Basic Math Questions and Answers

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?

In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the area polluted is circular, determine how fast the area is increasing when the radius of the circle is 38 ft and is increasing at the rate of 1 ft/sec?

Assume 520,000 people line up on the streets to see the Macy's Thanksgiving Parade. If attendance is expected to increase 25% next year, what will be the number of people lined up on the street to see the parade? Number of people

Why can't first differences be used to tell if the following data is linear? (2,8), (6,11), (8,14), (11,17) Choose the correct answer below. A. The first differences are not equal. B. The difference between inputs is not constant. C. The inputs and output values are all positive. D. The difference between inputs is constant.

Which inequality is true when the value of a is-18?

What color flag signified a comedy would be shown that night? A. A black flag signified a comedy would be shown that night. B. A white flag signified a comedy would be shown that night, C. A red flag signified a comedy would be shown that night, D. A brown flag signified a comedy would be shown that night.

Consider the force exerted by a spring that obeys Hooke's law. Find where U(xf) - U(x) = - SF₁.ds, Fs = -kx i, ds == dx i, and the spring constant k is positive. Express your answer in terms of k, xo, and xf.

Solve the equation. x+6/8 x + 53 What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is {x|x is a real number}. C. The solution set is Ø. .

The length of a new rectangular playing field is 9 yards longer than triple the width. If the perimeter of the rectangular playing field is 466 yards, what are its dimensions?

Puthina Unge bought a new Compaq computer system on sale for $1,990. It was advertised as 30% off the regular price. What was the original price of the computer? (Round to the nearest whole dollar.)

The percentage of families that were married couples with children between 1970 and 2000 is approximately where t is measured in decades, with t = 1 corresponding to 1970. (a) What percentage of families were married couples with children in 1980? (Round your answers to one decimal place.) (b) How fast was the percentage of families that were married couples with children changing in 1980? (Round your answers to

Find the domain and range of the relation Provide your answer below: domain: range: {(22, 21), (5, -16), (20, -24), (-17,4), (-9,2)).

Challenge A car is traveling at a steady speed. It travels travel in 41 minutes? In 1 hour? miles in 2 The car will travel miles in 41 minutes.

David has 3 cups of blueberries. He uses of a cup of blueberries to make a breakfast smoothie. He uses of tof the remaining blueberries to make blueberry pancakes. How many cups of blueberries does he use for the pancakes? A Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.

If f(x) = 3x + 2 and g(x)=x²-x, find each value. 14. f(4) 15. f(8) 16.)f(-2) 17.g(2) 18. g(-3). 19.f(-6) 20. f(2) + 1 21. f(1) - 1 23,g(-1) + 4 24. f(x + 1) 25. g(3b)

Jay Miller sold his ski house at Attitash Mountain in New Hampshire for $42,000. This sale represented a loss of 15% off the original price. What was the original price Jay paid for the ski house? (Round your answer to the nearest dollar.)

A rhombus is a four-sided figure with all sides the same length. Points F(-2,-2), G(-2, 3), and H(2, 6) are three vertices of rhombus FGHJ. Vertex J is directly below vertex H. a. Graph rhombus FGHJ. Label J with its coordinates. b. What is the perimeter of the rhombus? Show your work.

Riley is packing 144 pencils, 120 folders and 108 notebooks into as many boxes as possible. a. Find the greatest number of boxes that Riley could pack the items into. b. Find the number of pencils, folders and notebooks in each box.

Out of 5,600 colleges surveyed, 60% reported that SAT scores were not used as a high consideration in viewing their applications. How many schools view the SAT as important in screening applicants?

Earl Miller, a lawyer, charges Lee's Plumbing, his client, 25% of what he can collect for Lee from customers whose accounts are past due. The attorney also charges, in addition to the 25%, a flat fee of $50 per customer. This month, Earl collected $6,400 from three of Lee's past-due customers. What is the total fee due to Earl?

For the graph of a function y = f(x) shown to the right, find the absolute maximum and the absolute minimum, if they exist. Identify any local maxima or local minima. Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum of y=f(x) is f(1) = 4. (Type integers or simplified fractions.) B. There is no absolute maximum for y = f(x). Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum of y = f(x) is f() = B. There is no absolute minimum for y = f(x).