Basic Math Questions and Answers

Jigwill bha pic P 1 00 joajall heal ho If f x x e then y at x 1 is 2e a O 4e b O

Ji will ha plc P 1 00 j lle all who Ji The monod growth function is given by R N 5N 1 N then R 3 20 16 C

Jigwill ha pic P 20 Jigw 1 00 joajal hoi If f x x e then y at x 1 is 2e a O 4e b O 3e CO

Jigwill bha pic P 1 00 joajalla hoi One of the following functions is even y x 2x y 2x a O 21 x x 1 x y x x 3 CO p3 b O None d O e O r

The value of a that makes the following function continuous x 2a x 4 x 2 f x x 2 x 2 2 a O 0 b O 2 CO

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

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

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

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 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

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

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

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

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

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

14 4 15 9 A 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 D Simplify if possible Can the fraction O No O Yes 22 45 be simplified

roblem 6 Find the interval of convergence of the following power series x 6 n 5 n n 1 A 1 11 B 1 11 C 1 11 D 1 11 E 1 11 F 1 11 G 1 11 H 1 11 Problem 6 Select v

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board On the second square the King would place two grains of wheat on the third square four grains of wheat and on the fourth square eight grains of wheat If the amount of wheat is doubled in this way on each of the remaining squares how many grains of wheat should be placed on square 15 Also find the total number of grains of wheat on the board at this time and their total weight in pounds Assume that each grain of wheat weighs 1 7000 pound How many grains of wheat should be placed on square 15

How profitable are different sectors of the stock market One way to answer such a question is to examine profit as a percentage of stockholder equity A random sample of 30 retail stocks was studied for x profit as a percentage of stockholder equity The result was x 13 8 A random sample of 36 utility gas and electric stocks was studied for x profit as a percentage of stockholder equity The result was x 10 6 Assume that 4 4 and 3 1 a Categorize the problem below according to parameter being estimated proportion p mean difference of means H or difference of proportions P P2 Op OH OH H OP P b Let u represent the population mean profit as a percentage of stockholder equity for retail stocks and let 4 represent the population mean profit as a percentage of stockholder equity for utility stocks Find a 95 confidence interval for M M in Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place

A research group conducted an extensive survey of 2 865 wage and salaried workers on issues ranging from relationships with their bosses to household chores The data were gathered through hour long telephone interviews with a nationally representative sample In response to the question What does success mean to you 1 550 responded Personal satisfaction from doing a good job Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question Find a 90 confidence interval for p Enter your answer in the form lower limit to upper limit Include the word to Round your answers to three decimal places USE SALT

10 8 points Consider the systme of linear equations a x b y ci a2x b y c where a1 b1 C1 a2 b2 and c2 represent real numbers What must be true about the lines represen the equations when a b a2 b 0

What is the minimal sample size needed for a 95 confidence interval to have a maximal margin of error of 0 09 in the followin scenarios Round your answers up the nearest whole number USE SALT a a preliminary estimate for p is 0 32 b there is no preliminary estimate for p

Do you want to own your own candy store With some interest in running your own business and a decent credit rating you can probably get a bank loan on startup costs for franchises such as Candy Express The Fudge Company Karmel Corn and Rocky Mountain Chocolate Factory Startup costs in thousands of dollars for a random sample of candy stores are given below Assume that the population of x values has an approximately normal distribution 96 175 133 100 75 94 116 USE SALT X a Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviations in thousands of dollars Round your answers to four decimal places thousand dollars thousand dollars 100 85 b Find a 90 confidence interval for the population average startup costu for candy store franchises in thousands of dollars Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place thousand dollars

X PROBLEM 6 For a function f 0 R f x x In 3p find all asymptotes 5p examine monotonicity and find local extreme values 2p verify if it is surjective

14 4 15 9 1 Determine the LCD The LCD is 45 Determine the second step to subtract fractions when the denominators are different Choose the correct answer be OA Multiply the numerators and denominators by the LCD OB Subtract the numerators and keep the larger denominator OC Subtract the numerators and subtract the denominators Multiply by 1 using an appropriate notation to express each number in terms of the least common O D denominator

15 9 Determine the first step to subtract fractions when the denominators are different Choose the correct answer below A Find the least common multiple of the denominators That number is the least common denominator LCD OB Subtract the numerators and subtract the denominators n Multiply by 1 using an appropriate notation to express each number in terms of the least common n denominator CD Subtract the numerators and keep the larger denominator Determine the LCD The LCD is 0 0

100 10 8 OB Multiply by 1 using an appropriate notation to express each number in terms of the LCD n OC Simplify if possible D Find the least common multiple of the denominators That number is the least common denominator LCD The LCD is 40 What is the next step in adding fractions when denominators are different OA Add the numerators keeping the same denominators OB Simplify if possible OC Multiply by 1 using an appropriate notation OD Add the numerators and the denominators n to express each number in terms of the LCD n

One of the following functions is a solution of the second linear ODE y 9y 0 a y x cos 3x b y x cos 2x None O d y x cos r C

At noon a child s temperature is 101 2 F and is rising at an increasing rate At 1 p m the child is given medicine After 2 p m the temperature is still increasing but at a decreasing rate The temperature reaches a peak of 103 6 F at 3 p m and decreases to 100 F by 6 p m Draw a possible graph of the function T t the child s temperature at time t Choose the correct graph below O A AT t 105 100 noon 5 t 10 Q G OB AT t 105 100 noon Q Q O C 105 100 AT t noon Q OD 105 AT 1 100 noon Q G

Based on the given table of data compute each of the following derivatives f g 4 18 f g 4 2 fx g 4 80 f g 4 5 4 f 4 7 A g 4 7 X X f 4 10 g 4 8

7 A caterer prepares a mixed berry salad with 8 total amount of berries in the salad 7 9 qt of strawberries T www Let T be the total amount of berries in the salad To find the total amount add Translate the given information into an equation qt of raspberries and 4 16 qt of blueberries What is th

Simplify 21 27 The answer is Simplify your answer Type an inte

Find both the opposite or additive inverse and the reciprocal or the multiplicative inverse of the following number 13 Type the opposite of 13

Verbalize the following logical statements in a correct and simple natural language sentence in both Arabic and English vx 3y Student x A Course y A Passes x y A TaughtByly Rami A Taughtin y CS dept Smart x