n a survey, one out of three people named blue as their favorite color. Two out of seven named red. If 1,092 people were included in the survey how many named neither blue nor red as their favorite color?

416
432
540
512

2. The triangles below are similar find the value of X

14
12.5
13.5
12

For number two There are two triangles and one is big the right side says 21 same with the left side and the bottom says 24 for the other triangle both left and right are 10.5 and its a small one and the bottom is X

1-(1/3+2/7) = 21/21 - (7/21+6/21).

21/21 - 13/21 = 8/21 of those surveyed
chose neither color.

8/21 * 1092 = 416 Named neither blue nor red.

Why did the triangle go to therapy? Because it couldn't find its similar shape-mate, X!

But let's get serious for a moment. To find the value of X, we can set up a proportion:

(21/10.5) = (24/X)

Cross-multiplying, we get:

21X = 10.5 * 24

Simplifying further:

21X = 252

Dividing both sides by 21:

X = 252/21

After crunching the numbers, we find that X equals 12.

So the value of X is 12. But don't let that triangle's identity crisis get you down - you're doing great!

To solve the first problem, we can first find the number of people who named blue as their favorite color. Since one out of three people named blue, we can calculate this by dividing the total number of people (1,092) by 3:

1,092 / 3 = 364

So, 364 people named blue as their favorite color.

Next, we can find the number of people who named red as their favorite color. Two out of seven people named red, so we can calculate this by multiplying the total number of people (1,092) by the fraction of people who named red (2/7):

1,092 * (2/7) = 312

So, 312 people named red as their favorite color.

To find the number of people who named neither blue nor red as their favorite color, we can subtract the sum of people who named blue and people who named red from the total number of people:

1,092 - (364 + 312) = 1,092 - 676 = 416

So, 416 people named neither blue nor red as their favorite color.

Therefore, the correct answer is 416.

To solve the first question, we need to find the number of people who named neither blue nor red as their favorite color.

Let's start by finding the number of people who named blue as their favorite color. From the survey, we know that 1 out of 3 people named blue, so we can calculate this by dividing the total number of people in the survey by 3:

1/3 * 1092 = 364

Similarly, we can find the number of people who named red as their favorite color by dividing the total number of people by 7:

2/7 * 1092 = 312

Now, to find the number of people who named neither blue nor red, we subtract the number of people who named blue and red from the total number of people in the survey:

1092 - (364 + 312) = 416

Therefore, 416 people named neither blue nor red as their favorite color. So the correct answer is 416.

For the second question, we are given two similar triangles. We have the bigger triangle with sides labeled as 21, 21, and 24, and the smaller triangle with sides labeled as x, 10.5, and 10.5.

Since the triangles are similar, their corresponding sides are proportional. We can set up a ratio using the corresponding sides:

21/24 = 10.5/x

To solve for x, we can cross-multiply and then divide:

21x = 24 * 10.5
21x = 252
x = 252/21
x = 12

Therefore, the value of x is 12. So the correct answer is 12.