GED Math Test #8
Analyze the expression.
5x^2+4y^2
when x=−2 and y=−2
Instead of x and y, substitute 2 for each.
5x^2+4y^2
First, analyze the exponents.
=5(−2)^2+4(−2)^2
=5(4)+4(4)
=20+16
=36
How many degrees are there in a rectangle's four corners?
In a rectangle, all four angles are right angles (90 degrees each). Therefore, the sum of the four angles in a rectangle is: 360degrees.
Find the greatest common factor between the numbers 33 and 44.
A number's factors are the values that divide equally into it. Because 4 can be divided by each without leaving a leftover, the factors of 4 are 1, 2, and 4. To get the greatest common factor of 33 and 44, start by listing each number's factors:
Factors of 33 are: 1, 3, 11, 33
Factors of 44 are: 1, 2, 4, 11, 22, 44
The greatest number in both lists of factors is the most common factor: 11.
Kate worked 40 hours and earned $8.10 per hour. Janice is paid $10.80 per hour. How many hours would Janice have to work to earn the same amount as Kate over 40 hours?
Calculate Kate's total earnings after 40 hours as follows:
40 hours × $8.10 an hour = $324
To calculate the number of hours Janice would need to work, divide the sum by his hourly rate:
$324 ÷ $10.80 = 30 hours
Put this fraction in the lowest terms: 35/21
You should divide both the numerator and the denominator by the same integer in order to reduce a fraction to its lowest term. The answer is 5/3 since 35 divided by 7 equals 5, and 21 divided by 7 equals 3.
Jake walks 3,247 meters to the park, 582 meters to the store, and 1,634 meters to return to his home. By first rounding each number to the nearest 10, you may calculate the overall distance traveled.
To the nearest ten, round each number
3,247 - 3,250
582 -580
1,634 - 1,630
Add up the data:
3,250 + 580 + 1,630
= 5,460
For the following data points, compute the mean: 95,84,31
The mean is the average of the numbers, and finding it is simple: add up all the numbers, then divide by the total number of numbers.
95+84+31=210
210÷3=70
Compute for h and use the formula 3h+3=12.
Subtract 3 from both sides of the equation to move the constant term to the other side:
3h+3−3=12−3
Simplifying:
3h=9
Divide both sides by 3 to solve for
h= 3/9
Simplifying:
h=3
Analyze (5x+2y) when x=−2 and y=−3.
Instead of x and y, use -2 and -3.
5(−2)+2(−3)−10+(−6)
=−16
Find the greatest common factor among the numbers 16, 27, and 20.
Begin by listing the factors of each number to determine the highest common factor of the three numbers:
Factors of 16: 1, 2, 4, 8, 16
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 27: 1, 3, 9, 27
The greatest number that goes into EACH of the original values is the greatest common factor. As can be seen, 1 is the only number that divides each number evenly, hence 1 is the correct answer.
Convert the sentence into a mathematical expression that includes the specified variable. "9 times the sum of z and 2"
The result is then multiplied by 9 after the integers z and 2 have been added. The appropriate mathematical expression for the variable z is 9(z+2).
On a number line, the numbers 11.2 and 3.3 are plotted. What is the difference between these two points in terms of distance?
The absolute value of the difference between points A and B on a number line is the distance between them. The value of the distance is always positive. Calculate the difference between the two points before using the absolute value:
AB = |b − a| or |a − b|
= |−11.2 − 3.3|
= |−14.5|
= 14.5
Remember that a number's absolute value is its distance from 0.
A store is promoting the fact that anything customers buy there will be discounted by 14%. What was the item's marked price when John purchased it and paid $670.80 for it?
Let's denote the originally marked price as x. John receives a 14% discount on this price, so he pays 86% (100% - 14%) of the marked price. The amount John paid after the discount is $670.80, so we can set up the equation: 0.86x = 670.80 Now, let's solve for x to find the originally marked price: x = 670.80 / 0.86 ≈ 780
How many users can four one-foot rulers be divided among to leave each with 16 rulers?
4÷16 = 24
What percentage of a class plays tennis if 40% of the females are girls and 25% of the girls play tennis?
The percentage of female tennis players is:
40%×25% = 0.40×0.25 = 0.10 = 10%
Eighty percent of the members of a local yoga studio are women, while twenty percent are men. Women are on average 30 years old, while men are on average 40 years old. What is the average age of the entire group?
This is a dilemma with a weighted average, in which the average age of the women weighs 80 percent, and the average age of the men weighs 20 percent. The combined average age will be the sum of each group's contribution, which is calculated by multiplying the average of each group by its weight.
Begin by calculating the contribution of women to the overall average (remember that 80% = 0.8): 24 = 0.8 * 30
Next, look for the contribution of the men: 8 = 0.2 * 40
To get the overall average, add them all together: 32 = 24 + 8
It's worth noting that the combined average is split between the average age of women (30) and the average age of males (40), which makes sense given that both groups contribute to the overall average.
Which of the following equations must be positive if x is a tiny negative integer and y is a large positive integer?
Consider the properties of positive and negative integers before moving on to the answer options. When a positive integer is multiplied or divided by a negative integer, the result is always a negative integer. As a result, y x is the only viable answer choice that must be positive.
Choosing a tiny negative integer for x, 1, and a large positive integer for y, 100, and substituting these values into each of the answer choices is an alternative solution.
Put this fraction in the lowest terms: 15/12
You should divide the numerator and denominator of a fraction by the same number in order to reduce it to its lowest term. The right response is 5/4 because 15 divided by 3 equals 4, and 12 divided by 3 equals 4.
Lei wants to spend his $305 on as many bags of mulch as possible, and he wants them delivered to his home. The price of ach bag is $7.50, plus a $35.75 shipping fee. Only entire sacks of mulch are available for purchase. How many bags will Lei be able to purchase?
A flat $35.75 shipping charge is subtracted from Li's initial sum of $305:
$305 − $35.75 = $269.25.
The total number of bags Lei can buy is calculated by dividing this amount by the cost per bag:
$269.25 ÷ $7.50 = 35.9 bags. However, because the question specifies that the mulch can only be sold in whole bags, we must round our answer down to keep Li's budget in check.
Put this fraction in the lowest terms: 16/14
You should divide both the numerator and the denominator by the same integer in order to reduce a fraction to its lowest term. The answer is 8/7 since 16 divided by 2 equals 8, and 14 divided by 2 equals 7.