# GED Mathematical reasoning 2

#### Florida will be Lira's vacation destination. She moves at a speed of 63 km/h for five hours and 70 km/h for two hours. What was Lira's average speed over the 7-hour period?

Distance traveled at 70 km/h for 2 hours:

Distance1 = Speed1 * Time1 = 70 km/h * 2 hours = 140 km

Distance traveled at 63 km/h for 5 hours:

Distance2 = Speed2 * Time2 = 63 km/h * 5 hours = 315 km

Total distance traveled:

Total Distance = Distance1 + Distance2 = 140 km + 315 km = 455 km

Total time taken:

Total Time = Time1 + Time2 = 2 hours + 5 hours = 7 hours

Average speed:

Average Speed = Total Distance / Total Time = 455 km / 7 hours ≈ 65 km/h

So, Lira's average speed over the 7-hour time period was approximately 65 km/h.

#### Each year, a toy maker produces 15,000 toys. 300 toys are chosen at random by the company for inspection sampling. Five defective toys are found in the sample by the firm. How many of the 15,000 toys are expected to be defective based on the sample?

Substitute the given values:

5 / 300 = x / 15000

Now, solve for x:

5 * 15000 = 300 * x

75000 = 300 * x

Divide by 300 to find the estimated number of faulty toys in the total production:

x = 75000 / 300

x = 250

Based on the sample, it is estimated that there are likely 250 defective toys in the total production of 15,000 toys.

#### -11.2 and 3.3 are two points that are plotted on a number line. How far apart are these two locations?

The absolute value of the difference between points A and B on a number line is the distance between them. The value of distance is always positive. Apply the absolute value after determining the point differences:

AB = |b − a| or |a − b|

= |−11.2 − 3.3|

= |−14.5|

= 14.5

#### With his $305, Mark intends to purchase as many bags of mulch as he can and have them delivered to his home. The price of each bag is $7.50, and the shipping fee is $35.75. Mulch is only offered for sale in whole bags. What number of bags can Mark buy?

A flat delivery fee of $35.75 is subtracted from Mark's first payment of $305:

$305 − $35.75 = $269.25.

To determine the total number of bags Mark can purchase, we can divide this sum by the price per bag as follows:

$269.25 ÷ $7.50 = 35.9 bags. Since the question specifies that the mulch can only be sold in whole bags, we must round our response down to make sure Mark doesn't go over his allotted spending limit.

#### The equivalent of (7x + 3y)(8x + 5y) is which of the following?

When dealing with binomial expressions, this method is commonly referred to as the ""FOIL method"": multiply the first two terms, then the Outer two terms, then the Inner two terms, and then the last two terms, then combine like terms to arrive at the answer:

(7x + 3y)(8x + 5y)

56x² + 35xy + 24xy + 15y²

56x² + 59xy + 15y²

#### Figure out the x value that renders this fraction undefinable.

For any value when the denominator is equal to 0, a fraction is undefined. Set the denominator to 0 to begin solving for the variable x in this equation:

5 + x = 0

x = −5

#### Which of the following expressions must be true if x is a small negative integer and y is a large positive integer?

Since y is a large positive integer and x is a small negative integer, the value of y - x will be positive.

For example, let's say y = 1000 and x = -3:

y - x = 1000 - (-3) = 1000 + 3 = 1003

As we can see, the expression y - x results in a positive value.

This will hold true for any large positive integer y and any small negative integer x, making the expression y - x always positive.

#### Lisa worked 40 hours for an hourly wage of $8.10. Jamie's hourly wage is $10.80. How many hours would Jamie have to put in to earn what Lisa made working more than 40 hours?

Start by calculating Lisa's final 40-hour salary:

40 hours × $8.10 an hour = $324

To determine how many hours Jamie would need to work, divide this amount by his or her hourly wage:

$324 ÷ $10.80 = 30 hours

#### Rose needs to figure out her water bill each month. At a cost of $1.12 per hundred gallons, her family utilized 18,900 gallons. Additionally, each household must pay a $5.90 monthly account charge. What does she owe in total?

Calculate the cost of water usage:

Melody's family used 18,900 gallons of water at a rate of $1.12 per hundred gallons. To find the cost, we first need to convert 18,900 gallons to hundreds of gallons.

