Math

Problem 39001

a) Détermine les zéros de chacune de ces fonctions polynômes. 1) f(x)=x413x2+36f(x)=x^{4}-13 x^{2}+36 II) g(x)=6x57x33xg(x)=6 x^{5}-7 x^{3}-3 x

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Problem 39002

12. Laquelle de ces réponses représente l'opposé de 2x2x2 x^{2}-x ? A 2x2x-2 x^{2}-x B
C \square D 2x2+x2 x^{2}+x

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Problem 39003

Question 10
Find the domain of y=log(1+x)y=\log (1+x) using interval notation.
The domain is: (1,)(-1, \infty)

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Problem 39004

13. Modélise cette soustraction (3x2+4x)(2x2x)\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right) à l'aide d'un schéma.

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Problem 39005

stion list Iestion y estion 10 estion 11 estion 12 stion 13 stion 14 stion 15 tion 16 ion 17 ion 18 on 19 on 20 B. The function has two vertical asymptotes. The leftmost asymptote is , and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has three vertical asymptotes. The leftmost asymptote is \square, the middle asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote.
Determine the hole, if it exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice. There is a hole in the graph at the point (6,13)\left(6,-\frac{1}{3}\right). (Type an ordered pair using integers or simplified fractions.) B. There are no holes in the graph.
Determine the behavior of the graph on either side of any vertical asymptotes, if any exist. Select the correct choice and, if necessary, fill in any answer box(es) to complete your choice. A. It approaches \infty on one side of the asymptote(s) at x=\mathrm{x}=\square and -\infty on the other. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=\mathrm{x}= \square \square \square . Save Points: 0 of 1
Follow the steps for graphing a rational function to graph the function H(x)=4x2436x2H(x)=\frac{4 x-24}{36-x^{2}}. and the rightmost asymptote is \square

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Problem 39006

6 Résous ces inéquations. a) 8x+4<368 x+4<36 b) 5x7>2x+65 x-7>2 x+6 isx 14<3614<36 irouver la fater dun xx 5x7<2x+62x2x>63x7>73x>133x>4,33\begin{array}{c} 5 x-7<2 x+6 \\ -2 x-2 x>6 \\ 3 x-7>7 \\ 3 x>\frac{13}{3} \\ x>4,33 \end{array} c) 8b+4320\frac{8 b+4}{3} \leq-20 d) 0,5v+2,5>3v4(v+1,25)-0,5 v+2,5>3 v-4(v+1,25) 80+4<6080+4<-60 -4 0,5v+2,373v4v50,5v+2,5>v52,5\begin{array}{c} -0,5 v+2,373 v-4 v-5 \\ -0,5 v+2,5>-v-5 \\ -2,5 \end{array} 18b/6418 b /-64 1.8÷81.8 \div 8 0,5v6,5>7,50,5V>15\begin{array}{l} \frac{0,5 v}{6,5}>-\frac{7,5}{0,5} \\ V>-15 \end{array} e) 3b412<b4+25\frac{3 b}{4}-\frac{1}{2}<\frac{b}{4}+\frac{2}{5} f) 35b+5242b+45\frac{-35 b+5}{2} \leq \frac{42 b+4}{5}
530

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Problem 39007

on list
Follow the steps for graphing a rational function to graph the function H(x)=4x2436x2H(x)=\frac{4 x-24}{36-x^{2}}. tion y ion 10 on 11 n 12 13 14 15 16 7
B. The function has two vertical asymptotes. The leftmost asymptote is , and the rightmost asymptote is \square
(Type equations. Use integers or fractions for any numbers in the equations.) . The function has three vertical asymptotes. The leftmost asymptote is \square, the middle asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote. \square and the rightmost asymptote is \square
Determine the hole, if it exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice. There is a hole in the graph at the point (6,13)\left(6,-\frac{1}{3}\right). \square . (Type an ordered pair using integers or simplified fractions.) B. There are no holes in the graph.
Determine the behavior of the graph on either side of any vertical asymptotes, if any exist. Select the correct choice and, if necessary, fill in any answer box(es) to complete your choice. A. It approaches \infty on one side of the asymptote(s) at x=x=\square and -\infty on the other. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=x= \square . (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) . It approaches \infty on one side of the asymptote(s) at x=6x=-6 and -\infty on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) . It approaches either \infty or -\infty on both sides of the asymptote(s) at x=x=\square. \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no vertical asymptote.
Determine the horizontal asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, \square (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two horizontal asymptotes. The top asymptote is \square , and the bottom asymptote is \square \square. (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no horizontal asymptote.

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Problem 39008

6 Résous ces inéquations. a) 8x+4<368 x+4<36 b) 5x7>2x+65 x-7>2 x+6 isx 14<3614<36 irouver la fater dun xx 5x7<2x+62x2x>63x7>73x>133x>4,33\begin{array}{c} 5 x-7<2 x+6 \\ -2 x-2 x>6 \\ 3 x-7>7 \\ 3 x>\frac{13}{3} \\ x>4,33 \end{array} c) 8b+4320\frac{8 b+4}{3} \leq-20 d) 0,5v+2,5>3v4(v+1,25)-0,5 v+2,5>3 v-4(v+1,25) 80+4<6080+4<-60 -4 0,5v+2,373v4v50,5v+2,5>v52,5\begin{array}{c} -0,5 v+2,373 v-4 v-5 \\ -0,5 v+2,5>-v-5 \\ -2,5 \end{array} 18b/6418 b /-64 1.8÷81.8 \div 8 0,5v6,5>7,50,5V>15\begin{array}{l} \frac{0,5 v}{6,5}>-\frac{7,5}{0,5} \\ V>-15 \end{array} e) 3b412<b4+25\frac{3 b}{4}-\frac{1}{2}<\frac{b}{4}+\frac{2}{5} f) 35b+5242b+45\frac{-35 b+5}{2} \leq \frac{42 b+4}{5}
530

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Problem 39009

tion list
Follow the steps for graphing a rational function to graph the function H(x)=4x2436x2H(x)=\frac{4 x-24}{36-x^{2}}. stion y stion 10 stion 11 stion 12 stion 13 stion 14 tion 15 tion 16 tion 17 tion 18 tion 19 tion 20 A. There is a hole in the graph at the point (6,13)\left(6,-\frac{1}{3}\right). (Type an ordered pair using integers or simplified fractions.) B. There are no holes in the graph.
Determine the behavior of the graph on either side of any vertical asymptotes, if any exist. Select the correct choice and, if necessary, fill in any answer box(es) to complete your choice. A. It approaches \infty on one side of the asymptote(s) at x=x=\square and -\infty on the other. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=x= \square \square . (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. It approaches \infty on one side of the asymptote(s) at x=6x=-6 and -\infty on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=x=\square. \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no vertical asymptote.
Determine the horizontal asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. The function has one horizontal asymptote, y=0y=0.
(Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two horizontal asymptotes. The top asymptote is \square , and the bottom asymptote is \square (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no horizontal asymptote.
Determine the oblique asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one oblique asymptote, \square \square. (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is \square , and the oblique asymptote with a positive slope is \square \square. (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no oblique asymptote.

