Today, Jay ran 6 3/4 miles around the track and Nick ran 4 1/2 miles. How many times the length of Nick's was Jay's run?

On the first math test, Keiko answered 19 out of 25 questions correctly. On the

m_a_m_a [10]

Answer:

Keiko got a better answer on the test on her second test, and you could compare these two ratios as they are written.

Step-by-step explanation:

First: Convert each of the scores into percentages:

How do you convert ratios to percentages? Well, first we have to convert the ratio to a decimal or a fraction. Let's convert it to a fraction. So, 19 out of 25 will become $\frac{19}{25}$ , and 17 out of 20 will become $\frac{17}{20}$ . To convert a fraction to a percentage:

Divide the numerator by the denominator:

19 ÷ 25 = 0.76 AND 17 ÷ 20 = 0.85

Multiply your quotient by 100

0.76 x 100 = 76 AND 0.85 x 100 = 85

Add the percent sign

76% AND 85%

Now the two quantities are easier to compare. We can obviously see that 85% is bigger [and better] than 76%. So, the ratio that equals 85% - 17 out of 20 - is a better grade.

The second question was: Can you compare these two ratios as they are written? Explain why or why not.

Yes, you can compare these two ratios, just find the [positive] difference between the amount that she scored and the total number of scores that could be gained.

25 - 19 = 6

20 - 17 = 3

Since the equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Keiko got more right and less wrong, which means a greater mark which is also a greater quantity].

Thanks,

Topic: Quantity Relationships, Quantity Conversions

4 0

3 years ago

PROBLEM: Riley has a rectangular shaped patio that is 13 feet long by 15 feet wide. He wants to DOUBLE THE AREA of the patio by

photoshop1234 [79]

Answer:

1) The equation that represents the total area of Riley's proposed ratio is $A' = (\sqrt{2}\cdot x)\cdot (\sqrt{2}\cdot y)$ .

2) The length and width of the new patio are approximately 18.4 feet and 21.2 feet, respectively.

Step-by-step explanation:

1) From Geometry we remember that area formula for the rectangle is represented by:

$A = x\cdot y$ (1)

Where:

$A$ - Area, measured in square feet.

$x$ - Length, measured in feet.

$y$ - Width, measured in feet.

From statement we know that Riley wants to double the area, that is:

$A' = 2\cdot A$ (2)

By applying (1) in (2), we get the following expression:

$A' = 2\cdot x\cdot y$ (3)

Given that Riley wants to double the area of the pation by increasing the length and width by the same amount, we can rearrange (3) by algebraic means:

$A' = \sqrt{2}\cdot \sqrt{2}\cdot x\cdot y$