Basic Math Questions and Answers

Which of the following numbers best describes inequality above? A) [0,4/3) B)[4/3, ∞) C) (-∞, ∞) D) (-∞, -4]u[3, ∞)

Write the first term of the given expression as a perfect cube. The number 125 is a perfect cube which can be written in exponential form. 125 = 5 x 5 x 5 Substitute the exponential form found above into the given expression. Then, use the power of a product rule for exponents to write the first term in the form a³. 125x³ 1 = ( )^3 (x)³ - 1 = ( )^3 - 1

Determine which situation could be represented by the following system of linear equations. x + y = 70 8x + 5y = 410 A. Evaporated milk comes in eight-ounce cans and five-ounce cans. A grocery store sold 410 ounces of evaporated milk in 70 cans. B. At the floral shop, Mary buys eight large bouquets and five small bouquets for a total of $410. Mark buys one large bouquet and one small bouquet for $70 less than Mary pays. C. Packs of file folders cost $8 each and boxes of pens cost $5. An office manager ordered 70 more boxes of pens than packs of file folders and paid a total of $410. D. Each student at an elementary school is required to have five notebooks and eight pencils. One grade has a total of 70 school supplies and another grade has a total of 410 school supplies.

Which expression is equivalent to the given expression? 10g + 5 5q +5g +5 10q+5+5 5g + 10 5q +5

Can the following be factored? If so, factor it: 16x6-80y² Yes, (4x³+8y)(4x³-10y) Yes, (4x³+20y)(4x³-20y) Yes, (4x³+20y2)(4x³-20y²) Yes, (4x3+40y)(4x³-40y) Cannot be simply factored.

Solve the word problems using the RDW strategy. Show all of your work. Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave the leftovers to his friends. What fraction of the pie did he give to his friends?

An entertainment center is financed at a total cost of $2,364.99 including a down payment of $300. If the center is financed over 24 months, find the monthly payment. The monthly payment is $(Round to the nearest cent as needed.)

The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 8.6 and 14.6 lb? 0.3270 0.4032 0.0968 0.6730

This equation can be used to predict the population p (in thousands) of Barbaria, a mythical country, for a given year,t where t is the number of years since 1950: p = 15,498 + 446t a. To find the predicted population in 2020, what should you use for t? Compute the population predicted for 2020. Write the answer using the word "thousands." Without using the word "thousands." b. Compute the population predicted for 2021. In the answer, don't use "thousands." c. How much does the population increase each year?

Factor the difference of cubes. Recall that a difference of cubes can be rewritten such that a³ b³ = (a - b)(a² + ab + b²). Factor the difference of cubes. Then, simplify the terms. (4x³)3 - (3y)3

Serafina is solving a number puzzle that involves three integers, e, f, and g, where e is negative. The product of e and fis-15. The product of e and g is 6. The product of f and g is -10. What are the values of e, f, and g? Show your work.

Suppose the charge account of Black's Mailing Service at the local supply store had a 1.7% interest rate per month on the average daily balance. Find the Black's finance charge on April 1 if Black's had an unpaid balance on March 1 of $148.96, a payment of $25.00 posted on March 12, and a purchase of $27.06 posted on March 22. The billing cycle ends March 31. The Black's finance charge is (Round to the nearest cent as needed.)

Let B={-20, -19, 0, 19, 20}, and D = {-19}. Insert C or to make the following statement true. D ____ B Choose the correct answer below. A. Not every element of D is also an element of B, so D B. B. Every element of D is also an element of B, so D B. C. Not every element of B is also an element of D, so D B. D. Every element of B is also an element of D, so D B.

Oscar, Renee, Penny and Hugo, all turkeys, are wandering through the beautiful forest. They spot seven bees and five cockroaches, and in the trees, they see eight spiders. There are also four deer and four boars. Behind a bush, they can see a pair of antlers. How many legs are there in total?

ALGAE Ronald owns a fish tank in the shape of a rectangular box. The tank is 18 inches high, 14 inches deep, and 30 inches long. Ronald went on a one-month vacation. When he returned he found that the sides and bottom of his fish tank were covered with algae. What is the area that was covered?

