Math Questions

The diameter of a standard basketball is 9.5 inches. If the basketballs are covered in rubber, what is the minimum amount of rubber needed to manufacture a set of four basketballs?

A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 29-foot ramp, to the nearest tenth of a degree, if its final height is 7 feet. The ramp's angle of elevation is (Round the answer to the nearest tenth of a degree.)

Joshua is going to invest $680 and leave it in an account for 19 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Joshua to end up with $1,680?

Two cell phone plans offer differing text packages. The two plans are outlined below: Plan A: $6.00 per month charge along with a charge of $0.05 per text. Plan B: No per month charge, but a charge of $0.20 per text. Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.

Use the simplex method to maximize the following: Maximize f = 7x1 + 9x2 subject to 4x1 +5x2 ≤ 15 5x1 + 4x2 ≤ 32 4x1+5x2 ≤ 30 x1 ≥ 0, x2 ≥ 0 If no solutions exist enter DNE in all answerboxes. x1 = x2 = f =

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value. At a boating and sports store, the cost of renting a personal watercraft is $47.70 per half hour, which includes a 6% sales tax. Determine the cost of a half hour rental before tax. The equation is The cost of a half hour rental is $45 per half hour. (Type an equation using x as the variable.)

Jen collects toy sports cars. She has 784 red cars and 224 black cars. She wants to line up the cars in groups so that each group has the same number of cars and contains only red cars or only black cars. What is the largest number of cars that she can have in a group? The largest number of cars that Jen can have in a group is. (Simplify your answer. Type an integer.)

You are working with the following quadratic function: y = x² - 2x - 8 a) Write the quadratic in factored form: y= b) Complete the square to write the quadratic in vertex form: y = Identify the vertex of the parabola: Remember that the vertex is a point! Identify the y-intercept of the parabola: Remember that the y-intercept is a point! Identify the x-intercepts: and Remember that the x-intercepts represent points on the graph!

A publishing company sold 26,265,591 books last year. Round the number of books sold to the nearest ten million. A. 30,000,000 B. 26,000,000 C. 20,000,000 D. 26,270,000

The intelligence of the clones of Jango Fett are deteriorating at a rate that has a standard distribution. If the average I.Q of a clone is 90 with a standard diviation of 2.6, what percent of the clones are smarter than a clone with an I.Q of 85? (round to the nearest hundredth.) % are smarter than a clone with an I.Q of 85.

The power of Darth Vader using the force can lift a speeder 14m off the ground with a thought. The average Sith can lift a speeder 10 meters with a standard deviation of 1.2. This data fits a standard distribution. What is Vader's z-score? (Round to the nearest 10th.) Z= type your answer...

Give the associative property of addition and illustrate the property with an example. Choose the correct answer below. A. For any elements a and b, a+b=b+a. An example of this is 4+7=7+4. B. For any element a, a +(-a)= -a+a=0. An example of this is 2+(-2)=-2+2=0. C. For any element a, a +0=0+a=a. An example of this is 8+0=0+8=8. D. For any elements a, b, and c, (a+b)+c= a + (b+c). An example of this is (3+2)+6=3+(2+6).

A rectangular kitchen has an area of 160 square feet. The length is 12 feet more than the width. a. Write an equation that represents the area of the kitchen. b. Find the dimensions of the kitchen by completing the square.

Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20 year period. Recall that r is the monthly rate. Show your work and carefully evaluate the above formula for m.

There are 30 students in a high school senior class. In how many ways could the yearbook choose the winners of Most Athletic, Class Clown, and Best School Spirit?

The population is decreasing at a rate of 4 % per year. If the population is 28,000 today, what will the population be in 12 years? Round your answer to the nearest whole number, if necessary.

Consider the parabola given by the equation: f(x) = 4x² – 10x-4 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas:

A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 121 feet long and makes an angle of 62° with the ground. The other rope is 115 feet long. What is the distance between the points on the ground at which the two ropes are anchored (just give one of the answers rounded to the nearest whole number)?

Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?

The HMS Sasquatch leaves port on a bearing of N29°E and travels for 7 miles. It then changes course and follows a heading of S31°E for 4 miles. How far is it from port? Round your answer to the nearest hundredth of a mile. What is its bearing to port? Round your angle to the nearest degree. Distance = miles Bearing with angle rounded to the nearest degree is ?

Given the vector u equal to 5 (cos 255°, sin 255°) and vector v equal to 7 (cos 150°, sin 150°), find the sum u + v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree, 0° ≤0 < 360°.

The Marvel Costume Design Workshop employs 65 people. Eight of the 30 men and 21 of the 35 women work in the business office. What is the probability that an employee picked at random is a woman or works in the business office? A. 64/65 B. 21/65 C. 43/65 D. 10/13 E. 51/65

Consider the curve: y = 1-csc(2 (x-π)) (a) State the period of this curve. (b) State the phase shift of this curve, and whether it is to the right or to the left. (c) Sketch a sequence of 5 small separate graphs carefully labeled over a single period starting with y = sin(x) for x ∈[0,2π], moving one change at a time through 3 intermediate curves, and ending with the curve above, as we have done in class.

Brenda cuts her grass every 10 days and trims her shrubs every 24 days. If Brenda cut her grass and trimmed her shrubs on June 1, how many days will it be before she cuts her grass and trims her shrubs on the same day again? It will be days before Brenda cuts her grass and trims her shrubs on the same day again.

This question is not about solving the stated problem, but about understanding it. A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t) = 4.9t² + 1300t + 170. a) From what height was the rocket launched? b) What is the maximum height the rocket reaches? c) If the rocket will splash down in the ocean, when will it splash down?

The sales in thousands of a new type of product are given by S(t)=180-50 e -0.3t, where t represents time in years. Find the rate of change of sales at the time when t=3. Round to the nearest tenth. A. 6.1 thousand per year B.-36.9 thousand per year C.-6.1 thousand per year D. 36.9 thousand per year

Juan is going to invest $1,700 and leave it in an account for 14 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Juan to end up with $3,700?

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 4x-x². What rainfall produces the maximum number of mosquitoes? A. 16 inches B. 0 inches C. 2 inches D. Maximum number of mosquitoes does not exist E. 4 inches

Suppose the supply and demand for a certain DVD are given by p=1/6 q2 and p = -1/6q2+44, respectively, where p is price and q is quantity. Find the equilibrium price. A. $26 B. The supply and demand curves do not intersect. C. $24 D. $21 E. $22

Alexa invested $54,000 in an account paying an interest rate of 4% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $106,200?

Find the probability of the given event. A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. A randomly drawn marble is not blue. A. 6 B. None of these C. 1/2 D. 3/2 E. 1/3

Find the mean of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary. 22, 29, 30, 35, 18, 30, 31, 24, 28, 25, 25

At the beginning of an experiment, a scientist has 180 grams of radioactive goo. After 255 minutes, her sample has decayed to 5.625 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t)= How many grams of goo will remain after 17 minutes?

If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p = 66- x/36. How many bolts must be sold to maximize revenue? A. 1,188 bolts B. 2,376 bolts C. 1,188 thousand bolts D. 2,376 thousand bolts

Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?

If g(x) = 1/3 x3 + 2 1/4x²-5x and h(x) = 1 2/3x3 -3/4x2-3x then g(x) + h(x) = A) 11/3x3+3x²-2x B) 1 1/3x3-3x²-8x C) 2׳ +1 1/2x²-8x D) 2x³ + 1 3/4x² - 2x

The height y (in feet) of a ball thrown by a child is y=-1/14 x² + 2x + 3 where is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? feet (b) What is the maximum height of the ball? feet (c) How far from the child does the ball strike the ground? feet

Bella is going to invest $94,000 and leave it in an account for 9 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Bella to end up with $156,000?

