Basic Math Questions and Answers

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.

Use function notation to rewrite the function y = 25x using d as the function name. The function written in function notation is

Simplify the following expression. 64 -1/3

2. On a number line, which of the following is the greatest distance? The distance between -3 and 0. The distance between -1 and 2. The distance between -2 and 2. The distance between -3 and 0. All distances are equal. The distance between -2 and 2. The distance between -1 and 2.

Currency is used to claim a person's status in society make the exchange of goods or services easier

Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. Write an inequality showing how many bags (b) they would have to sell to make a profit of at least $3832. F 5.50b3832 G 5.50b> 3832 H 5.50b3832 J 5.50b> 3832

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. 6.022 x 1023 x 8.50 × 10² b.(6.6262x 10-34 x 2.998 x 108)/(1.71 x 10 -9) c. 1.388 x 10-2 +1.24 x 10-3 +1.947 x 10-¹ d.(1.00866 1.00722)/(6.02205 x 1023) e.(9.875 x 1029.847 × 10²)/(9.875 x 10²)x 100=(100 is exact)

Solve for x. -3/(x-2)=6/(2x-4)+1 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Solve -7.8=-2.6t. #18 i t = Which statement shows the correct justification for the step used to solve the equation? O Divide each side by -2.6. OMultiply each side by 2.6. O Divide each side by 1.6. O Multiply each side by -1.6.

Using the function defined by f(x) = -8x³ +16 − 3x² + x^9+ 13x², which of the following most accurately describes f? (A) The function is a polynomial of degree 3 with leading coefficient -8 (B) The function is a polynomial of degree -8 with leading coefficient 3 (C)The function is a polynomial of degree 9 with leading coefficient 1 (D) The function is a polynomial of degree 9 with leading coefficient -8

An ice block is in the shape of a rectangular prism. Danny cuts the block so that each side is its 1/2 original length. How do the volumes of the ice blocks compare? A. The new volume is 1/2 the original volume. B. The new volume is 1/4 the original volume. C. The new volume is 1/6 the original volume. D. The new volume is 1/8 the original volume.

Calculate the following using dimensional analysis. A farmer has 52 cows that he must milk daily. If each cow produces, on average, 50 lb of milk per day,and 8 pounds of milk is 1 gallon of milk, how many gallons of milk will the farmer have after 3 days of milking? gallons

Calculate the following using dimensional analysis. A swimmer does a full stroke every 1.5 seconds. He completes a 50-meter race in 1 minute. How many full strokes did he make per meter?

When written in scientific notation, the result of the following arithmetic expression has a digit term (a number between 1 and 10) and an exponential term (a power of 10 signifying the order of magnitude). Calculate: (7.340x10¹8) (4.618x106)/(7.519x10-17) When performing calculations involving powers of ten, use the EE or EXP key on your calculator to enter the power of ten. Do not use the 10x key.