In a random sample of 25 students at college, the average IQ was x = 103. Assume that the IQ of a student in college follows a Normal distribution with unknown mean and standard deviation = 15. A 90% confidence interval for u is (78, 128). (97, 109). (98, 108). (102, 104).

A bird traveled 72 miles in 6 hours flying at constant speed. At this rate, how many miles did the bird travel in 5 hours? 12 30- 60 14.4 I don't know (I need help with these type of questions)

A flagpole 94.4 ft tall is on the top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 35.7°, while the angle of elevation of the bottom of the flagpole is 25.4°. Find the height of the building.

Automatic transmissions and manual transmissions achieve the same goal: They use power to turn the wheels of a car. However, there are some differences between the two. An automatic transmission makes a car easy to drive; but stick shift drivers believe that automatics aren't quite as fun. There are other differences as well. A car with a manual transmission usually uses less fuel. This is because the driver has greater control over the car; it is the driver, not the car, who is "in the driver's seat." A manual transmission also has more power and can accelerate faster. This is why race cars have manual transmissions. Which organizational pattern is used in the passage? A. Sequential B. Problem-solution C. Cause and effect D. Compare and contrast

For a project in her Geometry class, Tamika uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 14.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then walks 4.2 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.65 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Consider the trinomial x² - 11x + 18. In preparation for factoring it by grouping, write -11 as a sum or difference of factors of 18.

Anthony works as a salesperson at an electronics store and sells phones and phone accessories. Anthony earns a $8 commission for every phone he sells and a $4 commission for every accessory he sells. On a given day, Anthony made a total of $80 in commission and sold 5 more accessories than phones. Graphically solve a system of equations in order to determine the number of phones sold, al, and the number of accessories sold, y.

Arnold Brown has a Visa Card with an annual percentage rate of 16.8 %. The unpaid balance for his June billing cycle is $1,054.33. During the billing cycle he purchased a printer cartridge for $43.72, books for $291.59 and gasoline for $17.06. He made a payment of $1,000. If the account applies the unpaid balance method, what are the finance charge and the new balance?

A total of 568 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 more student tickets sold than adult tickets. How many adult tickets were sold?

Solve the system of equations using Cramer's Rule if it is applicable. 3x - y = 10 2x + 2y = 12 Write the fractions using Cramer's Rule in the form of determinants. Do not evalua

1/9+5/6 Least multiple that is the same: Add using renamed fractions:

Peg and Larry purchased "no contract" cell phones. Peg's phone costs $25 plus $0.25 per minute. Larry's phone costs $35 plus $0.20 per minute. After how many minutes of use will Peg's phone cost more than Larry's phone?

A school is organizing a cookout where hotdogs will be served. The hotdogs come in small packs and large packs. Each small pack has 12 hotdogs and each large pack has 24 hotdogs. The school bought 4 times as many small packs as large packs, which altogether had 144 hotdogs. Graphically solve a system of equations in order to determine the number of small packs purchased, z, and the number of large packs purchased, y.

Karen, Dan, and Josh sent a total of 109 text messages over their cell phones during the weekend. Josh sent 4 times as many messages as Dan. Dan sent 5 more messages than Karen. How many messages did they each send? Number of text messages Karen sent: Number of text messages Dan sent: Number of text messages Josh sent;

The families "a", "b" and "c" are invited to dinner. The probabilities that each family will come are 0.8, 0.6 and 0.9, respectively. In addition, each family's decision is independent of the decisions of the other families. Find the probability that NONE of the families come. Define Event A: the family "a" comes; Event B: the family "b" comes; Event C: the family "c" comes.

On an exam for a class with 54 students, the mean score was 77.2 points. The instructor rescored the exam by adding 6 points to the exam score for every student. What was the mean of the scores on the rescored exam?