18,900 gallons = 18,900 / 100 = 189 hundreds of gallons

Cost of water usage = 189 hundreds of gallons * $1.12 per hundred gallons = $211.68

Add the monthly account fee:

Monthly account fee = $5.90

Calculate the total bill:

Total bill = Cost of water usage + Monthly account fee

Total bill = $211.68 + $5.90 = $217.58

#### What is the volume of a cube whose sides are 4 inches long?

To determine the cube's volume, use the specified side length and the volume of a cube formula.

V = s^3 where s is the side length

V = (4 in)^3 = 64 in^3

#### Determine 16, 27, and 20 greatest common factor.

List each number's factors first before determining the biggest common factor between the three:

16 factors are 1, 2, 4, 8, and 16.

20 factors are 1, 2, 4, 5, 10, and 20.

27 factors are 1, 3, 9, and 27.

The largest 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 into each number equally, hence 1 is the correct response.

#### In a nearby yoga studio, women make up 80% of the clientele while men make up 20%. The men are typically 40 years old, while the ladies are typically 30 years old. What is the average age of the group as a whole?

Start by calculating the contribution of women to the average (remember that 80% = 0.8): 0.8 * 30 = 24.

Find the contribution of the men: 0.2 * 40 = 8.

Combine these to find the overall average: 24 + 8 = 32

#### 15.05 ÷ 5 =

Put the decimal point in your answer right above the decimal point in the dividend (15.05) and rewrite the problem in long division form. The answer would be 3.01

#### The slope of a road represented as a percent rather than a fraction or decimal is known as the grade of a road.

A road is graded so that it rises 6 feet for every 40 feet of horizontal space. What is the road's grade?

The road's slope, expressed as a fraction, is 6/40 since the slope is the ratio of vertical change (rise) to horizontal change (run). To convert this to the corresponding percent, multiply by 100%: 6/40×100%=15%

#### Find 33 and 44 greatest common factor.

A number's components are values that split into it in an exact ratio. For instance, the factors of 4 are 1, 2, and 4 since each of them can be used to divide 4 without leaving a residual. List the factors of both 33 and 44 in order to find the greatest common factor:

The 33 factors are 1, 3, 11, and 33.

The 44 factors are 1, 2, 4, 11, 22, and 44.

The greatest number that appears in both lists of components, 11, is the factor that has the most in common.

#### The figure has 12 inches on each side. long. What does this shape's area measure?

It is best to initially evaluate all of the available information in situations like these where there are several paths to the solution. You may have noticed that although the solution options are given in feet squared, the side length of the shape is given in inches. The solution must be 5 feet squared since 12 inches equals 1 foot and the shape is made up of 5 identical 1 foot by 1 foot squares.

#### What is the slope of the line perpendicular to 3x+6y=93?

3x + 6y = 93

6y = -3x + 93

y = (-3/6)x + 93/6

y = (-1/2)x + 15.5

In this equation, the coefficient of x is -1/2, which represents the slope of the given line. The slope of a line perpendicular to this line will be the negative reciprocal of -1/2.

Reciprocal of -1/2 = -2/1 = -2

Negative of -2 = 2

#### Which of the following expressions is undefined in the set of real numbers?

The square root of a number is the value that when multiplied with itself gives the number inside the square root, for example: √16 = ±4, because 4 * 4 = 16, and −4 * −4 = 16. Just one answer option displays a negative value inside the square root, as you may have noticed. Since there is no real number that, when multiplied by itself, equals −9, this response,√−9, must be right.

The square root of a negative value is undefined in the set of real numbers since a positive integer squared is positive and a negative integer squared is positive.

#### What is the x-intercept of 2y+3x=159?

Remember that you must put y equal to zero in order to determine the x-intercept. As a result, you get:

3x=159

Simple math yields x=53.

#### There is a 90% likelihood that the Blue Comets soccer team will score the opening goal in each game. How likely is it that the Blue Comets will score the first goal in four straight games?

The Blue Comets have a 90% chance of scoring the opening goal in every given game, regardless of whether they do so in any prior games. This proves that taking the lead in back-to-back games is an independent event. Calculate the product of the probabilities of the occurrences in order to determine the likelihood that they will occur consecutively. The possibility that a team will score first in four successive games is as follows: 0.9 * 0.9 * 0.9 * 0.9 = 0.6561, which rounds to 0.656.