Mathematics - Computation

*91/216*

3 six-sided dice are rolled at once. What is the probability that the number 2 is rolled on any die?

*100,000*

An increase of five orders of magnitude is equal to an increase of how many times?

*72 square inches*

Find the area of a square with a diagonal of 12 inches.

*1/2* or *.5*

Four to the x power equals 2.

*1,440* degrees

How many degrees are in four complete revolutions?

*x=(ay)/c*

Solve for x if x over a is equal to y over c.

*27*

The sum of the ages of Will and John is 39 years. John is 3 years more than twice Will's age. How old is John?

*31,622,400*

To within 10 percent, how many seconds are in 1 leap year?

*90 degrees*

Two angles are both congruent and supplementary. What is the measure of each angle?

*One square centimeter*

What is the area of an isosceles right triangle with a hypotenuse of length two centimeters?

*1/2* or *.5*

What is the average value of the function f(x) = cos squared x?

*18 x squared*

What is the first derivative of six x cubed?

*24*

What is the value of four factorial?

*1/81*

9 to the negative 2 power.

*2 radical 3 inches*

A cube has a volume of 8 cubic inches. What is the length of the cube's diagonal?

*9*

A group of junior high school girls earned $522 during the month of January by doing "odd jobs" for people in their community. How many girls were in the group if each received $58 for her share of the effort?

*7 feet 0 inches*

A man is 5 and ¼ inches taller than his son. How tall is the man if his son's height is 68 and ⅔ inches? Express your answer in feet and inches.

*45 and a half minutes*

A one-hour TV program allows a total of 14 and a half minutes of commercials. How much time remains for the actual program?

*54 pi square inches*

A particular circle has a circumference of 18 pi inches. What is the area of a sector of this circle with a central angle of 240 degrees?

*21/500*

A production check at a General Electric plant revealed that 210 timers out of 5,000 were defected. What is the probability of selecting a defective timer from the lot?

*$2.45*

A small candle and a pen cost $4 together. The candle costs 90 cents more than the pen. How much does the candle cost?

*Pi*

A square of sides 2 has been circumscribed about a circle. What is the circle's area?

*2 pi*

A square of sides 2 has been circumscribed about a circle. What is the circle's circumference?

*2*

A square of sides 2 has been circumscribed about a circle. What is the circle's diameter?

*162 degrees*

Angle A and Angle B are supplementary angles. Angle A is nine times larger than B. What is the measure of A?

*y equals 2 times the quantity x minus the fraction 3 over 2, quantity squared, plus 4*

Answer the following about the equation, y equals two x squared minus six x plus the fraction, seventeen over two. Use no mixed numbers and no decimals. Complete the square, and give the resulting equation in the form y equals a times the quantity x minus h, quantity squared, plus k.

*1*

Benita needs to simplify this expression: the sine of x plus the cosine of x, quantity squared, minus 2 times the sin of x times the cosine of x. She begins expanding the quantity squared term, then applies a trigonometric identity that reduces the expression to a constant. What integer equals sine x plus cosine x, quantity squared, minus 2 times sine x times cosine x?

*130 feet*

Bob and Fred are walking on a path and come to a fork. Bob follows a flat path and Fred takes a path alongside it that leads up a steep hill. After walking for another 120 feet, Bob looks up and sees Fred 50 feet directly above him. How far has Fred walked up the steep path?

*$973.75*

Bob is trying to buy a baseball autographed by Mickey Mantle on E-bay. The latest bid is $2,375. Bob decides to wait two days before buying the ball and the price increases by 10 percent each day. At the end of that second day, Bob decides not to buy the ball and instead buys his fiancee diamond earrings for $1,900. Besides making his bride-to-be happy, how much money does Bob save?

*$2,873.75*

Bob is trying to buy a baseball autographed by Mickey Mantle on E-bay. The latest bid is $2,375. Bob decides to wait two days before buying the ball and the price increases by 10 percent each day. What is the bid price after the end of the second day?

*$1,306.25*

Bob is trying to buy a baseball autographed by Mickey Mantle on E-bay. The latest bid is $2,375. If Bob buys the ball, and its value decreases by 45 percent, what will it be worth?

*$2,731.25*

Bob is trying to buy a baseball autographed by Mickey Mantle on E-bay. The latest bid is $2,375. If Bob purchases the ball at the current bid price and then sells it for a 15 percent profit, for what price could he resell it?