Factor the following polynomial if possible. Hint: Using an identity will be helpful. 27x3+y³z³ Cannot be simply factored. (3x+yz) (9x²-3xyz + y²z²) (2x+yz)(4x²-2xyz + y²z²) (3x-yz) (9x²+3xyz + y²z²) (3x+yz) (9x²-3x²y²z²+²z²)

Which of the following sets of numbers could represent the three sides of a triangle? {10, 21, 32} {14, 24, 40} {13, 17, 32} {13, 16, 27}

A company manufactures electronic components that each must weigh from 29.5 grams to 30.5 grams, inclusive. Which of the following inequalities describes all acceptable weights x, in grams, for each component? (A) |30-x| ≤0.5 (B) |30-x| >0.5 (C) 30-x≤ 0.5 (D)30-x>0.5

Michael wishes to give his son a savings bond that will mature in 8 years. He would like the value of the savings bond to be $5,000 at maturity. If he can invest in a bond that has an annual interest rate of 4% compounded monthly, which of the following is the best approximation of the amount he should invest? (A) $3,200 (B) $3,350 (C) $3,500 (D) $3,650

Define a variable and write an inequality. Then sol Marlea received an inheritance of $10,000. She plans to invest some in a stock that pays 7% interest annually. She will deposit the remainder in a savings account that pays 5% interest annually. What is the least amount that Marlea can invest in stock if she wants to earn at least $550 on her investments for the year?

Caitlin had $402 in her bank account. She withdrew $15 each week to pay for a swimming lesson. She now has $237. a.Write an equation that can be used to find the number of swimming lessons that she paid for. b. Find the number of swimming lessons she paid for. C.The cost of a swimming lesson rises to $19. How many lessons can she pay for with the remaining $237?

Fabian is 1.65 meters tall. At 12 noon, he measures the length of a tree's shadow to be 18.35 meters. He stands 13.6 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Change the logarithmic equation to an equivalent equation involving an exponent. In x = 9 The equivalent exponential equation is

For a project in her Geometry class, Chloe uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 13.65 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then walks 4.7 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.65 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

A newsletter publisher believes that 26% of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer: Ho: Ha:

A half-century ago, the mean height of women in a particular country in their 20s was 62.4 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.28 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 28 of today's women in their 20s have mean heights of at least 63.33 inches? About of all samples have mean heights of at least 63.33 inches. (Round to one decimal place as needed.)

A boxer needs to lose 3 1/2 kg in a month to be able to compete as a flyweight. In three weeks, he lowers his weight from 55.5 kg to 53.8 kg. How many kilograms must the boxer lose in the final week to be able to compete as a flyweight?

Solve the linear programming problem using the simplex method. Maximize P=2x₁ + 3x₂ + 4x3 X₁ + X3 ≤24 subject to x2 + x3 ≤18 X1, X2, X3 20 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of P is B. There is no optimal solution.

The formula D=20 e -0.6h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered. When the number of milligrams reaches 4, the drug is to be administered again. What is the time between injections? The time between injections is hour(s). (Round to two decimal places as needed.)

Write inequalities to represent the situations below. To get the 10% discount, a shopper must spend more than $300. Used to represent the spending (in dollars) of a shopper who gets the discount. The temperature inside the lab refrigerator is no more than 35 °F. Use t to represent the temperature (in °F) of the refrigerator.

Type the missing number to complete the proportion. 18 plants in 1 row 72 plants in rows

A shipment of small lab mice arrives at an animal care facility. A sample of five mice is selected and weighed. The average weight of the sample is 10.2 g, and the standard deviation of weight among mice is 2 g. Find a 95% confidence interval for the mean weight of all the mice in the shipment. 10.2 ±2.48 10.2 ± 11 10.2 ± 2.30 10.2 1.75

A Potating, panoramic camera attached to a helium balloon can capture images of all the airspace below the balloon. The altitude, in feet, of the balloon m minutes after it is released, is equal to 4 more than the square root of the sum of 100m³ and m². A similar camera is attached to a drone and aimed upward to capture images of all the airspace above the drone. The altitude, in feet, of the drone m minutes after it is launched, is equal to the cube root of the sum of m² and 1,600m. Which system of inequalities represents the altitudes, in feet, of airspace which are captured by both cameras after m minutes?

On the graph of f(x) = sin x and the interval [-2π, 0), for what value(s) of x does the graph cross the x-axis? Choose all answers that apply. Select all that apply: