Analyze

Problem 9901

A sandwich store has a weekly cost of \ $575.00 and \$0.65 per roast beef sandwich. Find profit function$ P(x)$ and max profit.

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Problem 9902

For the function $P(x)=-0.74 x^{2}+22 x+75$ , what constraints ensure profits are at least \ $175,000? Options:$ -3.09 \leq x \leq 5.6 $or$ 0 \leq x < 5.6$?

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Problem 9903

Find the limit as $x$ approaches infinity for $\frac{4x - 1}{2x + 1}$ .

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Problem 9904

Which point is on the graph of the piecewise function $f(x)$ defined as: $f(x)=-9$ for $x<-6$ , $f(x)=1$ for $x=-6$ , and $f(x)=7x-1$ for $x>-6$ ? Options: $(-6,-9)$ , $(-6,-43)$ , $(1,-6)$ , $(0,-9)$ , $(-5,-36)$ , or None.

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Problem 9905

What is the best way to display data on college students' ages and car values from a survey of 300 students? A. Two-way table B. Pie chart C. Histogram D. Side-by-side boxplots E. Scatterplot

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Problem 9906

Determine the best way to display data from a study on TV violence and adult abuse: A. scatterplot B. boxplots C. two-way table D. histogram E. pie chart.

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Problem 9907

(1 point) A population $P$ obeys the logistic model. It satisfies the equation $\frac{d P}{d t}=\frac{3}{1300} P(13-P)$ for $P>0$ . (a) The population is increasing when $\square$ $<P<$ $\square$ (b) The population is decreasing when $P>$ $\square$

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Problem 9908

19. The graph of a cosine function is shown. a) What is the maximum value? the minimum value? b) What is the amplitude? c) What is the vertical translation? d) What is the period? e) What value of $k$ in the formula Period $=\frac{2 \pi}{k}$ will result in the required period? f) Explain why the phase shift can have more than one value. Suggest at least three possible values for the phase shift.

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Problem 9909

|EXERCISE SET 1.2
Reduced Echelon Form of a Matrix
1. Determine whether the following matrices are in reduced echelon form. If a matrix is not in reduced echelon form give a reason.
(a) $\left[\begin{array}{rrrr}1 & 0 & 3 & -2 \\ 0 & 0 & 1 & 8 \\ 0 & 1 & 4 & 9\end{array}\right]$ (b) $\left[\begin{array}{lllll}1 & 2 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 6 \\ 0 & 0 & 0 & 1 & 5\end{array}\right]$ $\left[\begin{array}{lllll}1 & 0 & 4 & 2 & 6 \\ 0 & 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{array}\right]$ (e) $\left[\begin{array}{lllll}1 & 0 & 2 & 0 & 3 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 2 & 0 & 7 \\ 0 & 0 & 0 & 1 & 3\end{array}\right]$ (f) $\left[\begin{array}{lllll}1 & 0 & 4 & 0 & 0 \\ 0 & 1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{array}\right]$ (g) $\left[\begin{array}{lllll}1 & 0 & 0 & 5 & 3 \\ 0 & 0 & 1 & 0 & 3 \\ 0 & 1 & 2 & 3 & 7\end{array}\right]$ (h) $\left[\begin{array}{lllll}0 & 0 & 1 & 0 & 4 \\ 0 & 0 & 0 & 1 & 5 \\ 0 & 1 & 0 & 0 & 3\end{array}\right]$ (i) $\left[\begin{array}{rrrrr}1 & 5 & -3 & 0 & 7 \\ 0 & 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0\end{array}\right]$

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Problem 9910

3LEM 9: THE HAWK PROBLEM A hawk is on top of a tree and spots a fish in the water. The hawks's pathway in metres is measured by time in seconds by the equation: $y=x^{2}-6 x+11$ a) When does the hawk enter the water? b) Explain why this is a problem? c) Sketch a graph

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Problem 9911

Consider the function $f(x)=16 x+81 x^{-1}$ . Give a list of the critical numbers of $f$ and any values for which $f$ is undefined. $x=$ $\square$ Determine the intervals on which $f$ is increasing and decreasing. $f$ is increasing on $\square$ $f$ is decreasing on $\square$ Determine the intervals on which $f$ is concave up and concave down. $f$ is concave up on $\square$ $f$ is concave down on $\square$ Determine the coordinates $(x, y)$ of any inflection points of $f$ . $(x, y)=$ $\square$ No inflection points.

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Problem 9912

Question 1 of 10 How did the Industrial Revolution motivate Europeans to claim colonies around the world? A. Europeans wanted to spread industrial technology to poor countries around the world. B. Europeans hoped to recruit scientists from around the world to help develop new technology. C. Europeans hoped to find natural resources to produce goods in factories. D. Europeans needed places to use the new technologies they had developed.

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Problem 9913

The graph of a quadratic function with vertex $(1,-4)$ is shown in the figure below. Find the domain and the range.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$

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Problem 9914

The graph of a quadratic function with vertex $(2,3)$ is shown in the figure below. Find the domain and the range.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$

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Problem 9915

Determine the amplitude of the periodic graph. * 1 po
Determine the period of the periodic graph. * 1 point

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Problem 9916

Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?
Tara Edward

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Problem 9917

Which of these statements is true for all exponential functions? a) The sign of the slope of the tangent is always the same for all values of $x$ on the function b) The slope is always positive c) The function changes from increasing to decreasing at the turning point d) The slope is always negative

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Problem 9918

5. Consider the sets of vectors of the following form. Determine whether the sets are subspaces of an appropriate vector space. If a set is a subspace give a basis and its dimension. (a) $a(1,2,3)$

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Problem 9919

Determine if triangle $J K L$ and triangle $M N O$ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
SSS: three sides proportionate SSS: three sides congruent SAS: two sides proportionate, included angle congruent SAS: two sides + included angle congruent AA: two angles congruent

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Problem 9920

Determine if triangle $R S T$ and triangle $U V W$ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answer Attempt 2 out of 2
SSS: three sides proportionate SSS: three sides congruent SAS: two sides proportionate, included angle congruent SAS: two sides + included angle congruent AA: two angles congruent

