# GED Mathematical Reasoning 3

#### What value does this numerical expression indicate?

The exponents in the square root must first be evaluated in accordance with the order of operations (PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), after which the total may be determined and the square root can then be evaluated. The formula is reduced to: 36=64 = 100 = 10.

#### Solve for the positive value of c.

9c^{2} - 11 = 718

^{2}- 11 = 718

Isolate the variable by adding 11 to both sides of the equation right away. You'll be left with:

9c2 = 729

Divide both sides by 9.

#### Which expression describes the distance between the two spots indicated on this number line most accurately?

Regardless of what the signs of the individual points are, keep in mind that distance is always a positive number. Therefore, an absolute value is required in the right response.

Since -1 is halfway between -2 and 0, it must be the starting point. Since it lies in the middle of points 4 and 6, the second point must be 5. To get the right response, divide one point by the other and nest the expression inside an absolute value:

AB = |b − a| or |a − b|

= |−1 − 5|

#### In 21 feet, how many meters are there?

3.25 feet equals one meter

1 foot = 1÷3.25 meters

21 feet = 21×1÷3.25 = 6.4615 meters

#### A great circle of a sphere lies on its surface and contains its center. What is the circumference of a great circle of a sphere that has a surface area that measures 1,476 square centimeters?

NOTE: Π (or Pi) equals 3.14.** ** (math4)

SA = 4Πr2 finds the radius.

4(3.14)r2 = 1,476cm2

12.56r2 = 1,476cm2

r2 = 117.51592356687898

r = 10.840476168825749 (or 10.84)

Place the value of the radius in the circumference formula (C = 2Πr)

C = 2(3.14)(10.84) = 68.0752 or approximately 68.1 (Answer 1).

#### What value of x results in y = 15 - 3x and y = 0?

y =15 – 3x and y = 0

15 – 3x = 0

3x = 15 x = 5

#### There are three books sold in different quantities. A $10 book sells six copies. A $5 book sells five copies. A $2 book sells three copies. What is the median price of all the books sold?

To determine the median, find the two middle numbers in numeric order (5 and 5) and divide by 2.

In this case, the numeric order is

2, 2, 2, 5, 5, 5, 5 ,5, 10, 10, 10, 10, 10, 10

#### A building can be painted in 5 days by 10 persons. How much of the building could 7 individuals paint in 5 days if they all painted as quickly as the others?

A building can be painted in 5 days by 10 persons. In 5 days, each person paints a 1/10 of the building. In 5 days, 7 individuals would paint 7 × 1/10 of the building, and 7 people would paint 7/10 of the building.

#### Identify mode for the following data:

2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 9, 9, 9, 11, 11, 13, 12, 9, 9, 9, 2, 7, 7, 7

7 occurs in the highest quantity in the 24-number pair (9 times). This makes it the mode.

#### What is the median of this data set?

17, 42, 53, 97, 102, 82

Take the two middle numbers in numerical order (53 and 82) and add them together. Then, divide by 2.

#### What is the mean of this data set?

8, 47, 13, 17, 26, 32

To determine the mean, add all numbers together and divide the sum (143) by the quantity (6).

#### Solve using the substitution method:

NOTE: Round long decimals to the nearest one hundredth.

y = 3x - 873x + 2y = 21

If y = 3x - 87, then the following is true per the substitution method:

3x + 2(3x - 87) = 21

3x + 6x - 174 = 21

9x = 195

x = 21.67

y = 3(21.67) - 87

y = -21.99

#### Arrange the following four fractions: 1/4, 2/3, 4/7, and 1/2 from smallest to largest.

The right order is evident if 1/4, 2/3, 4/7, and 1/2 are transformed to fractions with the common denominators 21/84, 56/84, 48/84, and 42/84.

#### The volume of the cylinder below, measured to the nearest cubic inch, is 6283 cubic inches with r = 10 inches. To the nearest inch, determine the cylinder's height.

This cylinder has a volume of 6283.

(pi)r2h = 6283. The height is h. (pi) is 3.14

h = 6283÷(pi)÷100 = 19.999…. h = 20

The cylinder has a 20-inch height.

#### 8.32 × 3.2 =

Decimal numbers can be multiplied together by right-aligning them vertically and multiplying the values as normal while disregarding the decimal points until the product is found. The amount of digits to the right of the decimal points in the values multiplied determines where the decimal point is placed in the product. In this case, there are three digits to the right of the decimal points: 32 and 2, so the product must also have three digits to the right of the decimal: 26624 becomes 26.624 to satisfy this condition.

#### What is the distance between -3/7 and -2/3 on a number line?

The absolute values |a| or abs(a) can be used to calculate the distance between two numbers.

The distance between these numbers is abs(-3/7 − -2/3 )

= abs(-(3/7 -2/3))

= abs(3/7 -2/3)

= abs(9/21 – 14/21)

= abs(-5/21 )

=5/21

#### The equation h=-t2+3t+10, where t is time in seconds and h is height above a platform and is in computer units, can be used to simulate the trajectory of a rocket on a computer screen. Find out how long it takes the rocket to arrive at the platform.

When h = 0, you reach the platform. You must find the solution to the equation 0 =-t2+3t+10. Rearranging this yields t2-3t-10 = 0. Consequently, (t - 5)(t + 2) = 0.

The answer to the equation is t = 5 or -2. It is impossible for t to be -2 since t is a time. The journey of the rocket to the platform lasts 5 seconds.

#### If the product of 6 and an integer, n, is increased by 13, the result is -14. What is the value of n?

Let n = the integer.

The product of two values is the result of multiplying them. "Increased by" means to use addition. Therefore, you get this equation:

6n + 13 = -14

Isolate the variable.

6n = -27

Divide both sides by 6.

n = -4.5

#### Solve for x:

-5x - 5 > 15

Isolate the variable by adding 5 to both sides.

-5x - 5 + 5 > 15 + 5

You're left with this: -5x > 20

Continue the operation, dividing both sides by -5 and reversing the comparison because we are dealing with a negative number.

x < -4

Now plug -4 into the original inequality.

-5(-4) - 5 > 15

20 - 5 > 15

15 > 15

Since 15 is equal to 15 and not greater than, we know that any number below -4 will cause the original inequality (-5x - 5 > 15) to be true; therefore, x > -4, so Answer 1 is correct.

#### Two of the sides of an isosceles triangle are equal. What is the triangle's perimeter if two of its sides are 5 inches and 2 inches?

In order for the two shorter sides to meet, the other side must be 5 inches long.

The triangle's perimeter is its circumference, which is 5 + 5 + 2 = 12.