Basic Math Questions and Answers

5 Does the following data show inverse variations Round to the nearest tenth in your calculations y 89 335 35 493 12 068 3 873 E 1 597 4 02 11 822 36 837 O no O yes

3 In business there is a formula used to find simple interest on an account The formula is rate x time x principle interest The rate is the percentage rate usually per year and time is in years with principle being the amount of money put into the account originally The interest will be the money earned on the account Determine whether the following statement is true or false Rate and interest are an inverse relationship assuming the remaining variables are kept constant O True O False

1 In business there is a formula used to find simple interest on an account The formula is rate x time x principle interest The rate is the percentage rate usually per year and time is in years with principle being the amount of money put into the account originally The interest will be the money earned on the account If I put 80 into an account offering 3 interest per year how much interest would I earn in three years

A video game company sends out shipments to its various stores with a mean cargo size of 75 games and a standard deviation of 4 8 games What is the probability that a store chosen at random will receive a shipment of between 65 and 85 games assume a normal distribution

1 Identify each of the following as having either a discrete probability distribution D or a continuous probability distribution C the number of red marbles drawn from a bag the height of the students in this room the volume of lemonade Mr Fisher drinks on a hot day the score in a hockey game

A biologist has 400 kg of nutrient A 600 kg of nutrient B and 300 kg of nutrient C These nutrients will be used to make 4 types of food whose contents in percent per kilogram of food and whose growth values are shown on the right Set up the initial simplex tableau that would be used to determine how many kilograms of each food should be produced in order to maximize total growth What is the objective function z 100 x 90 x 70 x3 50 x4 Set up the initial simplex tableau for the problem X X2 X4 S1 S2 S3 0 1 0 0 2 0 625 0 125 0 1 0 8 0 25 0 0 70 50 0 0 Type an integer or decimal for each matrix element 0 0 1 X3 0 0 1 400 ABC 0 Growth Value Let x be the number of kilograms of food type P Let x be the number of kilograms of Q Let x3 be the number of kilograms of R and let x4 be the number of kilograms of S 2008 8 P Q R S 0 12 5 87 5 20 62 5 12 5 100 80 25 0 70 50 100 90

ww aw SETS Interpreting Venn diagram cardinalities with Try Again b Your answer is incorrect A drug trial had 407 participants A survey was taken to determine how many had nausea as a side effect and how many had anxiety as a side effect The Venn diagram below shows the results Each number gives the number of participants who fall into that Venn diagram category All participants in the survey Had nausea 88 63 Had anxiety 197 59 a How many of the participants had anxiety 260 participants b How many of the participants had nausea or anxiety or both 222 participants c How many of the participants did not have both nausea and anxiety 344 participants X 3

Multiply 810 by 086 using the lattice algorithm identity the correct multiplication lattice Choose the correct answer below OA 8 6 1 0 O 6 S 1 OB OD 4 8 2 4 8 8 7 0 4 7 6 4 9 8 8 6 C 8 0 0 0 0 0 0 0 6 2 4 9 1 2 8 4 7 8 7 1 9 9 8 6

Find the slope of the line graphed below 17 5 3 ca He

Find the slope of the line graphed below S 4 en

6 The table shows Aleksei s December budget Fill in the blanks so that Aleksei s budget is balanced Income December 5 pay December 19 pay Total December Income Expenses 180 Phone 205 Save for driver training Save for car Family expenses Spending money Total December Expensos 55 50 100 100

Use short division to find the quotient and remainder for the division problems given below Check the result a 5 37 858 b 7 6816 a 5 37 858 R Type whole numbers

Boris s class measured the lengths of 9 leaves Draw a line plot for the lengths of the leaves 3 3 1 3 Lengths of leaves in inches 2 1 4 2 3 2 4 3 3 3 3 4 4 4 2 3 4 3 3 4

To receive full credit you should show all your work 100 points total 1 Define T R R by T the definition of linearity IL T2 T3 0 11 12 I3 Prove that T is linear by using

1 Find the lengths of the circ Assume r 9 and 0 114 S S 0 arc not 33 74 2 How many revolutions will a car wheel of diameter 18 in make as the car travels a distance of one mile Round your answer to the nearest whole number

3 Assuming a credit card bank fee of 2 35 of the net sales find the amount deposited into a tax accountant s checking account based on the following credit card transactions Credit Card Sales 125 00 125 00 125 00 179 00 179 00 652 16 673 00 Credit Card Refunds 35 00 25 00

x 3 matrix Find the k values that make the row vectors of the matrix A orthogonal to 3k A k 1 3k 0 5 Answer Solve the question on this paper below and write down your final answer here k each other

artesian product of finite and nonempty sets can be illustrated by the intersections of a crossing line pattern as shown to the right plain why the number of intersection points in the crossing line pattern for AxB is a b where a n A and b n B w the crossing line pattern for 0 A x ch of the lines coming from set A intersects each of the lines coming from set B GENERED

