Basic Math Questions and Answers

Use the difference of cubes formula to factor. Be sure to factor out any common factors. 8x^3 - 125 =

22) What would the graph of the following inequality look like? * x≤-4 Open circle, arrow towards the right Open circle, arrrow towards the left Closed circle, arrow towards the right Closed circle, arrow towards the left

Maria invests $13,000 at 8% simple interest for 10 year. How much is in the account at the end of the 10 years period?

Solve by using the strategies for solving application problems. It costs a manufacturer $9.99 to produce sunglasses that sell for $34.99. How many pairs of sunglasses must the manufacturer sell to make a profit of $18,125? Step 1 This real-world problem can be solved using a linear equation. Let x be the number of pairs of sunglasses. The sell price of one pair is $34.99. The revenue generated after selling x pairs is, therefore, Revenue = x dollars. It costs the manufacturer $9.99 to produce one pair of sunglasses. The total cost of producing x pairs is, therefore, Cost = x dollars.

Brad, Lance, Allen, and John are all brothers. They are measuring and comparing their heights. They have found that Lance is exactly 1 foot taller than Brad and John is exactly 1 foot taller than Allen. They also found that the product of Brad's and Lance's heights is equal to Allen's height and if they subtract 1 foot from both Brad's and Lance's height, the product is equal to John's height. Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not. A. There is only 1 solution, and it is viable. B. There are 2 solutions, and only 1 is viable. C. There is only 1 solution, and it is not viable. D. There are no solutions

The last 60 boat rentals at a boat rental company were 38 sunfish, 12 kayaks, and 10 rowboats. Use this information to complete parts (a) through (c). a) Determine the empirical probability that the next boat rental is a sunfish. b) Determine the empirical probability that the next boat rental is a kayak. c) Determine the empirical probability that the next boat rental is a rowboat. a) P(sunfish) = (Type an integer or a simplified fraction.)

You want to buy a $187,000 home. You plan to pay 15% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 5%? c) What will your monthly payments be if the interest rate is 6%?

Determine if the given relation is also a function. {(-4,- 6), (7, − 1), (-2,9), (3,6)} Is the relation a function? No Yes

The vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. P= (0,0); Q=(3,7)

Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem? (16,+∞) (-16,+∞) (-∞,16) (-∞, -16)

One of the early communication satellites was Telstar, launched in 1962 and inspiring a popular song on the radio. It followed an elliptical orbit that varied form about 1.00 x 10³ km to -6.00x10³km above the Earth. What was its orbital speed at its closest approach to Earth?

You want to be able to withdraw $40,000 each year for 15 years. Your account earns 7% interest. a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account? c) How much of that money is interest?

What is the length of the line segment that joins points (4, -1) and (7,5)? (A) 5 (B) √13 (C) √29 (D) √45

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = (x³ - 3x + 1)² 2 roots 3 roots 6 roots 9 roots

You deposit $1090 in a savings account paying 4.5% simple interest. How much interest will you earn in 6 years? How much is in the account at the end of 6 years?

A toy rocket is launched straight up into the air with an initial velocity of 60 ft/s from a table 3 ft above the ground. If acceleration due to gravity is -16 ft/s2, approximately how many seconds after the launch will the toy rocket reach the ground? h(t) = at² + vt + h0 0.05 s 2.03 s 3.80 s 3.70 s

Suppose you have $1800 in your savings account at the end of a certain period of time. You invested $1500 at a 7.85% simple annual interest rate. How long, in years, was your money invested?

A cooler contains 100 ice cream bars. There are 30 Vanilla bars, 20 Mint Chocolate Chip bars, 10 Strawberry bars, and 40 Rocky Road bars. If one bar is randomly selected determine the probability that the bar selected is Vanilla.

You owe $15,000 on student loans at an interest rate of 5.85% compounded monthly. You want to pay off the loan in 8 years. What will your monthly payments be? How much interest do you pay?

Each individual letter of the word Mississippi is placed on a piece of paper, and all 11 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a vowel is selected.

You have $2,000 on a credit card that charges a 12% interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

You have $400,000 saved for retirement. Your account earns 8% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 25 years?

A force with a magnitude of 100 pounds and another with a magnitude of 400 pounds are acting on an object. The two forces have an angle of 60° between them. What is the magnitude of the resultant force? 458.2575 pounds 435.8898 pounds 387.2983 pounds 360.5551 pounds 131.6074 pounds

The expected value when you purchase a lottery ticket is -$1.00 and the cost of the ticket is $7.00. Determine the fair price of the lottery ticket.

Find the next term of the given sequence. 1.31, 2.54, 3.77, ... 5.10 5.00 4.90

Select the only true statement below. A) The graph of an even function is symmetric with respect to the y-axis. B) The graph of an even function is symmetric with respect to the x-axis. C) The graph of an odd function is symmetric with respect to the x-axis. D) The graph of an odd function is symmetric with respect to the y-axis.

