Functions Questions and Answers

Would you favor spending more federal tax money on the arts Of a random sample of n 230 women 66 responded yes Another random sample of n 170 men showed that r 53 responded yes Does this information indicate a difference either way between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts Use 0 05 a What is the level of significance 0 05 State the null and alternate hypotheses Enter for as needed Ho P1 P USE SALT H P P b What sampling distribution will you use What assumptions are you making O It follows the Student s t sampling distribution The number of trials is sufficiently large It follows the standard normal sampling distribution We assume the population distributions are approximately normal Use the sample test statistic to find the corresponding z or t value as appropriate Test the difference p P Round your final answer to two decimal places O O It follows the Student s t sampling distribution We assume the population distributions are approximately normal O It follows the standard normal sampling distribution The number of trials is sufficiently large c Find the P value Round your answer to four decimal places P value O Sketch the sampling distribution and show the area corresponding to the P value 3 2 1 3 2 1 0 0 1 2 1 2 3 3 GO 00 2 3 3 1 0 1 2 3 0 1 2 1 2 3 G

Give the intervals on which the function is increasing decreasing or constant Simplify your answers completely Enter your answers using interval notation If an answer does not exist enter DNE Objective 1 increasing decreasing constant

The slope of a vertical line is Select ex The equation of the vertical line passing through 5 2 is

The slope of a horizontal line is Select The equation of the horizontal line passing through 7 6 is

In the following diagram suppose side f 9 19 cm and side g 31 5 cm Determine the AREA the triangle e D Round to the nearest tenth if needed Be sure to include proper units If the area cannot be determined put NULL in the answer box

2 Use an Euler diagram to determine whether the argument is valid or invalid b No rocker would do the mariachi All baseball fans do the mariachi No rocker is a baseball fan

40 00 35 28 Lebron received 55 800 of compensation from his employer and he received 635 of interest from a municipal bond What is the amount of Lebron s gross income from these items Multiple Choice 56 435 0 635 55 800 B

Work required Find the determinant 1 0 2 1 32 3 4 4

What is the additive inverse and the additive identity for the vector space V x y xeR y 0 Be sure you indicate which is which in your response or if the set does not contain the additive identity or inverse

Question 24 of 26 1 point I Question Attempt 1 of Unlimited Use transformations to graph the function f x x 4 6

By hand perform a single iteration of the secant method with initial guesses x 1 4 and 0 0 to find a solution of tan x 0 1 1 where x is in radians After 1 iteration report the exact values of your solution estimate x and its estimated relative error and the tolerance in function as a decimal floating point number in engineering notation with 7 mantissa digits Required submission Handwritten or printed all steps to obtain the answers incl the final answers submitted to Gradescope

Two functions are described below Function A A taxi driver charges customers a base amount of 3 00 and also an amount of 2 00 per mile x for a total charge y to a customer Function B The equation y 3x 2 represents the relationship between the number of miles x a taxi travels and the total charge y to a customer Which statement correctly compares the relationship between Function A and Function B A Function A has both a greater rate of change and a greater initial value Function B has both a greater rate of change and a greater initial value Function A has a greater rate of change than Function B but the initial value for Function A is less than the initial value for Function B B C D Function B has a greater rate of change than Function A but the initial value for Function B is less than the initial value for Function A A B C

Describe the zero vector the additive identity of the vector space P3 x x 3

Given the table of values of x and y find the slope and the y value of the y intercept X 2 6 11 y 20 40 65 a Slope b y intercept

The perimeter and area of an envelope are known to be 68 cm and 64cm respectively We can find the dimensions by solving the equation x 34x 64 0 Factored the left side of this equation gives O x4 x 16 O x 2 x 17 O x 2 x 32

Solve for x by rewriting in exponential form log 14 x 2 x

Factor fully 32x y 56x y O x4y 32y 56x O 8x4y 4x 7y O 8x4y 4y 7x 08 4x4y 7x5y

The inverse of the function f x ex 2 1 is None a O bo O x ln x 1 2 f x ln x 1 2 f x ln x 2 1 x ln x 2 1 b CO d O e O

One of the following functions is neither even nor odd O a sin x 1 x y 2 Ob y x cosx O c None d y cos sinx O e y 1 x sinx

10e limx 3e 5 O a a 2 O b 5 O c 0 O d 10 3

One of the following functions is odd O a y cost sing O b T y 1 z O c None O d Women sin x y Y 1 x sinx Oe Y 1 z y

The center of the circle y 2x 2y i 1 O a 1 1 O b 1 1 O C None O d 1 1

The value of a that makes the following function continuous f x O a 1 O b 1 Oc None O d 0 O e 2 x a T 1 I 19 x 1 I 1

If f x 2x 3 g x O a 14 O b 86 O c 5 O d None O e 31 5 then fog 3

Evaluate 5 5 3 5 3 Simplify your answer

Add the numerators 14 16 4 16 9 16 16

Subtract the numerators and subtract the denominators 42 20 22 45 45 45 Determine the final step to subtract fractions when the denominators are different Choose the correct answer below OA Subtract the LCD to the numerator and denominator OB Add the LCD to the numerator and denominator OC Multiply the LCD by the numerator and denominator OD Simplify if possible