*Cosecant squared x*

Complete the following Pythagorean identity by filling in the blank. 1 plus cotangent-squared x equals _________.

*(2, 0)*

Consider a circle that is described by the equation (x - 2) squared + y squared = 4. What are the coordinates of the center of the circle?

*4 pi*

Consider a circle that is described by the equation (x - 2) squared + y squared = 4. What is the area of the circle?

*4 pi*

Consider a circle that is described by the equation (x - 2) squared + y squared = 4. What is the circumference of the circle?

*2*

Consider a circle that is described by the equation (x - 2) squared + y squared = 4. What is the radius of the circle?

*35/12* or *2 and 11/12*

Consider the graph of the curve described by the equation y = x cubed + x squared -3. What is the area above the curve between the y-axis and the line x = -1?

*50 units*

Consider the isosceles triangle ABC. The altitude to the base, segment BC, measures seventy-five units. How far is the centroid from angle A, the vertex angle of the triangle?

*2*

Consider the polynomial: 2x to the 5th power y minus 4x squared y squared plus y. What is the coefficient of the first term?

*6*

Consider the polynomial: 2x to the 5th power y minus 4x squared y squared plus y. What is the degree of the polynomial?

*51*

Consider the polynomial: 2x to the 5th power y minus 4x squared y squared plus y. What is the value of the expression if x equals 2 and y equals 3?

*200 degrees*

Convert 10pi over 9 from radians to degrees.

*330 degrees*

Convert 11pi over 6 from radians to degrees.

*135 degrees 12 minutes*

Convert 135.2 degrees to degrees-seconds-minutes notation.

*16 degrees 30 minutes*

Convert 16.5 degrees to degrees-seconds-minutes notation.

*22.9 degrees*

Convert 2 pi over 4 radians to degrees.

*150 degrees*

Convert 5 pi over 6 radians to degrees.

*-45 degrees*

Convert negative pi over 4 radians to degrees.

*60 degrees*

Convert pi over 3 radians to degrees.

*45 degrees*

Convert pi over 4 from radians to degrees.

*Negative Cosine X*

Cosine of open parenthesis pi minus x closed parenthesis.

*Negative Cosine X*

Cosine of open parenthesis x minus pi closed parenthesis.

*Thirty nine plus ten times the square root of fifteen* or *Thirty nine plus ten times radical fifteen*

Divide six plus the square root of fifteen by four minus the square root of fifteen.

*1*

Evaluate sine squared pi plus cosine squared pi.

*-1*

Evaluate the sine of pi plus the cosine of pi.

*54*

Evaluate x squared minus three x when x equals negative 6.

*Cosine squared theta*

Express cosine theta secant theta minus sine squared theta in terms of a single trigonometric function.

*16 square root 3 square inches*

Express your answer in simplest radical form. What is the area of an equilateral triangle with one side measuring 8 inches?

*2(2x + y)(x - 5)*

Factor 4x squared minus 20x plus 2xy minus 10y completely.

*(x - 2) (3x + 7)*

Factor the following expression completely. 3x squared + x - 14.

*(x - 2)(5x + 7)*

Factor the following expression completely. 5x squared - 3x - 14.

*(x - 7) (x squared + 7x + 49)*

Factor the following expression completely. X cubed - 343.

*(x - 9) (x - 6)*

Factor the following expression completely. X squared - 15x + 54.

*(3x + y)(9x squared - 3xy + y squared)*

Factor the following expression completely: 27x cubed plus y cubed.

*(2x + 7)(3x - 4)*

Factor the following expression completely: 6x squared plus 13x minus 28.

*(3x squared + 2x + 2)(3x squared - 2x + 2)*

Factor the following expression completely: 9x to the 4th + 8x squared + 4.

*(x - 3)(x + 7)*

Factor the following expression: x squared plus four x minus twenty-one.

*4*

Find the 10th in the progression that begins 2048, 1024, 512.

*56*

Find the 8th term in the sequence that begins 0, 2, 6, 12, 20.

*64*

Find the 9th term in the sequence that begins 256, 225, 196, 169.

*144 pi square inches*

Find the area of a circle with a circumference of 24 pi inches.

*90 square inches*

Find the area of a regular hexagon with an apothem of 6 inches and one side length measuring 5 inches.