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Problem 9921

Determine if triangle $E F G$ and triangle $H I J$ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answer Attempt 1 out of 2 $\square$ SSS: three sides proportipnate SSS: three sides congruent SAS: two sides proportionate, included angle congruent SAS: two sides + included angle congruent AA: two angles congruent

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Problem 9922

\begin{align} &\text{Given the quadratic function:} \\ &y = -2x^2 - 4x + 3 \\ &\text{Calculate the first and second differences, } \Delta y \text{ and } \Delta^2 y, \text{ for the following values of } x: \\ &x = -3, -2, -1, 0, 1, 2, 3 \end{align}

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Problem 9923

3. The dataset GRADESINTROSTATS is a file that contains information from a random sample of 31 students who took Statistics at MacEwan University in a recent term. Your variables of interest are LCMT (lecture midtermgrade) and LCFE (lecture final exam grade). The data are given below; your instructor has calculated a column of differences for you. \begin{tabular}{|c|c|c|c|c|c|} \hline LCMT & LCFE & & \multicolumn{3}{|l|}{LCMT-LCFE} \\ \hline 81.58 & 69.74 & & 11.84 & & \\ \hline 68.42 & 68.42 & & 0 & & \\ \hline 71.05 & 65.79 & & 5.26 & & \\ \hline 60.53 & 60.53 & & 0 & & \\ \hline 65.79 & 68.42 & & -2.63 & & \\ \hline 55.26 & 61.84 & & -6.58 & & \\ \hline 63.16 & 69.74 & & $-6.58$ & & \\ \hline 84.21 & 50.00 & & 34.21 & & \\ \hline 89.47 & 88.16 & & 1.31 & & \\ \hline 81.58 & 73.68 & & 7.9 & & \\ \hline 92.11 & 78.95 & & 13.16 & & \\ \hline 86.84 & 84.21 & & 2.63 & & \\ \hline 97.37 & 81.58 & & 15.79 & & \\ \hline 68.42 & 63.16 & & 5.26 & & \\ \hline 68.42 & 68.42 & & 0 & & \\ \hline 52.63 & 65.79 & & -13.16 & & \\ \hline 63.16 & 60.53 & & 2.63 & & \\ \hline 97.37 & 98.68 & & -1,31 & & \\ \hline 68.42 & 60.53 & & 7.89 & & \\ \hline 78.95 & 84.21 & & -5.26 & & \\ \hline 73.68 & 64.47 & & 9.21 & & \\ \hline 86.84 & 80.26 & & 6.58 & & \\ \hline 52.63 & 56.58 & & -3.95 & & \\ \hline 50.00 & 71.05 & & -21.05 & & \\ \hline 78.95 & 76.32 & & 2.63 & & \\ \hline 44.74 & 68.42 & & -23.68 & & \\ \hline 73.68 & 76.32 & & -2.64 & & \\ \hline 71.05 & 65.79 & & 5.26 & & \\ \hline 71.05 & 57.89 & & 13.16 & & \\ \hline 81.58 & 67.11 & & 14.47 & & \\ \hline 68.42 & 59.21 & & 9.21 & & \\ \hline \end{tabular}
Note: the sample mean $\bar{x}_{d}=2.630968$ and the sample standard deviation $s_{d}=11.05528$ . The student may verify this with R or Excel or an online calculator, if desired, but it is not neoessary: (a) Why are these data best regarded as a paired sample? (2 marks)

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Problem 9924

Selected values of the function $f$ are shown in the table below. The function $f$ is continuous on the closed interval $[-3,2]$ and differentiable on the open interval $(-3,2)$ . Determine the validity of the following statement:
There exists a value $c$ in the open interval $(-3,2)$ such that $f^{\prime}(c)=6$ . \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline-3 & -9 \\ \hline-1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular}
Answer the statement must be true Submit Answer the statement must be false the statement could be either true or false

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Problem 9925

Discuss the statement and tell what possible misuse or misinterpretation may exist. In a study of patients with flu symptoms, each patient was found to have improved symptoms after taking apple cider vinegar. Therefore, apple cider vinegar cures the flu.
Discuss the statement and tell what possible misuse or misinterpretation may exist. Choose the correct answer below. A. The statement is not valid because having improved symptoms does not necessarily translate to the patients being cured of the flu. B. The statement is valid because the patients may have improved on their own without taking apple cider vinegar and having improved symptoms translates to the patients being cured of the flu. C. The statement is valid because each patient had improved symptoms which translates to the patients being cured of the flu. D. The statement is not valid because the patients may have improved on their own without taking apple cider vinegar and having improved symptoms does not necessarily translate to the patients being cured of the flu.

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Problem 9926

9. Using electronic graphing tools, graph $y=2 \sin (3[x-4])+5$ and $y=2 \csc (4 x-3)-1$ on the same axes. Find all points of intersection of the two functions between $-\pi$ and $\pi$ , with answers to 2 decimal places. Include an image of the graphs in your response. [ 6 marks]

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Problem 9927

Use the accompanying histogram to answer the following questions. a) How many homes were included in the survey? b) In how many homes were three televisions observed? c) What is the modal class? d) How many televisions were observed? e) Construct a frequency distribution from this histogram.
Televisions per Home a) There were 29 homes included in the survey. (Type a whole number.) b) There were 8 homes where three televisions were observed. (Type a whole number.) c) The modal class is 3 . (Type a whole number) d) There were 93 abserved televisions. (Type a whole number) e) Construct a frequency distribution from this histogram. \begin{tabular}{c|c} Televisions per home & Number of Homes \\ \hline 0 & $\square$ \\ 1 & $\square$ \\ 2 & $\square$ \\ 3 & $\square$ \\ 4 & $\square$ \\ 5 & $\square$ \\ 6 & $\square$ \end{tabular}

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Problem 9928

The following graph shows the average price of a movie ticket for the years 2008 and 2010. Complete parts (a) and (b) Average Pribe of a Movle Ticket below: a) Draw a bar graph that shows the entire scale from $\$ 0$ to $\$ 8$ . Choose the correct graph below. A.
Average Price of a Movie Ticket B. c.
Average Prioe of a Movie Ticket D. b) Does the new graph give a different impression? Explain. Choose the correct answer below. A. No, the price difference appears the same in the new graph. B. Yes, the price difference appears more reasonable in the old graph. C. No, the price difference appears more reasonable in the new graph. D. Yes, the price difference appears more reasonable in the new graph.

