Basic Math Questions and Answers

Use synthetic division to divide. (9x³ - 9x² +50x +15) ÷ (3x − 1) What is the quotient? What is the remainder?

An issue of Taunton's Fine Woodworking included plans for a hall stand. The total height of the stand is 69 inches. If the base is 47 inches, how tall is the upper portion of the stand?

The boiling point of water was measured at different locations of varying barometric pressures. A regression line of the data is y = 1.9x + 155.3, where y is the boiling point in degrees Fahrenheit and x is the pressure in inches of mercury. Which statement best describes the meaning of the slope in the regression line? A. For every 1 inch of mercury the pressure increases, the boiling point is expected to increase by 1.9 °F. B. For every 1 inch of mercury the pressure increases, the boiling point is expected to increase by 155.3 °F. C. For every 1.9 inches of mercury the pressure increases, the boiling point is expected to increase by 1.9 °F. D. For every 1.9 inches of mercury the pressure increases, the boiling point is expected to increase by 155.3 °F.

If f(x) = 2x² - 7x+1, find each of the following. (a) f(0) (b) f(-5) (c) f(2) (a) f(0) = 1 (b) f(-5) =

At the beginning of the year, Pina Colada Company had total assets of $968,000 and total liabilities of $586,000. Answer the following questions. (a) If total assets increased $135,000 during the year and total liabilities decreased $69,000, what is the amount of stockholders' equity at the end of the year?

The lowest point of the dry lake bed in the Example has an elevation of -18 3/4 ft. What number represents the change in elevation from the start of the path to the lowest point in the dry lake bed? Show your work.

Personal care aide is an occupation that is growing quickly. Assume that, in a certain region, there will be a need for 152,452 personal care aides in 2024, a growth of about 29% over 2014 levels. How many personal care aides were there in this region in 2014?

A friend has a 78% average before the final exam for a course. That score includes everything but the final, which counts for 25% of the course grade. What is the best course grade your friend can earn? What is the minimum score would your friend would need on the final to earn a 75% for the course?

Consider the following operations on the number 1.59 x 10-² Without using a calculator, decide which would give a significantly smaller value than 1.59 x 107, which would give a significantly larger value, or which would give essentially the same value. 1.59 x 10 +2.00 x 100 1.59 x 10-22.00 x 10-6 1.59 x 102x2.00 x 10-6 1.59 x 102 +2.00 x 10-6

Create an equation for the following real-life problem. Adrian needs to rent a car while on vacation. A-plus rentals charges $60 per day plus $0.60 per mile. The rental cost for Mavis Rentals is $70 per day and $0.50 per mile. The equation represents the mileage at which each of the rentals will be the same cost.

Sand falls from a conveyor belt at a rate of 15m3/ min onto the top of a conical pile. The height of the pile is always three-eighths of the diameter of the base. How fast is the height changing when the pile is & m high?

This problem is a checkpoint for solving linear equations (integer coefficients). It will be referred to as Checkpoint 1. Solve each equation. a. 3x+7=-x-1 C. 4x-2+x=-2+2x b. 1-2x+5=4x-3 d. 3x-4+1=-2x-5+5x

In this example, we should not report all the digits from the final calculation. By including all the numbers we imply that we were able to measure the dimensions with greater precision than actually possible with a standard inch ruler. We should round and report the diagonal calculation with two significant figures since the length and width values were given with two significant figures. If we round off in the middle of our calculation and square root 190, we will be removing valuable information that would otherwise provide a more accurate diagonal value. By rounding down midway we end up with a value that is less than the true diagonal value. You could argue that we are going to report our final answer with two significant figures anyway and end up at the same number, but it is a bad habit that can lead to unreliable data in other situations.

In proving the quadratic formula, what is the appropriate justification for the last step? ax+bx+c 0 Need to rewrite for common denominator of 2a Equivalent expressions c) Use completing the square to isolate squared term d) Keeping both sides equivalent e) The last step is incorrect

Simplify the fractions. a) 2/6 b) -4/2 c) 3/-3 d) 2/-4

Lexi runs the snack stand at Belleview Community Pool. This morning, she withdrew $150 from the stand's bank account to buy supplies. When the stand closed this evening, she deposited $437 from the day's sales. What was the total change in the stand's bank account relative to where it started?