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Problem 39010

Part 11 of 13 Points: 0 of 1 Save
Follow the steps for graphing a rational function to graph the function H(x)=4x2436x2H(x)=\frac{4 x-24}{36-x^{2}}. (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. It approaches \infty on one side of the asymptote(s) at x=6x=-6 and -\infty on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=x=\square. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no vertical asymptote.
Determine the horizontal asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, y=0y=0. (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two horizontal asymptotes. The top asymptote is \square, and the bottom asymptote is \square \square (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no horizontal asymptote.
Determine the oblique asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one oblique asymptote, \square (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is \square , and the oblique asymptote with a positive slope is \square . (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no oblique asymptote.
Determine points, if any, at which the graph of H intersects the horizontal or oblique asymptote, if one exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The graph of H intersects the horizontal or oblique asymptote at \square (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) B. The graph of H intersects the horizontal or oblique asymptote at infinitely many points. C. There is no point at which the graph of H intersects the horizontal or oblique asymptote. D. There is no horizontal or oblique asymptote.

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Problem 39011

Solve the following formula for the specified variable. A=14h(q+z) for qA=\frac{1}{4} h(q+z) \text { for } q q=q= \square (Simplify your answer.)

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Problem 39012

3. A tresuard at poettion L spots a swimmer lif troubic it one copner of the pool, S . She runs Bcen the lengen of the pool to poeltion P, and then dives in and swimt a distance d from P to S. a) Show thent the swiming distanco is siven by the relation d=wsecx.[/2k/U]d=w \sec x . \quad[-/ 2 \mathrm{k} / \mathrm{U}] b) Iy=2wI y=2 w, determine the range of values that xx may take on given that PP can be anywhere along the length of the pool.
L \qquad /3 APP1 c) Determine the range of values that dd may take on. (1)2APP)(1) 2 \mathrm{APP})

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Problem 39013

17. Complète la pyramide d'additions. Pour trouver la valeur à écrire dans une case, additionne les expressions qui sont dans les deux cases situées juste en dessous.

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Problem 39014

logab3+4loga(ac3)7\log _{a} b^{3}+4 \log _{a}\left(a c^{3}\right)-7, where a,b,c>1a, b, c>1, written as a single logarithm, is loga(b3c3)\log _{a}\left(b^{3} c^{3}\right) loga(bca4)\log _{a}\left(\frac{b c}{a^{4}}\right) loga(b3c12a4)\log _{a}\left(\frac{b^{3} c^{12}}{a^{4}}\right) loga(b3c12a3)\log _{a}\left(\frac{b^{3} c^{12}}{a^{3}}\right)

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Problem 39015

Answer the questions below about Line 1 and Line 2 shown below. \begin{tabular}{ll} 4+24+2 \\ 2+42+4 & Line 1 \\ Line 2 \end{tabular}
Answer Attempt 1 out of 2
The expression was rewritten using the \square Line 1 says \square ++ \square , which could be represented using dots as +\bullet \bullet \bullet+\bullet \bullet for a total of \square dots.
Line 2 says \square ++ \square , which could be represented using dots as +\bullet \bullet+\bullet \bullet \bullet for a total of \square dots.

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Problem 39016

CP Geometry Unit 2 Test For Questions 13 and 14, determine whether QVQ V and RMR M are parallel, perpendicular, or neither.
13. Q(3,8),V(5,12),R(2.5,1),M(5,2)Q(-3,-8), V(5,12), R(-2.5,1), M(-5,2)

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Problem 39017

Follow the steps for graphing a rational function to graph the function R(x)=x2+10x+16x+8R(x)=\frac{x^{2}+10 x+16}{x+8}. (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) C. The graph has neither xx-intercepts nor yy-intercepts. D. The graph has xx-intercept(s) \square and no yy-intercept(s). (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) Determine the behavior of the graph of RR at any xx-intercepts. Select the correct choice and, if necessary, fill in the answer box(es) within your choice. A. The graph will cross the xx-axis at x=x= \square and touch the xx-axis at x=x= \square (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. The graph will cross the xx-axis at x=2x=-2. \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. The graph will touch the xx-axis at x=x= \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no x-intercept.
Determine the vertical asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) within your choice. A. The function has one vertical asymptote, \square . (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \square , and the rightmost asymptote is \square (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has three vertical asymptotes. The leftmost asymptote is \square , the middle asymptote is \square , and the rightmost asymptote is \square . (Type equations. Use integers or fractions for any numbers in the equations.) D. The function has no vertical asymptote.
Determine the hole, if it exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice.
There is a hole in the graph at the point \square \square. (Type an ordered pair using integers or fractions.) B. There are no holes in the graph.

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Problem 39018

Suppose loga=6,logb=2,logc=3\log a=-6, \log b=2, \log c=3. Find log(a2b5c3)\log \left(\frac{a^{2}}{b^{5} c^{3}}\right). log(a2b5c3)=\log \left(\frac{a^{2}}{b^{5} c^{3}}\right)= \square

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Problem 39019

Consider the function given by f(x)=x2e2xf(x)=x^{2} e^{-2 x}
Determine the absolute maximum value and absolute minimum value of ff over the interval [1/2,3][-1 / 2,3]. FORMATTING: Give your answer with an accuracy of at least 3 decimal places.
Minimum value == \square Maximum value == Number

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Problem 39020

Halla el cociente. 64.48÷1664.48÷16=\begin{array}{r} 64.48 \div 16 \\ 64.48 \div 16= \end{array}

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Problem 39021

Alexander finalizó su reseña de un libro en 429 minutos. ¿Aproximadamente cuántas horas son?
Alexander tardó en completar su reseña de un libro aproximadamente \square horas.