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Problem 9929

Discuss the statement and tell what possible misuse or misinterpretation may exist. Suppose seventy-five percent of accidents occur within 13 miles of home. Therefore, it is safer not to drive within 13 miles of home.
Discuss the statement and tell what possible misuse or misinterpretation may exist. Choose the correct answer below. A. The statement is not valid because most accidents occur within 13 miles of home. B. The statement is valid because most accidents occur within 13 miles of home. C. The statement is not valid because people may drive within 13 miles of home more often. D. The statement is valid because people may drive within 13 miles of home more often.

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Problem 9930

When a national sample of heights of kindergarten children was taken, a student was told that she was in the 70 th percentile. Explain what that means.
Choose the correct interpretation below. A. She is taller than 70 kindergarten children. B. She is taller than 70 percent of all kindergarten children. C. She is shorter than 70 percent of all kindergarten children. D. She is taller than 30 percent of all kindergarten children.

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Problem 9931

Identify the sampling technique used to obtain a sample. A famous magazine chooses its "smartest-sounding celebrities" by compiling responses from readers who mail in a survey printed in the magazine.
What type of sampling is used? Random sampling Systematic sampling Convenience sampling Stratified sampling Cluster sampling

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Problem 9932

Use the frequency distribution to complete parts (a) through (e). a) Determine the total number of observations. b) Determine the width of each class. c) Determine the midpoint of the second class. d) Determine the modal class (or classes). e) Determine the class limits of the next class if an additional class were to be added. \begin{tabular}{cc} Class & Frequency \\ $12-22$ & 8 \\ $23-33$ & 0 \\ $34-44$ & 8 \\ $45-55$ & 8 \\ $56-66$ & 0 \\ $67-77$ & 7 \end{tabular} a) The total number of observations is $\square$ . b) The width of each class is $\square$ c) The midpoint of the second class is $\square$ . (Type an integer or a decimal.) d) The modal class(es) is/are $\square$ (Use a hyphen to separate the limits of a class. Use a comma to separate answers. Type the classes in order from smallest to largest.) e) The class limits of the next class if an additional class were to be added are $\square$ (Use a hyphen to separate the limits of a class.)

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Problem 9933

(1) $y=\frac{2 x-3}{3 x+4}$

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Problem 9934

The prices of the 19 top-rated all-season tires for a specific tire size, are as follows. Answer parts (a) - (c). \begin{tabular}{llllllllll} $\$ 88$ & $\$ 118$ & $\$ 97$ & $\$ 79$ & $\$ 82$ & $\$ 92$ & $\$ 94$ & $\$ 89$ & $\$ 94$ & $\$ 81$ \\ $\$ 109$ & $\$ 115$ & $\$ 103$ & $\$ 95$ & $\$ 85$ & $\$ 92$ & $\$ 75$ & $\$ 99$ & $\$ 91$ & \end{tabular} a) Determine $Q_{2}$ . $\mathrm{Q}_{2}=$ $\square$ b) Determine $Q_{1}$ . $Q_{1}=$ $\square$ c) Determine $Q_{3}$ . $Q_{3}=$ $\square$

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Problem 9935

$\begin{aligned} \text { mit } a \in \mathbb{R} \backslash\{0\} & \text { (das heißt, der Parameter a beinhaltet alle reellen Zahlen } \\ & \text { außer die Zahl Null) }\end{aligned}$
2. Berechnen Sie in Abhängigkeit von a die Schnittpunkte / Berührpunkte mit den Koordinatenachsen und geben Sie diese Punkte an.
3. Berechnen Sie in Abhängigkeit von a die Lage und Art der Extrema und geben sie diese Informationen an.
4. Berechnen Sie in Abhängigkeit von a die Lage und Art der Wendepunkte und geben sie diese Informationen an. Berechnen Sie ebenfalls die Funktion der Wendetangente( $n$ ) und geben Sie die Funktion(en) an. b) Ermitteln Sie die Ortskurve des Wendepunktes. c) Ermitteln Sie die Ortskurven der Extrema.
Für die folgenden Aufgabenteile gilt $\mathbf{a}=-4$ d) Zeichnen Sie den Graphen von $f_{a(x)}$ für $a=-4$

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Problem 9936

2. Der Luftdruck nimmt, wie rechts zu sehen, mit zunehmender Höhe ab. a) Begründen Sie, dass die Abnahme des Luftdrucks nicht gleichmäßig erfolgt. Wo ist die Abnahme am stärksten, wo ist sie am geringsten? b) Ermitteln Sie die durchschnittliche Abnahme zwischen 2 und 4 km Höhe und zwischen 8 und 10 km Höhe näherungsweise.

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Problem 9937

Contoh / Example 7 Cari julat nilai bagi $m$ jika persamaan kuadratik $x^{2}+m x+16=2(x+m)$ tidak mempunyai dua punca nyata. Find the range of values of $m$ if the quadratic equation $x^{2}+m x+16=2(x+m)$ does not have real roots.

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Problem 9938

If X is a discrete random variable. With the following CDF: $F(x)=\left\{\begin{array}{lc} 0, & x<2 \\ 0.2 & 2 \leq x<5 \\ 0.5 & 5 \leq x<7 \\ 0.8 & 7 \leq x<9 \\ 1 & 9 \leq x \end{array}\right.$
Select one: a. 0 b. 1 c. 0.2 a. 0.5 e 0.3

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Problem 9939

5. The number of real solutions for $x^{3}+x^{2}+x+1$ is

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Problem 9940

(d) [2 Points] On $1 / 6 / 2022$ " ABC " Company purchased equipment for $\$ 260,000$ . The equipment has an estimated useful life and salvage value of 20 years and $\$ 20,000$ , respectively. At the end of the financial period, the accountant recorded the adjusting entry for the depreciation by debiting depreciation expense $\$ 12,000$ and crediting equipment $\$ 12,000$