Three experiments investigating the relation between need for cognitive closure and persuasion were performed Part of the study involved administering a need for closure scale to a group of students enrolled in an introductory psychology course The need for closure scale has scores ranging from 101 to 201 For the 68 students in the highest quartile of the distribution the mean score was x 176 50 Assume a population standard deviation of a 7 53 These students were all classified as high on their need for closure Assume that the 68 students represent a random sample of all students who are classified as high on their need for closure Find a 95 confidence interval for the population mean score on the need for closure scale for all students with a high need for closure Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places

9 12 points Find the volume of the tetrahedron with the given vertices 0 0 0 0 2 0 3 0 0 1 1 4

The method of tree ring dating gave the following years A D for an archaeological excavation site Assume that the population of x values has an approximately normal distribution 1264 1264 1278 1292 1268 1316 1275 1317 1275 S USE SALT a Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s Round your answers to four decimal places X A D yr b Find a 90 confidence interval for the mean of all tree ring dates from this archaeological site Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to the nearest whole number

1 Draw and correctly label the following two production possibilities frontiers one for China and one for the United States The Y axis reflects units of tech goods produced the X axis reflects units of manufactured goods produced If China uses all its resources to make tech goods it will produce 4 if they use all their resources to make manufactured goods it will produce 24 If the US uses all its resources to make tech goods it will produce 48 if they use all their resources to make manufactured goods it will produce 48 China is currently producing 2 tech goods and 12 manufactured goods while the US is currently producing 24 tech goods and 24 manufactured goods

In a marketing survey a random sample of 724 shoppers revealed that 624 remained loyal to their favorite supermarket during the past year i e did not switch stores LAUSE SALT a Let p represent the proportion of all shoppers who remain loyal to their favorite supermarket Find a point estimate for p Round your answer to four decimal places b Find a 95 confidence interval for p Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to three decimal places The interval should have only two values Keport p along with the margin or error What is the margin of error based on a 95 confidence interval Round your answer to three decimal places

em 2 4 points Recall the pre lab candy situation consider two unopened bags of candy one Skittles the other M M s The manufacturers state the distribution of coloured candies is M M S MILK CHOCOLATE 24 blue 19 orange 17 green 13 yellow 13 red 14 brown SKITTLES colours are reportedly distributed evenly meaning each colour red orange green blue yellow and purple has a probability of Assume that both of these unopened bags have the same number of candies If they are opened and mixed and one candy is randomly selected what is the probability it is a Skittle Hint only focus on the colour you need P Skittle blue If rounding use at least four digits after the decimal in your answer

Given f x find the average rate of change of f x on the interval 3 3 h Your answer will be an expression involving h and must be simplified I x 1 14h 169 1 11

8 10 THE What is the first step in adding fractions when denominators are different A Find the least common multiple of the denominators That number is the least common denominator LCD OB Add the numerators keeping the same denominators n OC Multiply by 1 using an appropriate notation to express each number in terms of the LCD OD Simplify if possible The LCD is

The estimated and actual values are given Compute the percentage error Simplify your answer completely PE 0 059 and v 0 05

Claude estimates the average age of the participants in his aerobics class to be about 30 years The registration records show that the average age is 21 8 years a Compute the absolute error Simplify your answer completely AE Interpret the result Claude s estimate had this much error relative to the actual average age of participants Claude s estimate had this much percent error This proportion of participants in the class are older than Claude s estimate This is the ratio of Claude s estimate to the actual average age of participants in the class Claude s estimate for the average age of participants was this many years off of the actual average age b Compute the relative error Round to three decimal places Simplify your answer completely RE Interpret the result Claude s estimate had this much error relative to the actual average age of participants Claude s estimate had this much percent error This proportion of participants in the class are older than Claude s estimate This is the ratio of Claude s estimate to the actual average age of participants in the class Claude s estimate for the average age of participants was this many years off of the actual average age

Identify the correct graph for the following equation y 4x 1

Evaluate lim f x where f x X 5 4 5 5 4 Limit does not exist 0 6 x 25 x 2x 15 6 if x 5 if x 5

Evaluate lim f x where f x X 4 4 Limit does not exist 8 0 6 X 8 2 8 x 12x 36 if x 4 if x 4 if x 4

If f x O8 5 4 5 00 08 x39x 13 x 4 8 5 8 find f 1

The total monthly revenue R x in dollars generated from sales of Math t shirts is related to the amount x spent on advertising by R x 2x 24x 30x 60 where x is in hundreds of dollars Compute the rate of change of revenue with respect to the amount of money spent on advertising R x Is monthly revenue increasing faster when the amount of money spent on advertising is 320 dollars or 400 dollars 320 dollars 400 dollars

If g s 8 s 5 S g s S 20 compute g s

Determine the equation of the line tangent to the curve y 3x X y at the point 2 7

Your car has a 20 gallon gas tank and is full when you leave your house You are using gas at a constant rate and therefore the amount of gas in your car is a linear function of the time you are driving After traveling for two hours your car is half full Find the slope of the linear function Select one O a 5 O b 5 O c 5 2 O d 2 5