Let L be the line through the point Q 1 8 8 and direction vector a 1 2 2 Find the two distinct points R1 and R2 on L at distance 6 2 to the point P 2 1 4 2 R1 0 0 0 R2 0 0 0

measure of one angle is shown in the figure Given k find the measures of the other seven labeled angles

Service Lube oil and filter 5000 Tire rotation and brake 10000 inspection Wheel alignment inspection 25000 Discount Purchase Price Freight Tire Air Tax Deal Review New car MSRP or List Price Gas Fee Gas Tax Administration Fee Cooling system 50000 Tune up and emission 85000 control Automatic transmission 85000 51 175 In the first 3 years that Jill owns her sports car she drives 63 350 kms Jill maintains her vehicle according to the distance maintenance schedule below taking into consideration both kilometres driven and elapsed time The fuel consumption rating for her sports car is 8 3 L 100 km Each year Jill pays 1960 for insurance and 98 for her vehicle license plate registration During those 3 years Jill renews her driver s licence at a cost of 80 The average cost of fuel is 1 06 L Determine Jill s average monthly operating cost during the 3 years Use the table provided see attached to organize your answers Lien Payout Delivery Price MFG Rebate Down Payment Finance Fee Amount Financed 3 6 Taxable Subtotal Interest Rate Trade in Allowance Loan Term Taxable Total 15 Monthly Payment Module 5 Case Study 1 36 95 63 99 24 30 79 95 84 95 165 00

b Your answer is incorrect A county is planning to expand its train service In studying the current service the county planner looked at which train stations are along or not along various train lines The Venn diagram shows this information for three of the lines All county train stations Green Line stations Ulm Quilmes Explanation Blue Line stations Rechock Fes Graz Jena Trento Orange Line stations Metz Volos Warren Radom York Santos Ponce a Select all the train lines that have a stop at Haifa Green Line Orange Line Blue Line b How many stations are only along the Orange Line 7 c Which stations are along all three lines the Green Line the Orange Line and the Blue Line Choose all that apply Bern Graz Fes Ponce Metz Trento Ulm Quilmes Volos Halfa Jena Radom Santos Warren York 5 8

SETS Interpreting a Venn diagram with 3 sets for a real world situation All animals housed Treated by Dr Scott An animal sanctuary houses a variety of animals To understand the workload of the sanctuary s veterinarians the director looked at which types of animals are treated or not treated by various doctors The Venn diagram shows this information for three of the doctors Snakes Elks Frogs Goats Treated by Dr Hall Cats Otters Treated by Dr Torres Pigs Birds Dogs Llamas Horses Koalas Iguanas Turtles Quails a Select all the doctors who treat otters Dr Scott Dr Torres Dr Hall b How many types of animals are treated only by Dr Scott 0 c Which types of animals are treated only by one of the three doctors Dr Scott Dr Torres or Dr Hall Choose all that apply Cats Elks Birds Goats Dogs Iguanas Koalas Otters Quails Snakes Horses Pigs 10 5 Frogs Llamas Turtles Ang

Use formulas to find the area of the figure 4 km 3 km OA 16 km OB 22 km OC 32 km C 11 km 8 km

A certain field is a rectangle with a perimeter of 886 feet The length is 155 feet more than the width Find the width and length of the rectangular field The width is The length is

If construction costs are 157 000 per kilometer find the cost of building the new road in the figure shown to the right The cost of building the new road is Round to the nearest dollar as needed new road 4 000 m 3 000 m

Find the requested term Find the 3rd term of the sequence s 1 13n 1 53

Hans is taking out an amortized loan for 26 000 to buy a new car and is deciding between the offers from two lenders He wants to know which one would be the better deal over the life of the car loan and by how much Answer each part Do not round intermediate computations and round your answers to the nearest cent If necessary refer to the list of financial formulas a A savings and loan association has offered him a 6 year car loan at an annual interest rate of 8 9 Find the monthly payment b An online lending company has offered him a 5 year car loan at an annual interest rate of 8 7 Find the monthly payment c Suppose Hans pays the monthly payment each month for the full term Which lender s car loan would have the lowest total amount to pay off and by how much O Savings and loan association The total amount paid would be s O Online lending company The total amount paid would be less than to the online lending company Time Remaining 1 30 38 0 less than to the savings and loan association 4 X

Consider the following sequence 5 10 15 25 a Classify the sequence as arithmetic geometric Fibonacci type or none of these O arithmetic O geometric O Fibonacci type O none of these X b If arithmetic give d if geometric give r if Fibonacci type give the first two terms If Fibonacci type enter your answers as a comma separated list If none of these enter NON X c Supply the next term

2 0 3 5 A laptop computer is purchased for 1000 After each year the resale value decreases by 25 What will the resale value be after 4 years Use the calculator provided and round your answer to the nearest dollar X 6

A tennis ball is dropped from a height of 13 ft If the ball rebounds 2 3 of its height on each bounce how far will the ball travel before coming to rest Find the total distance that the ball will trav before it stops bouncing ft