*240 square inches*

Find the area of a rhombus with a perimeter of 68 inches and one diagonal measuring 16 inches.

*108 square inches*

Find the area of a rhombus with diagonals measuring 12 inches and 18 inches.

*256 square inches*

Find the area of a square with a perimeter of 64 inches.

*13.5 meters squared*

Find the area of a triangle with a base of 3m and height of 9m.

*13*

Find the distance between the coordinates (-2, 5) and (3, -7).

*3*

Find the distance from the origin to the line whose equation is: 3x + 4y + 15 = 0.

*y = 3x + 4*

Find the equation of the line in slope-intercept form that goes through the points (2, 10) and (9, 31).

*(4, 8)*

Find the midpoint between (3, 7) and (5, 9).

*8 centimeters*

Find the missing dimension of a cylinder if the volume is 640 pi cubic centimeters and the height is 10 centimeters. What is the base radius?

*30 centimeters*

Find the missing dimension of a rectangular prism if the volume equals 24,000 cubic centimeters, the length equals 20 centimeters, and the width equals 40 centimeters. What is the depth?

*6 centimeters*

Find the missing dimension of a triangular prism if the volume equals 180 cubic centimeters and the base dimensions are 5 by 12 by 13 centimeters. What is the height?

*f squared (x) = 4x - 4*

Give the derivative with respect to x of the function f(x) = 2x squared - 4x + 1.

*13 feet*

Give the diagonal for a rectangle with a length of 12 feet and a width of 5 feet.

*-8* and *5*

Give the two real number solutions to the following equation: x squared + 3x - 40 = 0.

*45 degrees*

Give the value of the smallest positive angle in degrees if the angle is in the first quadrant and the sine of the angle is the square root of 2 over 2.

*95%*

Give your answer as a percentage. The lengths of a mechanical component are distributed normally with a mean of 30 inches and a standard deviation of .2 inches. All components not within .4 inches of 30 inches are rejected. What percent of the components are acceptable?

*4 over 221*

Give your answer as a reduced fraction. Given a standard 52-card deck, what is the probability of drawing a club that is not an ace, and then without replacing the first card, drawing an ace of any suit?

*8/3* or *2 and 2/3*

Give your answer as a reduced fraction. Solve the following equation completely for x. 49 to the 3x-1 power equals 343 to the x plus 2 power.

*2 square root of 13*

Give your answer as a simplified radical expression. On a coordinate plane, what is the distance between the points (-6, 2) and (-2, -4)?

*(2 - square root of 3) / 4*

Give your answer as a single, reduced fraction. Evaluate sin squared (15 degrees). It may help you to use the trigonometric power formulas.

*3 times the square root of 2, pi/4)*

Give your answer in radians, as the smallest possible positive angle. Convert rectangular coordinates (3, 3) to plane coordinates.

*the square root of 3 over 2* or *radical 3 over 2*

Give your answer to the following question in simplified radical form. What is the sine of an 840 degree angle?

*40,320*

How many different ways can the letters in the word "question" be rearranged?

*80 liters*

How many liters of water must be added to 20 liters of a 75% acid to produce a solution that is 15% acid?

*4*

How many solutions are there for x to the 4th minus x to the 3rd plus x squared minus x equals 0?

*3*

How many solutions does the equation x cubed minus x squared plus 3x equals 7 have?

*20*

How old is David if his age six years from now will be twice his age seven years ago?

*Circle*

Identify the conic section with the following equation. 3x squared plus 3y squared equals 12.

*Hyperbola*

Identify the conic section with the following equation. 4x squared minus 6y squared minus 8x plus 8y equals 24.

*Parabola*

Identify the conic section with the following equation. 4x squared minus 8x plus 8y equals 24.

*10*

If 6 furlongs are equal to 3/4 of a mile, then how many furlongs are in 1 and 1/4 miles?

*Saturday*

If January 3rd is on a Monday, on what day of the week is January 29th?

*38.25 feet*

If a tree grows at a rate of 4.5 feet per year, how tall will the tree be in 8.5 years?

*2*

If the hypotenuse of a triangle is 12, then what is the distance from the midpoint of the hypotenuse to the triangle's centroid?

*3 days*

If two workers typed eight sets of Scholastic Bowl questions in 4 days, how long would it take 12 workers to type 36 sets?

*1/16*

If you flip a coin four times, what is the probability that the first head appears on the fourth flip?

