Basic Math Questions and Answers

Fill in the blank with the most appropriate term or phrase. A line that falls from left to right has a(n) slope.

If $P is invested for n years at a rate / (as a decimal), compounded annually, the future value that accrues is given by S = P(1 + i)", and the interest earned is I = S-P. Find S and I for the given P, n and i. (Round your answers to the nearest cent.) $1300 for 5 years at 11% S = $ I = $

Chocolate Bliss sells their box of chocolate candy for $2.00 per candy plus a $12 packaging fee. Expressions in Sweets sells their box of chocolate candy for $3.00 per candy plus a $10 packaging fee. If five boxes of Chocolate Bliss chocolate candy cost the same as four boxes of Expressions in Sweets chocolate candy, how many candies are in each box?

11 If a skyscraper has a height of 235 feet, could it be in the town described in problem 3? Explain why or why not.

Sonya drank 4 oz of juice and 8 oz of milk for breakfast; for lunch she had a 12 oz soda, then she drank another 12 oz soda mid- (use either proportion or afternoon. For dinner she drank 16 oz of water. The amount of fluid she drank equals dimensional analysis) liters

The length of a rectangle is 7 yd more than twice the width x. The area is 855 yd². Part 1 of 3 (a) Write an equation in terms of x that represents the given relationship. The equation is x (2x + 7) = 855 Part 2 of 3 (b) Solve the equation to find the dimensions of the given shape. The width is 19 yd. Part: 2/3 Part 3 of 3 The length is yd. X

What is the simplified expression for the expression below? (5x+20)-(4x-28) -2x+3 -2x-3 O-2x-8 -2x+8

Solve for v, where v is a real number. √v-10=6 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Tutorial Exercise Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (3x + 3y)³ = 27x³ + 27y³, (-1, 1) Step 1 Expand the term (3x + 3y)3 in (3x + 3y)3 = 27x3 + 27y³ and simplify. (3x + 3y)³ = 27x³ + 27y³ 27x3 + 81x²y + 81xy2 + 27y3 = 27x³ + 27y³ 81x²y + 81xy² x²y + = = 0

A physician orders 1/2 fl oz of medication for a patient. How many milliliters of medication should the patient be given? mL

Solve for w. -30w-25=9w² If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

5 6 Find the lateral and surface area of a cylinder with base area 49 m² and a height 2 meters less than the radius. The lateral area of the cube is The surface area of the cube is 2 3 m². m². 4 7 y.hrw.com/dashboard/

(a) Simplify s³s⁹ and write your answer without using negative exponents. (b) Simplify s³s-⁹ and write your answer without using negative exponents. (c) Simplify s-³s⁹ and write your answer without using negative exponents. (d) Simplify s-³s-⁹ and write your answer without using negative exponents.

Which conversion factors are used to multiply to 18 cm/s to get meters per minute? Select each correct answer. 0 1 m 100 cm 100 cm 1 m 60 s 1 min

Hans has scored 20, 17, and 24 points in his three basketball games so far. How many points does he need to score in his next game so that his average (mean) is 22 points per game?

Which description is represented by a discrete graph? O Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax? The temperature at 9 a.m. was 83° F and is heating up at an average rate of 6°F per hour. What is the temperature x hours later? O Juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. What is the total amount of calories he consumed? O A bottle contained 2,000 mL of liquid and is being poured out at an average rate of 300 mL per second. How much liquid is left in the bottle after x seconds?

Sonya, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $391 for 44 hours worked. What is her regular hourly rate? Sonya's regular hourly rate is $ per hour.

A small manufacturing company produces child-sized and adult-sized adirondack chairs. The company makes a profit of $40 on each child-sized chair and $75 on each adult-sized chair. The manufacturer can make a total of 150 chairs per week. It takes 1 hour of labor to make a child-sized chair and 2 hours of labor to make an adult-sized chair, and the company has 200 hours of labor available per week. Let x represent the number of child-sized chairs and y represent the number of adult-sized chairs. Determine how many child-sized and adult-sized adirondack chairs should be manufactured weekly to maximize production. O 50 child-sized chairs and 100 adult-sized chairs O 150 child-sized chairs and 0 adult-sized chairs O 0 child-sized chairs and 100 adult-sized chairs O 100 child-sized chairs and 50 adult-sized chairs

Is this equation an identity? 9n + 9 = 9n - 17 yes no

(a) Simplify 5.6 and write your answer without using negative exponents. (b) Simplify a (c) Simplify (d) Simplify 13 a and write your answer without using negative exponents. 2 p13 a and write your answer without using negative exponents. and write your answer without using negative exponents.