From 1983 to 2003, the number B of federally insured banks could be approximated by B(t) = 322.6t+13787 where t is the year and t=0 corresponds to 1983. How many federally insured banks were there in 1988? Find the slope of the graph of B. Interpret this slope as a rate of change. Choose the correct answer below. The number of banks increased by 12174 banks per year The number of banks decreased by 322.6 banks per year The number of banks increased by 322.6 banks per year The number of banks decreased by 13787 banks per year The number of banks decreased by 12174 banks per year The number of banks increased by 13787 banks per year Find the y-intercept of the graph of B. The y-intercept is Interpret the y-intercept. Choose the correct answer below. The y-intercept is the maximum number of banks allowed in the country The y-intercept is the number of banks in 1983 The y-intercept is the minimum number of banks allowed in the country The y-intercept is the number of banks in 1988 The y-intercept is the number of banks in 2003

Police use the formula: v = √20L to estimate the speed of a car, v, in miles per hour, based on the length, L, in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 208 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit. Answer: The car was traveling at approximately miles per hour.

Find the volume of a hemisphere with a great circle circumference of 37.7 centimeters. r= V =

In a high school basketball team there are 12 students competing to start a game. If 5 students can be chosen to start a game, how many different starting lineups can be formed from this group of 12 students? 3,991,680 95,040 120 792

Use the first derivative test to determine the location of each local extremum and the value of the function at that extremum. f(x) = (7-5x)4/3 +7 A. Local minimum at (7/5,7) B. Local minimum at (0,7) C. Local maximum at (7/5,7) D. No local extrema

Anne and Nancy use a metal alloy that is 18. 141% copper to make jewelry. How many ounces of an alloy that is 14% copper must be mixed with an alloy that is 25%, copper to form 85 ounces of the desired alloy? Round to the nearest whole number. A. 53 ounces B. 37 ounces C. 55 ounces D. 32 ounces

On the planet of Endor, the Ewoks are building a trebuchet to attack the Storm Troopers. The test their new weapon and decided it can launch 100 kgs of rocks 50 meters, with a margin of error of 7 meters. What is the range of the rocks they can throw?

Dylah is going to invest in an account paying an interest rate of 4.1% compounded continuously. How much would Dylan need to invest, to the nearest cent, for the value of the account to reach $19,000 in 7 years?

A driver filled the gas tank and noted that the odometer read 57,491.9. After the next filling, the odometer read 57,838.4. It took 17.5 gal to fill the tank. How many miles per gallon did the driver get? The driver got mpg. (Type a whole number or a decimal.)

In one state lottery game, you must select four digits (digits may be repeated). If your number matches exactly the four digits selected by the lottery commission, you win. a) How many different numbers may be chosen? b) If you purchase one lottery ticket, what is your chance of winning? a) There are different numbers that can be chosen. (Type a whole number.) b) There is a chance of winning. 1 in 10,000 1 in 9999 1 in 6561 1 in 100 1 in 1000

Minimize the following objective function subject to the given constraints. Find the corner points and state the minimum. Minimize: z = 10x + 4y subject to 2x + y ≥ 8 x + 3y ≥ 9 x≥0, y≥0 A. Corner Points: (8, 0), (0, 9), (3, 2) Minimum: 38 B. Corner Points: (0, 3), (4, 0), (3, 2), (0, 0) Minimum: 0 C. Corner Points: (0, 8), (9, 0), (2, 3) Minimum: 32 D. Corner Points: (8, 0), (0, 9), (2, 3) Minimum: 32 E. Corner Points: (0, 8), (9, 0), (3, 2) Minimum: 32

Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 5 ? (mod 9) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The positive number replacement(s) (less than the modulus) for the question mark is(are) (Use a comma to separate answers as needed.) B. There are no positive number replacements (less than the modulus) for the question mark that make the statement true.