Basic Math Questions and Answers

Which of the following represents the graph of the inequality? -20x - 15 ≥ -30x - 45 Open circle and shaded to the left Open circle and shaded to the right Closed circle and shaded to the left Closed circle and shaded to the right

Factor. Remove the largest possible common factor. Check your answer by multiplication. 25x8+10x7 +20x4 25x8+10x7 +20x =

Carmen tutors math. For each hour that she tutors, she earns 40 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H. Then use this equation to find Carmen's earnings after tutoring for 13 hours.

A ladder leaning against a wall makes an angle of 68 degrees with level ground. The foot of the ladder is 3 ft away from the wall. How far up the wall does the ladder reach?

Find the length of BOTH bases of the trapezoid with the given information. The area of the parallelogram is 95 m². The height is 10 meters. One base is 3 meters longer than the other. Shorter Base = Longer Base=

Find the exact and approximate area of a circle with the given radius r or diameter d. Use pi for π with no spaces in your exact answer. Round approximate answer to the nearest tenth. d = 16 ft A =

Is it possible for a solid to have a cross section that is a single point? If so, give an example. If not, explain why not. None of the other answers are correct No, it is not possible. You cannot have a cross section of a single point. There needs to at least be 2 dimensions in the cross section. Yes; a plane that intersects a solid figure at one of its vertices produces a cross section that is a single point.

The doubling time of a population of flies is 5 hours. By what factor does the population increase in 31 hours? By what factor does the population increase in 1 week? By what factor does the population increase in 31 hours?

Simplify. Assume that all variables are nonnegative real numbers. 3√128x³y^5 3√128x³y^5 = (Type an exact answer, using radicals as needed.)

bicycle riders start a race at the same time. The functions f(x) and g(x) give the distance in miles that each rider has traveled after x hours of riding. What does f(2)- g(2) = 5 mean in this context? A The riders are 2 miles apart 5 hours after the race starts. B The riders are 5 miles apart 2 hours after the race starts. C Both riders travel 2 miles in the first 5 hours of the race. D Both riders travel 5 miles in the first 2 hours of the race.

A child flies a kite at a height of 50 ft, the wind carrying the kite horizontally away from the child at a rate of 26 ft/sec. How fast must the child let out the string when the kite is 130 ft away from the child? The child must let out the string at a rate of___ft/sec when the kite is 130 ft away from the child. (Simplify your answer.)

The coins are placed in a cylindrical storage container that has a radius of 2 in and a height of 5 in. How much empty space is in the cylinder after all 225 coins are placed in? a. Volume of the container is 72.8 in³; Empty space 28.64 in³ b. Volume of the container is 52.5 in³; Empty space 21.64 in³ c. Volume of the container is 62.8 in³; Empty space 18.64 in³ d. Volume of the container is 102.1 in³; Empty space 58.64 in³

The sum of 5 times one number, x, and 6 times a second number, y, is 179. If the sum of the two numbers is 31, find the two numbers. Enter a system of equations to represent the situation, then solve the system. The system of equations is The first number is__and the second number is___

Find the area and perimeter of a rectangle with sides 5 and 7.9 mi None of the other answers are correct area is 12√6 mi² perimeter is 17.9 mi area is 58.5 mi² perimeter is 35 mi area is 39.5 mi² perimeter is 25.8 mi area is 36.24 mi² permeter is 12.9 mi

The following list gives the home run totals for Barry Bonds from 1986 through 2007 (his total career). 16 25 24 19 33 25 34 46 37 34 49 73 46 45 45 5 26 28 Construct a stem-and-leaf plot for the data. Enter the leaves in ascending order, without spaces betweenb them. If a stem has no corresponding leaves, leave that space blank.

Adam is also confused. He wonders why, if you take a rectangle and multiply the length of each side by 1.5. the area of the new rectangle isn't 1.5 times as big as the area of the old rectangle. How would you explain this to him?