Write the following expression in exponential form. -5•-5•-5•-5 -5•-5•-5•-5= (Use integers or fractions for any numbers in the expression.)

Abe earned a score of 144 on a test with a mean of 128 and standard deviation of 34. Bob earned a score of 90 on a test with a mean of 86 and standard deviation of 18. Caleb earned a score of 18 on a test with a mean of 15 and standard deviation of 5. a) Which student has the best relative position? Give an answer of Abe, Bob, Caleb, or none (if all performed the same)? b) To two decimal places, what is the standard score of the value chosen in part (a)? A/ 1

Matt invested $300 into an account that had an annual interest rate of 3.8% compounded monthly for 5 years. Chris invested $350 into an account that had an annual interest rate of 3.5% compounded continuously for 5 years. Determine which models could be used to determine how much money would be in each account after 5 years. O Matt: A = 300 (1 + 0.038) 60 12 Chris: A 350e (0.035.5) O Matt: A 300e(0.038.5) Chris: A = 350(1+0.35)5 Matt: A = 300 (1 + 5) Chris: A 350e (3.5-5) B Matt: A = 300 (1 + 0.035) 60 12 Chris: A350e(0.35-5)

A vacant city lot is being turned into a neighborhood garden. The neighbors want to fence in a triangular section of the lot and plant flowers there. The longest side of the triangular section is 7 feet shorter than twice the shortest side. The third side is 2 feet longer than the shortest side. The perimeter is 59 feet. How long is each side?

Graph f(x) = 6. Use the graphing tool to graph the function.

A 10-yr-old competes in gymnastics. For several competitions she received the following "All-Around" scores: 37.9, 37.4, 37.8, and 38.7. Her coach recommends that gymnasts whose "All-Around" scores average at least 36.3 move up to next level. What "All-Around" scores in the next competition would result in the child being eligible to move up?

Shen needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $170 and the labor is $40/hr. (a) Write a model that represents the cost of the repair C (in $) in terms of the number of hours of labor x. The model that represents the cost of repairs is C = (b) After how many hours of labor would the cost of the repair job equal the cost of a new toilet of $370? It would take hours of labor for the cost of the repair job to equal the cost of a new toilet.

A boat travels upstream for 288 miles in 4 hours and returns in 3 hours traveling downstream in a local stream of water. What is the rate of the boat in still water and the rate of the current? The rate of the boat in still water is The rate of the current is miles per hour. miles per hour.

Is this equation an identity? -2 3c + 2c = 9 - c - yes no

68. Mrs. Larson's math class is using cardboard to build a scale model of the Great Pyramid of Khufu in Egypt. The surface area of this pyramid is about 1,496,510 sq. feet. If the scale factor of the surface area of the model to the original is 1:100, how much cardboard will the class need to make the model?

The earnings of two employees are given below: Rachel: 7% on all sales Gunther: 4% commission on the first $60,000 and 7% on anything over $60,000. How much more does a straight commission employee make than the graduated commission employee for sales of $100,000?

Patrick spends on apples in a week. Then write an inequality that represents pound, Draw a graph that represents the possible amounts of money, m, that your graph. Show your work.

At his wellness checkup, Jacob was told that as a healthy male adult, he should drink about 3 liters of fluid every day. Jacob asked how many cups of fluid that would be, and the physician replied that he should drink of fluid per day. If the answer results in a mixed number be sure to include a space between the whole number and the fraction. Example: 1 1/4 (read as one and one-fourth). cups

Given that f(x) = 2(x - 3)² - 8, determine the true statement. The x intercepts of the graph of f(x) are (1,0) and (5,0). O The graph of f(x) is decreasing from (3, ∞). O The domain of f(x) is x > 3. O The range of f(x) is y> -8. O The graph of f(x) has a maximum point at (3, -8).

10 Given f(x) = 2x²-4, which of the following represents a point on the graph of the function? A. f(3) = 16; to eat the cake B. f(-5) = -46; they got to decorate C. f(4) = 28; the house looked festive D. f(-2) = -8; the internet was back on

Tiana cannot read traffic signs that are more than 50 m away. Which inequality represents the distances, d, at which Tiana can read traffic signs? A d > 50 B d≥ 50 C d < 50 D d≤ 50 Erik chose A as the correct answer. How might he have gotten that answer?

