# GED Math Test #5

#### How many separate three-person committees can be established from a group of five people?

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

#### Which is the best way to simplify (24 x 32)/(2 x 3)?

(2^4 x 3^2) / (2 x 3)= 2^4-1 × 3^2-1.

2^4-1 × 3^2-1 = 2^3 × 3^1

2^3 × 3^1 = 2^3 × 3

#### 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

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

#### Which of the following is equivalent to (√3 + √2)2 ?

(√3 + √2)2 = (√3 + √2)( √3 + √2)

=(√3 + √2)( (√3 + √2)

=√3×√3 + √3×√2 + √2×√3 + √3×√3

=√3×√3 + √3×√2 + √2×√3 + √3×√3

=3 + √6 + √6 + 2

=5 + 2√6

#### There were 466 pupils that showed up to take the test. What is accurate regarding the median score attained by test-takers?

The median will be determined by averaging the 233rd and 234th marks once the marks have been arranged in order, as there are 466 students. The 233rd and 234th places will both fall between the ages of 40 and 49.

Between 40 and 49 will be the average of these two marks.

#### Results of an international mathematics exam taken by senior students from a large high school.

A score of at least 40 is required to pass this test. How many kids at this high school did not succeed on this math test?

The score ranges that denote failure are 0–9, 10–19, 20–29, and 30-39. There were 23, 32, 45, and 67 marks in those categories. 23 + 32 + 45 + 67 = 167.

There were 167 pupils that didn't pass the test.

#### Solve for x as follows:

14.5x−5(x+2) ≤ 4+4 (4−1/8x)

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 percentage of a number is 44?

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

#### What is the value of (x2 + x + 3) / (x + 2) when x = -1?

(x2 + x + 3) / (x + 2) = ( (-1)2 + (-1) + 3) / ((-1) + 2) when x=-1

((-1)2 + (-1) + 3) / ((-1) + 2) = (1 – 1 + 3)/ (-1 + 2)

(1 – 1 + 3)/ (-1 + 2) = 3 / 1 = 3

#### Which of the following mark intervals has the largest proportion of those who took the test?

The highest number displayed in a mark interval is 128. This number falls between the range of 50-59. 32 + 45 = 77 students make up the grade range of 10-29. Greater than 77 is 128.

The mark range between 50 and 59 had the highest proportion of students who took the test, according to the mark intervals displayed.

#### If three of them must sit side by side, how many different ways may six individuals sit on a bench?

Treat the three people who want to sit next to each other as a single group. The group consists of 4 units, each with three individuals. 4 arrangements of the 4 units are possible! on the bench, positions.

The trio in the group can be arranged into threes. ways. There are four arrangements in total. × 3! = 144.

#### What follows has the same value as 10x2 - 11x + 3?

10x2 – 11x + 3 = 10x2 – 5x – 6x + 3

10x2 – 5x – 6x + 3 = 5x(2x – 1) – 3(2x – 1)

5x(2x – 1) – 3(2x – 1) = (5x – 3)(2x -1)

#### What is the chance that two randomly selected students who took the test would both receive a score of 70 or higher?

466 students took the test, which was administered in English. 28 people received a score of 70 or above. The likelihood that the first student will receive a score of 70 or higher is 28/466.

The likelihood that the second student will receive a score of 70 or higher is 27/465. The odds of both students receiving a score of 70 or higher are 28/466 × 27/465.

#### 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?

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

#### 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?

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

#### 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?

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%

#### What is the following line's slope:

y=3x−7

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.

#### Factor the equation to find the answer:

2x^2−2x−4=0

2x^2−2x−4=2(x2−x−2)=2(x+1)(x−2)=0

x+1=0 or x−2=0

x+1−1=0−1 or x−2+2=0+2

So, the solutions to the equation 2x^2 - 2x - 4 = 0 are x = 2 or x = -1.

#### 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?

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

#### What percentage of pupils who received a grade below 30 also received a grade below 20?

23 + 32 + 45 = 100 students received a grade of less than 30. 23 + 32 = 55 students received a grade of less than 20.

55/100 = 55% of pupils had a grade of less than 20, less than 30, or less than 30.