GED Math Test #5
Which of the following answer options depicts the order of the following integers from least to greatest?
0.4, 1/6, 1/3, 0.16, 3/22
Explanation:
To compare the fractions to the decimal values already provided, first convert them to decimals:
1/6=0.1667
1/3=0.333
3/22=0.13636
The correct order of the numbers will be:
0.13636
0.16
0.1667
0.333
0.4
What is the actual distance represented by 25 inches on a map if 10 inches on a map represents an actual distance of 100 feet?
Explanation:
A percentage can be utilized to solve for the unknown distance because the ratio of inches to actual distance is constant. Create a scale to depict the scenario. The question asks for the distance represented by 25 inches using a ratio of 10 inches to 100 feet. Write a proportion that equates the supplied and unknown data, making sure that the units of each ratio are consistent (all inches on top or all inches on bottom):
10 in/100 ft=25 in/x ft
To solve for the unknown, x feet, use cross multiplication as follows:
10x=25∗100
x=25∗100/10
x=250 ft
How many separate three-person committees can be established from a group of five people?
Explanation:
Given that the sequence in which committees are constituted has no bearing on the overall number of possible committees (committee A, B, C is the same as committee B, A, C), the total number of possible committees can be computed using a combination. The formula gives the number of possibilities to choose r elements from a group of n elements:
nCr = n!/r!(n−r)!
nCr = 5!3/!(5–3)!
nCr = 5∗4∗3∗2∗1/(3∗2∗1)(2∗1) = 5∗4/2∗1
nCr = 10
Solve for x as follows:
14.5x−5(x+2) ≤ 4+4 (4−1/8x)
Explanation:
To solve for x, perform the relevant operations to simplify the issue, then combine like terms. To get rid of the parentheses, start by dispersing the terms.
Through the parentheses, multiply the 5 and the 4:
14.5x−5x−10≤4+16−1/2x
Combine like terms on both sides of the inequality:
9.5x−10≤20−1/2x
Add 1/2x to both sides:
10x−10≤20
Add 10 to both sides:
10x≤30
Divide both sides by 10:
x≤3
It was not essential in this situation, but keep in mind that when both sides of an inequality are multiplied or divided by a negative number, the inequality's direction changes.
What is the following line's slope:
y=3x−7
Explanation:
A linear equation is an equation that connects an input variable to an output variable by raising both variables to the first power. The slope is the constant ratio of the change in y coordinates to the change in x coordinates in a linear equation. The algebraic expression for the slope is:
m=y2−y1x2−x1
The slope-intercept form of the equation for a line is y=mx+b, where m is the slope, b is the y-intercept, and (x,y) is a line point. The slope is 3 in this question, and the slope-intercept form of the line is provided.
Every month, a manufacturer makes 500 smartphones. Each phone has a $200 production cost. Which of the following inequalities will provide the sales price, Y, at which the factory must sell each phone in order to achieve the appropriate profit if the corporation wishes to make a total profit of $10,000 or more on the 500 phones?
Explanation:
The profit of a corporation is equal to the difference between its total revenue and total costs. The total revenue is calculated by multiplying the number of smartphones sold by the average cost per smartphone:
Total Revenue = 500 phones∗sales price,Y
Total Revenue = 500Y
The total cost is calculated by multiplying the number of smartphones sold by the cost of manufacturing each smartphone:
Total Cost = number of phones∗cost
Total Cost = 500∗$200
Total Cost = $100,000
The total profit is then:
Total Profit = Revenue−Cost
Total Profit = 500Y−$100,000
What percentage of a number is 44?
Explanation:
Using x to represent the unknown integer, convert the question into an equation:
44 = 0.8x
Divide both sides by the decimal:
44/0.8 = x
x = 55
George purchases 10 shares of Bling-Bling Inc. stock for $450 per share on May 15, 2015. On August 15, 2015, Bling-stock Bling's price increased to $600. What is the rounded-to-the-ninth-percentage-point increase in the value of George's stock?
Explanation:
Remember that the percentage change is equal to the difference between the new and original values, divided by the original value, and multiplied by 100%. The change is an increase if the new value is greater than the previous value. The change is a decline if the new value is less than the previous value. In algebraic form:
Percentage Increase =
Final Value − Original Value/Original Value ∗100%
Substitute the given values and evaluate to find the percentage increase:
=$600−$450/$450 ∗ 100%
=$150/$450 ∗ 100%
=33.3%
Sandra is on her way to Texas. For 2 hours, she goes at 70 kilometers per hour, and for 5 hours, she travels at 63 kilometers per hour. What was Sandra's average speed over the 7-hour period?
Explanation:
Use the following formula to calculate the average for the entire journey:
Average Speed = Total Distance/Total Time
Calculate the entire distance traveled first:
Total Distance = 2(70) + 5(63)
= 140+315
= 455 km
Next, find the total time:
Total Time=2 hours+5 hours
= 7 hours
To solve, enter these values into the average speed formula:
Average Speed = 455/7
= 65 km/h
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