Math Questions

A cone and a cylinder have the same radius and height. The volume of the cone is 100m cubic feet. What is the volume of the cylinder?

Which classification describes the following system of equations? 5x+y+2z-13 4x+3y+6z=17 x+2y=4 inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent

If the Laffite family deposits $8,500 in a savings account at 6.75% Interest, how much will the account make after 25 years if it is compounded... a) monthly? b) weekly? c) continuously?

Your credit card company uses the Unpaid Balance Method. Determine the finance charge at the end of the month for the following of transactions. Assume the interest rate is 12%. Previous Balance: $275.48 New Purchases: $429.95 . Return Credit: $106.99 Payment: $200.00

Which line is perpendicular to the line y = −1/2 x - 5 and passes through the point (-3, 2)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = − 3/4 x + 1, you would type your answer as y=(-3/4)x+1

What is the sales tax on a jacket priced at $325 if the sales tax rate is 7%? The sales tax is $.

Use Newton's method to approximate a root of the equation 3 sin(x) = x as follows. Let x1 = 2 be the initial approximation. The second approximation 2 is and the third approximation is

A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid? Select all that apply. A. a right triangle with one side 5 inches and the hypotenuse 13 inches. B. a 4-inch by 9-inch rectangle C, a circle with radius 4 inches D. a 3-inch by 4-inch rectangle E. a hexagon with an area of 36 square inches F. a square with side length 6 inches

A Toyota dealership receives a new shipment of Camrys and puts a sticker price of $23,485 in the window of each car. They arrived at this figure by marking up their cost for each car by 22%. What was the original cost that the dealership paid for the cars?

Boyle's law states that the volume of a gas varies inversely with applied pressure. Suppose the pressure on 60 cubic meters of gas is raised from 1 atmosphere to 3 atmospheres. What new volume does the gas occupy?

A town has an area of 10.4 mi². The town's population is 3619. What is the population density of the town? Round your answer to the nearest whole number. 37,368 people/mi² 348 people/mi² 1122 people/mi² 362 people/mi² None of the other answers are correct

According to Cavalieri's Principle, which pair of shapes would have equal volumes? A. a cylinder and a sphere with the same radius B. a cone and a pyramid with equal base areas and heights C. a cone and a cylinder with equal base areas and heights D. a cylinder and a right rectangular prism with equal heights

Carmen and Adela each spend the same amount of money at the dollar store. Carmen buys 3 bracelets and spends another $1.50 on candy. Adela buys one bracelet and a $5.00 hat. How much does one bracelet cost? A $1.17 B $1.50 C $1.75 D $2.00

Suppose you earn 3% on a $1,200 deposit for 5 years. Explain how the simple interest is affected if the rate is increased by 1%. What happens if the time is increased by 1 year?

Emily and Heather each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Emily spent $140 on 7 ft of grass sod and 10 geraniums. Heather spent $135 on 10 ft2 of grass sod and 5 geraniums. What is the cost of one ft2 of grass sod and the cost of one geranium?

An ant colony is growing according to an exponential growth model. The initial population of ants is 80 and after one day there are 92 ants. how many ants will be present after 30 days? * Approximately

Marcus finds that (3x² – 2y² +5x)+(4x² +12y²-7x) - 7x² - 10y²– 2x What error did Marcus make? He combined the terms 5x and -7x incorrectly. He combined the terms 3x² and 4x² incorrectly. He combined the terms -2y2 and 12y2 incorrectly. He subtracted the polynomials instead of adding.

Hector plays a game with a friend. They pay $1 and roll a 6-sided die. If the die comes up a number that is larger than 2, they win $7. If it doesn't, they win nothing. What is the expected value of the game? Give your answer to the closest cent (two decimal places).

Sani has at least 68 envelopes to address. He has addressed 17 of them. Write and solve an inequality that describes how many more envelopes, at most, Sani has left to address. n+ 172 68; n ≥ 85 n+ 17> 68; n> 51 n+ 17 ≤ 68; n ≤ 51 n+172 68; n ≥ 51

When treated with an antibiotic, 91% of all the dolphins are cured of an ear infection. If a group of 38 dolphins are treated with antibiotics, how many cured dolphins should be expected? The expected number of cured dolphins is

A county has a population density of 257 people per square mile. The county population is 4288. What is the area of this county? Round to the nearest square mile if necessary. None of the other answers are correct 1,102,016 mi² 283,218,112 mi² 6.5 mi² 16.7 mi^2

The geographic area of California is 1.637 x 105 sq. mi. The population of California, as of 2012, is approximately 3.804 x 107. What is the population density of California?? Note: Population/land area = population density. 232 per sq mi. 544 per sq mi. 3804 per sq mi. 1637 per sq mi

Central School is hosting a "Central Has Talent" show. They will award various prizes for the best 3 acts in the show. First place wins the most money, and each subsequent place after 1st wins $50 less than the previous place. Let x equal the amount of money first place wins. Which of the following expressions represents the total amount of prize money? Select all that apply.

Identify if the system of linear equations is parallel, perpendicular, coincident, or intersecting but, not perpendicular (IBNP). y = -3x = −3x − 2 Coincident Parallel IBNP Perpendicular

A company currently sells 905 units per year of a particular product, and sales are growing at a rate of 8% each year. How many years will it be until they are selling 3,218 units per year? Give your answer to two decimal places.

