Math Questions

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).

x2+5 – 2 When trying to factor, Sarita says this polynomial is PRIME. Why is she correct? there are no numbers with a product of -2, and a sum of 5 there are no numbers with a product 5, and a sum of -2 both 5 and -2 are prime numbers

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.)

Consider the line y=-7x+6. Find the equation of the line that is parallel to this line and passes through the point (2, 4). Find the equation of the line that is perpendicular to this line and passes through the point (2, 4). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of parallel line: Equation of perpendicular line:

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 company sells orange juice in spherical containers that look like oranges. Each container has a surface area of approximately 113 in². Use 3.14 for π. Part 1 out of 2 What is the volume of the container? Round to the nearest tenth. The volume of the container is approximately

Solve the quadratic equation by completing the square. x² +8x+14=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form:

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.

Round your answer to 3 decimal places when necessary. Find the probability of selecting either a non-smoker or a woman when you select a person at random from a group composed of 50 female smokers, 45 male smokers, 20 female non-smokers, and 45 male non-smokers. 0.125 0.844 0.719 0.178

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

Write the quadratic equation with the following transformations: Reflected over the x-axis Vertical shrink of 1/3 Translated up 2 units y = -3(x + 2)² y = -(1/3)x² + 2 y = -(1/3)(x + 2)² y = -3x² + 2

Let f(x)=x³-4x²+7x-6/x-2 a. Graph the function on the window xmin = -2, xmax = 4, ymin = 0, ymax = 10. b. What is the domain of the function? c. Find lim x⇒2 f(x). d. Write a very short paragraph about the importance of examining a function analytically as well as graphically. e. In light of part b, make sure your graph is correct.

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.

Use a sum or difference identity to find the exact value of the expression. tan 15° tan 15° = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

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?

Consider the line -7x+2y=2. Find the equation of the line that is parallel to this line and passes through the point (-6, 1). Find the equation of the line that is perpendicular to this line and passes through the point (-6, 1). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of parallel line: Equation of perpendicular line:

Which of the following is an attribute of any quadratic function? It has a constant rate of change. The function values increase as x increases. It is symmetric about a line through its vertex. The graph always intersects the x-axis twice.

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

The top of a gumball machine is a 20 in. sphere. The machine holds a maximum of 3,500 gumballs, which leaves about 56% of the space in the machine empty. Estimate the diameter of each gumball to the nearest whole number. The diameter of one gumball is about in.

Determine the center and radius of the following circle equation: x² + y² + 4x − 8y - 16 = 0

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.)

A vector s has initial point (5,-2) and terminal point (-1, -3). Writes in the form s = ai + bj.

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

Find each indicated quantity if it exists. Let f(x) = |x-11| / x-11 .Complete parts (A) through (D). (A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim f(x)= (Simplify your answer.) B. The limit does not exist.

Consider the line - 8x-2y=3. Find the equation of the line that is parallel to this line and passes through the point (3, -6). Find the equation of the line that is perpendicular to this line and passes through the point (3, -6). Note that the ALEKS graphing calculator may be helpful in checking your answer.

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

A city has a population of 300,000 people. Suppose that each year the population grows by 6.5%. What will the population be after 11 years? Use the calculator provided and round your answer to the nearest whole number.

A cardboard box without a lid is to have a volume of 5,324 cm³. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.) (x, y, z) =

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

- Which of the following rules describes the translation of point P(-5, -4) to point P'(-8, -7) a. (x,y) → (x-3, y + 3) b. (x, y) → (x-3, y-3) c. (x,y) → (x+3, y− 3) d. (x,y) → (x+3, y + 3)

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?

A spinner is used for which it is equally probable that the pointer will land on any one of twelve regions. Four of the regions are colored green, six are colored yellow, and two are colored red. If the pointer is spun twice, find the probability it will land on green and then red.

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 paper airplane is thrown from a height of 9 feet. The function y = -2x² + 3x +9 represents the path of the plane, where x is the distance traveled and H(x) is the height of the plane. At what distance does the plane hit the ground? 18 ft 3 ft 2 ft 9 ft

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