College Math - Others Questions

lim 0 x 4 sin x sin x O a 2 O b 3 O c 4 O d 1 O e None

The domain of the function f x 16 8x O a R O b 0 U 1 O C None d 4 4 O e 0 2 O f 0 0 U 1

If f x xtanx then f x O a O b 1 O c 1 O d T

If y f g x where f 2 8 f 4 5 g 3 4 g 3 8 then y at x 3 is O a 8 O b 24 O c 40 O d 12

The monod growth function is given by R N TAN ION O a 5 8 O b 5 16 O c 15 32 O d 5 10 then R 3 a

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

If x y 4x 22 then y at 1 3 is O a 1 O b 4 O c 1 O d 2

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

The concentration of Oxygen in blood at time t is given by C t sin 57t cos 5 t 9 then C 2 O a 57 O b 5 O C 10 O d 5T

Let f x x Inx then f e O a 2e O b 3e O c 0 O d 4e

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

Let y x sin 2x then y at x IS O a 3 O b 2 O c 0 O d 1

Let A 5 3 then the value of k so that A is singular matrix is 4 k O a 12 5 O b 12 O c 5 12 O d 3 2

limx 0 tan x sin 3x 1 3 O b 3 O a O c 0 d 2

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

Suppose the price of apples increases from 23 to 26 and in response quantity demanded decreases from 108 to 96 Using the mid point formula what is the price elasticity of demand Note your answer should be correct to two decimal places and be sure to express your answer as a positive number Your Answer

Suppose the price of gasoline decreases from 3 80 to 2 50 and in response quantity demanded increases from 10000 to 11400 Using the mid point formula what is the price elasticity of demand Note your answer should be correct to two decimal places and be sure to express your answer as a positive number Your Answer

The total cost of producing 25 tons of butter is 45000 If average variable cost is 825 then what is the firm s average fixed cost enter answer as just a number no commas dollar signs or the like Your Answer

Price 12 8 15 5 3 65 2 D PERPEe 220 400 Supply Demand Quantity ne market depicted above suppose a price floor holds the price at 8 15 ulate producer surplus for this situation Show your answer as a decimal e g

Lisa quit her 14000 per year job to start her own economics consulting firm At the end of her first year of operation her total revenues were 96000 Her total explicit costs were 46000 What was her economic profit for the year Give response as a number no commas decimals dollar signs or otherwise Your Answer

In response to a change in the price of good X from 10 to 6 the quantity demanded of good X increases from 100 to 150 units What is the price elasticity of demand for good X Use the midpoint formula and express as a decimal e g 0 2 A

The average total cost of producing electronic calculators in a factory is 28 at the current output level of 200 units per week If fixed cost is 765 per week then what is the firm s variable cost enter answer as just a number no commas dollar signs or the like Your Answer

2 On Tanya s phone bill 60 out of the 75 long distance calls were in state of the in state calls were to her parents What 3 fraction of all of her long distance calls were to her parents How many calls were to her parents What fraction of all of her long distance calls were to her parents of her long distance calls Simplify your answer Type an integer or a fraction

5 6 A certain recipe calls for cup of flour A chef is making an amount that is of the recipe How much flour should the 6 9 chef use To make of a recipe 6 9 cup of flour is needed Simplify your answer Type an integer or a fraction

8 7 pry OA Multiply the first numerator by the second denominator and multiply the second numerator by the first denominator and then find the sum of these two products OB Multiply the first numerator by the second denominator to get the new numerator and multiply the second numerator by the first denominator to get the new denominator C Multiply the numerators to get the new numerator and multiply the denominators to get the new denomina OD Add the numerators to get the new numerator and add the denominators to get the new denominator Set up the multiplication 5 3 5 3 8 7 8

Evaluate 5 5 3 5 3 Simplify your answer

Suppose again that checkable deposits started off at 1 300 000 in First Main Street Bank the required reserve ratio is 15 and no excess reserves and no cash leakage exist You know from the previous step that due to the sale of securities by the Fed the money supply in the economy contracted from 1 300 000 to 1 292 000 But the contraction of the money supply does not stop with First Main Street Bank It moves to other banks The loan repayment that Sharon made to First Main Street Bank was written on a check Second Republic Bank issued Then when the check cleared the reserves of Second Republic Bank declined and Second Republic Bank found itself reserve deficient as well It applied loan repayments to its reserve deficiency position The effect continued with other banks and so on The initial removal of funds in the amount of 8 000 will cause the money supply to contract by supply is Hint Round the results of your calculations to the nearest dollar Therefore the money Grade Final Step

