Algebraic Expressions
What is the term for a mathematical expression made up of variables, constants, and mathematical operations?
Algebraic Expression
What term is used to describe a comparison of two quantities using division, often expressed using a fraction or colon?
ratio
What is the term for a statistical measure that represents the middle value in a dataset, with half of the values falling below it and half above it?
median
What is the formula to find the area of a circle, and how would you find the area if the radius is 5 units?
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.
To find the area if the radius is 5 units, you would plug in the radius value into the formula and calculate the area: A = π(5)^2 A = π(25) A = 25π
Therefore, the area of the circle with a radius of 5 units is 25π square units.
whats The likelihood of rolling a 6 on a fair six-sided die?
1/6 or 16.67%
3x + 7 = 16
Solve for X
x=3
What is the formula for calculating a rate in mathematics?
(Change in Quantity) / (Change in Time) or y/x
is measure of central tendency is calculated by adding all the values in a data set and dividing by the total number of values.
mean
What is the formula for calculating the volume of a cylinder and how would you find the volume if the radius is 4 cm and the height is 10 cm?
The formula for calculating the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder.
To find the volume of a cylinder with a radius of 4 cm and a height of 10 cm, you would substitute these values into the formula.
V = π(4 cm)^2(10 cm) V = π(16 cm^2)(10 cm) V = π(160 cm^3) V ≈ 502.65 cm^3
Therefore, the volume of the cylinder would be approximately 502.65 cm^3.
The probability of rolling a prime number on a six-sided die?
1/2
2(3x + 5) - 4 = 10x?
Solve for x
x=-1
What is the rate at which a car travels if it covers a distance of 120 miles in 2.5 hours?
48 miles per hour.
What is the median of the following data set:
12, 15, 18, 23, 25, 29, 37, 41, 42, 45
29
What is the formula for finding the volume of a cone with a radius of 4 inches and a height of 9 inches, expressed as a fraction?
The formula for finding the volume of a cone is V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Given that the radius is 4 inches and the height is 9 inches, we can plug these values into the formula:
V = (1/3) * π * (4^2) * 9 V = (1/3) * π * 16 * 9 V = (1/3) * π * 144 V = (1/3) * 144π V = 48π cubic inches
Therefore, the volume of the cone is 48π cubic inches when expressed as a fraction.
What is the probability of rolling a sum of 7 on two twelve-sided dice
The probability of rolling a sum of 7 on two six-sided dice is 1/6.
3(4x + 2) + 2(3x - 1) = 30
Solve for X
X=1.5
What is the ratio of the sum of two numbers to their difference if one number is 6 times larger than the other
Let's say the two numbers are x and 6x (where 6x is 6 times larger than x).
The sum of the two numbers is x + 6x = 7x The difference of the two numbers is 6x - x = 5x
So the ratio of the sum of the two numbers to their difference is:
(7x) / (5x) = 7/5
So, the ratio is 7:5.
What is the mean of the following data set: 12, 15, 18, 22, 26, 29, 33, 36, 39?
25.56
What is the formula for the volume of a rectangular prism, and how would you calculate the volume if the dimensions are given as 5 1/2 feet by 7 1/3 feet by 3 3/4 feet?
The formula for the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height.
To calculate the volume of a rectangular prism with dimensions of 5 1/2 feet by 7 1/3 feet by 3 3/4 feet, first convert all the dimensions to fractions:
5 1/2 feet = 11/2 feet 7 1/3 feet = 22/3 feet 3 3/4 feet = 15/4 feet
Now, plug the dimensions into the volume formula:
V = (11/2) x (22/3) x (15/4) V = 11 x 22 x 15 / 2 x 3 x 4 V = 3630 / 24 V = 151.25 cubic feet
Therefore, the volume of the rectangular prism with dimensions of 5 1/2 feet by 7 1/3 feet by 3 3/4 feet is 151.25 cubic feet.
What is the probability of randomly selecting a 10th-grade student who has taken both AP Calculus and AP Physics and has a GPA of 3.8 or higher?)
If we let:
The probability can be calculated by: P = N1 / N3
(3/4)^2 * 6x - 10 when x = 1/2
(3/4)^2 * 6(1/2) - 10
Next, we simplify the terms:
(9/16) * 3 - 10 27/16 - 10 27/16 - 160/16 (27 - 160)/16 -133/16
Therefore, the value of the expression (3/4)^2 * 6x - 10 when x = 1/2 is -133/16.
What is the mathematical equation for finding the ratio of two numbers when the first number is 5 times the second number, and the second number is increased by 20% before finding the ratio?
Let the second number be represented by x.
The first number is 5 times the second number, so the first number is 5x.
The second number is increased by 20%, so the new second number is 1.2x.
The ratio of the first number to the new second number is given by:
Ratio = (5x) / (1.2x)
Simplifying this:
Ratio = 5 / 1.2
Ratio = 4.16666666667
Therefore, the mathematical equation for finding the ratio of two numbers when the first number is 5 times the second number, and the second number is increased by 20% before finding the ratio is:
Ratio = 4.16666666667
What statistical test is used to determine if a sample mean is significantly different from a population mean, assuming the sample data follows a normal distribution?
The statistical test used in this scenario is the one-sample t-test.
What is the formula for finding the volume of a frustum?
The formula for finding the volume of a frustum is:
V = (1/3) * π * h * (r1^2 + r2^2 + r1 * r2)
Where:
What is the probability of selecting a red card from a standard deck of 52 playing cards, without replacement, after selecting a black card on the first draw?)
The probability of selecting a red card from a standard deck of 52 playing cards is 1/4.