The ratio of forks to spoons in the cafeteria is 15:25. If the total

Mathematics

1 answer:

9966 [12]2 years ago

8 0

Answer:

30 forks

Step-by-step explanation:

Let's start by simplifying the given ratio. Since both 15 and 25 are multiples of 5, we can divide the whole ratio by 5.

Forks: spoons

= 15: 25

= 3: 5

This means that forks take up 3 units of the total number of utensils, while the number of spoons is 5 units of the total number of utensils.

Number of forks= 3u

Number of spoons= 5u

Units shall be represented by the letter u from this point forth.

Now, we can form an equation using the total number of utensils in the cafeteria.

Assuming that the utensils in the cafeteria are only forks and spoons,

number of fork and spoons= 80

3u +5u= 80

8u= 80

Let's solve for u.

Divide by 8 on both sides:

1u= 80 ÷8

1u= 10

This means that 1 unit represents 10 utensils.

Substitute the value of u into the expression of the number of forks:

Number of forks

= 3u

= 3(10)

= 30

Thus, there are <u>30 forks</u> in the cafeteria.

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Professor Halen teaches a College Mathematics class. The scores on the midterm exam are normally distributed with a mean of 72.3

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Answer:

14.63% probability that a student scores between 82 and 90

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 72.3, \sigma = 8.9$