Basic Math Questions and Answers

When entering numbers, leave off units (or dollar signs for money) unless the problem directs you to do otherwise. For example, if we want to know how much money you will have if you collect $100 from 200 people, the answer is $20,000. When entering this value, you should just give 20000 (or 100*200, or anything else which evaluates to 20000).

Solve |2x - 1| - 3 = 14 Enter your answer as a reduced fraction (like 5/3, not 10/6) or as an integer (like 4 or -2). Do not enter mixed numbers. Enter DNE for Does Not Exist, oo for Infinity Enter the smaller solution for an and the larger solution for x₂

The profit from the production and sale of specialty golf hats is given by the function P(x)=20x-4000 where x is the number of hats produced and sold. (a) Producing and selling how many hats will give a profit of $8000? (b) How many hats must be produced and sold to avoid a loss? (a) Producing and selling hats will give a profit of $8000.

It costs $44 per hour plus a flat fee of $29 for a plumber to make a house call. What is an equation of the form y = mx + b for this situation? A. y = 29x B. y = 44x C. y=29x +44 D. y=44x +29

Graph y=2x-4 by plotting points. Based on the graph, determine the intercept(s).

A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. observational study B. survey C. experiment D. theoretical study

Solve for y and graph the equation with a standard window on a graphing utility. x² + 2y = 8

What is the slope for the line that goes through the points (2,13) and (6,3)? Answer may need to be reduced. -4/6 -5/2 -4/10 -10/4 -2/5

Find the midpoint of the line segment joining the points P₁ and P₂ P₁ = (-3, 2); P₂ = (6, 0) The midpoint of the line segment joining the points P₁ and P₂ is [ (Simplify your answer. Type an ordered pair.)

The average monthly bill for wireless telephone subscribers from 1985 to 2008 can be modeled by B(x) = -1.275x+98.208, where x is the number of years after 1980. If this model remains valid, in what year will the average monthly bill be $48.48? The average monthly wireless phone bill would be $48.48 in the year

Find the domain of the following function. Give your answer in interval notation. f(x)=1/√8x - 16

When solving an absolute value equation, such as [2x+3|= 17, it is important to create two equations. 2x+3= Resulting in a = and 2x +3=

A building is 1 ft from a 7-ft fence that surrounds the property. A worker wants to wash a window in the building 10 ft from the ground. He plans to place a ladder over the fence so it rests against the building. (See the figure.) He decides he should place the ladder 7 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?

Penelope is playing a number game with her sister June. Penelope is thinking of a number and wants June to guess it. Five more than three times her number is between 11 and 29. Write a compound inequality that shows the range of numbers that Penelope might be thinking of.

5. Note: This is a knowledge of number theory question. Do not use a calculator for this question. (10 points) Circle the correct response to identify whether the following numbers are factors of 62,296,715,880 (2³ x 3² x 5 x 7 x 472 x 31 x 192) and explain why they are or are not factors using the given prime factorization. 15 IS/IS NOT a factor because: 16 IS/IS NOT a factor because: 75 IS/IS NOT a factor because: 94 IS/IS NOT a factor because: n = 19 x 31² IS/IS NOT a factor because:

The area of a rectangle is 45 nº, and the length of the rectangle is 1 it more than double the width. Find the dimensions of the rectangle.

A store is having a sale on chocolate chips and walnuts. For 2 pounds of chocolate chips and 5 pounds of walnuts, the total cost is $18. For 8 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $21. Find the cost for each pound of chocolate chips and each pound of walnuts. Cost for each pound of chocolate chips: Cost for each pound of walnuts:

A boat is moving away from shore in such a way that at time t hours its distance from shore, in kilometers, is given by the linear function d(t)=4.5t +6.3. What is the rate of change of the distance from shore? A. 4.5 km/hr B. 6.3 km/hr C. 4.5 m/s D. 6.3 m/s

The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give the coordinates after the translation. original coordinates final coordinates (b) Choose the general rule below that describes the translation mapping AABC to AA'B'C'.

An object thrown directly upward is at a height of s=-161²+1281+256 feet after t seconds (a) What is its initial velocity? (b) When does it reach its maximum height? (c) What is its maximum height? (d) When does it hit the ground? (e) with what speed does it hit the ground?

The length of a rectangle is 3 yd less than twice the width, and the area of the rectangle is 44 yd². Find the dimensions of the rectangle.

A town is using a storage container in the shape of an inverted cone to store salt for treating icy roads. If the town needs to store 10,000 cubic feet of salt, and the cone has a height equal to its diameter, what is the height of the storage container? 42.4 feet 67.4 feet 29.4 feet 33.7 feet

The Howard family and the Watson family each used their sprinklers last summer. The Howard family's sprinkler was used for 30 hours. The Watson family's sprinkler was used for 35 hours. There was a combined total output of 1650 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour? Note that the ALEKS graphing calculator can be used to make computations easier.

Plant Trellis You are building the wood trellis shown in the figure so that you can grow a vine up the side of your home. Write an expression for the total number of feet of wood needed to build the trellis. Hint: Write separate expressions for the number of feet of vertical pieces needed and the number of feet of horizontal pieces needed. Then find the total number of feet of wood needed if the trellis is 8 feet tall and 2 feet wide. xft- y ft

Let f(x) = 1/9 + 6x and g(x) = 7x - 2/9 Find all values of x for which g(x) ≥ f(x).

