Basic Math Questions and Answers

Consider the line - 6x+7y=4. Find the equation of the line that is perpendicular to this line and passes through the point (1, 5). Find the equation of the line that is parallel to this line and passes through the point (1, 5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Use the frequency histogram to complete the following parts. (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data. classes. (a) There are (Type a whole number.) (b) The least frequency is about (Round to the nearest whole number as needed.) The greatest frequency is about (Round to the nearest whole number as needed.) (c) The class width is (Type an integer or a decimal. Do not round.) (d) What pattern does the histogram show?

The population density of an area can be computed by dividing the total population by the total land area. The population density of Rhode Island is 870.5 people/square mile and the population is 1,055,046. What is the area of Rhode Island?

Make a box-and-whisker plot that represents the data. Describe the plot, in the area provided, by giving Q1,Q2,Q3, and Q4. If there are any outliers be sure to identify them. Newly planted tree heights (in inches): 16, 10, 10, 18, 18, 6, 24, 16

A technical machinist is asked to build a cubical steel tank that will hold 540 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m.

Which of the following is a true statement? a. A horizontal translation changes the x-coordinate of the endpoints of a figure but the y-coordinate remains the same. b. A vertical translation changes the x- coordinate of the endpoints of a figure but the y-coordinate remains the same. c. A horizontal translation changes the y-coordinate of the endpoints of a figure but the x-coordinate remains the same. d. A vertical translation changes both coordinates of the endpoints of a figure.

A space plane skims the edge of space at 4000 miles per hour. Neglecting altitude, if the circumference of the planet is approximately 20,000 miles, how long will it take for the plane to travel around the planet? How long will it take for the plane to travel around the planet? It will take__for a plane to travel around the planet. (Type an integer or a decimal.)

Suppose H (x)= (5x-2)6. Find two functions and g such that (fog)(x) = H (x). Neither function can be the identity function. (There may be more than one correct answer.) ƒ(x) = g(x)=

A plane flying a straight course observes a mountain at a bearing of 30.2° to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time later, the bearing to the mountain becomes 40.2°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)? 7 km 13.1 km 4.7 km 11.5 km

Chris has a job selling newspapers every morning. He receives a base pay of $10 per day and also gets 15 cents for every paper he sells. One morning he made $16.45. How many papers did he sell? A 39 B 43 C 52 D 64

Brent Pickett borrowed $4000 from his brother Dave. He agreed to repay the money at the end of 2 years, giving Dave the same amount of interest that he would have received if the money had been invested at 3.25% compounded quarterly. How much money did Brent repay his brother? Brent repaid his brother $ (Round to the nearest cent as needed.)

Read the sentence. Toni's father taught at two schools, Concordia College and University of Wisconsin-Madison. How does the underlined phrase function in the sentence? as an adverb prepositional phrase as an appositive with essential information as an appositive with nonessential information as an adjective prepositional phrase

A man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $29,000 for 4 years with a simple interest rate of 1.3%. Determine the amount of money the man must repay after 4 years. The man must repay $

Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of inches. If each side were exactly this length, the each side of the square pieces of paper must be approximately equal to area of each square would be square inches.

Which of the deals shown has the lesser unit price? Deal 1: 9 pairs of shorts for $89.01 Deal 2:8 pairs of shorts for $75.92 Choose the correct answer below. A. Deal 1 and Deal 2 have the same unit price. B. Deal 1 has the lesser unit price. C. Deal 2 has the lesser unit price.

A 150-pound person uses 5.1 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 210 calories? minutes in order to use at least 210 calories. A person must walk for at least (Round up to the nearest minute.)

Describe the transformation of f(x) = cosx to g(x) = cosx-4 A. (x) is shifted 4 units right to g(x). B.(x) is shifted 4 units left to g(x). C. (x) is shifted 4 units down to g(x). D. f(x) is shifted 4 units up to g(x).

The function h (t) = -16t(t-7) models the height of an object at any time t after it is launched, where t is measured in seconds. After how many seconds will the object hit the ground? 3.5 seconds 7 seconds 9 seconds 16 seconds

Gaines invested $11,000 in a money market account with an interest rate of 2.25% compounded semiannually. Three years later, Karen withdrew the full amount to put toward the down payment on a new house. How much did Karen withdraw from the account? Karen Karen withdrew $ (Round to the nearest cent as needed.)

You and your friend plan to meet for coffee in a town between your two towns. You both drive at a constant speed for 45 minutes, but your speed is 40 miles per hour and your friend's speed is 35 miles per hour. What is the total distance between your town and your friend's town? Justify your answer.

Suppose you take out a loan of $15,000 where interest on the loan accrues at an APR of 8.4% compounded monthly. a. If the loan is to be paid back in 12 years. What will the monthly payment of the loan be? b. What will the total interest on the loan be?

Use the simple interest formula to determine the missing value. p=$1275, r=?, t=2 years, i=$30.60 r= % (Do not round until the final answer. Then round to one decimal place as needed.)

A certain forest covers an area of 2300 km². Suppose that each year this area decreases by 3%. What will the area be after 13 years? Use the calculator provided and round your answer to the nearest square kilometer.

A cylinder and a sphere both have the same radius, 4. The height of the cylinder is equal to the diameter of the sphere. Select the expression that describes the volume of the cylinder that is not occupied by the sphere. (Use π=3.14) A. 39.67 B. 85.33π-128π C. 124.56 D. 128π-85.33π

A laptop computer is purchased for $2400. After each year, the resale value decreases by 25%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

Your class earned $110.00 Saturday afternoon by washing cars to raise money for a class trip. This is 1/4 of the money needed for the trip. What is the total amount needed? A $114 B $27.50 C $106 D $440

Find the average rate of change of f(x)=x²+3x+1 from x=-4 to x= 1. Simplify your answer as much as possible.