If possible find the sum of the infinite geometric series If not possible enter IMPOSSIBLE 3 2 2 X 9 4

A rotating flywheel is allowed to slow to a stop from a speed of 200 rpm While slowing each minute it rotates two thirds as many times as in the preceding minute How many wheel make before coming to rest revolutions

centimeters Write out your work for each calculation striking through units as they cancel 2pts Your height in centimeters cm From the procedure 3 Use the appropriate conversion factor to calculate your height in meters Write out your work for each calculation striking through units as they cancel 2pts Your height in meters m 5pts Calculation Uploads 5pts Upload images of your work for the calculation of the volume of the solid object and for the conversion of your height to metric units

A culture of bacteria increases by 100 every 24 hours If the original culture contains 1 million bacteria a P bacteria 1 million find a formula for the number of bacteria present P after d da

2 0 3 Round 8 41 to the nearest tenth 5 51 6

5 There are 3 green apples and 8 red apples in a basket 6 a What is the ratio of green apples to all apples in the basket 0 b What is the ratio of red apples to all apples in the basket 0 0 0

Ann borrowed money from her credit union to invest in the stock market She took out a personal amortized loan for 28 500 at an interest rate of 7 65 with monthly payments for a term of 1 year For each part do not round any intermediate computations and round your final answers to the nearest cent If necessary refer to the list of financial formulas a Find Ann s monthly payment b If Ann pays the monthly payment each month for the full term find her total amount to repay the loan 0 c If Ann pays the monthly payment each month for the full term find the total amount of interest she will pay 0 X 5 25

24 25 26 11 When ordering the Kids Lunch at Burger Universe the customer must choose a size a type of bun a side order and a type of fruit drink Here are the possibilities for each choice Choice Possibilities Junior Small Medium Large Size Type of bun White bun Wheat bun Side order Fries Onion rings Fruit cup Fruit drink Orange Grape How many Kids Lunches are possible 28 X

From the procedure Solve the addition and subtraction problems below reporting the answer with the correct number of significant figures 2pts 13 45 mL 0 4552 mL 2pts 145 5 m 86 58 m 1045 m 2pts 245 625 g 80 2 g 2pts 4 62 cm 0 885 cm

Games like Wheel of Fortune and Jeopardy have one winner and two losers A three team game tournament is illustrated by the figure If Jeopardy has a Tournament of Champions consisting of 27 players what is the necessary number of games games Need Help Bu

Use similar triangles to solve A person who is 6 foot tall is standing 182 feet from the base of a tree and the tree casts a 196 foot shadow The person s shadow is 14 feet in length What is the height of the tree 6 A

If construction costs are 150 000 per kilometer find the cost of building the new road in the figure shown to the right The cost of building the new road is S Round to the nearest dollar as needed new road 30 000 m 16 000 m

A school playground is in the shape of a rectangle 700 feet long and 500 feet wide If fencing costs 14 per yard what will it cost to place fencing around the playground BOCO

Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x Round to one decimal place 7 in 12 in O A 168 in OB 3 4 in OC 1 2 in O D 41 9 in 2 in www

24 25 26 Mathematics test score Frequency 550 to 599 5 11 13 11 600 to 649 650 to 699 700 to 749 750 to 799 27 28 29 30 31 32 33 34 Each year the newspaper America at a Glance writes an article about the performance of students on a particular nationwide math test Included in the article this year was the following frequency distribution It summarizes the test scores from a study which looked at 49 students who completed preparation program for the test 35 Based on the frequency distribution using the midpoint of each data class estimate the mean mathematics test score for the students in the study For your intermediate computations use four or more decimal places and round your answer to one decimal place

1pts 2 a What conversion factor s can you use to convert g to ug 1 10 Pg a b C d C 1 pts b Complete the conversion of 0 000059 g to g a b d 1 pts 3 a What conversion factor s can you use to convert ng to mg 1 10 ng and and a b d C 18 1000 pg 1 g 1g 1 10 pg 1g 1000 pg 1g 1 g 1pts b Complete the conversion of 2881 ng to mg 1x10 ng 1 mg 1pts 4 a What conversion factor s can you use to convert kg to Mg 1x10 g and 1x10 ng 1x10 ng 1 mg 1 kg 1 kg 1x10 g 1 10 g 1 kg 1 10 g 1 kg and 1000 mg 1g 1000 mg 18 and and 1x10 Mg 1 g 1 10 Mg 1g 1 Mg 1 106 g 1x100 g 1 Mg Choose Choose Choose

If you drive 3 miles south then make a left turn and drive 4 miles east how far are you in a straight line from your starting point Use the Pythagorean Theorem to solve the problem Use a calculator to find square roots rounding to the nearest tenth as needed OA 1 0 mi OB 2 6 mi OC 2 8 mi OD 5 0 mi

Use formulas to find the area of the figure 11 cm b OA 44 cm OB 72 cm OC 96 cm O 2 12

Use the formulas developed in this section to find the area of the figure 15