Find the distance d (P1, P2) between the points P₁ and P2 P₁=(1,-2), P₂=(2,6) (P₁, P₂) = (Simplify your answer. Type an exact answer, using radicals as needed.)

Deshaun is driving to Boston. Let y represent his distance from Boston (in miles). Let x represent the time he has been driving (in hours). Suppose that x and y are related by the equation -55x+275=y. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was Deshaun's distance from Boston when he began his drive? miles What is the change in Deshaun's distance from Boston for each hour he drives? miles

Painting Three weeks ago, an art supply store started selling a paint kit for 75% of the original price. Now the kit is 15% off of the sale price. The expression 0.75x -0.15(0.75x) represents the current price of the paint kit where x is the kit's original price (in dollars). Find the current price of the kit if it originally cost $48.

Add as indicated. 5x + 26 / 2x + 7 + 3x + 2 / 2x + 7 Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Motorcycle A can reach a top speed of 160 miles per hour. Motorcycle B can reach a top speed of 210 feet per second. Which motorcycle has a greater top speed? Motorcycle A Motorcycle B

Use the appropriate reciprocal identity to find the approximate value of sin 8 for the given value of csc 8. Use a calculator. csc 8=2.48003196

True or false: 2 = -5 is a solution to the inequality -2 |z-3|< -20. True False

For what questions is a HISTOGRAM most useful? What about a TABLE? A HISTOGRAM is most useful when I'm being asked . . . A TABLE is most useful when I'm being asked . . .

f(v) is the total revenue from the sale of v sofas. Which of the following does the slope f '(v) represent? Answer 2 Points Total cost of producing v sofas. Increase in total revenue if sales are increased to v + 1 units from v units. Rate of change in additional revenue when v sofas have been sold. Average rate of change in the revenue from the sale of v sofas.

Hong is driving to Miami. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Hong has 56 miles to his destination after 31 minutes of driving, and he has 44.8 miles to his destination after 47 minutes of driving. How many miles will he have to his destination. after 57 minutes of driving?

The area of a rectangle is 77 m², and the length of the rectangle is 10 m less than three times the width. Find the dimensions of the rectangle.

Members of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat. Nonmembers must pay $14.75 each time they rent a boat. How many times would a member and a nonmember have to rent a boat in order to pay the same amount?

Which of the following points lie on the line whose equation is y-4=3/5(x + 2)? (1,5) (-7, -1) (8, 11) (3.7) (-1,0)

Drag the linear equation that corresponds to each description. A line parallel to y = x +2. A line perpendicular to x = 3. A line perpendicular to y = 3x - 6.

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make a whole number product. How many solutions can you find?

Alan is loading a pallet with boxes that each weighs 65 pounds. The pallet can safely support no more than 2015 pounds. How many boxes can he safely load onto the pallet?

f(x) is the velocity in feet per hour a car is traveling at x hours. Which of the following does the slope f '(x) represent? Distance in feet the car has traveled in x hours. Average rate of change in the velocity of the car in feet per hour atx hours. Direction the car is traveling at x hours. Rate of change of the velocity of the car at x hours.

Julian is taking a multiple choice test with a total of 20 points available. Each question is worth exactly 2 points. What would be Julian's test score (out of 20) if he got 2 questions wrong? What would be his score if he got a questions wrong?

Write a linear expression with all rational coefficients such that simplifying the expression requires using the associative property of addition, the commutative property of addition, the Distributive property, the additive inverse property, and the additive identity property. Show your work and explain how your expression simplifies.

Select the correct definition of an observational study from the choices below. A study where subjects are selected based on convenience to the researcher. A study that rejects or fails to reject a statistical hypothesis about a population parameter. A study where neither the subjects nor the researchers know what treatments are being administered to which subjects. A study where researchers manipulate variables and impose treatments on the subjects in the study, then measure and record the responses of the subjects. A study where researchers measure and record data about the subjects in the study, but do not apply any treatments to the subjects or manipulate any variables.

Barbara's new lunch box is only 5 centimeters in height, so it fits in her backpack along with all her books. The lunch box has 3 sections for different types of food. The length and width of the lunch box are 22 centimeters and 14 centimeters. What is the volume of Barbara's new lunch box? cubic centimeters

Jordyn bought 7 shirts and spent $131. Fancy shirts cost $28 and plain shirts cost $15. Let x represent the number of fancy shirts bought and y represent the number of plain shirts bought. Determine which of the following system of equations model this scenario. x+y=7 28x + 15y = 131 x+y = 131 28x + 15y = 7 x+y=7 15x+28y = 131 7x + 7y= 131 28x + 15y = 131

Laura is now trying to come up with a number where three less than 8 times the number is equal to half of 16 times the number after it was increased by 1. She can't seem to find a number that works. Explain why.

Which of these expresses the rate at which she is earning credits? Select the correct answer below: 14 semesters per credit 15 credits per semester 3 credits per semester 14 credits per semester 7 semesters per credit 56 credits per semester

Make a sine wave with the given amplitude, period or frequency, and phase shift. Use the form y = A sin (B(t – C)). Amplitude 1, frequency 0.5, and phase shift 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.)