Correct answer: 12%
To find out what percentage A is of B, divide A by B and multiply the result by 100 percent:
10.16 ÷ 86.89 = 0.1169 × 100% = 11.69%
This is approximately 12%.
Correct answer: 5
The total number of buckets required will be determined by dividing the total area of the walls by the total area covered by each bucket. First, determine the size of the walls Jennie intends to paint. Two of the walls are 10 × 10 and the other two are 10 × 15:
2 (10 × 10) = 200 sq. ft.
2 (10 × 15) = 300 sq. ft.
As a result, the total area of the walls is 500 square feet.
If a half gallon of paint covers 55 square feet, each gallon covers 2 × 55 = 110 square feet. Four gallons can only cover 440 square feet. Five gallons will cover 550 square feet, which is enough to cover the entire wall area.
Correct answer: 648
First, determine distance the car travels in one hour:
360 km ÷ 5 hours = 72 km per hour
Then multiply this number by the total number of hours traveled:
9 hours × 72 km per hour = 648 km
It is important to note that the final calculation produces the correct units; this helps to confirm that the calculation is correct.
Correct answer: 1/3
The probability of a successful event is defined as the ratio of successful events to total events. A successful event in this case is selecting a yellow marble from the box. The number of events equals the number of marbles in the box:
P(Yellow) = Yellow Marbles/Total Marbles
P(Yellow) = 4/12
P(Yellow) = 1/3
Correct answer: 30
To begin, compute Robert's total earnings after 40 hours: 40 hours × $8.10 per hour = $324
Then, divide this total by John's hourly rate to determine how many hours John would need to work:
$324 ÷ $10.80 per hour = 30 hours
A prime factor is a prime number that exactly divides the given composite number without leaving a remainder. Prime factors are the building blocks of composite numbers because any composite number can be expressed as a product of prime factors.
A circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed center point. It has no beginning or end, and it is continuous, making it an infinite shape. The distance from the center of the circle to any point on its boundary is called the radius, and the distance across the center through any two points on the boundary is called the diameter, which is twice the length of the radius. Circles have many interesting properties and are fundamental in mathematics and geometry.
Correct answer: 6x + 15xy
Begin by taking note of the format in which the answer options are written. As there is no parenthetical expression in any of the answer choices, begin by distributing the 3x through the parentheses. Multiply each of the term inside the parentheses three times and combine any similar terms:
3x(2 + 5y)
= 3x(2) + 3x(5y)
= 6x + 15xy
Correct answer: 20
To keep things organized, create a table that compares the situation five years ago to the situation today.
Five years ago Today
Brian 10 - 5 = 5 10
Angel 3 x 5 = 15 15 + 5 = 20
Brian is now 10 years old, so he was 5 years old five years ago.
Angel was 3 times Brian's age five years ago, so Angel must have been 15 at the time.
To calculate Angel's current age, add 5 years to her age five years ago. Angel is now 15 + 5 = 20 years old.
Correct answer: (4y − 2)(3x + 2)
Any part of an expression that is shared by all of its terms can be factored out. (3x + 2) is a common term in this case and can be factored out of both parts of the expression:
4y(3x + 2) − 2(3x + 2) = (3x + 2)[4y − 2]
See that distributing (3x + 2) through [4y − 2] yields the original expression, which validates the answer.
An acute angle is an angle that measures less than 90 degrees. Acute angles are characterized by their openness and sharpness, as they are narrower than a right angle (90 degrees) and do not reach the measure of a straight angle (180 degrees). In an acute triangle, all three angles are acute, and in a right triangle, one angle is a right angle (90 degrees) while the other two angles are acute.
Vertical angles are a pair of non-adjacent angles formed by intersecting lines. When two lines intersect, they create four angles, and the two opposite angles among them are called vertical angles. These vertical angles are congruent, meaning they have the same measure.
Correct answer: 90
Multiply the number of options for each factor to determine the number of possible outfit combinations:
6×3×5=90
A dot plot is a graphical representation of data that uses dots to display individual data points along a number line or a specific axis. Each dot in the plot represents a single data point, and the dots are stacked above each other if multiple data points have the same value.
A right triangle is a type of triangle that has one angle measuring exactly 90 degrees, which is known as a right angle. The other two angles in a right triangle are acute angles, meaning they are both less than 90 degrees.