*1/32*

If you flip a coin six times, what is the probability that each flip after the first will have a different outcome than the one immediately preceding it?

*⅜*

If you flip a fair coin three times, what is the probability that there will be exactly one head?

*July*

In a leap year, the 200th day of the year is in what month?

*22.5 inches*

In a marching band, each member must learn the "8-to-5" step so that everyone can consistently find his or her place on the field. "8-to-5" means that there are 8 steps for every 5 yards. How long is each step in inches?

*97*

In the Gregorian calendar, how many leap years occur during any 400-year span?

*$112*

Joann is saving money to buy a birthday present for her mother. She has $28 now and adds $7 a week for 12 weeks. How much money will she have at the end of the 12 weeks?

*$624.00*

Joe makes a salary of $1,200 per week. Thirty-five percent of his paycheck goes to taxes. Joe saves 20 percent of the remaining income. How much money does Joe have in his budget to spend each week?

*128*

Lauren has not done her homework for the five-question quiz, and she will have to guess the answers randomly. Two of the questions are multiple choice questions with four options, and three are true-false questions. How many different ways could she possibly answer these five questions?

*3.5 years*

Little Cathy is 42 months old. How old is she in years?

*$79*

Lonnie earned $237 for mowing yards last summer. He gave his mother ⅔ of the money to put away for college. How much did he save for himself?

*28,800*

Louise completes 12 parts per minute on a factory assembly line. How many parts will she complete during one standard 40-hour work week?

*$2,500*

Mr. Owens invested $15,000, part at 7% and the remained at 9%, to insure a $1,300 yearly income. How much was invested at 7%?

*$23.20*

Mrs. Allen purchased four-dozen cans of dog food priced at 3 cans for $1.45. How much did the dog food cost?

*5.5 miles*

Mt. Everest is 29,030 feet tall. Express this height in miles, rounded to the nearest tenth.

*8 cents*

One dozen oranges and six grapefruit cost $2.46. Nine oranges and nine grapefruit cost $2.97. What is the cost of one orange?

*8*

One number is four times as large as another number. The sum of their reciprocals is 5/8 (five-eighths). What is the larger of the two numbers?

*5 cubed, 2 to the 7th power, 3 to the 5th power*

Place in order of size from smallest to largest: 3 to the 5th power, 5 cubed, and 2 to the 7th power.

*8x cubed + 60x squared + 150x +125*

Simplify the following expression. Give the polynomial in degree descending form. You may use exponents on variables, but work out exponents on all coefficients. Simply the quantity, 2x + 5, close quantity, quantity cubed.

*Sine X*

Sine of open parenthesis pi minus x closed parenthesis.

*Negative Sine X*

Sine of open parenthesis x minus pi closed parenthesis.

*x = -(3/10)*

Solve for x. ((2x)/3) + 1 = 4/5.

*x = 7/2*

Solve for x. ((3x)/4) - 2 = 5/8.

*x = -(7/4)

Solve for x. ((5x)/4) + 3 = 13/16.

*36*

Solve for x. (3/4)x + 16y = 27.

*-54*

Solve for x. -(1/2)x + 3y = 27.

*-2.7*

Solve for x. -x + 4.7y = 2.7.

*9*

Solve for x. 3x + 5y = 27.

*27*

Solve for x. x + 9y = 27.

*28*

The area of a rectangle is 40 square units. The length of the rectangle is 6 units larger than the width. What is the perimeter of the rectangle?

*20* and *4*

The difference between two numbers is 16. The sum is 24. What are these two numbers?

*y/2 minus 3x/2 equals 1*

The equation of a line in slope-intercept form is y equals 3x plus 2. Restate the equation in intercept form.

*8 centimeters*

The legs of an isosceles trapezoid measure 10 centimeters. What is the height of the trapezoid if the perimeter is 50 centimeters and the area is 120 square centimeters?

*3*

The logarithm of 81 to the base x equals 4.

*200*

The midpoint of the sides of a square are joined to create a new square. This process is repeated for each new square. Find the sum of an infinite series of the areas of such squares if the side length of the original square is 10.

*⅗*

The neighbors have five cats, two of which are black and 3 that are calico. What is the probability that the cat sleeping in the recliner is not black?

*$213.25*

The salary Barbara earns is directly proportional to the number of hours she works. One week she worked 18 hours, and her salary was $153.54. The next week she worked 25 hours. How much did she earn the second week?