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Problem 39022

Determine the domain on which the following function is decreasing.

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Problem 39023

Answer the questions below about Line 1 and Line 2 shown below. \begin{tabular}{ll} 2+62+6 & Line 1 \\ 6+26+2 & Line 2 \end{tabular}
Answer Attempt 1 out of 2
The expression was rewritten using the \square
Line 1 says \square ++ \square , which could be represented using dots as +\bullet \bullet+\bullet \bullet \bullet \bullet \bullet for a total of \square dots.
Line 2 says \square ++ \square , which could be represented using dots as +\bullet \bullet \bullet \bullet \bullet \bullet+\bullet \bullet for a total of \square dots.

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Problem 39024

8. Write each expression as a single trigonometric function. a) sin28cos35+cos28sin35\sin 28^{\circ} \cos 35^{\circ}+\cos 28^{\circ} \sin 35^{\circ} b) cos10cos7sin10sin7\cos 10^{\circ} \cos 7^{\circ}-\sin 10^{\circ} \sin 7^{\circ} d) sinπ3cosπ4cosπ3sinπ4\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\cos \frac{\pi}{3} \sin \frac{\pi}{4}

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Problem 39025

xponential Functions HW
Solve the equation for xx (18)x=512\left(\frac{1}{8}\right)^{x}=512
The solution set is J \square (Simplify your answer. Type an integer or a fraction.)

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Problem 39026

Question Watch Video Show Examples
Use the long division method to find the result when 6x37x2+23x76 x^{3}-7 x^{2}+23 x-7 is divided by 3x23 x-2. If there is a remainder, express the result in the form q(x)+r(x)b(x)q(x)+\frac{r(x)}{b(x)}.
Answer Attempt 1 out of 2 \square Submit Answer

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Problem 39027

Consider the function f:RRf: \mathbf{R} \rightarrow \mathbf{R} defined by f(x)=x3(1x)5f(x)=x^{3}(1-x)^{5} (a) Provide a list of all the critical numbers of ff. Separate the values by a semi-colon should there be more than one. Input the word "none" (without quotes or capitals) should there be none. x=x= \square (b) Provide a list of all the local minima of ff (following the same instruction). x=x= \square (c) Provide a list of all the local maxima of ff (following the same instruction). x=x=\square

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Problem 39028

Determine the domain on which the following function is increasing.

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Problem 39029

Practice: Probability and Distributions
1. Determine whether the following procedure results in a binomial distribution or a distribution that can be treated as binomial. If it is not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied. a. In a Pew Research Center survey of 50 subjects, the ages of the respondents are recorded. b. A basketball player who makes 71%71 \% of his free throws is asked to shoot free throws until he misses. The number of free throws attempted is recorded.

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Problem 39030

webassign.net/web/Student/Assignment-Responses/submit?pos=1\&dep=358210028tags=autosave\#question3170019_1 ur best submission for each question part is used for your score. [-/1.5 Points] DETAILS MY NOTES JMODD8 4.2.004.
Find the mean, median, and mode of the given set of raw data. (If more than one mode exists, separate your answers with commas. If an answer does not exist, enter DNE.)
Need Help? Read It Submit Answer View Previous Question Question 3 of 12 View Next Question Home My Assignments Request Extension

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Problem 39031

R-carvone is responsible for the characteristic minty odor and flavor of spearmint oil, and its structure is shown below:
Which two orbitals overlap to form the π\pi bond between C5 and C6? Assume that all of C4 C5 and C6 lie in the xz plane.

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Problem 39032

Question Watch Video Show Examples
Use the long division method to find the result when x47x329x2+17x3x^{4}-7 x^{3}-29 x^{2}+17 x-3 is divided by x210x+2x^{2}-10 x+2. If there is a remainder, express the result in the form q(x)+r(x)b(x)q(x)+\frac{r(x)}{b(x)}.
Answer Attempt 1 out of 2 \square Submit Answer

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Problem 39033

a) C=A=C=A=\begin{array}{l|l} C= & A= \\ C= & A= \end{array}

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Problem 39034

Question The graph below shows the graphs of several normal distributions, labeled A,BA, B, and CC, on the same axis. Determine which normal distribution has the largest standard deviation.
Select the correct answer below: A B C

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Problem 39035

Kevin compró 3 pinceles que costaron \3.25cadauno.Quierecomprar5frascosdepinturaquecuestan3.25 cada uno. Quiere comprar 5 frascos de pintura que cuestan \3.45 3.45 cada uno. Si Kevin tiene \$26 para empezar, ¿tiene suficiente dinero para comprar también los frascos de pintura? Explica.
El costo de los pinceles es de $9.75\$ 9.75^{\circ}. El costo de los frascos de pintura es de \$17.25.
Después de comprar los pinceles, a Kevin le quedan $\$ \square, lo que es \square el costo de los frascos de pintura. Por tanto, Kevin \square suficiente dinero para comprar los pinceles y la pintura.

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Problem 39036

The histogram shows the starting salaries (rounded to the nearest thousand dollars) for college graduates based on a random sample of recent graduates. Determine whether the following statement is true or false according to the graph.
More college graduates had starting salaries in the $61,000$65,000\$ 61,000-\$ 65,000 range than
Starting Salaries of Recent College in the $46,000$50,000\$ 46,000-\$ 50,000 range.
Choose the correct answer below. A. False, because the bar for 61-65 has the same height as the bar for 46-50. B. False, because the bar for 61-65 is shorter than the bar for 46-50. C. True, because the sum of the heights of the first two bars in the graph is greater than the sum of the heights of the last two bars. D. True, because the bar for 61-65 is taller than the bar for 465046-50.

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Problem 39037

For the following conversion: 6×101 km=? nm6 \times 10^{-1} \mathrm{~km}=? \mathrm{~nm}
In order, in the blanks below:
1. Report the orders of magnitude between the two prefixes. Report as a positive number. For instance there are 10 orders of magnitude between deci and giga.
2. Write the conversion factor. For instance 1 kg/103 g1 \mathrm{~kg} / 10^{\wedge} 3 \mathrm{~g}
3. Write the final answer. If the conversion is given in scientific notation, write the answer in scientific notation, using the correct number of significant digits.