Write the indicated amounts, using numerals and abbreviations. Two tablespoons

Lightning flashes and is followed by the sound of thunder. The formula that relates the time between seeing the lightning, hearing the thunder, and the distance from the storm is: t=3y, where = time (seconds) y = distance (kilometers) How far away is the lightning if you hear the thunder 8 seconds after you see the lightning? A3/8km B. 2 2/3 km C. 5 km D. 11 km E. 24 km

A chemist mixes 125 milliliters of a solution that is 18% acid with 500 milliliters of pure acid. Answer the questions below. Do not do any rounding. (a) How many milliliters of acid are in the resulting mixture? (b) What percentage of the resulting mixture is acid?

Tom's team takes 2 hours to build the machine, while Sara's team takes 3 hours to build the same machine. If they work together at the same rates, how long will it take them to finish the same machine? a) 20 minutes b) 30 minutes c) 50 minutes d) 5 hours e) Answer is not here

In a tiny country the current population is 200,000 and is increasing at 2.5% a year. Most of the people eat rice as a basic part of their diet, and the country can produce enough rice for 300,000 people. Assuming they continue to produce the same amount of rice each year, how long will it be before there are shortages in rice and they have to start importing it?

Which subset describes the following set of numb -5, -8, 11, 430 A. Whole Numbers B. Integers C. Both of the above D. None of the above

Jia is thinking of a number. She gives three clues about the number: the number is even, the number is less than-12, and the absolute value of the number is between 9 and 15. What is Jia's number? Explain how you know.

Consider the equation shown in the box, where p and q are real numbers. For what values does the equation represent a proportional relationship? p=0,q=1 p=0,9-2 p=1,9 -0 p=1,9-2 ypx +q

You can do this exercise as a thought experiment or follow along with a real piece of paper and a ruler. You're trying to determine the diagonal length of a piece of paper by two methods. One is to measure the diagonal with the ruler. Second method is to measure the width and length, then calculate the diagonal by using the Pythagorean theorem. Using the first method, you measure the diagonal as 14". Using the second method, you measure 8.5" by 11". squaring each and adding, you get 193.25 sq in, then you take the square root to determine the calculated diagonal length. The calculator shows the number, 13.901439. Should you write down all of these numbers in your answer? Why or why not? What happens if, instead of using 193.25, you round off in the middle of your calculation to 190 and take the square root?

A supermarket offers a delivery service. If a customer pays $9 per month, each delivery costs just $2. Write an equation that shows how the total cost for a month, y, depends on the number of deliveries, x.

It is the least four-digit number that can be rounded up to the nearest hundred as 4,100. Write it in expanded form:

A 16-foot ladder is leaning against a building If the bottom of the ladder is sliding along the pavement directly away from the building at 2 ft/sec, how fast is the top of the ladder moving down when the foot of the ladder is 4 feet from the wall? ft/sec when the foot of the ladder is 4 feet from the wall. The top of the ladder is moving down at a rate of (Round to the nearest thousandth as needed.)

A tour group is going sea diving. The ocean floor is at-18 ft relative to sea level. One diver is already at 11 ft. The tour guide is keeping watch on a platform 5 ft above sea level, directly above the diver. PART B Write an absolute value inequality comparing the distances of the tour guide and the diver to sea level. Who is closer to sea level? Explain how you know.

Ralph and Alphonse are shooting marbles. Ralph has five more marbles than Alphonse, and they have a total of 73 marbles. How many marbles does each of them have?

A rectangular prism is shown. How will doubling the length of each edge affect the surface area of the prism? A. The surface area will be 2 times the original surface area. B. The surface area will be 3 times the original surface area. C. The surface area will be 4 times the original surface area. D. The surface area will be 6 times the original surface area.

Jenna and Dom get married. They start off with $7,000 in their bank account. Jenna, being the bread-winner of the family, puts $250 per month into the account so their kids can go to college one day. Write the equation to model the amount of money m, that will be in the account after t months. How much will be in the account after their third year of marriage (and second child, might I add)?