*14.25 lbs.*

The three boys picked up 42 and ¾ pounds of pecans. What was the average pound weight picked up by each boy?

*1/36*

There's a box containing 4 red balls, 3 blue balls, and 2 white balls. If 22 balls are drawn at random without replacement from the box, what is the probability that both the balls will be white?

*0*

There's a box containing 4 red balls, 3 blue balls, and 2 white balls. If 3 balls are drawn at random without replacement from the box, what is the probability that all 3 will be white?

*5/9*

There's a box containing 4 red balls, 3 blue balls, and 2 white balls. If one ball is drawn at random from the box, what is the probability that it will be either blue or white?

*4/9*

There's a box containing 4 red balls, 3 blue balls, and 2 white balls. If one ball is drawn at random from the box, what is the probability that it will be red?

*5.86*

To the nearest hundredth, give the sum of the numbers 'e' and 'pi'.

*Pi over three radians* and *Five times pi over three radians*

Use an integer or a single simplified rational expression for your answers. Find all values of x in radians greater than or equal to zero but less than two pi, satisfying the equation, sin x equals cos x times the square root of three.

*1:12*

What a penny is tossed then a die is rolled, what is the probability there will be heads on the penny and a 6 on the die?

*25.12 square centimeters*

What is the area of a semicircle whose radius is 4 centimeters?

*16 radical 3*

What is the area of an equilateral triangle that has a perimeter of 24 inches?

*$14*

What is the cost of 84 items if each item costs 16 and ⅔ cents?

*0*

What is the derivative with respect to x of the expression cos squared x plus sine squared x?

*-28*

What is the determinant of a two-by-two matrix in which the first row has values of 4 and 8, and the second row has values of 3 and -1?

*1/x*

What is the first derivative of the natural log of x?

*17*

What is the length of a line drawn between points (-3, -7) and (5, 8)?

*8*

What is the median of following numbers? (1, 2, 2, 2, 3, 3, 4, 5, 5, 8, 8, 8, 8, 9, 9)

*6*

What is the median of the following numbers? (4.7, 6.2, 4.0, 5.3, 9.8)

*92*

What is the median of the following numbers? (93, 93, 92, 83, 100, 80, 79)

*3/13*

What is the probability of drawing a face card from a standard deck of cards?

*56*

What is the product of the cube root of 512 and the fourth root of 2401?

*2 inches*

What is the radius of the circle whose area in square inches equals its circumference in inches?

*68 degrees*

What is the remaining angle in a triangle if two of the angles measure 63 degrees and 49 degrees?

*20,100*

What is the sum of all the integers from 1 to 200?

*276*

What is the sum of the first 23 whole numbers?

*17 inches*

What is the sum of the legs of a right triangle if its hypotenuse is 13 inches and one leg is 5 inches?

*90*

What is the sum of the two largest prime numbers that are less than 51?

*5 square feet*

What is the surface area of the balance beam on which a gymnast performs, expressed to the nearest square foot, if the bar is 4 inches wide and 16.4 feet long?

*41*

What is the third number in the Pythagorean triple of 9 and 40?

*360 inches squared*

What is the total area of a regular square pyramid with a base of 10 inches and an altitude of a triangular face of 13 inches?

*1/49*

What is the value of 7 to the negative 2 power?

*30 pi centimeters cubed* or *94.2 centimeters cubed*

What is the volume of a cone that has a base with a diameter of 6 centimeters and a height of 10 centimeters?

*-1*

What is the y-coordinate of the point of intersection of the equations y equals 2x plus 1 and y equals -3x minus 4?

*1*

What number is equal to both the sine of 90 degrees and the cosine of 360 degrees?

*152 times pi cubic units*

You are trying to find the volume of a roughly cylindrical solid, six units tall, whose horizontal cross-section is always a circle. However, the radius r of the cross-section varies with the height h, according to the formula, r equals, six minus the fractions, h over three. What is the volume of the solid?

*¼*

You flip a coin until either two heads show up on consecutive flips, or tails show up on one flip and heads on the flip immediately following. What is the probability that two heads will show up consecutively in such a sequence of flips?

*2 times the square root of three*

cot(210 degrees) - tan(120 degrees).

*4/3* or *1 and ⅓*

csc squared (240 degrees).

*1 + the square root of three*

sin(90 degrees) + tan(60 degrees).