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Problem 39038

Let ff be the function given by f(x)=x23(x+0.5)(x23)(x+0.5)f(x)=\frac{\left|x^{2}-3\right| \cdot(x+0.5)}{\left(x^{2}-3\right)(x+0.5)}. On which of the following open intervals is ff continuous? (A) (2,1)(-2,-1) (B) (1,0)(-1,0)
C (0,1)(0,1) (D) (1,2)(1,2)

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Problem 39039

12. If a=3x+2y\vec{a}=3 \vec{x}+2 \vec{y} and b=5x4y\vec{b}=5 \vec{x}-4 \vec{y}, find x\vec{x} and y\vec{y} in terms of a\vec{a} and b\vec{b}.

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Problem 39040

cosx=2\cos x=2
13. [T2] State the domain of the function y=3tan[2(x+π4)]+1y=3 \tan \left[2\left(x+\frac{\pi}{4}\right)\right]+1

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Problem 39041

According to the Bronsted-Lowry theory, an acid is any substance (molecule or ion) that can transfer a proton ( H+\mathrm{H}^{+}ion) to another substance, and a base is any substance that can accept a proton. Acid-base reactions are proton-transfer reactions, as follows: HA+BBH++A acid acid base \begin{array}{l} \mathrm{HA}+\mathrm{B} \rightleftharpoons \mathrm{BH}^{+}+\underset{\text { acid }}{\mathrm{A}^{-}} \\ \text {acid base } \end{array}
Chemical species whose formulas differ only by one proton are said to be conjugate acid-base pairs. Thus, A\mathrm{A}^{-}is the conjugate base of the acid HA, and HA is the conjugate acid of the base A\mathrm{A}^{-}. Similarly, B is the conjugate base of the acid BH+\mathrm{BH}^{+}, and BH+\mathrm{BH}^{+}is the conjugate acid of the base B . The stronger the acid, the weaker the conjugate base, and the stronger the base, the weaker the conjugate acid.
What is the conjugate base of HSO3\mathrm{HSO}_{3}{ }^{-}? Express your answer as a chemical formula. View Available Hint(s) \square Submit
Part C
What is the conjugate acid of HPO22\mathrm{HPO}_{2}{ }^{2-} ? Express your answer as a chemical formula. View Available Hint(s) \square \qquad A chemical reaction does not occur for this question.

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Problem 39042

12. [T8] Algebraically solve secθ1+secθ=sec2θ2+secθ\frac{\sec \theta}{1+\sec \theta}=\frac{\sec ^{2} \theta}{2+\sec \theta} over the domain [π,π][-\pi, \pi]. Give exact values where possible, if not round to 2 decimal places.

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Problem 39043

f(x)={ebx for x21.5x+b for x>2f(x)=\left\{\begin{array}{ll} e^{b x} & \text { for } x \leq 2 \\ 1.5 x+b & \text { for } x>2 \end{array}\right. et ff be the function defined above. For what values of bb is ff continuous at x=2x=2 ? (A) 0.508 only (B) 0.647 only (C) -1.282 and 0.508
D -2.998 and 0.647

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Problem 39044

Question Watch Video Show Examples
Use the long division method to find the result when 4x48x3+x2+7x114 x^{4}-8 x^{3}+x^{2}+7 x-11 is divided by 2x2x52 x^{2}-x-5. If there is a remainder, express the result in the form q(x)+r(x)b(x)q(x)+\frac{r(x)}{b(x)}.
Answer Attempt 1 out of 2 \square Submit Answer

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Problem 39045

Suppose currency held outside banks is $230\$ 230 billion, and M1 is $500\$ 500 billion.
Do we know for sure how much checkable deposits equal? Yes, because to calculate checkable deposits, we simply need to add $230\$ 230 billion to $500\$ 500 billion. Yes, because to calculate checkable deposits, we simply need to subtract $230\$ 230 billion from $500\$ 500 billion. No, because to calculate checkable deposits, we also need to know the amount in traveler's checks. No, because to calculate checkable deposits, we also need to know the amount in money market mutual funds.

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Problem 39046

Two towns experience changes in population. Equations modelling the population of each town, where PP is population and tt is the number of years after January 1, 2021, are shown below.  Town A PA=7000(0.93)t Town B PB=2500(1.12)t\begin{array}{c} \text { Town A } \rightarrow P_{A}=7000(0.93)^{t} \\ \text { Town B } \rightarrow P_{B}=2500(1.12)^{t} \end{array}
The number of years, to the nearest tenth, that it will take for the population of the two towns to be the same. t= years t=\square \text { years }

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Problem 39047

Application
1. The angle of elevation of the sun is 6565^{\circ} when a tree casts a shadow of 18.3 m long. How tall is the tree? (3 marks)
2. The angle of elevation of the top of a mountain peak, PP, as observed from a point AA on a level plane below is 2222^{\circ}. The angle of elevation from a second point B, 1000 m closer to the base of the mountain is 3232^{\circ}. Find the height of the peak. ( 6 marks)
3. Football goal posts are measured and found to be 6.7 m apart. A player is to attempt a field goal from a point where the ball is 44 m and 42 m from the ends of the goal posts. Within what angle must the he kick the ball? ( 4 marks)

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Problem 39048

1. A constant horizontal force on a 200 N is applied to a box in contact with a vertical surface. The coefficient of static friction between the box and the surface is 0.6 , and the coefficient of kinetic friction is 0.4 . Several students are discussing the frictional force on the box 1 second after the force is first applied:
Al : "The frictional force is 60 N since the box will not be moving and the coefficient of static friction is 0.6 ." Brianna: "The frictional force is 100 N upward since the box has a weight of 100 N downward." Carlos: "The frictional force will be 120 N since the box will not be moving and the normal force will be 200 N." David: "The frictional force will be 40 N for the kinetic frictional force and 60 N for the static frictional force. The weight is 100 Nand the coefficient of kinetic friction is 0.4 , giving 40 N for the kinetic friction. Likewise,for the static frictional force it has a coefficient of static friction of 0.6 , giving a static frictional force of 60 N.60 \mathrm{~N} .{ }^{\text {" }}