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Problem 9941

b) $y<-2 x+1$
8 pour chacune des fonctions suivantes: 1) représentez graphiquement chaque situation; 2) déterminez son domaine, son codomaine, son ou ses abscisses à l'origine, son ordonnée à l'origine, son signe, sa variation et ses extremums, s'il y a lieu. a) $f(x)=-2[0,5(x-3)]-1$ b) $g(x)=(x+0,5)^{2}+2$ 1) 1) 2) Domaine: $\qquad$ 2) Domaine: $\qquad$ Codomaine: $\qquad$ Abscisses à l'origine: $\qquad$ Ordonnée à l'origine: $\qquad$ Signe: $\qquad$ Codomaine: $\qquad$ Abscisses à l'origine: $\qquad$ Ordonnée à l'origine: $\qquad$ $\qquad$ Signe: $\qquad$ $\qquad$ Variation: $\qquad$ Variation: $\qquad$ $\qquad$ $\qquad$ Extremum: $\qquad$ Extremum: $\qquad$ GARDER LE

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Problem 9942

Is it ever ethical to add bias to a statistical study? In a paragraph, why or why not? (4 marks)

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Problem 9943

Let $\mathbf{u}=\left[\begin{array}{c}-1 \\ 2 \\ 1\end{array}\right], \mathbf{v}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$ , and $\mathbf{w}=\left[\begin{array}{c}-4 \\ 2 \\ 16\end{array}\right]$ We want to determine by inspection (with minimal computation) if $\{\mathbf{u}, \mathbf{v}, \mathbf{w}\}$ is linearly dependent or independent. Choose the best answer. A. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other. B. The set is linearly dependent because one of the vectors is the zero vector. C. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space. D. The set is linearly dependent because two of the vectors are the same. E. The set is linearly dependent because one of the vectors is a scalar multiple of another vector. F. We cannot easily tell if the set is linearly dependent or linearly independent.

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Problem 9944

Which of the following trigonometric expressions are equivalent? Explain your answer. $\cos ^{2} \theta, \cos 2 \theta, \cos (\theta)^{2}, \cos \theta \cdot \cos \theta, \cos \left(\theta^{2}\right)$

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Problem 9945

لتكن لدينا المتتالية التالية : $2,-6,18,-54$ $\qquad$ أ- حدد فيما اذا كانت منتالية هندسية ام حسابية
ب- اساس المتتالية
ت- الحد الخامس للمنتالية

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Problem 9946

Jayden advises a local restaurant owner on reducing costs and increasing profitability. He collects data about the number of customers in the restaurant throughout the day and graphs the average for each hour on this line plot. Based on his data, what should Jayden recommend?
Average Number of Customers A) The restaurant should open an hour later. B) The restaurant should close from 5:00 p.m. to 6:00 p.m. C) The restaurant should stay open 2 hours later. D) The restaurant should open an hour earlier.

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Problem 9947

On se donne un jeu de données $\left(x_{1}, \ldots, x_{n}\right)$ de réalisations indépendantes d'une même variable aléatoire $X$ . On note $m=\mathbb{E}[X]$ et $\sigma^{2}=\operatorname{Var}(X)$ . Parmis les propositions suivantes, lesquelles permettent de réduire la taille d'un intervalle de confiance : a. Augmenter la moyenne $m$ b. Réduire la taille d'échantillon $n$ c. Réduire la moyenne $m$ d. Réduire le risque $\alpha$ e. Augmenter le risque $\alpha$ f. Augmenter la taille d'échantillon $n$

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Problem 9948

For the following exercises, find the horizontal and vertical asymptotes.
271. $f(x)=x-\frac{9}{x}$
272. $f(x)=\frac{1}{1-x^{2}}$
273. $f(x)=\frac{x^{3}}{4-x^{2}}$
274. $f(x)=\frac{x^{2}+3}{x^{2}+1}$
275. $f(x)=\sin (x) \sin (2 x)$
276. $f(x)=\cos x+\cos (3 x)+\cos (5 x)$
277. $f(x)=\frac{x \sin (x)}{x^{2}-1}$
278. $f(x)=\frac{x}{\sin (x)}$
279. $f(x)=\frac{1}{x^{3}+x^{2}}$
280. $f(x)=\frac{1}{x-1}-2 x$

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Problem 9949

4 Maggie's Electronics is having a big sale on their smart televisions (TVs). The scatterplot shows the relationship between days on sale and the number of TVs left in stock.
Select all statements that are true about this scatterplot. \& $\square$ About 7 televisions will be left in stock at the end of the $14^{\text {th }}$ sale day. Ax $\square$ At the end of the $13^{\text {th }}$ sale day, there will be about 20 TV left. * $\square$ The scatterplot shows a negative correlation. $4 \times \square$ The scatterplot shows a positive correlation. $4 \times \square$ As days on sale increase, the number of TVs left decreases. 4x As days on sale increases, the number of TVs left increases. 4 $\square$ There are about 15 TVs left at the end of the 9th sale day. $4 \times$ There are about 34 TVs left at the end of the $4^{\text {th }}$ sale day.

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Problem 9950

Consider the following frequency table representing the scores on a test. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Scores on a Test } \\ \hline Class & Frequency \\ \hline $20-39$ & 15 \\ \hline $40-59$ & 9 \\ \hline $60-79$ & 10 \\ \hline $80-99$ & 6 \\ \hline $100-119$ & 4 \\ \hline \end{tabular}
Step 3 of 5 : Determine the class width of each class.
Answer

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Problem 9951

Consider the following frequency table representing the scores on a test. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Scores on a Test } \\ \hline Class & Frequency \\ \hline $30-47$ & 3 \\ \hline $48-65$ & 10 \\ \hline $66-83$ & 14 \\ \hline $84-101$ & 11 \\ \hline $102-119$ & 4 \\ \hline \end{tabular}
Step 1 of 5 : Determine the lower class boundary for the fifth class.
Answer

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Problem 9952

Part 1 of 2 Points: 0 of 2
Explain what a P -value is. What is the criterion for rejecting the null hypothesis using the P -value approach?
Explain what a P-value is. Choose the correct answer below. A. A P-value is the probability of observing a sample statistic as extreme or more extreme than the one observed under the assumption that the statement in the null hypothesis is true. B. A P-value is the value used to designate the area $\alpha$ in either the left- or right-tail of the normal curve. C. A P-value is the number of standard deviations that the observed proportion is from the proportion stated in the null hypothesis.

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Problem 9953

Si un système est en mouvement rectiligne: (If a system is in rectilinear motion
Select one or more: Sa trajectoire est une droite. (Its trajectory is a straight line.) La norme de sa vitesse est constante. (The norm of its speed is constant) Le vecteur vitesse peut varier. (The velocity can vary)
Check

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Problem 9954

Le graphique $v(t)$ d'un corps en mouvement est donné par la figure ci-dessous. The graph $v(t)$ of a moving body is given by the figure below.
Quelle est l'accélération à linstant $t=3$ s? What is the acceleration at time $\mathrm{t}=3 \mathrm{~s}$ ?
Select one or more: $4 \mathrm{~m} / \mathrm{s}^{2}$ $-2 \mathrm{~m} / \mathrm{s}^{2}$ $-4 \mathrm{~m} / \mathrm{s}^{2}$ $2 \mathrm{~m} / \mathrm{s}^{2}$ $0 \mathrm{~m} / \mathrm{s}^{2}$

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Problem 9955

Dans une formule physique, on peut additionner des grandeurs qui n'ont pas les mêmes dimensions (Dans une formule physique, on peut ajouter des quantités qui n'ont pas les mêmes dimension'́).
Sélectionnez une option : Vrai Faux. (Faux)

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Problem 9956

La représentation de $x(t)$ pour un point en mouvement rectiligne uniforme selon l'axe x'x est donnée par: La représentation de $\mathrm{x}(\mathrm{t})$ pour un point en mouvement rectiligne uniforme le long de l'axe $\mathrm{x}^{\prime} \mathrm{x}$ est donnée par: Sélectionnez une option:

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Problem 9957

Le vecteur vitesse $v(t)$ est: (The velocity vector $v(t)$ is
Select one or more: La dérivée par rapport au temps t du vecteur accélération a(t). (The derivative with respect to time $t$ of the acceleration vector $a(t)$ . La dérivée par rapport au temps $t$ du vecteur position $O M(t)$ . (The derivative with respect to time $t$ of the position vector $O M(t)$ .) Toujours tangent à la trajectoire au point consideré. (Always tangent to the trajectory at the point considered)

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Problem 9958

فيما يلي بيانات حول دخل عمال مصنع معين بآلاف الدينارات: $\begin{array}{l} \text { 23-21-19-16-14-11-22-20-24-17-15-37-18-26-30 } \\ \text { 35-18-38-38-34-20-32-10-28-21-29-13-20-22 } \\ \text {.31-25-24-27-34-23-29-33-24-26-26 } \\ \text { المطلوب: } \end{array}$ 1.نظم هذه البيانات في جدول تكراري. 2.ماهو عدد ونسبة العمال الذين يقل دخلهم عن 25000دج. 3.ماهي نسبة العمال الذين لايزيد دخلهم عن 32000دج. 4.ضع منعنى كل من التكرار المتجمع الصاعد والنازل وماذا تمثل نقطة
التقاطع .

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Problem 9959

11-30 Closing and opening stores. Sanchez Corporation runs two convenience stores, one in Connecticut and one in Rhode Island. Operating income for each store in 2017 is as follows: \begin{tabular}{|c|c|c|} \hline & Connecticut Store & Rhode Island Store \\ \hline Revenues & \1,070,000 & \$860,000 \\ \hline \multicolumn{3}{|l|}{Operating costs} \\ \hline Cost of goods sold & 750,000 & 660,000 \\ \hline Lease rent (renewable each year) & 90,000 & 75,000 \\ \hline Labor costs (paid on an hourly basis) & 42,000 & 42,000 \\ \hline Depreciation of equipment & 25,000 & 22,000 \\ \hline Utilities (electricity, heating) & 43,000 & 46,000 \\ \hline Allocated corporate overhead & 50,000 & 40,000 \\ \hline Total operating costs & 1,000,000 & 885,000 \\ \hline Operating income (loss) & \$ 70,000 & \$ (25,000)$ \\ \hline \end{tabular}
The equipment has a zero disposal value. In a senior management meeting, Maria Lopez, the management accountant at Sanchez Corporation, makes the following comment, "Sanchez can increase its profitability by closing down the Rhode Island store or by adding another store like it."
1. By closing down the Rhode Island store, Sanchez can reduce overall corporate overhead costs by $\$ 44,000$ . Calculate Sanchez's operating income if it closes the Rhode Island store. Is Maria Lopez's statement about the effect of closing the Rhode Island store correct? Explain.
2. Calculate Sanchez's operating income if it keeps the Rhode Island store open and opens another store with revenues and costs identical to the Rhode Island store (including a cost of $\$ 22,000$ to acquire equipment with a one-year useful life and zero disposal value). Opening this store will increase corporate overhead costs by $\$ 4,000$ . Is Maria Lopez's statement about the effect of adding another store like the Rhode Island store correct? Explain.

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Problem 9960

Part 7 of 7 HW Score: $39.75 \%, 32.2$ of 81 points Points: 0 of 1 Save
For the polynomial function below. (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of $f$ resembles for large values of $|x|$ . $f(x)=-2(x-9)(x+9)^{2}$ the mulupicity or the splanet cero is <. (Type a whole number.) (b) The graph crosses the $x$ -axis at the larger $x$ -intercept.
The graph touches the $x$ -axis at the smaller $x$ -intercept. (c) The maximum number of turning points on the graph is 2 . (Type a whole number.) (d) Type the power function that the graph of f resembles for large values of $|\mathrm{x}|$ . $\mathrm{y}=\square$

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Problem 9961

A charter flight charges a fare of $\$ 300$ per person plus $\$ 5$ per person for each unsold seat on the plane. The plane holds 100 passengers. Let $x$ represent the number of unsold seats. Complete parts (a) through (d). (a) Find an expression for the total revenue received for the flight $R(x)$ . (Hint: Multiply the number of people flying, $100-\mathrm{x}$ , by the price per ticket) $R(x)=30000+200 x-5 x^{2}$ (b) Choose the correct graph of the function, $\mathrm{R}(\mathrm{x})$ , below. A. B. c. D. (c) The number of unsold seats that will produce the maximum revenue is 20. (Round to the nearest whole number as needed.) (d) The maximum revenue is $\$$ $\square$ (Round to the nearest whole number as needed.)

