Question

In preparation for the school dance, the administration surveys randomly selected students about their preferred color combination. The table shows the results:

red and black: 8

silver and gold: 6

black and silver: 15

purple and white: 9

There are 304 students in the school. How many students can the administration expect to prefer red and black color combination?

Answer 1

are you sure that is the answer

Answer 2

To find out how many students the administration can expect to prefer the red and black color combination, we first need to calculate the total number of responses recorded in the survey. We can do this by adding the number of students who preferred each color combination:

- Red and black: 8
- Silver and gold: 6
- Black and silver: 15
- Purple and white: 9

Now, let's add those numbers:

\[
8 + 6 + 15 + 9 = 38
\]

Thus, there were 38 students who responded to the survey.

Now, we can determine the proportion of students who preferred the red and black color combination. The proportion is given by the number of students who preferred red and black divided by the total number of responses:

\[
\text{Proportion of red and black} = \frac{8}{38}
\]

Next, we want to find out how many students in the entire school of 304 students can be expected to have the same preference. We calculate this by multiplying the proportion by the total number of students in the school:

\[
\text{Expected number of students} = \frac{8}{38} \times 304
\]

Calculating this step by step:

First, compute the proportion:

\[
\frac{8}{38} \approx 0.2105
\]

Now multiply by the total number of students:

\[
0.2105 \times 304 \approx 64.00
\]

Thus, the administration can expect approximately **64 students** to prefer the red and black color combination at the school dance.

Answer 3

Let’s re-evaluate the calculations step by step to ensure accuracy.

1. First, we already added the preferences correctly:
- Red and black: 8
- Silver and gold: 6
- Black and silver: 15
- Purple and white: 9

Total responses:
\[
8 + 6 + 15 + 9 = 38
\]

2. Next, we determine the proportion of students who preferred red and black:
\[
\text{Proportion of red and black} = \frac{8}{38}
\]

3. Now, we multiply this proportion by the total number of students in the school (304):
\[
\text{Expected number of students} = \frac{8}{38} \times 304
\]

Let's calculate:
- \(\frac{8}{38} = 0.210526315789474\) (approximately)
- Now, multiply this by 304:
\[
0.210526315789474 \times 304 \approx 64.0
\]

To simplify the multiplication step:
\[
\text{Expected number of students} = \frac{8 \times 304}{38}
\]
Calculating the numerator:
\[
8 \times 304 = 2432
\]
Now, divide by 38:
\[
\frac{2432}{38} \approx 64
\]

Thus, upon re-evaluation, the expected number of students who prefer the red and black color combination remains approximately **64 students**.

So yes, the answer is indeed valid and correctly calculated. Thank you for your patience!