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Problem 39049

2. At grocery Store A, 5 cans of baked beans cost $3.45\$ 3.45. At grocery 5 tore B,7\mathrm{B}, 7 cans of bake beans cost $5.15\$ 5.15. At grocery Store C, 4 cans of baked beans cost $2.46\$ 2.46. At grocery Stoman 6 cans of baked beans cost $4.00\$ 4.00. How much money would you save th you bought 20 cat of baked beans from grocery store C than if you bought 20 cans of baked beans from groce store A? (A) $175\$ 175 (b) $1.25\$ 1.25 (c) $1.50\$ 1.50 (1) 95

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Problem 39050

Let ff be the function given by f(x)=x+tan(x5)10f(x)=x+\tan \left(\frac{x}{5}\right)-10. The Intermediate Value Theorem applied to ff on the closed interval [12,15][12,15] guarantees a solution in [12,15][12,15] to which of the following equations? (A) f(x)=10f(x)=-10 (B) f(x)=0f(x)=0 (C) f(x)=4f(x)=4 D. f(x)=14f(x)=14

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Problem 39051

Answer the questions below about Line 1 and Line 2 shown below. 7(2+1)72+71\begin{array}{c} 7 \cdot(2+1) \\ 7 \cdot 2+7 \cdot 1 \end{array} Line 1 Line 2
Answer Attempt 1 out of 2
The expression was rewritten using the \square 7(2+1)7 \cdot(2+1) equals 77 \cdot \square which equals \square . 72+717 \cdot 2+7 \cdot 1 equals \square ++ \square which equals \square .

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Problem 39052

Don has two jobs. For Job 1, he earns $7.55\$ 7.55 an hour. For Job 2, he earns $8.45\$ 8.45 an hour. 6 week he worked at the flist job for 10 hours and at the second job for 15 hours. What he his average earnings per hour? (1) $8.00\$ 8.00 (C) $8.09\$ 8.09 (C) $8.15\$ 8.15 (5) $8.13\$ 8.13

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Problem 39053

Answer the questions below about Line 1 and Line 2 shown below. \begin{tabular}{ll} 1+51+5 & Line 1 \\ 5+15+1 & Line 2 \end{tabular}
Answer Attempt 1 out of 2
The expression was rewritten using the \square
Line 1 says \square ++ \square , which could be represented using dots as +\bullet+\bullet \bullet \bullet \bullet \bullet for a total of \square dots.
Line 2 says \square ++ \square , which could be represented using dots as +\bullet \bullet \bullet \bullet \bullet+\bullet for a total of \square dots.

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Problem 39054

Go online for Step-by-Step Solutions
Find each number. Round to the nearest tenth if necessary. (Examples 1-3)
1. What percent of 60 is 15 ? 25%25 \% 1560=n100150060=60n60\begin{array}{c} \frac{15}{60}=\frac{n}{100} \\ \frac{1500}{60}=\frac{60 n}{60} \end{array} \begin{array}{l} 6 0 \longdiv { 1 5 0 0 } \\ \frac{1201}{388} \\ -\frac{608}{300} \end{array}
2. What number is 15%15 \% of 60 ? \qquad ertel? ! 5 p60=15100\frac{p}{60}=\frac{15}{100} =6045300+100p100=9001009=\frac{60}{} \frac{45}{300}+\frac{100 p}{100}=\frac{900}{100}-9
4. 12%12 \% of 72 is what number? \qquad 7575^{\circ} qω=12120010090012=1212P=75\begin{array}{c} \frac{q}{\omega}=\frac{12}{\frac{1200}{100}} \frac{900}{12}=\frac{12}{12} \\ P=75 \end{array} \begin{tabular}{r} 775 \\ 12 कै० \\ -841 \\ \hline 60 \\ -60 \end{tabular} +n72=12100100n100+\frac{n}{72}=\frac{12}{100} \frac{100 n}{100}
5. What percent of 50 is 18 ? \qquad 36%36 \%
6. 12 is 90%90 \% of what number? \qquad
7. A pair of sneakers is on sale as shown. This is 75%75 \% of the original price. What was the original price of the shoes? (Example 4) \qquad
8. Of the 60 books on a bookshelf, 24 are nonfiction. What percent of the books are nonfiction? (Example 4) \qquad

Find each number. Round to the nearest hundredth if necessary.
9. 40 is 50%50 \% of what number? \qquad 10. 12.5%12.5 \% of what number is 24 ? \qquad

11 What percent of 300 is 0.6 ? \qquad 12. What number is 0.5%0.5 \% of 8 ? \qquad

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Problem 39055

Go online for Step-by-Step Solutions
Find each number. Round to the nearest tenth if necessary. (Examples 1-3)
1. What percent of 60 is 15 ? 25%25 \% 1560=n100150060=60n60\begin{array}{c} \frac{15}{60}=\frac{n}{100} \\ \frac{1500}{60}=\frac{60 n}{60} \end{array} \begin{array}{l} 6 0 \longdiv { 1 5 0 0 } \\ \frac{1201}{388} \\ -\frac{608}{300} \end{array}
2. What number is 15%15 \% of 60 ? \qquad ertel? ! 5 p60=15100\frac{p}{60}=\frac{15}{100} =6045300+100p100=9001009=\frac{60}{} \frac{45}{300}+\frac{100 p}{100}=\frac{900}{100}-9
4. 12%12 \% of 72 is what number? \qquad 7575^{\circ} qω=12120010090012=1212P=75\begin{array}{c} \frac{q}{\omega}=\frac{12}{\frac{1200}{100}} \frac{900}{12}=\frac{12}{12} \\ P=75 \end{array} \begin{tabular}{r} 775 \\ 12 कै० \\ -841 \\ \hline 60 \\ -60 \end{tabular} +n72=12100100n100+\frac{n}{72}=\frac{12}{100} \frac{100 n}{100}
5. What percent of 50 is 18 ? \qquad 36%36 \%
6. 12 is 90%90 \% of what number? \qquad
7. A pair of sneakers is on sale as shown. This is 75%75 \% of the original price. What was the original price of the shoes? (Example 4) \qquad
8. Of the 60 books on a bookshelf, 24 are nonfiction. What percent of the books are nonfiction? (Example 4) \qquad