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Problem 9962

. Use Technology a) Predict the form of the graph of $y=\tan x+2$ .
Verify your prediction using graphing technology. b) Predict the form of the graph of $y=3 \tan x$ .
Verify your prediction using graphing 24. technology. c) Predict the form of the graph of $y=\tan \left(x-\frac{\pi}{4}\right)$ . Verify your prediction using graphing technology. d) Predict the form of the graph of $y=\tan 3 x$ . Verify your prediction using graphing technology.

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Problem 9963

\begin{tabular}{l|l} $t=48 \div 6$ & $t=48 \times 6$ \\ $48=t \times 6$ & $t=6 \times 48$ \end{tabular}

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Problem 9964

Question 14(Multiple Choice Worth 2 points) (Linear Relationships LC) Which linear equation shows a proportional relationship? $y=-2$ $y=3 x+1$ $y=\frac{3}{2} x$ $y=\frac{1}{2} x-3$

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Problem 9965

Exercice 3 Soient $f$ et $g$ deux fonctions définies par: $f(x)=x^{2}-2 x+3$ et $g(x)=\sqrt{x+1}$ 展共 Donner les tableaux de variations des fonctions $f$ et $g$ . b. Représenter les courbes représentatives $\left(C_{f}\right)$ et $\left(C_{g}\right)$ dans un repère orthonormé ( $O, \vec{i}, \vec{j}$ ) CVI Déterminer graphiquement $g([-1 ; 0])$ et $g([0 ;+\infty[)$ 2 Soit $h$ la fonction définie sur $[-1 ;+\infty[$ par : $h(x)=x+4-2 \sqrt{x+1}$ al Vérifier que : $(\forall x \in[-1 ;+\infty[) ; h(x)=(f \circ g)(x)$ 5 Étudier la monotonie de la fonction $h$ sur les intervalles $[0 ;+\infty[$ et $[-1 ; 0]$ à partir de celle de $f$ et $g$ . Puis déduire les extremums de $h$ sur l'intervalle $[-1 ;+\infty[$ s'ils existent. $\left.\gamma \varepsilon_{k}\right]$ Montrer que : $\left(\forall a \in\left[-1 ;+\infty[) ; \sqrt{a+1}-\sqrt{a} \leq \frac{1}{2}\right.\right.$

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Problem 9966

(ii) Construct a stacked bar graph like the one in part A.(iv), using the data for Quebec's alpine skiers. (Hint: Create a 100\% Stacked Column graph in Excel and ensure the legend is descriptive.)
(iii) After examining the bar graph in part B, (ii), do you believe that finishing place is independent of event for Quebecois alpine skiers? Explain.
(iv) Test at the $5\%$ significance level the claim that finishing place is independent of event. Are certain events more significant than other events? Explain.
(v) Using your results from the bar graph and hypothesis test, describe the performance of Quebec's alpine skiers in national competitions. Describe to the Quebecois coach how these results can help inform their training decisions.

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Problem 9967

\begin{enumerate} \item[(iii)] After examining the bar graph in part B. (ii), do you believe that finishing place is independent of event for Quebecois alpine skiers? Explain. \item[(iv)] Test at the $5\%$ significance level the claim that finishing place is independent of event. (Hint: Use the test of independence.) Do Quebecois alpine skiers appear to be better at certain events than other events? Explain. \end{enumerate}

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Problem 9968

If $r>0$ is a rational number, let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x):=x^{r} \sin (1 / x)$ for $x \neq 0$ , and $f(0):=0$ . Determine those values of $r$ for which $f^{\prime}(0)$ exists.

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Problem 9969

Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for 19 customers at the bank. Here are the 19 waiting times (in minutes). $2,3,4,5,6,6,6,7,10,11,12,12,15,15,17,21,27,29,37$ Send data to calculator Send data to Excel
Answer the questions below. \begin{tabular}{|l|l|} \hline (a) For these data, which measures of & Mean \\ central tendency take more than one value? & Median \\ Choose all that apply. & Mode \\ \hline \begin{tabular}{l} (b) Suppose that the measurement 37 \\ largest measurement in the data set) were \end{tabular} & Mone of these measures \\ \hline \end{tabular}

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Problem 9970

3. $\sum_{n=1}^{\infty} \frac{5 n^{3}}{n^{4}+7}$

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Problem 9971

Listed below are the numbers of cricket chips in 1 minute and the corresponding temperatures in ${ }^{\circ} \mathrm{F}$ . Construct a scatterplot, and find the value of the linear correlation coefficient $r$ . Is there sufficient evidence to conclude that there is a linear comelation between the number of chips in 1 minute and the temperature? Use a significance level of $\alpha=0.05$ . \begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline Chirps in 1 min & 889 & 1172 & 1092 & 857 & 1207 & 1027 & 958 & 919 \\ \hline Temperature ( F ) & 71 & 92.2 & 83.6 & 75.1 & 87.8 & 81.3 & 71.1 & 79.4 \\ \hline \end{tabular}
Construct a scatterplot. Choose the correct graph below. A. B. c. D.
What are the null and alternative hypotheses? A. $H_{0}: \rho=0$ $H_{1}: \rho<0$ B. $H_{0}: \rho \neq 0$ $H_{1}: \rho=0$ c. $H_{0}: \rho=0$ $H_{1}: \rho \neq 0$ D. $H_{0}: \rho=0$ $H_{1}: \rho>0$
The linear correlation coefficient $r$ is $\square$ 0.88 (Round to three decimal places as needed.) The test statistic t is 4.54 . $\square$ (Round to two decimal places as needed.) Next

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Problem 9972

A store surveyed 250 customers on service satisfaction by gender. Which is the best way to display this data? A. Two-way table B. Side-by-side boxplots C. Histogram D. Pie chart E. Scatterplot

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Problem 9973

Find numbers to exclude from the domain of these rational expressions: 1. $\frac{7}{x-3}$ , 2. $\frac{13}{x+9}$ , 3. $\frac{x+5}{x^{2}-25}$ , 4. $\frac{x+7}{x^{2}-49}$ , 5. $\frac{x-1}{x^{2}+11 x+10}$ , 6. $\frac{x-3}{x^{2}+4 x-45}$ .

