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goldfiish [28.3K]
3 years ago
7

Find the value of x and pls explain!!❤❤❤

Mathematics
1 answer:
AlexFokin [52]3 years ago
5 0

Answer:

x = 52 degrees.

Step-by-step explanation:

Here we make use of the fact that the interior angles of any triangle add up to 180 degrees.  Before this we must find an algebraic expression for interior angle RQS:  

Since angle RQS + x + 72 = 180 degrees, angle RQS is equal to 180 -72 - x, or 108 - x.

The sum of the three interior angles is then

108 - x + 90 + 34, or 232 - x degrees, and this sum must equal 180 degrees.

Then 232 - x = 180.  Solving for x, we get x = 52 degrees.

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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
How much would $200 invested at 7% interest compounded annually be worth after 5 years? Round your answer to the nearest cent.
e-lub [12.9K]
A= P(1 + r) n (n to the power of) 

<span>A= final balance </span>
<span>P= initial quantity </span>
<span>n= number of compounding periods </span>
<span>r= percentage interest rate </span>

<span>P= $200 </span>
<span>n= 9 years </span>
<span>r= 5%= 0.05 </span>

<span>=$200 (1 + 0.05)9 (power of) </span>
<span>=$310.26</span>
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The sum of a number x and -7 is less than or equal to 18.
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Step-by-step explanation:

x + (-7) ≤ 18

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x ≤ 18 + 7

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Value of x is less than or equal to 25

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6 times some number equals 30
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