One-third of the students in class scored 90% or better on a test. Two-fifths of the students scored 80% - 89% on the test. The rest of the students scored below 80% on the test. What fraction of the students scored below 80% on the test?

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Answer 1

Let's denote the total number of students in the class as $N$.

1. Students who scored 90% or better:
   $$\frac{1}{3}N$$

2. Students who scored between 80% and 89%:
   $$\frac{2}{5}N$$

Now, to find the fraction of students that scored below 80%, we first need to determine the total fraction of students accounted for by those who scored 90% or better and those who scored between 80% and 89%.

Adding these two fractions: $$\frac{1}{3}+\frac{2}{5}$$

To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15.

Converting each fraction:
$$\frac{1}{3}=\frac{5}{15}\text{and}\frac{2}{5}=\frac{6}{15}$$

Now, adding them: $$\frac{5}{15}+\frac{6}{15}=\frac{11}{15}$$

This means that $\frac{11}{15}$ of the students scored 90% or better or between 80% and 89%.

To find the fraction of students who scored below 80%, we subtract this result from 1: $$1-\frac{11}{15}=\frac{15}{15}-\frac{11}{15}=\frac{4}{15}$$

Therefore, the fraction of students who scored below 80% on the test is: $$\boxed{{\displaystyle \frac{4}{15}}}$$

Answer 2

3 of 83 of 8 Items

Question
The boiling point of oxygen is −182.9 °C
, and the boiling point of hydrogen is −252.87 °C
. What is the difference between the boiling point of oxygen and hydrogen?

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Answer 3

To find the difference between the boiling points of oxygen and hydrogen, we will subtract the boiling point of hydrogen from the boiling point of oxygen:

1. Boiling point of oxygen: $-182.9,°C$

2. Boiling point of hydrogen: $-252.87,°C$

Now we can calculate the difference:

$$\text{Difference}=\text{Boiling point of oxygen}-\text{Boiling point of hydrogen}$$

Substituting in the values:

$$\text{Difference}=-182.9-(-252.87)$$

This simplifies to:

$$\text{Difference}=-182.9+252.87$$

Now, performing the addition:

$$\text{Difference}=252.87-182.9=69.97$$

Therefore, the difference between the boiling points of oxygen and hydrogen is:

$$\boxed{{\displaystyle 69.97}}$$

Answer 4

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Question
In September, Claire weighed 187.4 pounds. By March, she weighed 163.5 pounds. What rational number represents the change in Claire’s weight? (Think about the sign).

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Answer 5

To find the change in Claire's weight, we subtract her weight in March from her weight in September.

1. Weight in September: $187.4$ pounds
2. Weight in March: $163.5$ pounds

The formula for the change in weight is:

$$\text{Change in weight}=\text{Weight in March}-\text{Weight in September}$$

Substituting in the values:

$$\text{Change in weight}=163.5-187.4$$

Now, we perform the subtraction:

$$\text{Change in weight}=163.5-187.4=-23.9$$

The negative sign indicates that Claire's weight decreased. Therefore, the rational number representing the change in Claire's weight is:

$$\boxed{{\displaystyle -23.9}}$$