See Solution

Problem 9974

Compare refrigerator prices:
(a) Superstore markup of $40\%$ on \$699. How much does Sam pay?
(b) Department store with $20\%$ discount. What’s the price?
(c) Which is true? Superstore more expensive, department store more, or same price?

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Problem 9975

Ann wants to buy golf clubs for \$369. Calculate prices at a pro shop and a distributor, then compare them.
(a) Pro shop marks up by 10% then 40%. What is the final price? (b) Distributor marks up by 50%. What is the final price? (c) Which is cheaper? Pro shop, distributor, or the same?

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Problem 9976

Calculate the CPI for year 2 given 3 shirts and 2 pants. Prices: year 1: shirts \$25, pants \$20; year 2: shirts \$26, pants \$21.

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Problem 9977

For which values of $c$ and $d$ does $c x - 2 = 7 x + d$ have no solution? Choose all that apply: $c=-7, d=-2$ ; $c=7, d=-2$ ; $c=7, d=0$ ; $c=7, d=2$ .

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Problem 9978

What does inflation do to prices? A. Decrease B. Double C. Increase D. Stay the same

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Problem 9979

Identify the mistake in $\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b}$ and correct the right side of the equation.

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Problem 9980

Find the median of the scores: $2,3,4,4,5,5,5,6,6,7$ for discrete and continuous variables. Provide two decimal places for continuous.

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Problem 9981

Fill in the blank: If $\mathbf{a}<\mathrm{b}$ , then $\mathrm{a}$ is located to the ___ of $b$ on a number line.

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Problem 9982

Which scenario shows a $3\%$ annual inflation rate? A. Computer: \$325 to \$328 B. Soda: \$0.75 to \$0.78 C. Game: \$10 to \$10.03 D. Sofa: \$500 to \$515.

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Problem 9983

Determine if this statement is true or false: The sum of a positive integer and a negative integer is always positive.

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Problem 9984

Is the statement "The product of a positive integer and a negative integer is never a positive integer" true or false?

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Problem 9985

Plot the point $-4$ on the number line.

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Problem 9986

Identify the initial value in Joanna's savings equation: $5,000\left(1+\frac{0.04}{12}\right)^{12 t}$ .

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Problem 9987

What is the monthly growth rate in the expression $f(x)=12(1.035)^{x}$ for a drama club? A. $0.35\%$ B. $1.035\%$ C. $3.5\%$ D. $12\%$

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Problem 9988

Find the account with the highest effective annual interest rate among four options with different compounding frequencies and rates.

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Problem 9989

Select $<$ or $>$ to make the statement true: $-14 ? 1$ . Choose: $<$ or $>$ .

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Problem 9990

Which option describes an annuity? A. $\$ 1,000$ lump sum B. $\$ 5,000$ in a one-year $C D$ C. $\$ 500$ savings D. $\$ 100$ regular deposits

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Problem 9991

Find the quotient of $\frac{-11}{0}$ or state if it's undefined. A. $\frac{-11}{0}=\square$ B. Undefined.

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Problem 9992

Which account has the highest annual interest rate: A. $3.28\%$ , B. $3.25\%$ , C. $3.10\%$ , D. $3.15\%$ , E. $3.25\%$ ?

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Problem 9993

Determine the growth type of an investment account with balances: Year 1: \$1,200, Year 2: \$1,260, Year 3: \$1,323, Year 4: \$1,389.15. Options: A, B, C, D, E.

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Problem 9994

Analyze the investment account balances: Year 1: \$1,200, Year 2: \$1,260, Year 3: \$1,323, Year 4: \$1,389. Which growth statement is correct?

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Problem 9995

Select the correct interpretation of $10,785(1.0275)^{x}$ for an investment with annual compounding interest.

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Problem 9996

Select the correct answer: What describes the relationship between nominal and real interest rates? A, B, C, D, or E?

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Problem 9997

Fluorine has how many protons?

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Problem 9998

Interpret the expression $10,785(1.0275)^{x}$ : What are the initial investment and growth rate? Choose A, B, C, D, or E.

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Problem 9999

Calculate the windchill temperature difference at $10^{\circ} \mathrm{F}$ for wind speeds of 5 mph and 25 mph.

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Problem 10000

Which statement is NOT true about atoms? 1) Mostly empty space, 2) Same element has different masses, 3) Nucleus is positive, 4) Isotopes have different protons.

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1 ...97 98 99 100 101 102 103 ...161

Analyze

Problem 9901

A sandwich store has a weekly cost of \575.00and$0.65perroastbeefsandwich.Findprofitfunction575.00 and \$0.65 per roast beef sandwich. Find profit function 575.00and$0.65perroastbeefsandwich.FindprofitfunctionP(x)$ and max profit.

Problem 9902

For the function P(x)=−0.74x2+22x+75P(x)=-0.74 x^{2}+22 x+75P(x)=−0.74x2+22x+75, what constraints ensure profits are at least \175,000?Options:175,000? Options: 175,000?Options:-3.09 \leq x \leq 5.6or or or0 \leq x < 5.6$?

Problem 9903

Find the limit as xxx approaches infinity for 4x−12x+1\frac{4x - 1}{2x + 1}2x+14x−1​.

Problem 9904

Problem 9905

What is the best way to display data on college students' ages and car values from a survey of 300 students? A. Two-way table B. Pie chart C. Histogram D. Side-by-side boxplots E. Scatterplot

Problem 9906

Determine the best way to display data from a study on TV violence and adult abuse: A. scatterplot B. boxplots C. two-way table D. histogram E. pie chart.

