Basic Math Questions and Answers

A farmer has 1200 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 per acre to grow wheat, and $50 per acre to grow soybeans. Because of market demand, the farmer will grow twice as many acres of wheat as of com. He has allocated $63,750 for the cost of growing his crops. How many acres of each crop should he plant? Be sure to include units.

How many widgets should Jesaki Inc. produce and sell in order to maximize revenue? widgets. Round to the nearest widget.

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there? 10 pigs and 0 ducks 2 pigs and 8 ducks 3 pigs and 7 ducks 8 pigs and 2 ducks

A movie theater sells two different sizes of candy. Small boxes cost $4.20 and large boxes cost $9.00. a. Complete the table to the right. b. If the theater sold 45 boxes of candy in one hour, write an equation relating the number of boxes sold. c. If the theater earned a total of $309 in that one hour, write an equation relating the total amount earned. Categories Value Number Amount Small box 4.20 x .... Large box 9.00 y ...

A boat travels between two cities that are 7 miles apart. When going downstream, with the current, the trip takes 1/2 hour(s). Returning upstream, against the current, the boat covers the same 7/6 hour(s).

The perimeter of the rectangle below is 170 units. Find the value of y.

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take Graham and Max to meet at the same altitude? a. Equation: b. Solution: c. At what altitude will Graham and Max meet? text

A rocket is fired upward with a velocity (v) of 580 feet per second. Find how many seconds pass before the rocket reaches the ground (S=0) again. Use the quadratic equation S= - 16t² +580t.

This is page 6 of 6 in section II. Use the "Jump to: Page" links to navigate among the pages. Do not use your browser's " back" button or you will lose any answers entered on the current page. 51. An equation for the line with slope that passes through the point (-6, 3) is A. 2x + 4y = 12 B. 2x - 4y = -12 C. 4x + 2y = -18 D. 2x + 4y = 0 E. 2x - 4y = -24

Find the x-intercepts (horizontal intercepts) of the function: f(x) = 4|x + 4| − 2 The intercepts are at x = Separate values with commas.

The solution of the inequality (x +50)/4 < 2 is A. x < -58 B. x < 42 C. x < -42 D. x < -46 E. x < 58

If x+a/b = 2.5 and a = 28, b = 4 then x = A. 38 B.-18 C.-27.375 D. -28.625 E. -38

In planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $2175.

An equation for the line with slope that passes through the point (-6, 3) is A. 2x + 4y = 12 B. 2x - 4y = -12 C. 4x + 2y = -18 D. 2x + 4y = 0 E. 2x - 4y = -24

The volume V, in liters, of air in the lungs during a four-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t2 0.0374t3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to four decimal places.)

A woman uses a loan program for small businesses to obtain a loan to help expand her vending machine business. The woman borrows $22,000 for 4 years with a simple interest rate of 1.3%. Determine the amount of money the woman must repay after 4 years.

Lollipops are selling for $5.00 a pound. Tootsie Rolls are selling for $2.50 a pound. Wendy wants to spend exactly $80 to get a total of 30 pounds of candy. How many pounds of each should she get?

Jason is planning to build a gazebo in the shape of a regular octagon. He is laying out his blueprints on a coordinate plane where each grid mark represents 1 foot. Two consecutive vertices are located at (1,4) and (4,8). He wants to enclose the gazebo with fencing. What is the perimeter of the gazebo?

Jenny applied for an $8,000 home improvement loan, which she will start paying back after the interest has accumulated. One bank offered her a simple annual interest rate of 7% for fi years. She decided to consider other options. Which of the following change will decrease the interest she pays the most? (8.1A, 8.1B, 8.1C, 8.1G) A Simple interest, annual rate of 7.2%, term of 5 years B Simple interest, annual rate of 6.75%, term of 5 years C Simple interest, annual rate of 7%, term of 4.75 years D Compound interest, annual rate 7%, term of 5 years

Marissa Chambers wants to open a savings account, but the bank requires a $250.00 initial deposit. She breaks her piggy bank, which contains 4 ten-dollar bills, 7five-dollar bills, 24 one-dollar bills, 11 quarters, 14 dimes, 29 nickels, and 72 pennies. She also has a check from her uncle for $100. If she deposits all her money, how much more will she need to meet the bank's required amount? The required amount is $

Let f(x) = (x - 3)² Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f restricted to this domain. f ¹(x) =

The following data provides the number of Calories of various types of frozen bars. (28, 35, 200, 280, 80, 80, 90, 40, 45, 50, 50, 60, 90, 100, 120, 40, 45, 60, 70, 350} a. Draw a histogram to represent the data. b. Find the measures of center.

The price of a gallon of gasoline is $4.05. The price when Ryan's mother started driving was 9 of the current price. What was the price of gasoline when Ryan's mother started driving? A. $1.40 B. $0.90 C. $3.83 D. $4.27

. A child starts a piggy bank with $2. Each day, the child receives 25 cents at the end of the day and puts it in the bank. If A represents the amount of money and d stands for the number of days then 4(d)=2+0.25d gives the amount of money in the bank as a function of days (think about this formula). (a) Evaluate 4(1), A(7), and 4(30). (b) For what value of d will A(d) = $10.50. (c) Explain why the domain does not contain the value d = 2.5. (d) Explain why the range does not include the value A = $3.10.

