directions: solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. do not linger over problems that take too much time. solve as many as you can; then return to the others in the time you have left for this test. you are permitted to use a calculator on this test. you may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator. note: unless otherwise stated, all of the following should be assumed. 1. illustrative figures are not necessarily drawn to scale. 2. geometric figures lie in a plane. 3. the word “line” indicates a straight line. 4. the word “average” indicates arithmetic mean. do your figuring here. 1. cameron took 4 tests, and his scores were as follows: 100, 60, 80, and 30. cameron took another test that was scored x. the mean score of the 5 tests he took is 72. what is the value of x? a. 54 b. 67.5 c. 68.4 d. 90 2. in the venn diagram below, circles s, c, and p represent farms raising sheep, cows, and pigs, respectively. how many of the 47 farms represented in the diagram do not raise cows? venn diagram with circles s, c, p: s has 12, overlap of s and c has 13, c has 10, overlap of s and p has 2, overlap of all three has 1, overlap of c and p has 4, p has 5 f. 15 g. 17 h. 18 j. 19

Question

Accepted Answer

### Problem 1
# Explanation:
## Step1: Recall the formula for the mean
The arithmetic mean (average) of a set of numbers is given by the sum of the numbers divided by the count of the numbers. For 5 tests, the mean is 72, so we can write the equation: $\frac{100 + 60 + 80 + 30 + x}{5}=72$.

## Step2: Simplify the numerator
First, calculate the sum of the first four scores: $100 + 60 + 80 + 30 = 270$. So the equation becomes $\frac{270 + x}{5}=72$.

## Step3: Solve for $ x $
Multiply both sides of the equation by 5: $270 + x = 72\times5$. Calculate $72\times5 = 360$. Then, subtract 270 from both sides: $x = 360 - 270 = 90$.

# Answer: D. 90

### Problem 2
# Explanation:
To find the number of farms that do not raise cows, we need to sum the regions in the Venn diagram that are not part of circle $ C $ (the circle representing cows). The regions not in $ C $ are the parts of circle $ S $ (sheep) not overlapping with $ C $, the parts of circle $ P $ (pigs) not overlapping with $ C $, and the region only in $ P $ (the 5).

The region only in $ S $ is 12, the region in $ S $ and $ P $ but not $ C $ is 2, the region only in $ P $ is 5, and the region in $ P $ and $ S $? Wait, no, let's look at the Venn diagram:

- Only $ S $: 12
- $ S $ and $ P $ but not $ C $: 2
- Only $ P $: 5
- $ P $ and $ S $? Wait, no, the regions not in $ C $ are:

From the Venn diagram:

- Only $ S $: 12
- $ S \cap P $ (not $ C $): 2
- Only $ P $: 5
- Wait, also, is there a region only in $ S $ and $ P $? Wait, the Venn diagram has:

Circle $ S $: 12 (only $ S $), 13 ($ S \cap C $ not $ P $), 2 ($ S \cap P $ not $ C $), 1 ($ S \cap C \cap P $)

Circle $ C $: 10 (only $ C $), 13 ($ S \cap C $ not $ P $), 4 ($ C \cap P $ not $ S $), 1 ($ S \cap C \cap P $)

Circle $ P $: 5 (only $ P $), 2 ($ S \cap P $ not $ C $), 4 ($ C \cap P $ not $ S $), 1 ($ S \cap C \cap P $)

So the regions not in $ C $ are:

- Only $ S $: 12
- $ S \cap P $ (not $ C $): 2
- Only $ P $: 5

Wait, no, wait: the total regions not in $ C $ are:

Only $ S $: 12

$ S \cap P $ (not $ C $): 2

Only $ P $: 5

Wait, but also, is there a region in $ S $ and $ P $ and not $ C $? Wait, the 2 is $ S \cap P $ not $ C $, the 5 is only $ P $, the 12 is only $ S $. Wait, let's add them up: 12 (only $ S $) + 2 ( $ S \cap P $ not $ C $) + 5 (only $ P $) + is there another? Wait, no, let's check the numbers:

