Questions

USE SALT a Use the binomial distribution to find the probability of exactly 10 successes Round your answer to three decimal places b Use the normal distribution to approximate the probability of exactly 10 successes Round your answer to four decimal places X c Compare the results of parts a and b These results are fairly different These results are almost exactly the same

5n 2n n 4n6 5n5 2n 5n 3 5p Find lim 3 5p Find lim n n 5n n 1 3p Show that lim tg x 2 g x 7 x 0 does not exist

Determine the point on the graph of the unit circle that corresponds to T findcos 2 andsin COS T and state which functions are undefined for The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction The functions that are undefined for 2 2 are RIN and 2 T T 2 0 Simplify your answer sin Simplify your answer RIN 2 Then 1 0 2 Ay 2 0 1 10 1 0 1

Question Consider the curve f y y Jour for 1 y 2 Find the arc length of the curve 4y

K Find the circular function values for the given number s State which functions are undefined for s Do not use calculator 3x 2 S A sin 3x 2 A cos OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice Type an integer or a fraction 3r 2 Type an integer or a fraction 1 0 2

Find m G 3x 2 K H

Choose the correct graph of the function y 2cos x Choose the correct graph below O A N Ay 10 G OB 10 Q O C Ay 10 Q OD 10 10

Let x represent the dollar amount spent on supermarket impulse buying in a 10 minute unplanned shopping interval Based on a newspaper article the mean of the x distribution is about 26 and the estimated standard deviation is about 10 USE SALT a Consider a random sample of n 100 customers each of whom has 10 minutes of unplanned shopping time in a supermarket From the central limit theorem what can you say about the probability distribution of x the average amount spent by these customers due to impulse buying What are the mean and standard deviation of the x distribution The sampling distribution of x is not normal The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean 26 and standard error 0 1 26 and standard error 1 26 and standard error o x 10 Is it necessary to make any assumption about the x distribution Explain your answer It is not necessary to make any assumption about the x distribution because n is large It is necessary to assume that x has an approximately normal distribution It is necessary to assume that x has a large distribution It is not necessary to make any assumption about the x distribution because is large b What is the probability that x is between 24 and 28 Round your answer to four decimal places Probabilities should be between 0 and 1 c Let us assume that x has a distribution that is approximately normal What is the probability that x is between 24 and 28 Round your answer to four decimal places 0 1587 d In part b we used x the average amount spent computed for 100 customers In part c we used x the amount spent by only one customer The answers to parts b and c are very different Why would this happen The standard deviation is larger for the x distribution than it is for the x distribution The mean is larger for the x distribution than it is for the x distribution The sample size is smaller for the x distribution than it is for the x distribution The x distribution is approximately normal while the x distribution is not normal The standard deviation is smaller for the x distribution than it is for the x distribution In this example x is a much more predictable or reliable statistic than x Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer How does the central limit theorem tell us that the average customer is much more predictable than the individual customer The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation Thus the average customer is more predictable than the individual customer The central limit theorem tells us that small sample sizes have small standard deviations on average Thus the average customer is more predictable than the individual customer

Graph one period of the given function y sin x x Choose the graph of y sin x x O A 2 Ay n L OB Ay HT S K HKT HTT o o LY www O C Ay H2 Ch 24

3 x 125 125 5 14 14 256 256 4

Match the function y cos 2x with its graph Which is the correct graph of the equation O A B A OON O C

A European growth mutual fund specializes in stocks from the British Isles continental Europe and Scandinavia The fund has over 121 stocks Let x be a random variable that represents the monthly percentage return for this fund Suppose x has mean 1 7 and standard deviation 0 6 LAUSE SALT a Let s consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks Is it reasonable to assume that x the average monthly return on the 121 stocks in the fund has a distribution that is approximately normal Explain Yes is x is a mean of a sample of n 121 stocks By the central limit theorem approximately normal b After 9 months what is the probability that the average monthly percentage return x will be between 1 and 2 Round your answer to four decimal places 0 9330 c After 18 months what is the probability that the average monthly percentage return x will be between 1 and 2 Round your answer to four decimal places X the x distribution d Compare your answers to parts b and c Did the probability increase as n number of months increased Why would this happen Yes probability increases as the standard deviation increases No the probability stayed the same Yes probability increases as the standard deviation decreases Yes probability increases as the mean increases e If after 18 months the average monthly percentage return x is more than 2 would that tend to shake your confidence in the statement that 1 7 If this happened do you think the European stock market might be heating up Round your answer to four decimal places x This would be very unlikely The probability that x was greater than 2 is than 5 of all such samples have means more than 2 One would suspect because less that the European stock market

Use transformations to graph the following function y 4 sinx Select the graph that represents the given function O A Ay K 2x G OB K 2x G O C Ay 10 21 G O

