Basic Math Questions and Answers

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

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 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.

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)]

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.

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 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?

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?

A principal of $3300 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 6 years? Use the calculator provided and round your answer to the nearest dollar.

You're constructing a ball pit for a local preschool. You find online that a circular ball pit with diameter 5 feet and depth 3 holds 456 balls. You want to build a 7 by 9 by 3 rectangular ball pit. How many balls will that ball pit hold? Round your answer to the closest whole number.

One hundred students out of 1100 at a school were surveyed. The results are recorded in each problem below. For the statements below, predict the number of students in the population that would answer similarly. Thirty-two students said they drove to school. Show the setup of the problem (blank 1) and the answer (blank 2). Blank # 1 Blank # 2

Mr. and Mrs. Steele deposited $8,000 to open a college savings account for their granddaughter on the day she was born. The account pays 5% simple interest annually. If they made no other deposits or withdrawals since then, how much money would be in the account after 18 years? A $7,200 B $8,000 C $15,200 D $19,253

Coast Guard Station Able is located L=120 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E.

The square root of 105 would lie between which two consecutive integers? A 9 and 10 B 10 and 11 C 104 and 106 D 9 and 11

Suppose the demand function for a product is given by the function: D(q)=-0.012q + 52.8 Find the Consumer's Surplus corresponding to q = 3, 700 units. (Do not round the results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4, 400.)

A water tank is in the shape of a cylinder with a height of 21 feet and a diameter of 8 feet. What is the volume, in cubic feet, of the water tank? 352 cubic feet 1,056 cubic feet 4,224 cubic feet 5,544 cubic feet

Find the flux of the vector field F (y, — z, x) across the part of the plane z = 2 + 4x + y above the rectangle [0, 4] × [0, 5] with upwards orientation.

Use the right triangle shown in the figure. Then, using the given information, solve the triangle. a=13, b=4; find c, A, and B

Let f be a scalar field (a function) and F a vector field. For each expression, decide first if it's meaningful, and if so, whether the result is a scalar field or vector field.

The current balance in Marianne's savings account is $525. The account pays 3.5% compounded annually. If she makes no deposits or withdrawals for the next 4 years, her savings account balance will be- A $588.00 B $590.89 C $598.50 D $602.45

A Formula 1 race car is re-created as a toy car, reduced by a scale of 1/12. If the model version is 7.8 cm tall, how tall is the race car? Hint: take note of the units a. 0.75 m b. 1.13 m c. 0.94 m d. 0.56 m

An equilateral triangle is shrinking, with its area decreasing at a rate of 2 m² per hour. The rate at which a side length of the triangle is changing, at the moment when the side length is 66 m, is: m/sec

The radius and height of a cylinder are multiplied by 5. What is the effect on the volume? None of the other answers are correct The volume is multiplied by 125. The volume is multiplied by 1/5. The volume is multiplied by 5. The volume is multiplied by 25.

The radius of the moon is about 1.738 megameters. The formula for the volume of a sphere is V = 4/3πr³. Approximately what is the volume of the moon? (Use 3.14 as an approximation for pi.) 2.75 cubic megameters 5.49 cubic megameters 12.64 cubic megameters 21.98 cubic megameters

A 124 foot fir tree and a 70 foot redwood were growing side by side in northern California. The fir is growing at the rate of 3.2 feet per year. The redwood grows at the rate of 6.2 feet per year. When will the redwood pass the fir in height?

The total cost of attending a state university is $18,500 for the first year. Stephen's grandparents will pay one-half of this cost. A football scholarship will pay another $7,000. Which amount is closest to the minimum that Stephen will need to save every month in order to pay off the remaining cost at the end of 12 months? A $2,250.00 $187.50 $958.33 $770.83

The time, t (in minutes), you need to type a certain paper varies inversely with the rate, r (in words per minute), that you can type. When typing 40 words per minute, you can finish in 50 minutes. Find the constant of proportionality and write an equation relating t and r. t = ?/?

Michelle has a balance of $950 in a savings account that pays 3% interest compounded annually. If Michelle makes no deposits or withdrawals, how much money will be in her savings account after 2 years? A $954.81 B $1,004.00 C $1,007.00 D $1,007.86

The sun produces 3.8 x 10^27 joules of energy per second. How much energy is produced in a year? (NOTE: A year is approximately 31,000,000 seconds, or 3.1 x 10^7) 1.178 x 10^35 1178 x 10^30 11.78 x 10^34 1.178 x 10^34

King Neptune bought 200 shares of a stock at $35.25 a few years ago. His broker charged her a 0.4% commission. He then sold all of his shares at $41.29, using an online broker who charges $18 per transaction. What were King Neptune's capital gains, including broker fees?

Brandon has saved $1,220 for college. He expects the total cost of his first year to be $9,850. He will receive a scholarship for $2,120. How much money should Brandon save each week in order to have enough money in 2 years to pay for his first year of college? A $62.60 C $103.37 B $74.33 D $271.25

Joe Biden and Donald Trump recently went skydiving. Each tested the given pair of hypotheses; Joe Biden committed a Type I error while Donald Trump committed a Type II error. Consequently, one of the skydivers died. Who was it? Explain your reasoning. Ho: My parachute will function properly. H₁: My parachute will not function properly.

Jonathan Deman's income this month is $2000 after taxes. He has $1000 in fixed expenses which include his car payment and rent and $600 in variable expenses including groceries, entertainment and clothing purchases. He deposits $100 in his savings account each month. Suppose that Jonathan's refrigerator breaks during the month and he has to decide whether to repair it for $500 or purchase a new refrigerator on credit for $300 a month over the next year. What should he do? a. He can purchase or repair the fridge now with no changes to his budget b. He does not have enough money to do either of these options c. He has enough money in his budget to repair the fridge, but not to purchase a new one d. He will need to make changes to his variable expenses in order to repair the fridge, but he could buy one on credit and still meet his budget.

A company packages apples by weight. One of the weight grades is Class A apples. Class A apples have a mean weight of 105 g, and there is a maximum allowed weight tolerance of 5% (7.5 g) above or below the mean for apples in the same consumer package. A batch of apples is selected to be included in a Class A apple package. Given the following apple weights of the batch, does the fruit company comply with the Class A grade weight tolerance requirements? Conducts the appropriate hypothesis test at the 1% level of significance. 158 g, 167 g, 149 g, 169 g, 164 g, 139 g, 154 g, 150 g, 157 g, 171 g, 152 g, 161 g, 141 g, 161 g, 172 g