Basic Math Questions and Answers

Nathan drew a circle on a grid with a radius of 4 units and the point (2, -1) as its center. Which of the following pairs of coordinates represent points on the circle? A (2,-5) and (6, -1) B. (4,0) and (0,4) C. (8,-4) and (6, -3) D. (2, 3) and (-1, -1)

Which of the following is NOT a characteristic of all parallelograms? a) Diagonal bisect each other b) Diagonals are angle bisectors c) Opposite angles are congruent d) Opposite sides are congruent

The Business Entity Concept means A business is an important legal entity Businesses can be stand alone or combined The entity is an profit earning business The accounting for a business is separate from that of its owners or other businesses .

Your grandparents invested $1500 in a college fund paying 7.2% interest when you were starting first grade. a) What is the equation that you would write to represent this situation? (annual interest, not compounded continuously) b) If you don't pull any money out of the account, how much money will you have when you enter college? Show the equation you used to answer this question. c) If you don't pull any money out of the account, how long will it take to reach $5000? Show your algebraic work.

A new motorcycle costs $5500 and depreciates at a rate of 18 % each year. How many years will it be until the motorcycle is worth $1000? (round to the nearest 3 decimal places)

Pietro is planning a patio using paving stones that are circles, semicircles, and quarter-circles. All stones have a radius of 10 inches. What is the area of one pattern of stones that has 5 circles, 10 semicircles, and 100 quarter-circles? Then, select the total area. total area= 8,164 in² 5 circles = 1,570 in² total area = 10,990 in² 5 circles= 2,198 in² 10 semicircles = 1,570 in² 100 quarter circles= 2,826 in² 100 quarter-circles = 7,850 in² 10 semicircles= 2,198 in²

Diane buys candy that costs $4 per pound. She will spend more than $20 on candy. What are the possible numbers of pounds she will buy? Use p for the number of pounds Diane will buy. Write your answer as an inequality solved for p.

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?

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

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?