Math Questions

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

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

A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 185 pounds with a margin of error of 6 pounds. Write a confidence interval for the true mean weight of the residents of the town.

Julia can make a key chain in 2 minute(s) 54 seconds. At this rate, which is closest to the amount of time she will need to make 9 key chains? Choose the correct answer below. A. 2 minutes B. 18 minutes C. 27 minutes D. 3 minutes

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?

The equation y = 8x + 12, where x is the number of hours and y is the total cost, represents what the surf instructor charges for lessons. Use this information to describe how to draw the line on a graph.

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?

The height in feet of a ball thrown in the air from a ledge 112 feet high is represented by the function f(x) = -16x²+96x +112, where x is the number of seconds since the ball has been thrown. How many seconds does it take the ball to reach the ground? 256 7 3 112

Write an algebraic equation and use it to solve the problem. Five-sevenths of a number is -20. What is the number? The equation is.

If a linear combination is the method used to solve the system of equations, what is the result of the first step? x + y = 6 x - y = 2 A. 2y = 8 B. 2x = 8 C. x + y = 8 D. x - y = 8

Fern bought groceries that cost $14.38. She paid the store clerk, Ping, with a $20 bill. 2 pennies makes the total $14.40. 6 dimes makes it $15.00, and 6 dollars makes it $20. Did the clerk make a mistake in giving Fern her change? You may use the scratchpad to show your work. A No, she received $6.62 in change. B Yes, Ping should give Fern 6 pennies and 2 dimes. C Yes, Ping should give Fern 3 dimes and 8 pennies. D Yes, Ping should give five one-dollar bills, not six.

Four golfers will be randomly split into 2 groups of 2 for a tournament. If Jill and Ramona are among the 4, what is the probability that they will be paired together? F. 1/12 G.1/8 H. 1/6 J. 1/4 K. 1/3

A shirt priced at x dollars is discounted before tax is added. The final price in dollars is described by the expression below. 1.05(x -0.6x) What is the sales tax for the shirt? 0.05(0.4x) 1.05 (0.6x) 1.05 (0.4x) 0.05(0.6x)

Given y = 4x + 21-3 if a is multiplied by 3 what happens to the vertex? a. The vertex remains the same. b. The vertex shift to the right 3 units. c. The vertex shifts to the left 3 units. d. The vertex shifts down 3 units.

Tyler stands at the top of a 40 meter tall vertical cliff. Down below, Susie stands some distance away from the base of the cliff. Tyler's angle of depression to Susie is 34°. How far is Susie from the base of the cliff? Round answer to the nearest tenth. You must draw the picture to represent the situation. (3 pts)

A tennis club offers two payment options. Members can pay a monthly fee of $9 plus $6 per hour for court rental time. The second option has no monthly fee, but court time costs $7.50 per hour. Answer parts a through d. a. Write a linear function that models the total monthly costs for each option for x hours of court rental time. The linear function that models total monthly cost for the first payment option is f(x) = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression.)

A banana peel weighs 1/6 of the total weight of a banana. If an unpeeled banana balances a peeled banana of the same weight, plus 5/6 of an ounce, how much does the banana weigh with the peel? The weight of the banana with the peel is oz.

The graph of: y = 11x³ + 22x² + 14x / (5x² + 1)(11x + 7) has one vertical asympote and one horizontal asymptote. An equation for the vertical asymptote is: An equation for the hoizontal asymptote is:

The price of a dress is reduced by 60%. When the dress still does not sell, it is reduced by 60% of the reduced price. If the price of the dress after both reductions is $80, what was the original price? The original price of the dress was $ (Type an integer or a decimal.)

Carter found the discriminant of this quadratic function. F(x)=6x²-5x +3 According to the discriminant, which best describes the roots of F(x)? One real root Two real roots Two complex roots One complex root

agrees to pay a student 6¢ for every problem in this chapter that the student solves correctly, and fines the student 5¢ for every problem done incorrectly. If at the end of 33 problems they do not owe each other any money, how many problems did the student solve correctly? problems correctly.

A parabola can be drawn given a focus of (1, 2) and a directrix of x = -11. What can be said about the parabola? The parabola has a vertex at

9/7x+35=9/x+5-6/7 aWhat is/are the value or values of the variable that make(s) the denominators zero? x= (Simplify your answer. Use a comma to separate answers as needed.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A The solution set is {}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution set is {x) x is a real number}. C. The solution set is Ø.