ply 3 11 The answer is 0 Type an integer or a si

As a result of the Fed s sale of 8 000 worth of government securities to First Main Street Bank the bank becomes reserve deficient Suppose that Sharon a First Main Street Bank s customer re pays back the 8 000 loan she took out a few months ago Which of the following most accurately describes First Main Street Bank s actions O The bank creates a 8 000 loan O The bank keeps the 8 000 as reserves The bank keeps the 1 200 as reserves The bank creates a 187 000 loan The money supply in the economy is s

Suppose again that checkable deposits started off at 400 000 in First Main Street Bank the required reserve ratio is 15 with no excess reserves and no cash leakage First Main Street Bank takes the entire 8 000 in excess reserves that resulted from the open market purchase by the Fed and creates a loan for Susan in a form of a new checkable deposit with a balance of 8 000 The money supply now is s Then Susan writes a check for 8 000 to Alex who immediately deposits the full amount into his checking account at Second Republic Bank Complete the following table to show the effect of Alex s deposit on the Second Republic Bank s balance sheet Liabilities Reserves Loans Assets Alle donncit on the Second Republic Bank s balance sheet The money supply now is s Checkable Deposits Now Second Republic Bank uses the entire 6 800 in excess reserves that resulted from Alex s deposit to create a loan for Becky in the form of a checkable deposit Suppose Second Republic Bank lends all its new excess reserves to Clancy who writes a check to Eileen who deposits the money into her account at Third Fidelity Bank Then Third Fidelity lends all its new excess reserves to Hubert Assume this process continues with each successive loan deposite into a checking account and no banks keeping any excess reserves Under these assumptions the 8 000 injection into the money supply results in an overall increase of in checkable deposits

After graduating from college with a bachelor of business administration you begin an ambitious plan to retire in 25 58 years To build up your retirement fund you will make quarterly payments into a mutual fund that on average will pay 10 20 APR compounded quarterly To get you started a relative gives you a graduation gift of 2 588 43 Once retired you plan on moving your investment to a money market fund that will pay 5 28 APR with monthly compounding As a young retiree you believe you will live for 33 64 more years and will make monthly withdrawals of 9 184 73 YOUR WITHDRAWALS ARE AT THE BEGINNING OF THE MONTH To meet your retirement needs what quarterly payment should you make

For every 1 increase in price 10 fewer tickets will be sold Determine the price that should be charged so that revenue is maximized Let x represent the price of a season ticket Q1 1 Q 1 1 17 Points Determine a formula for the linear function relating the price x and quantity y of concert ticket sold Consider writing two points price quantity first Define all variables Include units Upload a pdf in the correct orientation for CREDIT Please select file s Select file s Save Answer Q1 2 17 Points Set up a simplified equation to represent the monthly revenue Define all variables Include units

2 Determine whether the following mathematical models differential equations are ODE or PDE What is the order of the ODES a x 4x 16x 6t 5 a p a p b a1 x c C ap x t p x d x 5x 25 du x t at

The demand for a product of Carolina Industries varies greatly from month to month The probability distribution in the following table based on the past two years of data shows the company s monthly demand Unit Demand 300 400 500 600 Probability 0 16 0 27 0 42 0 15 a If the company bases monthly orders on the expected value of the monthly demand what should Carolina s monthly order quantity be for this product The monthly order quantity should be units b Assume that each unit demanded generates 63 in revenue and that each unit ordered costs 53 How much will the company gain or lose in a month if it places an order based on your answer to part a and the actual demand for the item is 389 units Select your answer

The following table provides a probability distribution for the random variable y a Compute E y to 1 decimal X 5 2 b Compute Var y and a to 2 decimals Var y X X E Y 35600 8 f y 0 20 0 30 0 40 0 10

5 In how many ways can we put 15 identical silver coins into five numbered boxes so that i every box contains at least one coin ii every box contains an odd number of coins ie 1 3 5 etc iii every box contains an odd number of coins and there are more coins in box 1 than in box 2 REMARK If the answer is eg 3 50 you don t have to compute the numerical answer 546875 Just write 3 50 as the final answer