Jackson is conducting an experiment for his Physics class. He attaches a weight to the bottom of a metal spring. He then pulls the weight down so that it is a distance of 6 Inches from its equilibrium position. Jackson then releases the weight and finds that it takes 4 seconds for the spring to complete one oscillation. Which function best models the position of the weight? A) s(t) =6Sin(2πt) B) s(t) =6Cos(π/2)t C) s(t) =6Sin(π/2)t D) s(t) =6Cos(2πt)

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2 She makes these two Statements: (1) As x increases infinitely, the y-values are continually doubled for each single increase in x. (2) As x decreases infinitely, the y-values are continually halved for each single decrease in x. She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine's statements and her conclusion? (1) Statement 1 is incorrect because the y-values are increased by 2, not doubled. (2) Statement 2 is incorrect because the y-values are doubled, not halved. (3) The conclusion is incorrect because the range is limited to the set of integers. (4) The conclusion is incorrect because the range is limited to the set of positive real numbers.

A small bakery called Taestry opens today. They expect to make profits continuously, at a rate of s(t) = t2/10 + 100 thousand dollars per year, where t is the time in years since they opened. (a) (3 points) Over their first ten years of operation, what will be the average value of Taestry's profit rate S(t)? Call this average value "A". Please show all of your reasoning. Answer: Over their first ten years of operation, Taestry's average profit rate will be A= thousand dollars per year.

Read the excerpt. At the beginning of the mission, since our priority was to identify the origin of the alien's signal. What is the most accurate way to describe the excerpt? (1)It is a complex sentence. (2)It is an independent clause. (3)It is a dependent clause. (4)It is a compound sentence.

It will take Cody 3 months to save up enough money to purchase a stereo. He has a credit card with a 12% interest rate. Cody's friend Mark says it will cost Cody less money if he saves for 3 months instead of using the credit card. Is Mark correct?

Stacy hits the jackpot one day at the gumball machine. She puts in a quarter and gets 4 gumballs rather than 1. The radius of each gumball is 6 mm. What is the total volume of all 4 gumballs? _________mm³

The Roth family has liquid assets of $10,000, use assets of $150,000 and investment assets of $34,000. They also have liabilities totaling $108,000. If their total liabilities increase by $7,000 over the next year, by how much would the Roth family need to increase their assets in order to have a net worth of $100,000? (a) $7,000 (b) $14,000 (c) $21,000 (d) $28,000

6900 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 26 years, to the nearest cent?

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax² + bx + c, is shown. Step 1: -c = ax² + bx Which best explains or justifies Step 1? subtraction property of equality completing the square factoring out the constant zero property of multiplication

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?y=6x x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6. y=6x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6. y=x+6; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6. y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6

Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount How much did tydla pay for the shirt? $42 $36.60 $34 $33,60

A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 30 cm. To the nearest tenth, what is the area of the wheel? 71.6 cm2 286.6 cm2 23.6 cm2 143.3 cm2

A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment? f(x) = 5000(0.4)^x, with a horizontal asymptote of y = 0 f(x) = 5000(0.6)^x, with a vertical asymptote of x=0 f(x) = 5000(1.4)^x, with a horizontal asymptote of y = 0 f(x) = 5000(1.6)^x, with a vertical asymptote of x=0

Peaches are being sold for $2 per pound. The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y? The values of both x and y can be any real number. The values of both x and y will be real numbers greater than or equal to 0. The value of x and y will always be zero The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.

The CEof a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees? 000-250 001-250 0-250 1-250

Your friend just purchased a new sports car for $32,000. He received $6,000 for his trade in and he used that money as a down payment for the new sports car. He financed the vehicle at 6.76% APR over 48 months with a monthly payment of $619.15. Determine, from the given information, the finance charge. (A) $3,719.20 (B) $5,476.10 (C) $4,610.64 (D) $6,000

A study was done in 2015 that collected data on teenagers and text messaging. * In 2015, there were about 22 million teenagers (aged 13-17) in the United States. * They each sent an average of 900 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation. No rounding.

Sarah sells fruit trays at a salad shop. Last week, she sold 450 fruit trays for $8 per tray. In previous weeks, she found that for ever $0.85 Increase in the price, she sold 15 fewer fruit trays. Which equation can be used to find Sarah's weekly sales Income in dollars, y, after x price increases of $0.85? (A) y = –12.75x2 + 262.5x + 3,600 (B) y = –12.75r2 + 482.5x + 3,600 (C) y = –12.75r2 + 272.5x + 3,600 (D) y = –12.75r2 + 502.51 + 3,600

Jerry has taken a random sample of students and determined the number of electives that each student in his sample took last year. There were 19 students in the sample. Here is the data on the number of electives the 19 students took: 6, 6 8,7,7,7,8,9,10,8,7,6 ,9,6,8, 7,9,7, 10. The mean of this sample data is 7.63. What is the sample proportion of students who took fewer than the mean number of electives? (A) 10/19 (B) 6/19 (C) 7/19 (D) There is not enough data to answer this question.

