Basic Math Questions and Answers

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.

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.

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 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.

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

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.

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