Basic Math Questions and Answers

We usually write numbers in decimal form or base 10 meaning numbers are composed using 10 different digits 0 1 9 Sometimes though it is useful to write numbers hexadecimal or base 16 Now there are 16 distinct digits that can be used to form numbers 0 1 9 A B C D E F So for example a 3 digit hexadecimal number might be 2B8 a How many 3 digit hexadecimals are there in which the first digit is E or F b How many 4 digit hexadecimals start with a letter A F and end with a numeral 0 9 c How many 6 digit hexadecimals start with a letter A F or end with a numeral 0 9 or both

of China s exports of automobiles and parts in billions of dollars is approximately f x 1 8208e0 33872 where x 0 corresponds to 1998 In what year did will the exports reach 8 billion Give your answer as the year with at least one decimal place

Simplify 3b 5 2a 2 b 7 2 Write your answer using only pos

Question 4 Divide the following polynomial f x 6x 3 32x 2 5x 25 x 5 6x 2 2x 5 6x 2 5x 5

2 Given the function below what would be the domain of the function s inverse 0 5 x 0 5 SX 0 75 x 2 0 5 0 25 0 0 25 0 5 0 75 All values of x except x TI T n n Z 311 2 2TT

sure to check for non real solutions x 2 y 2 8 2x 2 5y 2 12

A couple received a 137 000 inheritance the year they turned 49 and invested it in a fund that earns 6 6 compounded semiannually If this amount is deferred for 13 years until they retire how much will it provide at the end of each half year in dollars for the next 20 years after they retire Round your answer to two decimal places

If 2 drops of flavoring are needed for 5 dozen cookieg how many drops of flavoring are needed for 6 dozen State your answer as a mixed fraction

K Suppose three balls are drawn without replacement from a bag that contains 5 blue balls and 6 orange balls The number of orange balls is counted Complete parts a and b belo a Determine the histogram for the number of orange balls in the sample Choose the correct histogram below O A AP x 0 5 0 0 1 2 3 Q Q OB AP x 0 5 0 1 2 3 b What is the expected number of orange balls in the sample Round to two decimal places as needed Q Q G O C AP x 0 5 0 1 2 3 Q O D AP x 0 5 L 0 1 2 3 Q

Find the expected payback for a game in which you bet 3 on any number from 0 to 399 If your number comes up you get 500 The expected payback is Round to the nearest cent as needed

5 A fair coin is flipped 10 000 times Use the Central Limit Theorem Normal Approximation to estimate the probability that the number of heads is between 4850 and 5100

4 a A certain type of storage battery lasts on average 3 0 years with a standard deviation of 0 5 years Assuming that battery life is normally distributed find the probability that a given battery last less than 2 3 years I

Find the first five terms of the sequence an 2 5 M 11 32 83 34 as Determine whether the sequence is geometric If it is geometric find the common ratio r If the sequence is not geometric e T Express the nth term of the sequence in the standard form anar 1 If the sequence is not geometric enter DNE

The nth term of an arithmetic sequence is given an 12 24 n 1 a Find the first five terms of the sequence 31 a2 a3 a4 a5 b What is the common difference d

Find the nth term of the arithmetic sequence with given first term a and common difference d What is the 10th term a 7 d 5 an a10

Find the nth term of the geometric sequence with given first term a and common ratio r a 5 r 2 an What is the fourth term a4

y AC If AB has length 4 find the length of AC and BC BC 45 A 45 Your answers need to be in exact form do not use decimal approximations To enter a number like 3 use sqrt 3

AC AB F 30 A 11 X If BC has length 11 find the length of AC and AB 60 Your answers need to be in exact form do not use decimal approximations To enter a number like 3 use sqrt 3

The following table gives the the approximate amount of emissions E of nitrogen oxides in millions of metric tons per year in the US Let t be the number of years since 1940 and E f t a Using left endpoints estimate the integral f t dt z b Using right endpoints estimate the integral 1 f f t dt Be sure that you know what the units of your answer are and what its meaning is Original data from the Statistical Abstract of the US 1992 t 1940 1950 E 1960 1970 1980 1990 7 4 9 3 13 3 18 1 21 3 19 6

x values for which the expression is 3 6x 2 13x 5 6x 2 23x 7

v 6 3 32 0 where v is a vour answer in simplified radi

The system of equations 2y x 0 y is graphed below x y y hof 8 6 2 5 Use the graph to find the solutions of the system Assume that points of intersection fall on the grid x y smaller x value X larger x value

John wrote a book and his deal allowed him to receive a 15 royalty based on the total sales of the book Last year the book sold for 12 and 30 000 copies were sold How much did he receive in royalty payments Round to the nearest whole dollar For your answer do NOT include symbols commas words etc Answer x 54000 Question 51 0 1 point Chris sells computer equipment for his company He receives a base pay of 300 plus commission on his sales He receives 10 for the first 5000 in sales and 15 anything over 5000 Last week he sold 12000 in computer equipment Find his gross pay Round to the nearest whole dollar

Simplify the following units g x m s x m g x m s g x m s gx m s gx m s

The price in of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher Supply p 0 004x Demand p 0 007x 220 a Solve the system of equations defined by the supply and demand models b What is the equilibrium price c What is the equilibrium quantity

Berthold s Sporting Goods just purchased 375 worth of tennis gear from one of its vendors to restock its inventory What accounts would be debited and credited in this transaction A Inventory would be debited 375 Accounts Payable would be credited 375 B Inventory would be credited 375 Accounts Payable would be debited 375 OC Both Inventory and Accounts Payable would be credited 375 OD Both Inventory and Accounts Payable would be debited 375