Wait, the Venn diagram:

- Only $ S $: 12
- $ S \cap C $: 13
- Only $ C $: 10
- $ C \cap P $: 4
- $ S \cap C \cap P $: 1
- $ S \cap P $ (not $ C $): 2
- Only $ P $: 5

So the regions not in $ C $ are:

Only $ S $: 12

$ S \cap P $ (not $ C $): 2

Only $ P $: 5

Wait, but also, is there a region in $ P $ and $ S $ and not $ C $? Wait, the 2 is $ S \cap P $ not $ C $, the 5 is only $ P $, the 12 is only $ S $. Wait, let's sum these: 12 + 2 + 5 = 19? Wait, no, wait:

Wait, the total number of farms not raising cows is the sum of all regions that do not include $ C $. Let's list all regions not in $ C $:

1. Only $ S $: 12
2. $ S $ and $ P $ (not $ C $): 2
3. Only $ P $: 5
4. Wait, is there a region in $ P $ and $ S $ and not $ C $? Wait, the 2 is $ S \cap P $ not $ C $, the 5 is only $ P $, the 12 is only $ S $. Wait, but let's check the answer choices. The options are F.15, G.17, H.18, J.19.

Wait, let's re - examine the Venn diagram:

- Only $ S $: 12
- $ S \cap P $ (not $ C $): 2
- Only $ P $: 5
- Wait, also, is there a region in $ P $ and $ S $ and not $ C $? Wait, no, the regions not in $ C $ are:

From the Venn diagram, the areas not in circle $ C $ are:

- The part of circle $ S $ not overlapping with $ C $: 12
- The part of circle $ P $ not overlapping with $ C $: 2 ( $ S \cap P $ not $ C $) + 5 (only $ P $)

Wait, no, let's calculate:

Regions not in $ C $:

- Only $ S $: 12
- $ S \cap P $ (not $ C $): 2
- Only $ P $: 5
- Wait, is there a region in $ S $ and $ P $ and not $ C $? Wait, the 2 is $ S \cap P $ not $ C $, the 5 is only $ P $, the 12 is only $ S $. Now, sum these: 12 + 2 + 5 = 19? Wait, but let's check again.

Wait, the Venn diagram:

Circle $ S $: 12 (only $ S $), 13 ($ S \cap C $), 2 ($ S \cap P $ not $ C $), 1 ($ S \cap C \cap P $)

Circle $ C $: 13 ($ S \cap C $), 10 (only $ C $), 4 ($ C \cap P $), 1 ($ S \cap C \cap P $)

Circle $ P $: 2 ($ S \cap P $ not $ C $), 1 ($ S \cap C \cap P $), 4 ($ C \cap P $), 5 (only $ P $)

So the regions not in $ C $ are:

- Only $ S $: 12
- $ S \cap P $ (not $ C $): 2
- Only $ P $: 5
- Wait, but also, is there a region in $ P $ and $ S $ and not $ C $? Wait, the 2 is $ S \cap P $ not $ C $, the 5 is only $ P $, the 12 is only $ S $. Now, sum these: 12 + 2 + 5 = 19? Wait, but let's check the answer choices. The options are F.15, G.17, H.18, J.19. So J is 19. Wait, but let's do it another way. The total number of farms is 47. Let's calculate the number of farms that raise cows and subtract from 47.

Number of farms that raise cows: only $ C $ (10) + $ S \cap C $ (13) + $ C \cap P $ (4) + $ S \cap C \cap P $ (1) = 10 + 13 + 4 + 1 = 28. Then, the number of farms that do not raise cows is 47 - 28 = 19.

# Answer: J. 19

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QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Recall the formula for the mean

Step2: Simplify the numerator

Step3: Solve for \( x \)

Answer:

Problem 2