An athlete runs 7 miles in 45 minutes and then changes their pace to run the next 3 miles in 15 minutes. Overall, what is the average time in minutes it takes the athlete to run 1 mile?

To form an equation from the word problem, first break the given statement into smaller statements.

First, we are given the width of the rectangle as x. We are told, the length is three times width. Mathematically, this means

Length=3*width=3*x=3x

Again, the length is 4 less than 3 times width of the rectangle. Thus, the length of rectangle in terms of width becomes:

Length =3x-4

This is the required equation.

Scatter plots can depict three correlations: positive, negative and no correlation. A positive correlation scatter plot reveals that as one variable increases, the other variable also increases as shown below

To solve this problem, we need to have all options in fraction form.

74  95 = 

7/8 = 3/8

0.72 = 72/100

74% = 74/100

Now, find the least common denominator of 95, 8, and 100. The least common denominator is 3800, which we multiply by each fraction as follows:

74/95*3800=2960

7/8*3800=3325

72/100*3800=2736

74/100*3800=2812

We can see that the fraction 7/8 is the greatest among the given options.

A ratio is of the form a : b but can also be converted to a fraction of the form a/b, where b is not equal to zero. Besides, to in ration means per in fraction form.

In the class of 40 students, 22 are girls and 18 are boys. Thus, the ratio of girls to boys becomes:

The above fraction can be reduced further since 2 is a common factor in both 22 and 18. Thus

In ratio form, girls: boys=11:9

Thus, the ratio of girls to boys in a class of 40 students is 11 to 9.

We are required to find the percent equivalent of the given fraction.

We multiply 7/8 by 100 to convert it to percent. You convert fraction to percent.

Thus 7/8 is equal to 87.5%.

In this problem, we need to find the amount of gratuity the couple will leave. The gratuity is 16% of the total bill. Before solving the problem, the following are terms and their meaning in percent problems:

• Is means equals
• Of means multiply
• What means unknown (variable)

If we let x be the amount of gratuity, then translating the given problem into a mathematical equation becomes:

Now we evaluate the above equation noting that of means multiply.

So, the value of x=9.376 and to the nearest cent, x=9.38

There, a couple will leave a gratuity of $9.38.

We solve for the value of x by following the order of operations

3(x-2)=15

Divide both sides of the equation by 3

Add 2 to both sides of the equation

Thus, the value of x is 8.

We two conversions when asked to convert between kg and lb

And

We need kg equivalent of 220 lb, therefore we use option 1 and carry out the conversions as follows:

Thus, 100kg is equal to 220lb.

To change between L and mL, the following two options are used.

The initial step is to convert the decimal numbers into fractions.

5.2 becomes 52/10

5.15 becomes 515/100

Next, find the least common denominator of 3, 10, and 100, which is 300. We use this value and multiply each fraction.

7/3*300=700

52/10*300=1560

13/3*300=1300

515/100*300=1545

From the above, 1560 is the greatest value which corresponds to 52/10. Thus, 5.2 is the greatest value of all the choices given.