EACH PROBLEM WILL BE GRADED 0 15 1 For how many elements n 0 1 600 is the following statement true n is divisible by 8 or by 12 and n is not divisible by 5

poin Suppose the price of gasoline decreases from 3 90 to 2 60 and in response quantity demanded increases from 10200 to 11200 Using the mid point formula what is the price elasticity of demand Note your answer should be correct to two decimal places and be sure to express your answer as a positive number

For how many natural numbers n EN 0 is the following sentence false if n is divisible by 6 or by 9 then n is greater than 920

2 How many elements ne 101 102 1000 satisfy the following state ment n is divisible by 5 or by 6 and n is not divisible by 9 Y Z by 1

A GREST VER CURVE AT A POINT Q the station is 13 55 CONNECTS THE 204 2 fl 205 21 206 2x4 GRADE of 2 1 4 75 the MIST NEARLY WHAT IS THE ELE AT POINT B ON THE CURVE AT STA 17 00 A20324 the ELEVATION IS 2 10 6 ft

In a marketing survey a random sample of 724 shoppers revealed that 626 remained loyal to their favorite supermarket during the past year i e did not switch stores LUSE 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 Give a brief explanation of the meaning of the interval We are 5 confident that the true proportion of loyal shoppers falls within this interval We are 95 confident that the true proportion of loyal shoppers falls within this interval We are 95 confident that the true proportion of loyal shoppers falls outside this interval We are 5 confident that the true proportion of loyal shoppers falls above this interval c As a news writer how would you report the survey results regarding the percentage of supermarket shoppers who remained loyal to their favorite supermarket during the past year Report p along with the margin of error Report the margin of error Report the confidence interval Report p What is the margin of error based on a 95 confidence interval Round your answer to three decimal places

The previous experiment is not bound to involve only two forces Suppose you were to add two force vectors F 0 98 N 20 and F 1 96 N 120 We want to know what a third force F3 would be to obtain a zero net force 98 1 96 x C

Alyssa and Gabriel play the following game Alyssa rolls a die If she rolls a 1 2 or 3 Gabriel gives Alyssa 4 If Alyssa rolls a 4 or 5 Gabriel gives Alyssa 1 However if Alyssa rolls a 6 she gives Gabriel 13 a Determine Alyssa s expectation b Determine Gabriel s expectation a Alyssa s expectation is Round to the nearest cent dollars www

In a random sample of 500 judges it was found that 287 were introverts USE SALT a Let p represent the proportion of all judges who are introverts Find a point estimate for p Round your answer to four decimal places b Find a 99 confidence interval for p Enter your answer in the form lower limit to upper limit Include the word to Rou your numerical values to two decimal places Give a brief interpretation of the meaning of the confidence interval you have found We are 1 confident that the true proportion of judges who are introverts falls above this interval We are 99 confident that the true proportion of judges who are introverts falls within this interval We are 1 confident that the true proportion of judges who are introverts falls within this interval We are 99 confident that the true proportion of judges who are introverts falls outside this interval c Do you think the conditions np 5 and ng 5 are satisfied in this problem Explain why this would be an important consideration No the conditions are not satisfied This is important because it allows us to say that p is approximately normal Yes the conditions are satisfied This is important because it allows us to say that p is approximately binomial Yes the conditions are satisfied This is important because it allows us to say that p is approximately normal No the conditions are not satisfied This is important because it allows us to say that p is approximately binomial

Add the numerators 14 16 4 16 9 16 16

A study of parental empathy for sensitivity cues and baby temperament higher scores mean more empathy was performed Let x be a random variable that represents the score of a mother on an empathy test as regards her baby Let x be the empathy score of a father A random sample of 38 mothers gave a sample mean of x 68 36 Another random sample of 38 fathers gave X 58 70 Assume that a 10 99 and 10 88 a What distribution standard normal or Student s t should be used to construct a confidence interval for Explain A Student s t should be used because o and are known A standard normal should be used because and are known A standard normal should be used because o and are unknown A Student s t should be used because and are unknown b Let be the population mean of x and let 2 be the population mean of x Find a 99 confidence interval for Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places

A caterer prepares a mixed berry salad with qt of strawberries qt of raspberries and total amount of berries in the salad 8 4 Add the numerators 14 16 16 16 What is the next step in adding fractions when denominators are different A Add the numerators keeping the same denominators B Add the numerators and the denominators OC Rewrite each fraction so the numerators are in terms of the LCD OD Simplify the fractions 4 T 9 16 qt of blueberries What