Jamie and Margie need to divide a couch and a hot tub. Using the Method of Sealed Bids, Jamie bids $530 on the couch and $160 on the hot tub, while Margie bids $490 on the couch and $180 on the hot tub. Jamie will get the couch, and Margie will take the hot tub and will also get a little bit of money from Jamie. To make the division fair, how much money will Jamie have to give to Margie?

At a festival, stunt devils are launched in large catapults and air cannons. On one launch, the height of the stunt devil in feet above the ground after t seconds is modeled by y = -16t² + 60t +8. How long does it take the stunt devil to hit the ground? 10.2 sec 15 sec 3.8 sec 16 sec

Determine the total amount and the interest paid on $4000 with interest compounded monthly for 5 years at a) 2%. b) 4%. c) 8%. d) Is there a predictable outcome in either the amount or the interest when the rate is doubled? a) The total amount accumulated at 2% is $ (Round to the nearest cent as needed.)

If a ball is thrown into the air with a velocity of 46 ft/s, its height in feet t seconds later is given by y = 46t - 16t². (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (b) Estimate the instantaneous velocity when t = 2.

Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 6 people. Hudson booked a total of 19 rooms which can accommodate 87 guests altogether. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system.

A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter? 0.9 m 46.82 m 57.75 m 1.11 m

Determine the simple interest. Assume 360 days in a year. p=$39,632, r=0.0625% per day, t = 90 days The simple interest is $. (Do not round until the final answer. Then round to the nearest cent as needed.)

Use the power reducing formulas to rewrite sin3x in terms of the first power of cosine. Simplify your answer as much as possible. To indicate your answer, first choose one of the four forms below. Then fill in the blanks with the appropriate numbers.

If you inflate a beach ball with 14,130 cubic inches of air, what will its radius be? Use 3.14 for π. Round to the nearest whole number if necessary. 15 inches 17 inches 24 inches 58 inches

Jessica is collecting aluminum cans during the summer for a recycling project. She collected 120 aluminum cans in June and 150 aluminum cans in July. What is the percentage change of the number of cans she collected in June to the number of cans she collected in July? A. a 25% increase B. a 20% decrease C. a 20% increase D. a 25% decrease

What is the factored form of the trinomial below? 25x² +10 xy + y²=0 (Note: When factoring polynomials with two variables, one of them can be treated as a constant.) (5x-y)² (5x + y)² (25x + y)² (25x - y)²

Determine the effective annual yield for $1 invested for 1 year at 7.3% compounded quarterly. The effective annual yield is %.

Claire is writing a report about kangaroos. The report must bedwo full pages. If she can fit 20 lines on each page with about 20 words per line, approximately how many words in all will Claire's report be?

Reason A race is 10 kilometers long. Markers will be placed at the beginning and end of the race-course and at each 500-meter mark. How many markers are needed to mark the course for the race?

A cylinder has a radius of 25 cm and a height of 2 cm. Find the height of another cylinder that has a radius of 5 cm and the same surface area as the first cylinder. The other cylinder has a height of cm.

A couple found a house selling for $112,500. The taxes on the house are $1300 per year, and insurance is $320 per year. They are requesting a conventional loan from the local bank. The bank is currently requiring a 15% down payment and 3 points, and the interest rate is 10%. The couple's gross monthly income is $4850. They have more than 10 monthly payments remaining on a car, a boat, and furniture. The total monthly payments for these items is $430. Their bank will approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners' insurance that is less than or equal to 28% of their adjusted monthly income. Complete parts a) through g) below. a) Determine the required down payment. The required down payment is $.

A company determined that for each $1 increase in the price of their product, the number of items sold will decrease by 2. Their predicted weekly profit with a price increase of x dollars is represented by the function f(x)=-3x²+18x+120. By how many dollars should they increase the price of their product to maximize their weekly profits? 3 147 10 120

Which could describe two quadrilaterals that have all pairs of corresponding angles congruent but are not similar? Two rectangles, both having a perimeter of 3.5 feet A square with a perimeter of 14 feet and a square with a perimeter of 54 centimeters Two rhombi, each having at least one 90° angle A parallelogram with adjacent sides 9 and 12 centimeters and an angle of 88, and a parallelogram with adjacent sides 9 and 12 inches and an angle of 92°

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school collected during the two days. 12x + 4y = 152 32x+12y = 420 In the equations, x represents the cost of a chicken lunch and y represents the cost of a vegetarian lunch. Which is the cost of the vegetarian lunch? $9 $11 $13 $21

Based on f(x) = lxl, describe the transformations of the function g(x) = -|x +4| +3 a. g(x) is f(x) translated 4 units to the left and 3 up units b. g(x) is f(x) reflected across the x-axis translated 4 units to the left and 3 up units c. g(x) is f(x) reflected across the x-axis translated 3 units to the left and 4 up units d. g(x) is f(x) reflected across the y-axis translated 4 units to the right and 3 up units

Determine the simple interest. (The rate is an annual rate unless otherwise stated. Assume 360 days in one year.) p=$775, r= 6.5%, t = 90 days The simple interest is $ (Round to the nearest cent as needed.)

A helicopter is hovering 2500ft above the ground. The pilot looks down at a 43-degree angle with respect to the horizon to see a pedestrian. If the helicopter lands by descending directly down, how far away from the pedestrian will the helicopter have landed?

Mary forgot the security code to her home. She knows there is a 0, 2, and 8 in some order. a.) List all the possible three-digit security codes. b.) What percent of the security codes start with the number 2 or 8?