Basic Math Questions and Answers

Show all work as you answer each question below and round solutions to the nearest hundredth 1 Whitney buys a latte in a cylindrical cup that has a cardboard sleeve so the cup isn t too hot to hold If the sleeve has a diameter of 9 cm and a height of 5 cm find the number of square centimeters of the cup covered by the sleeve in his back yard to make a tire swing He rolls the tire 5 full aboc

If you make 42 500 and get 1700 raises each year in how many years will your salary double Assume you do not receive a raise the year you are hired yr

Solve the following recurrence relation find a closed form formula by iteration then prove your answer is correct by using induction xk xk 1 3k 1 for all integers k 1 with base condition given by x0 2

Find the solution to the recurrence relation T n 6T n 1 8T n 2 with base condition T 0 2 and T 1 3

1 If 7 000 is invested at 9 5 compounded continuously find the future value after 4 years Round your answer to the nearest cent 2

MY NO A homeowner planning a kitchen remodeling can afford a 300 monthly payment How much can the homeowner borrow for 4 years at 6 compounded monthly and still stay within the budget Round your answer to the nearest cent

With a present value of 120 000 what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7 4 compounded quarterly Round you answer to the nearest cent

How many permutations of the letters in catnip would contain the character string act somewhere inside them For the toolbar press ALT F10 PC or ALT FN F10 Mac

How many 4 letter words i e character strings which may be nonsense words can w make from the letters in the word beatnik

What interest will be earned if 6300 is invested for 7 years at 11 compounded monthly Round your answer to the nearest cent

Answer the questions below about the quadratic function f x 3x 2 30x 74

QUESTION 1 Write in exponential form Assume all variables are positive real numbers oot 2 x 3

7 How many five cards hands with no pairs each card is one of a kind are there

Solve the following recurrence relation with initial conditions T n 4T n 1 4T n 2 T 0 1 T 1 3

Annual sales for a furniture store are 375 000 and are increasing at a rate of 6 75 each year 9 years

Find the slope intercept form for the line passing through 1 4 5 6 and 1 8 4 5

LINEAR SYSTEMS Graphing a system of two linear inequalities Oraph the solution to the following system of inequaliti y 2x 3 y 5x 6

se common logarithms or natural logarithms and a calculator to evaluate the following log 1589 5 valuate the expression log 1589 5 Type an integer or a decimal Do not round until the final answer Then round to four decimal places as needed

What does it mean if the average rate of change of the gross domestic product is negative

An isosceles triangle has base b 86mm We inscribe in this triangle two equal circles of radius r 12mm Calculate the heighth of the triangle h

A farmer has 80 meters of fencing to enclose a rectangular garden that has one side of the garden against a barn Let I represent the length of the rectangular garden in meters Notice that the 80 meters of fencing is needed for only 3 sides of the garden a Suppose the length of the garden is 15 meters l 15 i What is the width of the garden meters ii What is the area of the garden square meters b Write an expression in terms of I that represents the width of the garden in meters c Write an expression in terms of I that represents the area of the garden in meters

A circle with a radius of 4 8 cm is centered at the vertex of an angle a Suppose the angle has a measure of 120 degrees i What is the radian measure of this angle 120pi 180 radians Preview 11 What is the length in cm of the arc subtended by the angle s rays along the circle cm Preview b Suppose represents the varying degree measure of the angle Write an expression that represents the length cm of the are subtended t the angle s rays along the circle Enter theta for 8 theta pi 180 4 8 cm Preview

3 Consider the table below showing the number of cells in a flask vs time days Day 3 5 6 1 1000 5000 15000 19000 Number of cells 2 2500 9000 a Estimate the growth rate of the cells ie cells day on day 4 b Determine an equation for the tangent line at day 4 7 21000

An investment will generate income continuously at the constant rate of 10 000 per year for 7 years If the prevailing annual interest rate remains fixed at 1 3 compounded continuously what is the present value of the investment

Watch help video Which system of equations has the same solution as 3x 3y 6 x 6y 32 6x 6y 6 3x 6y 12 x 6y 32 x 6y 32 6x 6y 12 6x 3y 12 x 6y 32 x 6y 32

Your answer is incorrect Find an equation of the parabola with vertex 5 4 and focus 5 6 x 5 8 4 0 0 U

Find the perimeter of the triangle whose vertices are 5 3 7 3 and 7 2 Write the exact answer Do not round Answer 2 Points

Rewrite sin60 in terms of the appropriate cofunction Answer 2 Points

Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ D Enter each matrix in the form row 1 row 2 where each row is a comma sepa list A 1 1 1 1 0 0 2 0 0 6 2 2 2 2 ASK YOUR TEACH X

rev Tom just hopped on the edge of a merry go round What are his linear and angular speeds if the diameter of the merry go round is 11 feet and takes 4 seconds for it to make a complete revolution Round the solutions to two decimal places Answer 2 Points rad s Keyp Keyboard Shor