Jimmy brings $24 to the county fair for rides. Roller coaster rides are $2, and the spinning cup rides cost $3. But Jimmy knows that he gets queasy if he takes more than 6 roller coaster rides or more than 8 spinning cup rides. Let r represent the number of roller coaster rides and let s represent the number of spinning cup rides. In addition to r ≥ 0; s ≥ 0, which is a set of inequalities that Jimmy can use to guide his choice of rides? Ar+s≤ 24; r ≤ 6; s < 8 Br+s≤ 24 C2r + 3s ≤ 24; r ≤ 6; s ≤ 8 D 2r ≤ 6; 3s ≤ 8

A physician whose patient suffers from severe arthritis wrote a prescription for 100 mg of Celebrex twice daily for 90 days. At the end of the 90 days, the patient will have taken of Celebrex grams

A vendor at a craft show sold items for $4.50, $6.00, and $7.50. Altogether, the vendor sold 87 items for a total of $489. The vendor sold 5 more items for $6.00 than for $7.50. Which system of equations could you use to determine how many of each item were sold? Ax + y + z = 87 z = y + 5 4.5x + 6y + 7.5z = 489 B) x + y + z = 87 y = z + 5 4.5x + 6y + 7.5z = 489 x + y + z = 489 y = z + 5 4.5x + 6y + 7.5z = 87 Dx + y + z = 489

Two companies, Chocolate Bliss and Expressions in Sweets, sell a special heart shaped box of chocolate candy for Valentine's Day containing the same number of candies. Chocolate Bliss sells their box of chocolate candy for $2.00 per candy plus a $12 packaging fee. Expressions in Sweets sells their box of chocolate candy for $3.00 per candy plus a $10 packaging fee. If five boxes of Chocolate Bliss chocolate candy cost the same as four boxes of Expressions in Sweets chocolate candy, how many candies are in each box? Define the variables and write the equations. Solve for your variables: Check your work: Explain what your answer means in the context of the problem

Find the domain and range of the function. (Enter your answers using interval notation.) g(x) = x² - 8 domain range

2. Greg received a 95 on his last math test. The only question that he got wrong is listed below. (a) Read through Greg's work and circle his mistake. Evaluate: ²-2(x-3) when x = 3. Greg's work: (b) Explain what Greg did wrong. = *²-2(x-3) = 3²-2(3-3) 3²-2(0) = 9-2(0) = =7(0) = 0 (c) Revise Greg's work and state the correct value of the expression.

Solve the inequality algebraically. Graph the solution set. Verify your results using a graphing utility. |2x+3|-5≥-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution is the empty set.

While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars O44.70 US dollars 73.06 US dollars 136.87 US dollars O140.41 US dollars

Consider the provided five-number summary: Minimum = 4, Q₁ = 8, M = 12, Q3 = 15, Maximum = 19. Which set of seven numbers have the same five-number summary? 4, 8, 9, 12, 14, 15, 19 4, 8, 10, 12, 17, 16, 20 4, 8, 11, 13, 11, 14, 19 1, 5, 12, 11, 13, 15, 19

The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p) = -12p2 + 186p, where p is the price charged per pet (in dollars). (a) Find the revenue earned for each price per pet given below. R($2) $324 R($6) $684 R($7) $714 (b) Find the unit price that yields a maximum revenue. $ 7.75 per pet What is the maximum revenue? $ 645 x Explain.

Let P(t) represent the number of cars in a school parking lot t hours after 7 a.m. P(0) = 8 and P'(0) = 12, which of the following statements must be true? 1. The instantaneous rate of change in the number of cars in the parking lot is 12 cars per hour at 7 a.m. II. The number of cars in the parking lot is increasing at 7 a.m. III. There are 20 cars in the parking lot at 8 a.m. Onone Olonly OI and II only II and III only

It took Sharon 4 hours to drive to her grandmother's house. Her grandmother lives 140 miles from Sharon. What was Sharon's average speed for this trip? 30 mph 35 mph 136 mph 560 mph

What is the slope of the line through (-8, 9) and (5,9)? If the slope is undefined, type undefined. What is the slope of the line through (-6, 9) and (-7,10)? If the slope is undefined, type undefined.. What is the slope of the line through (-10, 1) and (-10,2)? If the slope is undefined, type undefined.

Ross had an annual earned income of $48,000 last year. He also had a passive income of $3,500, and capital gains of $4,000. What was Ross' total gross income for the year?