Math Problems

336

70% of 480

112

84 is 75% of what number

270 square feet

A gardener mowed two-fifths of a lawn on Monday, and then mowed three-quarters of the remaining portion on Tuesday. If the lawn's total area is 1,800 square feet, how many square feet were still unmowed after Tuesday?

9/20 [After Monday, 1 - (2/5) = 3/5ths of the lawn was unmowed; 3/4ths of that fraction is (3/5) × (3/4) = 9/20.]

A gardener mowed two-fifths of a lawn on Monday, and then mowed three-quarters of the remaining portion on Tuesday. What proportion of the entire lawn did the gardener mow on Tuesday?

3/20

A gardener mowed two-fifths of a lawn on Monday, and then mowed three-quarters of the remaining portion on Tuesday. What proportion of the entire lawn was still unmowed after Tuesday?

676 π

Give your results in π, find the surface area of a sphere with a radius of 13 meters. SA of a sphere = 4πr2

600

210 is 35% of what number

14 feet by 28 feet

A rectangular family room is twice as long as it is wide, and its perimeter is 84 feet. Find the dimensions of the family room.

40%

Ben has earned an average of 80% on 5 tests each worth the same number of points. If Ben earned an average of 90 percent on the first four tests, what percentage did he earn on the 5th test? (90 x 4) + x = 80

30x to 4th plus 4

Bethany needs to find the second derivative of the function y equals x to the sixth power plus 2x squared plus 3x. By applying the power rule twice, she is able to compute what second derivative of y equals x to the sixth plus 2x squared plus 3x?

4 (2, 3, 5, 7)

Between 1-10, who many are prime numbers are there?

64

Consider a cube whose sides each have a length of 4 Compute the volume of the cube. [V = s3}

32/3 pi [The sphere will have a diameter of 4 and thus a radius of 4/2 = 2; V = (4/3) × pi × r3 = (4/3) × pi × 23 = (4/3) × pi × 8 = 32/3 pi.]

Consider a cube whose sides each have a length of 4. The volume of the cube is 64. What is the volume of a sphere that is inscribed within the cube?

3 - 4i

Consider the complex number 3 + 4i. What is the conjugate of this number.

55

Consider the integers 1 from to 10, inclusive. What is the sum of these integers? (Pair up 1 and 10, 2 and 9, etc)

$340

Debbie earned 51 dollars in tips yesterday, which was 15 percent of the pre-tip value of her customers' orders. To find the value of her customers' orders, one can either use an algebraic equation or ratios. Find the pre-tip value of the orders. [0.15x = 51]

20

Each side of a regular hexagon has a length of 10. What is the length of the hexagon's longest diagonal? It may help to divide the hexagon into congruent triangles. (The inside of a hexagon can be divided into 6 equilateral triangles and the longest diagonals will incorporate 2 sides of those triangles.)

60

Each side of a regular hexagon has a length of 10. What is the perimeter of the hexagon? (Hexagon has six sides)

-7 + 24i

Find the square of the complex number 3 + 4i

6

Find the y-intercept of the line given by the equation 2y - 7x = 12 2y = -7x + 12

pi

In 1882 Ferdinand von Lindemann proved that this number is transcendental. Ptolemy estimated it as 377 over 120; other approximations include the square root of 10 and 22/7. Name this constant, the ratio of the circumference to the diameter of a circle, equal to about 3.14.

64

In how many ways can a six question true-false exam be answered. Assume that no questions are omitted. (2 to the 6th)

22%

Kari needs to know, to the nearest whole number, what percentage of her wages goes into her savings account. Each week she earns $450, of which $100 is automatically put into savings. By setting up a ratio, she finds what percentage? (100/450)

39

Kira needs to find the tenth term of the arithmetic sequence whose first three terms are 3, 7, and 11. She can either write out the first 10 terms or multiply the common difference by the number of iterations. Find the tenth term of the sequence. a10 = a1 + (4 x (10-1)) a10 = 3 + (4 x 9)

25

Multiply 3 + 4i by its conjugate (3 - 4i)

45 degrees [3600 - 3285 = 315, so 360 - 315 = 45 degrees]

Pete needs to find the angle between zero degrees and 360 degrees that is coterminal with an angle of 3,285 degrees. He knows that coterminal angles are separated by a number of 360-degree turns, so he subtracts as many multiples of 360 as possible. Since 10 turns equal 3,600 degrees, he is able to compute what angle that is coterminal with an angle of 3,285 degrees?

x = 195

Solve t he following equation, expressing your answer in lowest terms. 2/3x + 15 = 4/5x -11

line

Standard form is a x plus b y equals c. Name this figure in the plane.

vertical

This type of line cannot be expressed in slope-intercept form, because its slope is undefined

-7, 4

Two answers required, for what 2 integer values of x does x times the quantity x plus 3 equal 28. x2 + 3x - 28 = 0 (x+7) (x-4) = 0

6

What is the coefficient of the third term in the expression of the binomial 2x + 1 to the third power?

4

What is the imaginary part of the complex number 3 + 4i?

6

What is the length of the shorter diagonal of a rhombus whose area is 90 and whose longer diagonal has a length of 30? A = 1/2 x d1 x d2 = 90

75 pi

What is the volume of a right circular cone whose base has a radius of 5 and whose height is 9? V = 1/3(B)(H) or V = 1/3 (pi) (r squared) (h)

24%

What percent of 300 is 72?

18

What product results from multiplying together the complex conjugates 3 plus 3i times 3 minus 3i? (Use FOIL)

slope-intercept form

y = mx + b expresses a line in this common form, named for what m and b represent.