7T Find the area of the sector of a circle of radius 9 m with a central angle of 5 AnswerHow to enter your Round the solution to two decimal places

Solve for the remaining angles and side of the one triangle that can be created Round to the nearest hundredth A 70 a 7 5 b 3 Answer How to enter your answer opens in new window 2 Points B C

Your backpacker s guide contains a grid map of Paris with each unit on the grid representing 0 125 kilometers If the Arc de Triomphe is located at 3 5 and Les Invalides is located at 7 8 what is the direct distance not walking distance which would have to account for bridges and roadways between the two monuments in kilometers Round your answer to two decimal places if necessary AnswerHow to enter your answer opens in new window 2 Points Keypad

4x y 8 3x 5y 2 15 Use the graphing tool to graph the system Click to enlarge graph Click the graph choose a tool in the palette and f 10 8 6 4 2 Ay 10 8 6 4 2 2 4 6 6 X 8 10

A ball is thrown into a lake creating a circular ripple that travels outward at a speed of 5 cm per second Express the area A of the circle in terms of the number of seconds t that have passed since the ball hits the lake A 25mt A 25m A A 5nt None of the above

E ev Determine the amplitude period and phase shift of the following trigonometric equation Sy cos 2mx 8 Answer 2 Points Selecting an option will display any text boxes necessary to complete your answer Amplitude Phase Shift O no phase shift Oshifted to the right Oshifted to the left Period

A national census bureau predicts that a certain population will increase from 31 4 million in 2000 to 62 3 million in 2060 Complete parts a through c below a Find an exponential function of the form f t yob for these data in which t 0 corresponds to 2000 and f t is im millions f t Use integers or decimals for any numbers in the expression Round to four decimal places as needed b What is the projected population in 2030 In 2050 million In 2030 the population is projected to be Round to one decimal place as needed In 2050 the population is projected to be Round to one decimal place as needed million

Consider the following pair of points 6 5 and 2 6 Step 2 of 2 Determine the midpoint of the line segment joining the pair of points Answer 2 Points

Solve for the remaining angle and sides of the triangle described below Round to the nearest hundredth C 10 A 40 c 3 AnswerHow to enter your answer opens in new window 2 Points B a

Use trigonometric identities to simplify the expression Answer 2 Points tan t tan 1 sin 1

48 Given that cose and cote is negative determine and cot Enter the angle in degrees from the interval 0 360 Write the exact 8 answer Do not round Answer 2 Points 0 Key Keyboard Sho

Given 9 4 and x 8 find all x such that the distance between these two points is 13 Separate multiple answers with a comma Answer 2 Points

Consider the following 6 15 A Find all eigenvalues of the matrix A 2 2 7 Give bases for each of the corresponding eigenspaces smaller value span larger 2 value span 1 2 2 1 Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ D Enter each matrix in the form row 1 row 2 where eac separated list D Q 7 0 0 2 2 1 1 2 X

The ramp of a moving truck touches the ground 16 feet away from the end of the truck If the ramp makes an angle of 12 relative to the ground what is the length of the ramp Round your answer to two decimal places Answer 2 Points Keyp Keyboard Short

A preschool has Campbell s Chunky Beef soup which contains 2 5 g of fat and 15 mg of cholesterol per serving cup and Campbell s Chunky Sirloin Burger soup which contains 7 g of fat and 15 m of cholesterol per serving By combining the soups it is possible to get 18 servings of soup that will have 99 g of fat and 270 mg of cholesterol How many cups of each soup should be used beef cups burger cups

A clothing manufacturer has factories in Atlanta Chicago and New York Sales in thousands during the first quarter are summarized in the matrix below Atl Chi N Y Coats 42 64 12 Shirts 82 51 41 Pants 7 19 9 Ties 8 7 7 During this period the selling price of a coat was 250 of a shirt 40 of a pair of pants 60 and of a tie 25 Use matrix multiplication to find the total revenue in dollars received by each factory Atlanta Chicago New York

Burnem Inc manufactures thumb drives and sells them to a distributor Burnem s total cost and total revenue in dollars for x thumb drives are given by the following equations Total cost 5x 5340 and Total revenue 17x How many thumb drives must Burnem sell to break even X thumb drives

une 2017 Central High School had five members on their swim team in 2010 Over the next several years the team increased by an average of 10 members per year The same school had 35 members in their chorus in 2010 The chorus saw an increase of 5 members per year Write a system of equations to model this situation where x represents the number of years since 2010 M 10 Graph this system of equations on the set of axes below 5 95 85 75 65 55 45 25 15 35 y BY MCS bass 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Explain in detail what each coordinate of the point of intersection of these equations context of this problem

Itranscript Suppose that IQ scores have a bell shaped distribution with a mean of 96 and a standard deviation of 17 Using the empirical rule what percentage of IQ scores are between 79 and 113

transcript Suppose that IQ scores have a bell shaped distribution with a mean of 96 and a standard deviation of 17 Using the empirical rule what percentage of IQ scores are between 79 and 113