Write each power of 1+i in the form a + bi, where a and b are real numbers. If a or bis zero, you can ignore that part of the number. For example, 0+3i can simply be expressed as 3i. a. (1 + i)⁰ b. (1 + i)¹ c. (1 + i)² d. (1 + i)³ e. (1 + i)4

Cher is making cupcakes for her class at school. She already has 12 cupcakes that she made yesterday and her teacher told her that she can bring fewer than 82 cupcakes into her class tomorrow. If each batch makes 8 cupcakes, what are the possible numbers of batches of cupcakes that Cher can make today for her class to be following the teacher's guidelines? Write an inequality to represent the number of possible batches Cher might make today. Use x for the variable.

Ruth's grandmother gave her a beautiful hand-carved cedar chest for storing sweaters. The chest is shaped like a rectangular prism and has a volume of 12 cubic feet. It is 3 feet long and 2 feet wide. Which equation can you use to find how deep the chest is, d? How deep is the chest?

The length of a rectangular picture is 5 inches more than three times the width. Find the dimensions of the picture if its perimeter is 74 inches.

A study determined that 9% of children under 18 years of age live with their father only. Find the probability that at most 2 persons selected at random from 10 children under 18 years of age lived with their father only.

A principal of $800 is placed in a savings account at 3.5% compounded annually. Use your equation to find how much money will be in the account after 6 years

A system has two linear equations with two variables. The graphs of the equations have the same slope and same y-intercepts. How many solutions does the system have? The system has infinite solutions because the equations are parallel. The system has one solution because the equations are perpendicular. The system has infinite solutions because the equations are intersecting, but not perpendicular. The system has one solution because the equations are coincident. The system has no solution because the equations are perpendicular. The system has no solution because the equations are coincident.

Find the center and radius of the circle given the equation below. Write the center as an ordered pair and the radius as a number. (x + 6)² + (y + 6)² = 9

Abigail Henderson has $2130.00 budgeted for spending money on an upcoming trip to Country A and Country B. Country A's currency is trading at $1.40 per currency A, and Country B's currency is trading at $1.50 per currency B. She plans to spend more time in Country A, so she wants to have four times as much of currency A as currency B. Set up and solve a system of equations to model this problem, and explain what the answer means in practical terms

Given the system of equations 2x - 3y - 9z = -15 x + 3z = -3 - 3x + y - 4z = 12 (a) determine whether the system is inconsistent or dependent; Your answer is (input inconsistent or dependent) (b) if your answer is dependent in (a), find the complete solution. Write and y as functions of z. x = y =

The standard IQ test has a mean of 101 and a standard deviation of 16. Determine the required sample size if we want to estimate the population mean with 98% confidence to within 4 IQ points of the true mean. 87 1 10 188

Use Newton's Method to estimate a root of the function f(x) = 5x + 2 - ex Use the initial estimate x1 = 0.5: x1 = 0.5 x2 x3 X4 X5 = x6 X7

The equation models the position and range of a tornado alert siren. Describe the position and range of the siren. (x+6)² + (y-8)² = 144 The position of the alert siren is

Suppose that the delivery times for a local pizza delivery restaurant are normally distributed with an unknown mean and standard deviation. A random sample of 24 deliveries is taken and gives a sample mean of 27 minutes and sample standard deviation of 6 minutes. The confidence interval is (24.47, 29.53). Find the margin of error, for a 95% confidence interval estimate for the population mean.

A survey of the community is conducted by asking the first 25 persons passing through the entrance gate to the football field if the school should drop the sports programs.

Timothy wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each 75 randomly selected students in the school. What is the statistic? the 75 randomly selected students the mean number of siblings for all students in the school the mean number of siblings for the randomly selected students the specific number of siblings for each randomly selected student all the students in the school

2/3 x 7 = 2/3 x 7/1 = 14/3 = 4 2/3 Multiply: 7 x 2/3 =

Given P(A) = 0.36, P(B) = 0.2 and P(An B) = 0.122, find the value of P(AUB), rounding to the nearest thousandth, if necessary.

A student of elite distance runners found a mean body weight of 63.1 kg, with a standard deviaiton of 4.8 kg. What proportion of runners have body weights below 60 kg? Round your answer to the nearest integer.

Two kickers are having a kicking competition to see who kicks farther. Bill kicks his ball with an initial velocity of 70 ft/sec at an angle of 38. Ben kicks his ball with an initial velocity of 63 ft/sec at an angle of 45°. Which kicker kicked the ball farther? Justify your answer.

William Base's employer withheld $16772 in federal income tax. After completing his return, William determined that his tax responsibility is $11814. Will William get a refund or does he owe the government money?

The functions fand g are defined as follows. f(x)=-3x³-2 g(x)=-3x+2 Find f(-3) and g (5).

The volume of a box, V(x), is represented by the function V(x) = x(20-2x)(302x), where x represents the width of the box. What is the domain of V(x)? A. all real numbers greater than 0 B. all real numbers greater than 0 and less than 10 C. all real numbers greater than 0 and less than 15 D. all real numbers greater than 0 and less than 20 E. all real numbers greater than 0 and less than 30

Mike needs to buy a water tank. The tank must fit inside a storage box that is shaped like a cube with the side lengths of 30 feet. Water tanks are available in cylinders, cones, square pyramids, and spheres. Mike wants to buy the tank that has the largest capacity.

A data set list the number of olives on each pizza ordered in the last few hours at a pizza shop. For this data set, the minimum is 4, the median is 16, the third quartile is 19, the interquartile range is 4, and the maximum is 20. Construct a box plot that show the number of olives. Submit a jpg file (picture) of your box plot.