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Archy [21]
3 years ago
7

Use trigonometry to solve for x. Round to the nearest tenth.

Mathematics
1 answer:
mel-nik [20]3 years ago
5 0

Answer

12

Step-by-step explanation:

You need to use cosine because the side length needed is adjacent and you have the hypotenuse.Set up a proportion of "cos23 = x/13" and solve by cross multiplying. Then just round.

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Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale
nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) Z = 1.05

e) Z = -1.10

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

Normal probability distribution

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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

\mu = 515, \sigma = 100

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

\mu = 515, \sigma = 100

This is Z when X = 620. So

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

Z = \frac{620 - 515}{100}

Z = 1.05

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

\mu = 515, \sigma = 100

This is Z when X = 405. So

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

Z = \frac{405 - 515}{100}

Z = -1.10

3 0
3 years ago
Help a girl out!!!!!
anzhelika [568]

Answer:

I believe the answer is D. 20\frac{3}{4} Hope i'm right

Step-by-step explanation:

4 0
2 years ago
What is the sign of f on the interval -7/3
Greeley [361]

Answer:

C is the answers for the question

7 0
2 years ago
At a food festival, 3/8 of the dishes were from china. Another 12.5% of the dishes were from japan. What percent of the dishes w
MrMuchimi

Answer: 50%

Step-by-step explanation:

Let x = Total dishes.

Dishes from China = \dfrac38x

Dishes from Japan  = 12.5\% \text{ of }x= 0.125x

Total dishes  from China and Japan = \dfrac38 x+0.125x=0.375x+0.125x=0.5x

Dishes from other countries = x- 0.5x= 0.5x

Percent of dishes from other countries= \dfrac{0.5x}{x}\times100\%= 50\%

Hence, dishes from other countries = 50%

5 0
3 years ago
Slope for (1,5) (3,4)​
frez [133]

Answer:

-1,2

Step-by-step explanation:

4-5=-1

3-1=2  

y2-y1

x2-x1

8 0
2 years ago
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