Math Questions

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.

You have 4500 cubic centimeters of wax. How many cylindrical candles can you make from the wax if each candle is 15 centimeters tall and has a diameter of 10 centimeters? None of the other answers are correct 0 3.8 3 4

A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S=0.60M+ 14.95, where Mis the number of miles driven. The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I = 0.25M-3.70. Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

A random sample of house sizes in major city has a sample mean of 1204.9 square feet and a sample standard deviation of 124.6 square feet. Use the Empirical rule to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 square feet. Round your answer to the nearest whole number (percent).

A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury. The charge E (in dollars) to rent an economy car is given by the function E= 0.70M+ 14.95, where Mis the number of miles driven. The charge I (in dollars) to rent a luxury car is given by the function L = 1.05M+17.30. Let C be how much more it costs to rent a luxury car than an economy car (in dollars). Write an equation relating C to M. Simplify your answer as much as possible.

A laundry detergent company's 32-ounce bottles pass inspection 98/100 of the time. If the bottle does not pass inspection, the company loses the unit cost for each bottle of laundry detergent that does not pass inspection, which is $3.45. If 800 bottles of laundry detergent are produced, about how much money can the company expect to lose?

Analyze the polynomial function f(x) = (x+8)2 (1-x) using parts (a) through (e). (a) Determine the end behavior of the graph of the function.

expression can be used to find the difference of the polynomials? (10m – 6) – (7m – 4) [10m +(-7m)] + [(-6) + 4] (10m + 7m) + [(−6) + (−4)] [(-10m) + (-7m)] + (6 + 4) [10m +(-7m)] + [6 + (−4)]

Nine hundred (900) high school freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (GPA) was 2.7, and the standard deviation was 0.4. What is the margin of error, assuming a 95% confidence level? (round to the nearest thousandths place)

Austin will donate up to $460 to charity. The money will be divided between two charities: the City Youth Fund and the Educational Growth Foundation. Austin would like the amount donated to the Educational Growth Foundation to be at least three times the amount donated to the City Youth Fund. Let x denote the amount of money (in dollars) donated to the City Youth Fund. Let y denote the amount of money (in dollars) donated to the Educational Growth Foundation. Shade the region corresponding to all values of x and y that satisfy these requirements.

Which line is perpendicular to the line y = x + 5 and passes through the point (-7, 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

Solve the equation x/3x9 -2 = 1/ x-3 Does the equation have a solution? Input Yes or No here: If your answer is Yes, input your solution here: x =

The circumference is 2.6 mm. Area in in decimal form: ____ A ≈ 8.16 cm² A ≈ 5.31 mm² A ≈ 16.33 cm² A ≈ 21.23 cm²

Find the area of the circle. Find the solution into decimal form rounded to the nearest hundred. The circumference is 0.67π miles. A = 1.13 mi² A = 0.09 m² A = 3.77 mi² A = 1.2 mi² A = 0.28 mi² A = 0.367 mi²

A set of nine data points is shown below. 8, 11, 12, 10, 9, 7, 5, 3, 9 Which statement is true if a tenth data point of 45 is added to the data set? The mean and median will both increase. The mean will increase and the median will decrease. The mean will increase and the median will remain the same. The mean and median will both decrease.

For the following function, one zero is given. Find all the others. tx)=x³-6x² +10x-8; 1-i The zeros of f(x) are 1-i. __,and ___ (Simplify your answers. Type any nonreal complex zeros first. Type exact answers, using radicals and i as needed.)

The functions and are defined as follows. q(x)=3x-2 r(x)=-3x-3 Find the value of r(q (2)).

here are two Statistics class in the high school. Andrea is in the AP class with 12 students and Drew is in the regular class with 18 students. If one student from each class will be chosen, what is the probability that both Andrea and Drew will be chosen.

For each data, match the type of data which best fits it. Number of people attending a university football A. Quantitative Continuous game. Favorite color B. Qualitative The weights of apples for sale at the store. C. Quantitative Discrete The number of pairs of shoes that you wear every day. D. Quantitative Discrete The number of people in your household who have have purchased a new phone in the last year.

The equation of a line is given below. 11x+4y=22 Find the X-intercept and the -intercept. Then use them to graph the line. X-intercept: y-intercept:

Suppose that z = z(t) and y = y(t) are both functions of t. If y² + x = 20, and dy/dt = -2 when z = 4 and y = -4, what is dx/dt?

The density of seawater is about 0.001027 kg/cm³. A tropical fish tank measures 50.8 centimeters by 30.5 centimeters by 30.5 centimeters. What is the mass of the seawater in the tank? Round to the nearest hundredth if necessary. 48.53 kg 43.63 kg 47.26 kg 51.19 kg None of the other answers are correct

In a baseball stadium, there is a certain number of fans. In the football stadium down the street, there are 300 more than twice the number of fans in the baseball stadium. There are 16,344 fans combined between the two stadiums. How many fans are at each stadium?

Suppose h" is continuous at x = 5.h' (5)= 0, and h" (5) > 0. What can you say about the behavior of h at x = 5? Inflection point Inflection point at a horizontal tangent Relative (local) maximum Relative (local) minimum

The number of math problems Phaedra has completed varies directly with the amount of time she has been working on homework. She completed 8 in the first 6 minutes. How many will she have completed after 27 minutes? A 20 B 29 C 35 D 36

A phone company offers two monthly plans. Plan A costs $21 plus an additional $0.11 for each minute of calls. Plan B costs $9 plus an additional $0.16 for each minute of calls. For what amount of calling do the two plans cost the same? minutes What is the cost when the two plans cost the same? $0

Ellie is building a dollhouse. She has boards that are two different lengths. A long board is 17 inches longer than the short board. a. Draw a picture showing how the short and long boards are related. The length of the long board is 50 inches. The length of the short board is unknown. b. Write an equation that shows how the length of the long board is related to the length of the short board. Remember to define your variable first. c. Ellie estimates that the length of the short board is between 30 and 40 inches. Test at least three values in this range in your equation. Were any of the values you tested a solution? How do you know? d. What is the length of the short board? Is there more than one possible answer?