In case the ball doesn't reach Martice, in the previous problem, Coach Kelly will place Nick at the midpoint. Where is Nick on Coach Kelly's grid? Coach Kelly drew his football team's next play on a coordinate grid. He placed Jon at (6,3). He will be passing the ball to Martice at (-6,9). (6, 1) (0, 6) (6, -1) (-6, 6)

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car. Equation:____= 648.45 t =

Calculate the following using dimensional analysis. A chef is adding a new dessert for his restaurant. For every 100 servings of the dessert, he will need a bag of flour. How many bags of flour will he need per week if he is open six nights per week for dinner, and he expects to serve dessert to 40 guests per night?

Graham uses a hot water bottle on an injury to his back he incurred playing basketball. He fills the bottle with water that is a temperature of 100°F. After 25 minutes, Graham finds that the bottle has cooled and he stops using it.

A group of students stood in a circle to play a game. The circle had a diameter of 22 meters. Which measurement is closest to the circumference of the circle in meters?

Isabella filled her pool with water at a constant rate. The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes). How fast did Isabella fill her pool?

Hassan invests some money into an account that pays 6% interest per year and the rest in an account that pays 4% per year. He invests twice as much money into the account that pays 6% interest than the account that pays 4% interest. If he earns $120 in interest after one year, how much money was in each account?

A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z-score corresponding to the given value and use the z-score to determine whether the value is significant. Consider a score to be significant if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A. -17.6; significant B. 1.6; not significant C. -1.6; significant D. -1.6; not significant

A shipping company sells large boxes and small boxes. The dimensions of the large box are 3 times the dimensions of the small box. How does the volume of the large box compare to the volume of the small box? A. The volume of the large box is 3 times the volume of the small box. B. The volume of the large box is 6 times the volume of the small box. C. The volume of the large box is 9 times the volume of the small box. D. The volume of the large box is 27 times the volume of the small box.

State whether the data described below are discrete or continuous, and explain why. The numbers of people looking at a website at different times Choose the correct answer below. A. The data are continuous because the data can only take on specific values. B. The data are continuous because the data can take on any value in an interval. C. The data are discrete because the data can only take on specific values. D. The data are discrete because the data can take on any value in an interval.

-4.24x² +3.72x + 1.94 = 0 is solved, the two values of the unknown z are and

A park is studying how its population of deer grows over time. The regression line of their data is y= 15x+1200, where z represents the number of years since the study began and y represents the number of deer. What does the slope of the regression line represent? A. The deer population will reach 1, 200 in 15 years. B. The deer population grows by 1,200 every 15 years. C. There were 15 deer in the park at the beginning of the study. D. For every 1 year, the deer population increased by an average of 15. E. For every 1 year, the deer population increased by an average of 1,200.

In a recent awards ceremony, the age of the winner for best actor was 31 and the age of the winner for best actress was 51. For all best actors, the mean age is 43.7 years and the standard deviation is 6.3 years. For all best actresses, the age is 34.9 years and the standard deviation is 12.3 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain. Since the z score for the actor is z = (Round to two decimal places.) and the z score for the actress is z = the had the more extreme age.

Four snail friends are out racing. They are able to go fast at the beginning, but they become tired and their distances from the starting point are modeled by the following equations: k(x) = -log(x) + 3, 3 g(x) = log(x) + log(x-1), h(x) = log(2x) - log(x+1), and f(x) = 2log(x). When will the slowest one get to 5 miles if x represents time in minutes? a) About 5.27 hours d) About 1.90 years b) About 5.28 hours e) Answer is not there c) About 5 hours

Lena's paycheck this week was $21.56 less than her paycheck last week. Her paycheck this week was $125.48. How much was Lena's paycheck last week?

For her grandfather's birthday, Valeria is baking cupcakes. With every egg she can find, she can bake 6 cupcakes. Write an equation that shows how the total number of cupcakes Valeria can bake, y, depends on the number of eggs she can find, x.

The function W(d) = 0.112d approximates the amount, in centimeters, of water that results from d cm of snow melting. Find the amount of water that results from snow melting from depths of 16 cm, 30 cm, and 67 cm. 16 cm of snow melting produces___cm of water.

Meiling and Jackie are playing a game of chance with a six-sided number cube. The sides of the cube are numbered 1 to 6. Meiling scores a point each time she rolls a number greater than 4. Which would give Jackie an equally likely chance for a point? A Jackie rolls a number that is greater than 2. B. Jackie rolls a number that is less than 2. C. Jackie rolls a number that is greater than 3. D. Jackie rolls a number that is less than 3. OE. Jackie rolls a number that is less than 4.