Math Questions

How much heat is required to boil 45.0 g of water at it's boiling point? a. 50.2 J b. 102 J c. 18800 J d. 102000 J

A certain forest covers an area of 3500 km. Suppose that each year this area decreases by 6%. What will the area be after 5 years?

The dollar value v (t) of a certain car model that is t years old is given by the following exponential function. v (t) = 26,000(0.92)^t Find the initial value of the car and the value after 12 years.

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9.50. There was a total of $883.50 in revenue from all ticket sales and the drama club sold 27 more adult tickets than student tickets. Determine the number of student tickets sold and the number of adult tickets sold.

Scott is using a 12-foot ramp to help load furniture into the back of a moving truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck?

In a certain Algebra 2 class of 26 students, 21 of them play basketball and 7 of them play baseball. There are 2 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

A company is considering expanding their production capabilities with a new machine that costs $60,000 and has a projected lifespan of 6 years. They estimate the increased production will provide a constant $11,000 per year of additional income. Money can earn 1.4% per year, compounded continuously. Should the company buy the machine?

A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is 54, the cost per minute is $0.20, and the cost per mile is $1.30. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed $10.30 and remarked that the number of minutes was four times the number of miles. Find the number of minutes and the number of miles for this trip.

A fishbowl shaped like a sphere is filled with water. The fishbowl has a diameter of 16 inches. Which measurement is closest to the volume of water in the fishbowl in cubic inches? A 2,144.66 in.³ B 17,157.28 in.³ C 5,461.67 in.³ D 6,433.98 in.³

Carter bought a pair of shoes online for $64. He used a coupon code to get a 10% discount. The website also applied a 5% processing fee to the price after the discount. How much did Carter pay, in the end?

Given the demand function d(p) = 27 – p², and the supply function s(p) = 6p. Calculate the following: a) The equilibrium price: b) The gains from trade is the sum of the consumer and producer surplus. Calculate the gains from trade

A plane can fly 340 miles in the same time as it takes a car to go 120 miles. If the car travels 110 mph slower than the plane, find the speed of the plane.

A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year. 1. Write an exponential function that models the value y of the car over x years. 2. To the nearest cent, what will be the value of the car after eight years?

An electrician charges a $20 house call fee plus $30 per hour of work. Which equation represents this relationship? A. y=20+30 B. y=20x + 30 C. y = 30x + 20 D. y = 50x

Frederick's salary varies directly with the hours he works. Last week he earned $328.30 and worked 33.5 hours. If he works 35 hours this week, what will be his salary? A $314.23 B $329.80 C $343.00 D $357.14

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 10 hours. How lo it take the pipe to fill the pool if the drain is left open?

Add and/or subtract and then simplify completely: 3p/p²-81 + p/p+9

Subtract and simplify: 7x + 5/5x² - 1x + 5/5x² Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Add and/or subtract and then simplify completely: 4p + 3/p² - 6p+8 + 1/P-4 Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Simplify the expression 2x - 3 / x - 3 + 3 - x / x - 3 and give your answer in the form of f(x) / g(x) Your answer for the function f(x) is : Your answer for the function g(x) is :

Simplify the expression x^2- 8x +12 / x^2- 5x + 6 and give your answer in the form of f(x)/g(x) Your answer for the function f(x) is : Your answer for the function g(x) is:

Tuition for one year at a state university is about $14,000. Denim would like to attend this university and will save money each month for the next 4 years. His parents will give him $6,500 for his first year of tuition. Which plan shows the minimum amount of money Denim must save to have enough money to pay for his first year of tuition? Save $625.00 per month for the next 4 years. Save $156.25 per month for the next 4 years. Save $1,875.00 per month for the next 4 years. Save $250.00 per month for the next 4 years.

A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3121 tickets overall. It has sold 222 more $20 tickets than $10 tickets. The total sales are $58,770 How many tickets of each kind have been sold? How many $10 tickets were sold? How many $20 tickets were sold?

Evaluate the sine, cosine, and tangent of the angle without using a calculator. (If an answer is undefined, enter UNDEFINED.) -135° sin θ = cos θ = tan θ =

Suppose that y varies directly with x, and y=8 when x = 20. (a) Write a direct variation equation that relates x and y. Equation: (b) Find y when x = 7. y =

A lemonade seller calculates that it costs $20 to produce 100 glasses of lemonade and $35 to produce 400 glasses of lemonade. Assume the relationship between the cost and the number of glasses of lemonade produced is linear. Of the choices given, what is the most reasonable estimate for producing 700 glasses of lemonade? $35 $40 $50 $70

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 m/s². If the force is changed to 18 N, what will be the acceleration of the object?

Simplify the expression 5x³ -6x²-8x/6x² - 15x + 6 and give your answer in the form of f(x)/g(x). Your answer for the function f(x) is: Your answer for the function g(x) is:

Suppose a hiker finds himself in a forest 3 miles from the nearest point on a straight road. He wants to walk to his car which is parked 10 miles down the road. He can walk 4 mph along the road, but only 2 miles per hour through the forest. Toward what point, in miles, on the road should he walk in order to reach his car in the least time? Note: Round to the nearest thousandth.