Problem 9907

Problem 9908

Problem 9909

Problem 9910

3LEM 9: THE HAWK PROBLEM A hawk is on top of a tree and spots a fish in the water. The hawks's pathway in metres is measured by time in seconds by the equation: y=x2−6x+11y=x^{2}-6 x+11y=x2−6x+11 a) When does the hawk enter the water? b) Explain why this is a problem? c) Sketch a graph

Problem 9911

Problem 9912

Problem 9913

Problem 9914

Problem 9915

Determine the amplitude of the periodic graph. * 1 poDetermine the period of the periodic graph. * 1 point

Problem 9916

Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?Tara Edward

Problem 9917

Problem 9918

5. Consider the sets of vectors of the following form. Determine whether the sets are subspaces of an appropriate vector space. If a set is a subspace give a basis and its dimension. (a) a(1,2,3)a(1,2,3)a(1,2,3)

Problem 9919

Problem 9920

Problem 9921

Problem 9922

\begin{align*} &\text{Given the quadratic function:} \\ &y = -2x^2 - 4x + 3 \\ &\text{Calculate the first and second differences, } \Delta y \text{ and } \Delta^2 y, \text{ for the following values of } x: \\ &x = -3, -2, -1, 0, 1, 2, 3 \end{align*}

Problem 9923

Problem 9924

Problem 9925

Problem 9926

Problem 9927

Problem 9928

Problem 9929

Problem 9930

Problem 9931

Problem 9932

Problem 9933

(1) y=2x−33x+4y=\frac{2 x-3}{3 x+4}y=3x+42x−3​

Problem 9934

Problem 9935

Problem 9936

Problem 9937

Contoh / Example 7 Cari julat nilai bagi mmm jika persamaan kuadratik x2+mx+16=2(x+m)x^{2}+m x+16=2(x+m)x2+mx+16=2(x+m) tidak mempunyai dua punca nyata. Find the range of values of mmm if the quadratic equation x2+mx+16=2(x+m)x^{2}+m x+16=2(x+m)x2+mx+16=2(x+m) does not have real roots.

Problem 9938

Problem 9939

5. The number of real solutions for x3+x2+x+1x^{3}+x^{2}+x+1x3+x2+x+1 is

Problem 9940

Problem 9941

Problem 9942

Is it ever ethical to add bias to a statistical study? In a paragraph, why or why not? (4 marks)

Problem 9943

Problem 9944

Problem 9945

لتكن لدينا المتتالية التالية : 2,−6,18,−542,-6,18,-542,−6,18,−54 \qquad أ- حدد فيما اذا كانت منتالية هندسية ام حسابيةب- اساس المتتاليةت- الحد الخامس للمنتالية

Problem 9946

Problem 9947

Problem 9948

Problem 9949

Problem 9950

Problem 9951

Problem 9952

Problem 9953

Problem 9954

Problem 9955

Dans une formule physique, on peut additionner des grandeurs qui n'ont pas les mêmes dimensions (Dans une formule physique, on peut ajouter des quantités qui n'ont pas les mêmes dimension'́).Sélectionnez une option : Vrai Faux. (Faux)

Problem 9956

Problem 9957

Problem 9958

Problem 9959

Problem 9960

Problem 9961

Problem 9962

Problem 9963

A sandwich store has a weekly cost of \ $575.00 and \$0.65 per roast beef sandwich. Find profit function$ P(x)$ and max profit.

For the function $P(x)=-0.74 x^{2}+22 x+75$ , what constraints ensure profits are at least \ $175,000? Options:$ -3.09 \leq x \leq 5.6 $or$ 0 \leq x < 5.6$?

Find the limit as $x$ approaches infinity for $\frac{4x - 1}{2x + 1}$ .

3LEM 9: THE HAWK PROBLEM A hawk is on top of a tree and spots a fish in the water. The hawks's pathway in metres is measured by time in seconds by the equation: $y=x^{2}-6 x+11$ a) When does the hawk enter the water? b) Explain why this is a problem? c) Sketch a graph

Determine the amplitude of the periodic graph. * 1 po
Determine the period of the periodic graph. * 1 point

Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?
Tara Edward

5. Consider the sets of vectors of the following form. Determine whether the sets are subspaces of an appropriate vector space. If a set is a subspace give a basis and its dimension. (a) $a(1,2,3)$

\begin{align} &\text{Given the quadratic function:} \\ &y = -2x^2 - 4x + 3 \\ &\text{Calculate the first and second differences, } \Delta y \text{ and } \Delta^2 y, \text{ for the following values of } x: \\ &x = -3, -2, -1, 0, 1, 2, 3 \end{align}

(1) $y=\frac{2 x-3}{3 x+4}$

Contoh / Example 7 Cari julat nilai bagi $m$ jika persamaan kuadratik $x^{2}+m x+16=2(x+m)$ tidak mempunyai dua punca nyata. Find the range of values of $m$ if the quadratic equation $x^{2}+m x+16=2(x+m)$ does not have real roots.

5. The number of real solutions for $x^{3}+x^{2}+x+1$ is

لتكن لدينا المتتالية التالية : $2,-6,18,-54$ $\qquad$ أ- حدد فيما اذا كانت منتالية هندسية ام حسابية
ب- اساس المتتالية
ت- الحد الخامس للمنتالية

Dans une formule physique, on peut additionner des grandeurs qui n'ont pas les mêmes dimensions (Dans une formule physique, on peut ajouter des quantités qui n'ont pas les mêmes dimension'́).
Sélectionnez une option : Vrai Faux. (Faux)

\begin{tabular}{l|l} $t=48 \div 6$ & $t=48 \times 6$ \\ $48=t \times 6$ & $t=6 \times 48$ \end{tabular}

Question 14(Multiple Choice Worth 2 points) (Linear Relationships LC) Which linear equation shows a proportional relationship? $y=-2$ $y=3 x+1$ $y=\frac{3}{2} x$ $y=\frac{1}{2} x-3$

If $r>0$ is a rational number, let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x):=x^{r} \sin (1 / x)$ for $x \neq 0$ , and $f(0):=0$ . Determine those values of $r$ for which $f^{\prime}(0)$ exists.

3. $\sum_{n=1}^{\infty} \frac{5 n^{3}}{n^{4}+7}$

Compare refrigerator prices:
(a) Superstore markup of $40\%$ on \$699. How much does Sam pay?
(b) Department store with $20\%$ discount. What’s the price?
(c) Which is true? Superstore more expensive, department store more, or same price?