Basic Math Questions and Answers

Diana has 440 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

A right circular cone is shown. The base of the cone is a circle with the center at point A. The distance from point A to point C is 16 inches. The distance from point to point B is 20 inches. What is the diameter, in inches, of the base of the cone?

It has been said that newspapers are disappearing, replaced by various electronic media. In 2001, newspaper circulation (the number of copies distributed in a day) in a country was about 58 million. In 2011, this ad dropped to 46 million. Assume that the relationship between time, x, and circulation, y, is a linear relationship. Write an equation describing the relationship between time and circulation. Use ordered pairs of the form (years past 2001, number of newspapers circulated in millions). Use this equation to predict newspaper circulation in 2015. The equation describing the relationship is type your answer in slope-intercept form. Use integers or decimals for any numbers in the equation.) million. In the year 2015, the newspaper circulation will be implify your answer. Type an integer or a decimal.)

The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 3 child tickets for a total of $69. The school took in $91 on the second day by selling 5 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?

Solve the system by the method of your choice. x²+2y² = 36 x+y = 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an ordered pair, using integers or simplified fractions for the coordinates. Use a comma to separate answers as needed.) B. There is no solution.

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

The area of a parallelogram is 18 square units. One side of the parallelogram is 24 units long. The other side is 6 units long. Which could be the parallelogram's height? Select all that apply. A 3/4 units B 4/3 units C 3 units D 4 units E 12 units

A 300. L kiln is used for vitrifying ceramics. It is currently operating at 1065 °C, and the pressure is 0.9250 atm. How many moles of air molecules are within the confines of the kiln?

Determine if the conclusion follows logically from the premises. All children are energetic. Some actors are children. Therefore, some actors are energetic. Valid argument Invalid argument All flowers need water. Roses need water. Therefore, roses are flowers. Valid argument Invalid argument

When factoring, which of of the following is the rule we follow? We just guess until we get something that works. We find what multiplies to "c" and adds to "b" We find what multiples to "a" and adds to "b" We find what multiples to "b" and adds to "c"

Describe and correct the error a student made when graphing y +5=-3/4(x-8)

Find the roots of the quadratic function: f(k)= 2k² - 3k - 9.

Graph the line through the point (0, -3), having a slope of 3/4

The mathematics faculty at a college consists of 4 professors, 7 associate professors, 5 assistant professors, and 9 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.

Supply a conclusion to make each argument valid. 1. All shrimp are appetizing. Tiger is a shrimp. Therefore, Tiger is appetizing. 2. All flowers smell good. All things that smell good are tasty. Therefore, all flowers are tasty. 3. No New Yorker likes pecan pie. All Southerners like pecan pie. Select an answer 4. All sailors are big spenders. No big spenders are miserly. Select an answer 5. All violets are blue. Some flowers are violets. Select an answer

A company found that an experienced surveyor can survey a roadbed in 5 hours. An apprentice surveyor needs 8 hours to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.

A figure containing STU is dilated by a scale factor of 2/3 to form a new figure which contains S'T'U'. STU measures 140°. What is the measure of S'T'U'?

Solve the system by the substitution method. x+y = - 12 y = - 4x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. C. There is no solution.

Maya arranges some tiles in different arrays. One array has 4 rows with 3 tiles in each row. The other array has 2 rows with 6 tiles in each row. Maya says that she can use the Commutative Property of Multiplication to show that the arrays both have 12 tiles. Is she correct? Explain.

A ferris wheel is 15 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y = What is the Period? How High are you off of the ground after 4 minutes?

Kimani plans to paint the background of a mural on a wall in her school's cafeteria. The mural will be in the shape of a parallelogram. One quart of paint covers 100 square feet. How many quarts of paint does Kimani need? Show your work.

Use a transformation of the graph of y=x4 to graph the function. f(x) = (x+2)4 Which transformation is needed to graph the function f(x) = (x + 2)4? Choose the correct answer below. A. The graph of y=x4 should be shifted vertically up 2 units. B. The graph of y=x4 should be shifted horizontally left 2 units. C. The graph of y=x4 should be shifted vertically down 2 units. D. The graph of y=x4 should be shifted horizontally right 2 units.

An object is dropped from a tower, 163 ft above the ground. The object's height above ground t sec into the fall is s=163-161². a. What is the object's velocity, speed, and acceleration at time t? b. About how long does it take the object to hit the ground? c. What is the object's velocity at the moment of impact?

plot the intercepts to graph the equation. 3x-6y=-6

Solve the system by the method of your choice. x²+2y² = 324 x+y = 18

A pencil cup with a capacity of 40 in.3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 12¢/in.² and the material for the base costs 49¢/in.2, what should the dimensions of the cup be to minimize the construction cost (in ¢)? Round your answer to two decimal places, if necessary.

A rectangular picture frame measures 20 cm by 30 cm. A matte is made of uniform width to go inside the frame and make a nice border for the picture. The area of the matte is to be equal to the area of the picture. What is the width of the matte?

Every week at the Cougar Scouts meeting, Jenna is in charge of the craft activity. This week, she decides to make pinecone bird feeders. At the meeting, Jenna divides a bag of birdseed evenly among 15 Cougar Scouts, and each scout gets 1/3 of a cup of birdseed. Use an equation to find the amount of birdseed in the bag .

A plane can fly 1260 miles in the same time as it takes a car to go 420 miles. If the car travels 120 mph slower than the plane, find the speed of the plane. Using r as your variable to represent the speed of the plane in miles per hour, write an equation using the information above that can be solved to find the answer to this problem.

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 0.01x -0.02y = 0.006 0.03x -0.04y = 0.06 Select one: a. {(-4.8, -2.1)} b. {(4.8, 2.1)} c. { }; The system is inconsistent. d. {(x, y) 1 0.01x -0.02y = 0.006); The equations are dependent.

The famous iris dataset (the first sheet of the spreadsheet linked above) was first published in 1936 by Ronald Fisher. The dataset contains 50 samples from 3 iris species: setosa, virginia, and versicolor. Four features are measured, all in cm: sepal length, sepal width, petal length, and petal width. What is the equation for the least square regression line where the independent or predictor variable is petal length and the dependent or response variable is petal width for iris setosa?

5 1/4 yards of ribbon cost $9.17.

Jim began a 209-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 9 hours. If Jim walks at a rate of 3 miles per hour and rides at 31 miles per hour, find the amount of time he spent on the bicycle.

A car travels 292 miles in the same time that a motorcycle travels 252 miles. If the car's speed is 10 miles per hour more than the motorcycle's, find the speed of the car and the speed of the motorcycle.

For log430, (a) Estimate the value of the logarithm between two consecutive integers. For example, log2 7 is between 2 and 3 because 2² <7<2³. (b) Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. (c) Check the result by using the related exponential form.

Of the cartons produced by a company, 8% have a puncture, 5% have a smashed corner, and 0.8% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed comer.

Answer the questions below about the quadratic function. g(x)=2x² + 12x+22 Does the function have a minimum or maximum value? What is the function's minimum or maximum value? Where does the minimum or maximum value occur?

Justin notices that his electric bill reflected a monthly fee of $40 as well as a charge of $0.0743 kilowatt-hour of electricity used. a) Write a function that will help Justin determine the monthly cost of his electricity bill.

The Football Boosters bought pizza for $900 to sell at the game. They kept 10 pizzas to feed the players after the game and sold the rest for $1040. There were 8 slices in each pizza. Their profit was 50 cents a slice a) How many pizzas were in the original order? What was the original price of each pizza? b) What did they charge per slice? c) If they bought plain cheese pizza, the original price would be $10 per pizza. What would this make their profit be per slice if they sold it for the same price as before and still saved 10 pizzas for the players?

For the function f(x)=2x-9, determine whether f(x) is one-to-one. If so, (a) write an equation for the inverse function in the form y=f(x). (b) graph fand f¹ on the same axes, and (c) give the domain and the range of f and if the function is not one-to-one, say so.

Bridget wants to purchase a mix of candy. She decides to make a mix of jelly beans worth $18 per kg and chocolate worth $21 per kg. Together, she gets 84 kg of the mixture worth $19 per kg. How many kg of each type of candy did she buy?

Susan invested her savings in two investment funds. The $12,000 that she invested in Fund A returned a 10% profit. The amount that she invested in Fund B returned a 3% profit. How much did she invest in Fund B, if both funds together returned a 6% profit?

What is the relationship between the value of the 4 in the circle and the value of the 4 in the square in the number above?? A. The value of the 4 in the circle is 10 times the value of the 4 in the square. B. The value of the 4 in the circle is 100 times the value of the 4 in the square. C. The value of the 4 in the circle is 1/100 the value of the 4 in the square. D. The value of the 4 in the circle is 1/100 the value of the 4 in the square.

The height of an object t seconds after it is dropped from a height of 300 meters is s(t) = -4.9t² + 300. (a) Find the average velocity of the object during the first 6 seconds. (b) Use the Mean Value Theorem to verify that at some time during the first 6 seconds of fall, the Instantaneous velocity equals the average velocity. Find that time

Suppose that after a company introduces a new product, the number of months before its market share is x percent is given by m = 20 In ( 40/40 - X), where x < 40. After how many months is the market share more than 37%, according to this model?

From an elevation of 4.5 m below the surface of the water, a dolphin dives at a rate of 1.6 m/s. What is the function rule for this if the dolphin's depth, d, and time, t? A d = (-4.5)t + (-1.6) · B d = (-1.6)t + (-4.5) C d = (-1.6t) + 4.5 D d = 1.6t+ 4.5

their annual reunion should take place, they found that out of all the family members, 7 would not go to a park, 7 would not go to a beach, 9 would not go to the family cottage, 2 would go to neither a park nor a beach, 3 would go to neither a beach nor the family cottage, 4 would go to neither a park nor the family cottage, 1 would not go to a park or a beach or to the family cottage, and 1 would go to all three places. What is the total number of family members? There are total family members. (Simplify your answer.)

The flight path of a rocket, launched from the ground, is modeled by y = 0.25(60x-x²), where y is the height of the rocket in meters from the ground and x is the time in seconds after it was launched. Find the vertex of the parabola and explain what it represents in terms of the context. (30, 225); rocket reaches maximum height of 225 feet after 30 seconds (60, 0); rocket lands at 0 feet after 60 seconds (30, 225); rocket reaches maximum height of 30 feet after 225 seconds (60, 0); rocket reaches 60 feet after 0 seconds

Diana has 160 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

A ball is inside a glass case in the shape of a cube. The diameter of the ball and length of the glass case are both 3.4 cm. What is the volume of the air outside the ball that is inside the glass case? Use the π button on your calculator.