A solid with surface area 50 square units is dilated by a scale factor of k to obtain a solid with surface area 200 square units Find the value of k 4 1 O2

t the following radian measure to degree measure

ert the following degree measure to radians 90 radians Simplify your answer

Question Consider the curve f y 6y 1 over the interval 2 y 6 Which of the following integrals represents the arc length of the graph of f y Select the correct answer below O 6 24y 1 dy 6 6y 1 dy 576y 1 dy 6y 2 dy 6y 1 1 dy

In the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities Suppose it is estimated that 3 3 of the general population will live past their 90th birthday In a graduating class of 785 hig school seniors find the following probabilities Round your answers to four decimal places LUSE SALT a 15 or more will live beyond their 90th birthday 0 9887 b 30 or more will live beyond their 90th birthday X c between 25 and 35 will live beyond their 90th birthday d more than 40 will live beyond their 90th birthday 0 0018

e figure at the right shows an angle 0 in andard position with its terminal side 7 24 ersecting the unit circle at P 25 25 valuate the circular functions at 0 n0 ype an integer or a simplified fraction Os 0 ype an integer or a simplified fraction n0 an integer or a simplified fraction 0 P 1 0 G

Calculate the amount of work done to lift an object and cable Question How much work in foot pounds is done when a 45 foot long cable with a weight density of 7 pounds per foot is wound up 34 feet Do not include any units in your answer

The formula 0 can be rewritten as 0 wt Using wt for 0 changes s r0 to s rot Use the formula s rot to find the value of the missing variable t T s 5 cm r 4 cm w radian per sec 8 t sec Type an integer or a fraction

Let x y be any two vectors in space Which of the following are properties of the cross product x x y Select all that apply x x y is orthogonal to the plane determined by x and y xxy y xx x xx y 0 and y x x y 0 Oxxy y x x x x y is the area of the paralellogram determined by x and y Oxxx yx y 0

Convert the following degree measure to radians 90 90 radians Simplify your answer Type an exact answer u

Given triangle JKL which of the following is a proper representation of the sine law a sin K I k sin L b kx sin K I x sin L Oc sinsink J K K Od sink sin L Question 16 1 point Saved Corinne invested 3200 in a three year regular interest CSB that earns 7 annually How much will her investment be worth at the end of the term a 6720 b 6192 c 3872

Which relation is a function O a O b O c O d S4 3 2 1 1 3 2 1 4 a 5 4 3 2 3 S4 3 2 1 1 2 1 3 2 2 1 3 4 2 3 2 4 3 2 14 A 2 1 2 3 3 3 4 INN 4 5 5 5

The graph of a piecewise defined function is given Write a definition for the function that best describes this graph B 3 0 0

Which of the following expressions is equivalen to x x A x10 B x 5 C X25 D X 30

What are the peaks of a periodic function O a the highest points of the graph Ob the x intercepts of the graph Oc the extremes of the graph d the lowest points of the graph Question 5 1 point Which function represents f x x 5 4 written in standard form O a f x x 10x 21 Ob f x x 10x 29 Oc f x x 10x 21 d f x x 10x 21

The concentration of a solution is defined as the amount of a substance divided by the volume of the solution Suppose a vat contains 18 kg of salt and 50 liters of water At t 0 water is added at a rate of 25 liters minute while salt is added at a rate of 9 kg minute A function giving the concentration after t minutes will be C t kg liter express as a function of t As time passes the concentration will Decrease Increase

What is the shortest interval in which a periodic function will complete one cycle Ob a period A C a B bd a wavelength c Question 21 1 point an action d an event b a Given triangle ABC above if DA 38 and b 4 47 cm determine a to the nearest hundredth a 5 67 cm b 7 26 cm c 3 52 cm d 2 75 cm

The graph below is the function f x 5 4 3 2 1 3 2 7 lim H 2 f 2 f x 2 123 4 5 lim f x x 2 lim f x x 2 1 1 Q Find the following If no value exists enter DNE C 2 3 4 5

lim sin x 4 sin 4 0 H 0 sin x 4 sin a cos 4 cos x sin 4 sin r sin 4 cos x cos 4 sin r sin 4 cos z cos 4 sin z cos 4 cos z sin 4 So sin 4 sin 4 So sin x cos 4 sin 4 cos r 1 sin r cos 4 cos x sin x sin x 4 sin 4 H 0 sin z cos 4 sin 4 cos z 1 sin 4 lim 2 0 H sin 4 H sin z 4 H 1 sin 4 H lim 2 0 sin x cos 4 K O lim 2 0 Part 2 of 5 Part 3 of 5 Part 4 of 5 Part 5 of 5 sin 4 cos z 1

lim sin 2 4 sin 4 2 0 sin x 4 sin z cos 4 cos z sin 4 sin z sin 4 cos z cos 4 sin a sin 4 cos z cos 4 sin z cos 4 cos z sin 4 So sin 4 sin 4 sin z cos 4 sin 4 cos z 1 sin z cos 4 cos z sin 2 sin z 4 sin 4 F So 0 sin z cos 4 sin 4 cos z 1 Um z in 4 z z lim sin z cos 4 lim Part 2 of 5 Part 3 of 5 Part 4 of 5 Part 5 of 5 sin 4 cos z 1

