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2 years ago

N/4 < -1 on a number line -10x>-100 on a number line 5x>20 on a number line

1 answer:

4 0

N/4 < -1 — we can multiply both sides with 4, so we dont have to deal with fractions.

N < -4

So, our N goes left from -4 on a number line.

-10x<-100 — divide both sides by 10
-x < -10
x > 10

X is from 10 rightwards.

5x>20 — divide both sides by 5
x > 4

X is rightwards from 4.

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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

2x+2y = 5<br> 3x + 3y = 7<br> How many solutions does the system of equations above have?

Anastaziya [24]

Answer:

No solutions

Step-by-step explanation:

5 0

2 years ago

The Great Pyramid in Giza, Egypt, is a square pyramid. The dimensions of the pyramid at the time of its completion are shown in

Ann [662]

Hey there look like you need some help.
If I give you the correct answer mark me brainleist

First you would find the area of the square: 230*230= 52,900Next you would find the area of one on the triangles: 230*187=43,010 * 1/2= 21,505Then you would multiply the area of the one triangle by four: 21,505*4= 86,020Finally, you would add the area of the square to the combined area of the triangles: 86,020+ 52,900=138,920

7 0

3 years ago

Help me please?? solve using proportion

gulaghasi [49]

9514 1404 393

Answer:

2 1/2 cups

Step-by-step explanation:

A proportion says the ratio of one thing to another is the same for different amounts. Here, we want cups, so we can use the proportion ...

cups/people = 2/12 = x/15 . . . . . where x is the number we want to find

Multiplying by 15 gives ...

x = 15(2/12) = 5/2 = 2 1/2

You will need 2 1/2 cups of zucchini to feed 15 people with the same recipe.

6 0

2 years ago

When an opinion poll selects cell phone numbers at random to dial, the cell phone exchange is first selected and then random dig

Sav [38]

Answer:

Step-by-step explanation:

When an opinion poll selects cell phone numbers at random to dial, the cell phone exchange is first selected and then random digits are added to form a complete telephone number. When using this procedure to generate random cell phone numbers, approximately 55%55% of the cell numbers generated correspond to working numbers. You watch a pollster dial 1515cell numbers that have been selected in this manner.What is the mean number of calls that reach a working cell number?A. 0.550.55B. 1515C. 8.258.25D. 3030

6 0

3 years ago