Fiona is pricing two bicycles. One is $175 with 10% off, and the other is $225 with 35% off. Which bicycle can she afford if she has $150 to spend? (1) Fiona can afford the $175 bicycle. It will cost $146.25. (2) Fiona can afford the $175 bicycle. It will cost $96.25. (3) Fiona can afford the $225 bicycle. It will cost $146.25. (4) Fiona can afford the $225 bicycle. It will cost $96.25.

Which of the following actions can be accomplished with electronic banking? A. pay bills without going to the bank B. transfer funds C. view our account status D. foreign exchange transactions

Olive oil is a cooking ingredient. The density of olive oil is 0.92 grams per cubic centimeter. An olive farmer wants to sell bottles that contain 460 grams of oil. What is the volume of the smallest container that holds 460 grams of oil? (A) 423 cubic centimeters (B) 460 cubic centimeters (C) 500 cubic centimeters (D) 552 cubic centimeters

Use the percent formula, A = PB, where A is P percent of B, to solve problem. 31% of what number is 49.6? The answer is (Type an integer or decimal rounded to the nearest tenth as needed.)

Sarah wants to study the time it takes to complete a lab in a regular biology course compared to the time it takes to complete a lab in an honors biology course. Which quantities could Sarah use to make her comparisons? Check all that apply. (1) amount of time needed to complete a cell lab in a regular biology course (2)amount of time needed to complete a cell lab in an honors biology course (3)number of students taking a regular biology course number of students taking an honors biology course (4) amount of time needed to write a cell lab report in a regular biology course (5)amount of time needed to write a cell lab report in an honors biology course

A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix. Which statement is true about the box plots? (A)The interquartile range of the trail mix data is greater than the range of the cracker data (B) The value 70 is an outlier in the trail mix data. (C) The upper quartile of the trail mix data is equal to the maximum value of the cracker data. (D)The number of calories in the packs of trail mix has a greater variation than the number of calories in the packs of crackers

Several ordered pairs from a continuous exponential function are shown in the table. What are the domain and range of the function? x y 0 4 1 5 2 6.25 3 7.8125 (1)The domain is the set of integers, and the range is y> 4. (2) The domain is the set of integers, and the range is Y>O. (3) The domain is the set of real numbers, and the range is y> 0. (4)The domain is the set of real numbers, and the range is y> 4.

Caylan is making baked goods for a charity bake sale. He places a tray of scones, a tray of muffins, and a tray of cookies in the oven. The scones bake for 15 minutes, the muffins bake for 12 minutes, and the cookies bake for 10 minutes. When one tray is done, he removes it and replaces it with another tray of the same item. How many minutes after Caylan puts the trays in the oven will he first remove the scones, muffins, and cookies at the same time? __________ minutes

Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. The pretzel requires 2.5 cups of flour to make. How much flour is in each loaf of raisin bread? Explain the steps to follow to get the answer

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of x, the distance of 1 lap around the path at the park?

Adult tickets to the fall play cost $6 and student tickets cost $3. The drama class sold 25 more student tickets than adult tickets to the fall play. If the class collected $660 from ticket sales, how many student tickets were sold? The drama class sold_____student tickets.

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book. What are the slope and y-intercept of the line represented by the points shown in the table? x y 0 -20 5 -10 10 0 15 10 20 20 (A) slope: 2, y-intercept: -20 (B) slope: 2, y-intercept: 10 (C) slope: 5, y-intercept: -20 (D) slope: 5, y-intercept: 10

A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. What is the height of the pole? (1) 12 ft (2) 12/3ft (3) 18 ft (4) 18/2 ft

Find the LCD for the list of rational expressions. 9x + 1/x²+5x-6, 5x/x²+4x-5 The LCD is ______

Kurtis had purchased a renters insurance policy for his new apartment at an annual premium of $588.00. The items covered in the policy included a bicycle kept locked to the railing in front of the apartment. When the bicycle was stolen, the insurance company covered the replacement cost of the bicycle, but told Kurtis that, because of the loss, his premium would increase by 35% if he wished to continue with the policy. What would Kurtis' new annual premium be if he chose to keep the policy. (1) $36.75 (2) $66.15 (3) $441.00 (4) $793.80