Find each number. Round to the nearest hundredth if necessary.
9. 40 is 50%50 \% of what number? \qquad 10. 12.5%12.5 \% of what number is 24 ? \qquad

11 What percent of 300 is 0.6 ? \qquad 12. What number is 0.5%0.5 \% of 8 ? \qquad

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Problem 39056

62 26 mph (4) myth (1) 4 mph
Q 30 minh

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Problem 39057

The Eefmont race track known es "Big Sandy" is 14, miles long. In 1973, Secretariat won the Belmont Stakes race in 2 minutes and 30 seconds. Assuming lie ran on "Big Sandy", what wets tha unit sposan? (C) 10 mph (1) 40 mph
036 mph (3) 38 mph

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Problem 39058

Answer the questions below about Line 1 and Line 2 shown below. (8+7)+38+(7+3)\begin{array}{l} (8+7)+3 \\ 8+(7+3) \end{array}
Line 1
Line 2
Answer Attempt 1 out of 2
The expression was rewritten using the \square (8+7)+3(8+7)+3 equals \square +3 which equals \square . 8+(7+3)8+(7+3) equals 8+8+ \qquad which equals \square .

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Problem 39059

Which transformation would take Figure A to Figure B?
Answer A counterclockwise rotation of 270270^{\circ} about the origin A counterclockwise rotation of 9090^{\circ} about the origin A reflection over the y -axis A reflection over the x -axis

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Problem 39060

The graph of the function ff is shown above. On which of the following intervals is ff continuous? (A) (1,1)(-1,1) (B) (1,2)(1,2) (C) (2,3)(2,3)
D (3,5)(3,5)

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Problem 39061

*) aly mun ( 45 mant cathety const thy tha munca? (a) 14e ram ave (4) at 7ey pxas ort (a) 15 2 secr m .

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Problem 39062

Tyler is on his school's swim team. During his 2-week winter break, he swims 30 laps each week to stay in shape. If each lap is 25 yards, how many feet does he swim during his winter break?

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Problem 39063

Jump to Problem:[ 11 2 1]]
Problem 1. (1 point) Find yy as a function of tt if y(0)=5,y(0)=8y(t)=6y+33y=0\begin{array}{ll} y(0)=5, \quad y^{\prime}(0)=8 \\ y(t)= & 6 y^{\prime \prime}+33 y=0 \\ & \end{array}
Note: This particular weBWorK problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.

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Problem 39064

13 ounce box of cereal costs $3.99\$ 3.99. What is the unit price per pound? (4) ahout $1.23\$ 1.23 (about \2.66(about2.66 ( about \4.30 4.30 Fatout \$4 91

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Problem 39065

3. Football goal posts are measured and found to be 6.7 m apart. A player is to attempt a field goal from a point where the ball is 44 m and 42 m from the ends of the goal posts. Within what angle must the he kick the ball? (4 marks)

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Problem 39066

The function ff is continuous on the interval 1<x<3-1<x<3 and is not continuous on the interval 1x3-1 \leq x \leq 3. Which of the following could not be an expression for f(x)f(x) ? (A) x+1x3\frac{x+1}{x-3} (B) x3x+1\frac{x-3}{x+1}
C (x+1)(x3)(x+1)(x-3) (D) 1(x+1)(x3)\frac{1}{(x+1)(x-3)}

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Problem 39067

Let x represent one number and let y represent the other number. Four times a first number decreased by a second number is -13 . The first number increased by twice the second number is 17 . Use the given conditions to write a system of equations. Solve the system and find the numbers.

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Problem 39068

Divide. 223+114=2 \frac{2}{3}+1 \frac{1}{4}=
Select the correct answer. 2152 \frac{1}{5} 113151 \frac{13}{15} 3133 \frac{1}{3} 22152 \frac{2}{15}

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Problem 39069

b) tan2xsinxsinx3=0\tan ^{2} x \sin x-\frac{\sin x}{3}=0

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Problem 39070

Two towns experience changes in population. Equations modelling the population of each town, where PP is population and tt is the number of years after January 1,2021 , are shown below.  Town A PA=7000(0.93)t Town B PB=2500(1.12)t\begin{array}{c} \text { Town A } \rightarrow P_{A}=7000(0.93)^{t} \\ \text { Town B } \rightarrow P_{B}=2500(1.12)^{t} \end{array}
The number of years, to the nearest tenth, that it will take for the population of the two towns to be the same. t=t= \square years

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Problem 39071

1. We wish to improve yearling weight (YW) in our cow herd. h2h^{2} for WW=.42\mathrm{WW}=.42 mean of the selected bulls =1130lb=1130 \mathrm{lb} mean of all bulls =1097lb=1097 \mathrm{lb} mean of selected cows =820lb=820 \mathrm{lb} mean of all cows =813lb=813 \mathrm{lb} overall herd mean =955lb=955 \mathrm{lb}
Calculate: - Selection differential for: o Males - Females - Overall - Response to selection - New herd mean for YW

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Problem 39072

1. [-/2 Points] DETAILS MY NOTES SCALCET9 11.9.003.MI.
Find a power series representation for the function. (Center your power series representation at x=0x=0.) f(x)=17+xf(x)=n=0()\begin{array}{r} f(x)=\frac{1}{7+x} \\ f(x)=\sum_{n=0}^{\infty}(\square) \end{array}
Determine the interval of convergence. (Enter your answer using interval notation.) \square Submit Answer

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Problem 39073

v2+2v13=5v^{2}+2 v-13=-5

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Problem 39074

\begin{enumerate} \item An office manager wants to determine if there is a relationship between the number of hours each week employees exercise and the number of sick days that they take each year. The data for the number of hours of exercise and sick days is given as follows: \begin{itemize} \item Hours of exercise: 1.5, 3, 2, 3.5, 2, 3.5, 4, 4.5, 2.5 \item Sick days: 16, 5, 9, 4, 12, 3, 2, 2, 11 \end{itemize} \item Find the correlation coefficient, rr. Round values to the nearest thousandth. \item Use the correlation coefficient and the scatter plot to determine if a relationship exists between these variables. Interpret this relationship. \item Can it be determined that this relationship is a cause-and-effect relationship? Why or why not? Are there other reasons this relationship might exist? If so, list some of these reasons. \end{enumerate}

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Problem 39075

f(x)={c+cxx2 for x<37 for x=32c+3x2 for x>3f(x)=\left\{\begin{array}{ll} c+c x-x^{2} & \text { for } x<3 \\ 7 & \text { for } x=3 \\ 2 c+\frac{3}{x-2} & \text { for } x>3 \end{array}\right.
Let ff be the function defined above. For what value of cc, if any, is ff continuous at x=3x=3 ? (A) 2 (B) 4 (C) 6
D There is no such C .