The displacement, d, in millimeters of a tuning fork as a function of time, f, in seconds can be modeled with the equation d=0.6sin(3520 st). What is the frequency of the tuning fork? 1/ 3520 Hz 1/1760 Hz 1760 Hz 3520 Hz

Using vertices to represent states and edges to represent borders, which graph models the bordering relationship among the states shown?

You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the account in 10 years?

Replace the values of m and n to show the solutions of this equation. x² + 6x 5 = 0

A monk crossbred plants, which can have purple or white flowers, and obtained 617 plants with white flowers and 280 plants with purple flowers. Find the empirical probability that a plant had each type of flower.

A total of 690 tickets were sold for the school play. They were either adult tickets or student tickets. There were 60 fewer student tickets sold than adult tickets. How many adult tickets were sold?

You want to buy a $160,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan at 3.9% interest for the rest. The bank will charge 3 points on the amount financed. a) What is the amount of the down payment?

An 8 in. by 8 in. square air vent is shown where AG = 8 inches. BF is the midsegment of ADG and CE is the midsegment of DBF. Which of the following is measure of CE? 2 inches 3 inches 4 inches 6 inches

A cylinder has a volume of 18 πin³. Which are possible dimensions of the cylinder? Radius: 1 inch Height: 2 inches Radius: 2 inch Height: 3 inches Radius: 3 inch Height: 2 inches Radius: 3 inch Height: 6 inches

Each exterior angle of a regular polygon measures 20°. How many sides does the polygon have? A. 16 B. 18 C. 15 D. 20

A class is learning about ratios and percentages. The teacher tells the class that at last Friday night's football game there were between 800 and 1000 people. Of those at the football game, about 13-17 percent of the people had blonde hair. Which of the following is the most reasonable estimate of the number of people at the football game with blonde hair? A. 170 B. 135 C. 100 D. 200

A rectangular park is 115 meters long and 70 meters wide. Give the length and width of another rectangular park that has the same perimeter but a larger area.

You deposit $2000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years?

You deposit $2000 each year into an account earning 4% interest compounded annually. How much will you have in the account in 25 years?

You invest $125,000 in an account that earns 4.75% annual interest, compounded continuously. a. What is the value of the account after 15 years? b. What is the value of the account after 30 years?

The height y, in feet, of a football x seconds after it is thrown is modeled by the equation y = -16x² + 24x + 1. What information does the zero of the equation 6 = -16x² + 24x + 1 represent? the height of the ball after 6 seconds when the ball is 6 ft above the ground the initial upward velocity of the ball the horizontal distance traveled by the ball when it is 6 ft above the ground

You want to buy a $183,000 home. You plan to pay 15% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 6%? c) What will your monthly payments be if the interest rate is 7%?

You can afford a $350 per month car payment. You've found a 4 year loan at 5% interest. How big of a loan can you afford?

Melanie used cross multiplication to correctly solve a rational equation. She found one valid solution and one extraneous solution. If 3 is the extraneous solution, which equation could she have solved? A. The equation is 4/(x-3)=x/10 because 3 makes a denominator equal to zero and is not a solution of the equation derived from cross multiplying. B. The equation is (x-3)/4=2x/4x because 3 makes a numerator equal to zero and is not a solution of the equation derived from cross multiplying. C. The equation is 8/(x^2-9)=5/(2x-6) because 3 makes a denominator equal to zero and is not a solution of the equation derived from cross multiplying. D. The equation is 8/(x+3)=12/4x-3 because 3 is a soluiton of both the original equation and equation derived from cross multiplying.

Select the correct answer. The value of m varies inversely as the square of n. When = 3, m = 6. What is the positive value of n when m = 13.5? A 18 B. 4 C 2 D. 9

The relationship between voltage E, current I, and resistance Z is given by the equation E = IZ. If a circuit has a current i = 3 + 2i and a resistance Z = 2-i, what is the voltage of the circuit? 4-i 4+i 8+i 8+7i

It takes Greg and Nikki a total of 40 minutes to paint a room if they work together. If Greg works alone, he takes 18 minutes longer to paint he room than Nikki takes if she works alone. When x represents the number of minutes it takes Nikki to paint the room working alone, the situation is represented by this equation: 1/x + 1/x+18 = 1/40 Which value is a solution of the rational equation that must be discarded because of the context? A. x=0 B.. X=-10 C. x= -18 D. X=-72

Which survey is most likely affected by bias? a survey of teenagers about their favorite colors a survey of students about vacation policies in a school district a survey of supermarket shoppers about products they would like to see added a survey of bike riders on whether they wear helmets

An airplane ascends at an angle of elevation of 22° for a ground distance of 7850 feet. What height does the plane gain during this ascent? Draw a picture on paper to support your answer, and round your answer to the nearest whole foot.