A truck driver operates a delivery service in a southern city. His start-up costs amounted to $2600. He estimates that it costs him (in terms of gasoline, wear and tear on his truck, etc.) $5.00 per delivery. He charges $7.50 per delivery. Let x represent the number of deliveries he makes. (a) Express the cost C as a function of x. (b) Express the revenue R as a function of x. (c) Determine analytically the value of x for which revenue equals cost. (d) Graph y₁ = C(x) and y₂ = R(x) on the same xy-axes and interpret the graphs. (a) C(x) =

Ralph Chase plans to sell a piece of property for $170000. He wants the money to be paid off in two ways - a short-term note at 11% interest and a long-term note at 8% interest. Find the amount of each note if the total annual interest paid is $16300. The amount of the 11% note is $ and the amount of the 8% note is $

The function D(t) can be used to approximate the total average credit card debt in a U.S. household (in thousands of dollars) t years after 1995. Interpret the meaning of the statement: D(24) = 20.9. In the year the total average credit card debt for a U.S. household will be $

Find the distance between the pair of points (0.-√14) and (√31,0). If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is 3√√5 units. The distance between the given points is approximately units.

If all the components of a vector are equal to 1, then that vector is a unit vector. True False

What is the radian measure of the angle whose degree measure is 210°? A. 150/180 π B. 180/210 π C. 330/ 180 π D. 30/ 180 π E. 210 / 180 π

Clark has 7 1/2 feet of wire. Part A: How many foot pieces can Clark cut from the 71/2 feet of wire? Show your work. Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given. (5 points)

A pizza company is building a rectangular solid box to be able to deliver personal pan pizzas. The pizza company wants the volume of the delivery box to be 480 cubic inches. The length of the delivery box is 6 inches less than twice the width, and the height is 2 inches less than the width. Determine the width of the delivery box. 4 inches 6 inches 8 inches 10 inches

Use the diagram below to fill in the blanks for the following explanation: Reflect right triangle ABC across line BC. Classify triangle ACA' according to its side lengths. Explain how you know.

Convert the expression x² + 12x + 27 into vertex form.

Find the intersection points of the parabola y = -x² - 2 and the line -x + y = -4. Give your answer as two ordered pairs separated by a comma. For example, if you found that the solutions were (1, 2) and (3, 4) you would enter (1, 2), (3, 4).

Compute the specified quantity. Your total payment on a 8 year loan, which charged 9% annual simple interest, amounted to $20,260. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.) $

Which inequality is true when the value of k is -1? k-3>4 -k-3<-4 -k-3>4 -k-3>4

The following passage from Julius Caesar is in reverse word order. Which answer best describes its meaning? BRUTUS: Thus must I piece it out A. Thus, I give out pieces B. Thus, I must figure it out C. Thus, I must be out of pieces

A coin is to be flipped four times, in sequence. What is the probability that the number of tails will never exceed the number of heads? The sequence HHTH satisfies the description, as does HTHT. However, in each of the sequences THHH and HTTH there is a point at which the number of tails exceeds the number of heads.

For f(x) = 9x and g(x)=x+6, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(4); d. (gof)(4)

A board is cut into 8 pieces. This requires the carpenter to make 7 cuts. Each cut produces a kerf, destroying a small amount of wood. If each kerf destroys 5/32" of the board, what total length of board will be lost to kerf once all cuts have been made?

A 6 year bond costs $20,000 and will pay a total of $2,000 in interest over its lifetime. What is its annual interest rate r (as a percent)? (Round your answer to three decimal places.)

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. We let P be any point on line 1, but different from point X. X Given: px is the bisector of YZ Prove: YP = ZP Send To Proof Send To Proof

What are the coordinates of the point of intersection of y = 5x -5 and y=2 - 2x? The coordinates of the point of intersection are (Type an ordered pair.)

Use the Segment Addition Postulate to find the missing length if the given points are collinear and appear in alphabetical order.

Write the linear equation in slope-intercept form y=b+mx. What are the values of m and b? y=100-2(x - 25) y=

Yesterday in Juneau, Alaska it was -20 degrees and in San Dieg California it was 75 degrees. What was the difference in temperature between these two cities? Select one: a. -20 degrees b. 55 degrees C. 75 degrees d. 95 degrees

You have decided to start saving for college and open up a 529 account. You invest $5,000 into the account at a 4% interest rate compounded monthly. How much money will you have after 7 years? $11,533.61 $13,482.02 $6,579.66 $6,612.57

Hurricane Bob is currently located at (18N, 53W). It is traveling at 11 knots. How far away from Galveston is it if Galveston is at (29N, 95W)? How long would it take to get there in hours and in days? You must show work to get credit.

If 4 is decreased to 1, the decrease is what percent of the original number?