The function f is given by the equation f x x 3 x 21 The graph of the function g x is shown below Express the function g x in terms of f x 4 2 4 2 2 6 a a

Suppose 0 If 2 then lim x 0 lim 0 lim sin u sin u 0 u lim H 0 U sin 2x I sin 2 1 2 2 2 U 2 OF OF X

Suppose an x distribution has mean 2 Consider two corresponding x distributions the first based on samples of size n 45 and the second based on samples of size n 81 LAUSE SALT a What is the value of the mean of each of the two x distributions for n 49 distribution for n 81 distribution b For which x distribution is P x 2 50 smaller Explain your answer The distribution with n 49 because the standard deviation will be larger The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be smaller The distribution with n 81 because the standard deviation will be larger c For which x distribution is P 1 50 x 2 50 greater Explain your answer The distribution with n 81 because the standard deviation will be larger The distribution with n 49 because the standard deviation will be smaller The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be larger

Question Consider the curve f x x 1 for 1 x 4 Find the arc length of the curve 2x Enter an exact answer Provide your answer below

Solve the right triangle with A 37 degrees and b 54 9

1 point What is the cycle of a traffic light with respect to time a 3 Ob the time it takes to repeat Oc infinite O d gro

Which of the following is equal to 2x 3x 2x sin 2x 2x sin 3x 3x sin 2x 3x sin 3x 2 sin x 3 sin x sin 2x 3x sin 2x 2x Which of the two expressions can be multiplied to obtain more expressions 2x sin 3x 3x sin 3x sin 2x lim 2 0 2x sin 2x sin 3x 2z lim 2 0 sin 32 assume x0 Select all that apply Part 1 of 3 2x sin 2x 2x sin 3x Part 2 of 3 Select two or Part 3 of 3

Let f x be the number in thousands of computers sold when the price is x hundred dollars per computer Interpret the statements f 14 80 and f 14 2 Then estimate the number of computers sold if the price is set at 1425 per computer T What does f 14 80 imply O A When the price per computer is 1400 for every 100 price increase the sales increase by 80 000 computers OB 80 000 computers are sold when the price is set at 1400 OC When the price per computer is 8000 for every 100 price increase the sales increase by 14 000 computers OD 80 000 computers are sold when the price is set at 140

Use the washer method to find the volume of a solid of revolution around Question 2 A solid is formed by revolving the region bounded by the graphs of f x 0 3e0 x g x x 2 and x 7 about the x axis Which of the following gives the volume of the solid Select the correct answer below Oxf 0 09e xx dx 0 0 09e 46 dx 2 0 6 0 3e0 dx

Suppose that f 600 6000 and f 600 10 Estimate each of the following a f 601 b f 600 5 c f 599 d f 598 e f 599 75 a f 601 Simplify your answer Type an exact answer

Suppose a student finds the following values of x and f x x If f X 1 9 10 1 99 344 1 999 8197 L these values would make us DOUBT the claim that lim f x x 2

Suppose the following plate is placed on a vertical wall so that the top of the plate is 1 m below the surface of a pool that filled with water Compute the force on the plate A plate shaped like an isosceles triangle with a height of 1 m and a base of length 1 2 m If a y axis in the vertical direction is drawn on the face of the triangle where the origin is the vertex of the trianglo find surface 1 2 m

An object moving in a straight line travels s t kilometers in t hours where s t 7t 5t a What is the object s velocity when t 6 b How far has the object traveled in 6 hours c When is the object traveling at a rate of 6 km h a The object s velocity when t 6 is km h

Find the mass of the following thin bar A 5 m bar with a density in g m of p x 250c For a thin bar or wire represented by the interval a sxsb with a density function p with units of mass per length what is the mass of the object d OA m P x dx OB m m b Sp x dx 8 d dx P x OC m for 0 x 5 b OD m xp x d Sxp x dx

Evaluate 6 for 0 6 3 12 6 54 2 6 a 2 Ob 54 O co d

A survey about social media reported that 77 of B2B marketers marketers that focus primarily on attracting businesses plan to increase their use of social media as compared to 56 of B2C marketers marketers that primarily target consumers The survey was based on 1 426 B2B marketers and 1 618 B2C marketers The accompanying table summarizes the results Complete parts a through d below Click the icon to view the contingency table about social media use and marketers a What is the probability that a randomly selected respondent plans to increase use of social media Round to three decimal places as needed U P O DE E SE ELEV

Which of the following is the surface area of the right cylinder below 1 6 15 OA 225 units OB 540 units C 252 units