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Problem 39076

12(23)19=13(23)\frac{1}{2}\left(\frac{2}{3}\right)-\frac{1}{9}=\frac{1}{3}\left(\frac{2}{3}\right)

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Problem 39077

7. For each triangle, determine the length of the hypotenuse to the nearest tenth of a metre. a)

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Problem 39078

5. What percent of 50 is 18 ?
6. 12 is 90%90 \% of what number?
7. A pair of sneakers is on sale as shown. This is 75%75 \% of the original price. What was the original price of the shoes? (Example 4) \qquad sale price $51\$ 51
8. Of the 60 books on a bookshelf, 24 are nonfiction. What percent of the books are nonfiction? (Example 4) \qquad

Find each number. Round to the nearest hundredth if necessary.
9. 40 is 50%50 \% of what number? \qquad 10. 12.5%12.5 \% of what number is 24 ? \qquad

11 What percent of 300 is 0.6?0.6 ? \qquad 12. What number is 0.5%0.5 \% of 8 ? \qquad

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Problem 39079

Autonomous27: Problem 2 Previous Problem Problem List Next Problem (1 point) Dead leaves accumulate on the ground in a forest at a rate of 3 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 80 percent per year. A. Write a differential equation for the total quantity QQ of dead leaves (per square centimeter) at time tt : dQdt=\frac{d Q}{d t}= \square B. Sketch a solution to your differential equation showing that the quantity of dead leaves tends toward an equilibrium level. Assume that initially (t=0)(t=0) there are no leaves on the ground. What is the initial quantity of leaves? Q(0)=Q(0)= What is the equilibrium level? Qeq=Q_{e q}= \square Does the equilibrium value attained depend on the initial condition? A. yes B. no

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Problem 39080

Solve the following equation: 70(1.29)w=654570(1.29)^{w}=6545
Write your answers exactly (i.e. no decimal approximations and simplified if possible), separated by a comma. w=w=
Write your answers as decimals rounded to four decimal places. ww \approx

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Problem 39081

The average production cost for major movies is 67 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 11 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of XX ? X N(X \sim \mathrm{~N}( \square \square ) b. What is the distribution of xˉ?xˉN(\bar{x} ? \bar{x} \sim N( \square , \square ) c. For a single randomly selected movie, find the probability that this movie's production cost is between 68 and 71 million dollars. \square d. For the group of 11 movies, find the probability that the average production cost is between 68 and 71 million dollars. \square e. For part d), is the assumption of normal necessary? Yes
No

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Problem 39082

Directions: First, determine if the three side lengths could form a triangle. (Recall from earlier, the sum of the two smaller sides must be greater than the third side). If yes, classify the triangle further as acute, right, or obtuse.
3, 7, 9 \square ++ \square \square \square \square \square \square 2 \square 2+{ }^{2}+ \square 2 \square \square \square \square Not a triangle \square Acute - Right - Obtuse \square Next

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Problem 39083

Previous Problem Problem List Next Problem (1 point) A population PP obeys the logistic model. It satisfies the equation dPdt=81300P(13P)\frac{d P}{d t}=\frac{8}{1300} P(13-P) for P>0P>0. (a) The population is increasing when \square <P<<P< \square (b) The population is decreasing when P>P> \square

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Problem 39084

b) tan2xsinxsinx3=0\tan ^{2} x \sin x-\frac{\sin x}{3}=0 c) cos2x+(122)cosx24=\cos ^{2} x+\left(\frac{1-\sqrt{2}}{2}\right) \cos x-\frac{\sqrt{2}}{4}=

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Problem 39085

(1 point) According to a simple physiological model, an athletic adult male needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer calories than those required to maintain his weight, his weight changes at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight; the constant of proportionality is 1/35001 / 3500 pounds per calorie. Suppose that a particular person has a constant caloric intake of HH calories per day. Let W(t)W(t) be the person's weight in pounds at time tt (measured in days). (a) What differential equation has solution W(t)W(t) ? dWdt=\frac{d W}{d t}= (Your answer may involve W,H\mathbf{W}, \boldsymbol{H} and values given in the problem.) (b) If the person starts out weighing 150 pounds and consumes 3100 calories a day. What happens to the person's weight as tt \rightarrow \infty ? WW \rightarrow
Note: You can earn partial credit on this problem.

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Problem 39086

The average production cost for major movies is 67 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 11 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of XX ? X N(X \sim \mathrm{~N}( 67 \square 0 s) \square \checkmark, \square , \square 0 b. What is the distribution of xˉ?xˉN(\bar{x} ? \bar{x}-\mathrm{N}( 67 , c. For a single randomly selected movie, find the probability that this movie's production cost is between 68 and 71 million dollars. \square d. For the group of 11 movies, find the probability that the average production cost is between 68 and 71 million dollars. \square e. For part d), is the assumption of normal necessary? O Yes No

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Problem 39087

(1 point) Recall that one model for population growth states that a population grows at a rate proportional to its size. (a) We begin with the differential equation dPdt=12P\frac{d P}{d t}=\frac{1}{2} P. Find an equilibrium solution: P=P= \square Is this equilibrium solution stable or unstable? A. stable B. unstable
Describe the long-term behavior of the solution to dPdt=12P\frac{d P}{d t}=\frac{1}{2} P when P(0)P(0) is positive. A. The value of PP approaches zero. B. The value of PP oscillates and does not approach a limit. C. The value of PP approaches a nonzero constant. D. The value of PP increases without bound. E. None of the above