Suppose you had $6.00 to buy bananas and apples. Bananas cost $0.49 per pound and apples cost $0.34 per pound. Write a linear equation that represents the different amounts of fruit you could buy 49x +34y = 300 49x + 34y = 600 None of the other answers are correct 49x - 34y = 600 7x + 17y=300

Given the differential equation dy/dx = 2x^2+5/3y^2, find the particular solution, y = f(x), with the initial condition f(-3) = -2.

Skylar repairs washing machines. Her revenue, in dollars, can be modeled by the equationy = 80 +24x, where x is the number of hours spent repairing microwaves. Her overhead cost, in dollars, can be modeled by the equation y=x²-100, where x is the number of hours spent repairing washing machines. After how many hours does she break even?

Use linear approximation, i.e. the tangent line, to approximate 1/0.103 as follows: Let f(x) = 1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.103. Then use this to approximate 1/0.103.

(a) A star is 5.37 light-years from Earth. If 1 light-year is about 5.9 trillion miles, how many miles is the star from Earth? The star is about miles from Earth. (Simplify your answer. Use scientific notation.) (b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of this star? The parallax of the star is about (Simplify your answer. Round to six decimal places as needed.)

Olive bought a candle for her grandmother. She wants to mail it to her, but she only has $3. It costs $3 to mail a package with the volume of 150 in³. If the candle she bought for her grandma has a diameter of 6 inches and a height of 5 inches, will she have enough money to mail the package? Show your work in the box below to justify your answer.

The equations of three lines are given below. Line 1: 10x-4y=-6 Line 2: y=-2/5x+8 Line 3: 5y=-2x+6 For each pair of lines, determine whether they are parallel, perpendicula Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=40°, and from a second position L = 50 feet farther along this path it is B = 30°. What is the height of the tree? The height of the tree is approximately ft. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Write the equation of a sine function that has the following characteristics. Amplitude: 9 Period: 9π Phase shift: 1/9 Type the appropriate values to complete the sine function. y=sin(x-)

4. Brady deposited $600 into a new savings account that earns 2.5% simple interest. If Brady makes no other deposits or withdrawals, how much interest will the account have earned after 5 years? A $15 B $70 C $75 D $125

The classrooms at Lincoln Middle School are painted every summer. If 7 gallons of paint are needed to paint 4 classrooms, how many gallons of paint are needed to paint 16 classrooms? 20 gallons 24 gallons 32 gallons 28 gallons

Surface area is: a. the amount of matter contained in a three-dimensional object. b. the area covering the surfaces of a three-dimensional object. C. the amount of space occupied by a three-dimensional object. d. the area covered by a two-dimensional object.

A triangular plot of land has one side along a straight road measuring 289 feet. A second side makes a 62° angle with the road, and the third side makes a 56° angle with the road. How long are the other two sides? The longer side of the triangular plot is feet. The shorter side of the triangular plot is feet. (Round to the nearest hundredth as needed.)

The equation x² + y² - 4x + 2y = b describes a circle. Part A Determine the y-coordinate of the center of the circle. The y coordinate of the center is Part B The radius of the circle is 7 units. What is the value of bin the equation? The value of bis

A local bank offers an investment option with a simple interest rate of 3.60% per annum. If you invest $3200.00, how much interest will you earn in 7 years? a. $967.68 b. $806.40 c. $791.73 d. $645.12

Find the average rate of change of g(x) = -x² + 5x+1 from x=2 to x = 7,

Find the average rate of change of h(x) = 2x²-7x from x = 1 to x = 5.

Decide whether the sampling method could result in a biased sample. Explain your reasoning. A representative of a mall surveys every fifth person walking into an electronics store to ask if they would like there to be a new store that sells audio equipment in the mall.

The slope of a ramp leading into a grocery store is 1:6 What is the angle of elevation of the ramp? Hint: you might have to use trigonometry a. 10.5° b. 80.5° c. 9.5° d. 64.4°

Peter Elzinga is a Dutch competitive archer who was ranked number 1 in the world in 2004. The probability that he makes a bullseye (i.e. a 10 point shot) on any given shot is 0.95. Assuming that the probability of making a bullseye on a given arrow is independent of results on other arrows, what is the probability that Peter Elzinga will make two bullseyes in a row followed by missing the bullseye on the third shot (i.e., the probability of making a bullseye on the first and second shots and something other than a bullseye on the third shot)? Note: Round to the nearest thousandth if necessary.

Suppose that a recent poll found that 64% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 250 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is (Round to the nearest whole number as needed.) The standard deviation of X is. (Round to the nearest tenth as needed.) (b) Interpret the mean. Choose the correct answer below. A. For every 250 adults, the mean is the minimum number of them that would be expected to believe that the overall state of moral values is poor. B. For every 250 adults, the mean is the range that would be expected to believe that the overall state of moral values is poor. C. For every 250 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. D. For every 160 adults, the mean is the maximum number of them that would be expected to believe that the overall state of moral values is poor. (c) Would it be unusual if 148 of the 250 adults surveyed believe that the overall state of moral values is poor? Yes No