Basic Math Questions and Answers

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?

When f(x) = 6x²-2x - 6, evaluate f(-3) f(-3) =

The number of streetlights in a town is growing linearly. Four months ago (n = 0) there were 130 lights. Now (n = 4) there are 146 lights. If this trend continues, how many months will it take to reach 200 lights?

Express the fact that x differs from 11 by less than 6 as an inequality involving absolute value. Solve for x. Express the given sentence algebraically as an inequality involving absolute value.

Write the first five terms of the sequence. f(0) = 3: f(n) = f(n-1) 2 f(0) = f(1) = f(2)= f(3) = f(4) =

Identify all the numbered angles that are congruent to the given angle. List the numbers of any angles that are congruent to the given angle.

What words describe how Anthony should build the next model in his series of concrete representations of this situation? O The pool should be 3 squares by 5 squares, and the border should be 4 squares by 6 The pool should be 3 squares by 5 squares, and the border should be 4 squares by 7 squares. squares. O The pool should be 3 squares by 5 squares, and the border should be 5 squares by 7 squares.

The position of a model train, in feet along a railroad track, is given by s(t) = 2.5t + 17 after t seconds. (a) How fast is the train moving? ft/sec (b) Where is the train after 4 seconds? feet along the track (c) When will the train be 32 feet along the track? t= sec

(a) Write an equation representing the fact that the product of two consecutive odd integers is 195. Use x to represent the smaller integer. (b) Solve the equation from part (a) to find the two integers. Part 1 of 2 (a) The equation is (x + 15) (x - 13) = = 0 Part: 1 / 2 Part 2 of 2 (b) Find the pair(s) of consecutive odd integers. If there is more than one pair, use the "or" button. and or X

A pump removes 1000 gallons of water from a pool at a constant rate of 50 gal/min. Write an equation to find the amount of water, w, in the pool after t minutes. How long will it take for the pool to become half-empty?

bstitution to Identify Solutions of Inequalities Read and try to solve the problem below. Pilar has a gift card for a sporting goods store. She has $42.50 left on the card. She plans to buy one pair of yoga socks for $8. There are four other items that she is looking at. Use the inequality x + 8 = 42.50, where x is the price of an item, to determine which of the other four items Pilar can buy. Yoga Socks 58.00 BUT HER Bike Helmet 530.00 ** BUT NOW Baseball Bat $38.50 BUT NOW Running Shoes 535.50 BUY NOW Swim Goggles $28.50 SUY NOW

Is the graph of the function f(x) = 9x5 + 7x symmetric with respect to the origin? O Yes, the graph is symmetric about the origin. O No, this graph has no symmetry. O No, but the graph is symmetric about the x-axis. O No, but the graph is symmetric about the y-axis.

An insurance policy on an electrical device pays a benefit of $5500 if the device fails during the first year. The amount of the benefit decreases by $1100 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.42. Find the expected benefit under this policy,

Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces? O(-3,-18) O (-0.5, -3) O (0,0) O (0.5, 3)

(1) Cora cut 3 shelves of equal length using 2/3 of a yard of wood. How long was each shelf? ◄) Write your answer as a fraction or as a whole or mixed number. D yards

Two lengths of stereo speaker wire total 32.5 ft. One length is 2.9 ft longer than the other. How long is each length of speaker wire?

Select the correct third step and reasoning: O -4; Division Property of Equality O x = 2; Division Property of Equality O x = -4; Multiplication Property of Equality O X x = 2; Multiplication Property of Equality X =

Given that an investment into a college fund is represented by A = 12, 000e(0.023.12) match each value to the correct description of the value in the context of the question. The amount of money in the av The amount of money in the account at the end of the time given. The initial amount of money invested into the college fund The amount of years the money is invested. The interest rate. The interest is compounded continuously.

Find the derivative of the function without using the Quotient Rule. 12/13x² Step 1 Rewrite the equation so the variable is not in the denominator. y =12x/13

Your college professor tells you he will give a 30 % -30% -40% split on grades between homework, quizzes, and test. However whichever category you have the highest average in will be the 40% category. What will your final grade be if your homework average is 57, you quiz average is 97, and your test average is 86? Type your answer...

We want to solve the equation x² - 8x +15=0 First, factor x² - 8x + 15: By the zero product property we know: And therefore we know that: Do not use decimal approximations in your answer. Use fractions instead.