Use a graphing calculator to do the following an an 1 an 2 and a 5 a 3 a Find the first 10 terms of the sequence a1 a2 a3 a4 a5 a6 a7 ag ag a10

Find the first four terms and the 100th term of the sequence whose nth term is given an 67 a1 11 a2 a3 34

What fraction of a turn around a circle is 210 degrees

Solving equations Show all work for credit 1 2 x 1 4 x 2 x 3 5X 100 5 2x 1 81 7 x 3x 1 4 X 9 x x 2 5x 3 0 2 x 7x 6 4 5 4 100 6 1 2 x 4 5 X 8 14 2 5 120 10 6x 162

At Alice s Restaurant a Taco Plate has 2 tacos and 1 chile relleno and costs 7 The combination platter comes with 3 tacos and 3 chiles rellenos and costs 14 25 What will the Party Platter cost if it contains 10 tacos and 14 chiles rellenos A 120 B 95 50 C 57 50 D 48 75

Jackie has two summer jobs She works as a tutor which pays 12 per hour and she works as a lifeguard which pays 9 50 per hour She can work no more than 20 hours per week but she wants to earn at least 220 per week Which of the following systems of inequalities represents this situation in terms of x and y where x is the number of hours she tutors and y is the number of hours she works as a lifeguard A 12x 9 5y 220 x y 2 20 B 12x 9 5y 220 x y 20 C 12x 9 5y 2 220 x y 20 D 12x 9 5y 2 220 x y 20

5 Sketch a sin function which contains the following characteristics k2 C4marks An amplitude of 2 A period of 2 3 T A phase shift of to the right 3 A vertical translation of 2 units down

2 Show all work to determine the exact value of sin 5 1 6 K3 C1 marks

2 Show all work to determine the exact value of sin 3 6 K3 C1 marks

1 Solve the following trigonometric equations K4 marks COS 2x 2

Fixit Corporation Issued 34 000 shares of 10 par value common stock at its current market price of 30 How does this event affect total stockholders equity Multiple Choice It Increases by 1 020 000 It is unaffected It Increases by 680 000 It Increases by 340 000

In a study of 10 000 car crashes it was found that 5140 of them occurred within 5 miles of home based on insurance company data Use a 0 01 significance level to test the claim that more than 50 of ca crashes occur within 5 miles of home Use this information to answer the following questions a Which of the following is the hypothesis test to be conducted OA Ho p 0 5 H p 0 5 O c Ho p 0 5 H p 0 5 OE Ho p 0 5 H p 0 5 b What is the test statistic Z Round to two decimal places as needed c What is the P value www OB Ho p 0 5 H p 0 5 OD Ho p 0 5 H p 0 5 OF Ho p 0 5 H p 0 5 P value Round to four decimal places as needed d What is the conclusion O There is sufficient evidence to support the claim that more than 50 of car crashes occur within 5 miles of home O There is not sufficient evidence to support the claim that more than 50 of car crashes occur within 5 miles of home C

Determine whether the samples are independent or dependent A data set includes the list price and selling price for each of 190 randomly selected homes Choose the correct answer below OA The samples are dependent because there is not a natural pairing between the two samples OB The samples are dependent because there is a natural pairing between the two samples OC The samples are independent because there is not a natural pairing between the two samples OD The samples are independent because there is a natural pairing between the two samples

Which of the following scatterplots indicates a strong negative linear relationship between X and Y Choose the correct answer below O A Y O C X GEREIR B Y OD X

Current Attempt In Progress An Investment center generated a contribution margin of 360000 fixed costs of 200000 and sales of 2800000 The center s average operating assets were 800000 How much is the return on Investment 20 O 170 O 45

Current Attempt In Progress Allowances should not be made in the direct labor quantity standard for O cleanup O rest perlods O machine downtime Himn

Current Attempt In Progress Assume that actual sales results exceed the planned results for the second quarter This favorable difference is greater than the unfavorable difference reported for the first quarter sales Which of the following statements about the sales budget report on J 30 Is true O The year to date results will show an unfavorable difference O The difference for the first quarter can be ignored The sales report is not useful If It shows a favorable and unfavorable difference for the two quarters The year to date results will show a favorable difference

Mr Young built a greenhouse 42 feet wide 110 feet long 5 feet to the eaves and 14 feet to the ridge cap How many square feet of plastic does it take to enclose the greenhouse O 5015 square ft 6215 square ft O 6915 square ft O 5915 square ft

U 3 3 a Find u v u v b Find the angle between u and v to the nearest degree 0 180 Submit Answer Viewing Saved Work Revert to Last Response DETAILS PREVIOUS ANSWERS Determine whether the given vectors are perpendicular 0 7 v 9 0

Find the equation for the hyperbola whose graph is shown DETAILS 10 F 4 0 5 10 0 10 F2 4 0 10 X

Sketch the given vector with initial point 1 4 u 5 3 30 10 Find the terminal point x y y 10 y 10 X X 10 10 10 10 y 10 X 10 x 10

u 0 7 v 9 0 Yes No DETAILS 00 Determine whether the given vectors are perpendicular u 3 4 v 2 5 Yes No

7 Write the given vector in terms of i and j u 1 6 U DETAILS Write the given vector in terms of i and j 8 0 U UM

Find the indicated quantity assuming u 7i j v i 3j and w 3i 6j u v w