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Problem 39088

Mary's restaurant has 5 full-time cooks each getting $140\$ 140 on Friday night and work from 5:00 to 11:00 PM You also have some part-time cooks that can start any time from 6:00 and work for 3 hours for $50\$ 50 a night. You use the character FF for fulltime cooks and PP for the different cooks starting in 1 hour intervals. You need to have at least 3 cooks from 5:00 to 6:00, 6 from 6:00 to 7:00, 8 from 7:00 to 8:00, 8 from 8:00 to 9:00, 4 from 9:00 to 10:00, and 5 from 10:00 to 11:00. You also do not want more than 9 part-time employees.
What is the constraints equation for number of employee from 8:00 to 9:00 PM?
F+P1+P2+P38F+P 1+P 2+P 3 \geq 8 F+P1+P28F+P 1+P 2 \leq 8 F+D1+D2+D2>RF+D 1+D 2+D 2>R

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Problem 39089

Use the following information to answer question 12. The graph of y=f(x)y=f(x) is shown below.
12. When comparing the graph of y=f(x)y=f(x) with the graph of the transformation y=f(x)y=\sqrt{f(x)}, the X-intercepts are \qquad and the y-intercept is \qquad ii .

The statement above is completed by the information in row \begin{tabular}{|c|c|c|} \hline Row & ii & iii i \\ \hline A. & different & different \\ \hline B. & different & the same \\ \hline C. & the same & different \\ \hline D. & the same & the same \\ \hline \end{tabular}

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Problem 39090

Let ff be the function defined by f(x)=3x204ex+8x20f(x)=\frac{3 x^{20}}{4 e^{x}+8 x^{20}} for x>0x>0. Which of the following is a horizontal asymptote to the graph of ff ? (A) y=0y=0
B y=38y=\frac{3}{8} (C) y=34y=\frac{3}{4} (D) There is no horizontal asymptote to the graph of ff.

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Problem 39091

(b) Let's now consider a modified differential equation given by dPdt=12P(3P)\frac{d P}{d t}=\frac{1}{2} P(3-P).
Find a stable equilibrium solution: P=P= \square Find an unstable equilibrium solution: P=P= \square If P(0)P(0) is positive, describe the long-term behavior of the solution to dPdt=12P(3P)\frac{d P}{d t}=\frac{1}{2} P(3-P). A. The value of PP approaches a nonzero constant. B. The value of PP approaches zero. C. The value of PP increases without bound. D. The value of PP oscillates and does not approach a limit. E. None of the above
Note: You can earn partial credit on this problem.

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Problem 39092

Find the standard deviation for the following group of data items. 6,11,11,196,11,11,19
The standard deviation is approximately \square (Round to two decimal

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Problem 39093

The table below shows the function f(x)=2x5f(x)=-2 x-5. Fill in the missing values. \begin{tabular}{|r|r|} \hline x\mathbf{x} & \multicolumn{1}{|c|}{y\mathbf{y}} \\ \hline\square & -1 \\ \hline-1 & \\ \hline & \\ \hline & \\ \hline 1 & \\ \hline 2 & \\ \hline & \\ \hline \end{tabular}

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Problem 39094

The sum of three numbers is 16 . The sum of twice the first number, 4 times the second number, and 5 times the third number is 54 . The difference between 7 times the first number and the second number is 44 . Find the three numbers. first number: \square second number: \square third number: \square

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Problem 39095

Previously, we developed the Product Rule and studied how it is employed to differentiate a product of two functions. In particular, recall that if ff and gg are differentiable functions of xx, then ddx[f(x)g(x)]=f(x)g(x)+g(x)f(x)\frac{d}{d x}[f(x) \cdot g(x)]=f(x) \cdot g^{\prime}(x)+g(x) \cdot f^{\prime}(x) (a) For each of the following functions, use the Product Rule to find the function's derivative. Notice the label of the derivative (e.g., the derivative of g(x)g(x) should be labeled g(x)g^{\prime}(x) ). (i) If g(x)=xsin(x)g(x)=x \sin (x), then g(x)=g^{\prime}(x)= \square (ii) If h(x)=xexh(x)=x e^{x}, then \square == \square . (iii) If p(x)=xln(x)p(x)=x \ln (x), then \square \square . (iv.) If q(x)=x2cos(x)q(x)=x^{2} \cos (x), then \square == \square . (v.) If r(x)=exsin(x)r(x)=e^{x} \sin (x), then \square \square 1. (b) Use your work in (a) to help you evaluate the following indefinite integrals. Use differentiation to check your work. (Don't forget the " +C+C ".)

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Problem 39096

15. A science experiment involves launching a small röcket. The following measurements are taken: Initial height: 0.61 m Initial vertical velocity: 36.85 m/s36.85 \mathrm{~m} / \mathrm{s} a) Create a quadratic model for the height, in metres, of the rocket after a given number of seconds. b) Verify the following results of the experiment: Total time in the air: 7.54 s Maximum height: 69.89 m c) Sketch a graph of this relation and label the key information as in Example 1 of this section.

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Problem 39097

8. Bill placed a mirror on the ground 5 m from the base of a flagpole. He stepped back until he could see the top of the flagpole reflected in the mirror. Bill is 1.5 m tall and saw the reflection when he was 1.25 m from the mirror. How high is the flagpole? lagpole

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Problem 39098

2. We wish to improve weaning weight (WW) in our cow herd. h2h^{2} for WW=.38W W=.38 herd mean for W W=587lbW \mathrm{~W}=587 \mathrm{lb} \% saved (males) = 1 \% saved (females) = 15 Standard deviation for WW = 23 lb Calculate: - Overall selection intensity - Response to selection - Generation interval for: - Males - Females o Overall - Generation interval - Response per year
Assume we keep our cows for 9 calf crops starting at 2 years of age and we use our bulls for 3 calf crops starting at 2 years of age.

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Problem 39099

2(x+6)=2-2(x+6)=2

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Problem 39100

A cordless leaf blower has a price-demand equation given by p=D(x)=33752.7x2p=D(x)=3375-2.7 x^{2} dollars, which gives the price per leaf blower when xx leaf blowers are demanded. The price-supply equation for the leaf blower is given by p=S(x)=1.05x2p=S(x)=1.05 x^{2} dollars, which gives the price per leaf blower when xx leaf blowers are supplied. Find the consumers' surplus and the producers' surplus.
The consumers' surplus is \square . M̄our answer must begin with \$.)
The producers' surplus is \square (Your answer must begin with \$.)

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