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2 years ago

What is 7 times the sum of a squared and b minus 4 times the sum of a squared and b

1 answer:

7 0

The sum of a squared and b is given by
$a^2+b$

7 times the sum of a squared and b is given by
 $7(a^2+b)$
while 4 times the sum of a squared and b is given by
 $4(a^2+b)$

Therefore, 7 times the sum of a squared and b minus 4 times the sum of a squared and b is given by

$7(a^2+b)-4(a^2+b)=3(a^2+b)$

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The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean

Marysya12 [62]

Answer:

a) 15.87% of the scores are expected to be greater than 600.

b) 2.28% of the scores are expected to be greater than 700.

c) 30.85% of the scores are expected to be less than 450.

d) 53.28% of the scores are expected to be between 450 and 600.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 500, \sigma = 100$

a. Greater than 600

This is 1 subtracted by the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% of the scores are expected to be greater than 600.

b. Greater than 700

This is 1 subtracted by the pvalue of Z when X = 700. So

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

$Z = \frac{700 - 500}{100}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of the scores are expected to be greater than 700.

c. Less than 450

Pvalue of Z when X = 450. So

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

30.85% of the scores are expected to be less than 450.

d. Between 450 and 600

pvalue of Z when X = 600 subtracted by the pvalue of Z when X = 450. So

X = 600

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 450

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

0.8413 - 0.3085 = 0.5328

53.28% of the scores are expected to be between 450 and 600.

6 0

2 years ago

In 10 seconds, Lauren counts 5 vehicles passing by her house. At that rate, how many vehicles would pass by in one hour?

Anna007 [38]

6 x 60 x 5 would be the equation and all of that put together would be 1,800 vehicles would pass by in an hour.

7 0

3 years ago

Select all the expressions that are equivalent to 4 - x.

Andre45 [30]

Im pretty sure it’s A,B,D

5 0

2 years ago

Henry can type 3500 words in 70 minutes. Colin can type 1500 in 30 minutes. Brian can type 2200 words in 40 minutes. Who types a

Snezhnost [94]

Given:

Henry can type 3500 words in 70 minutes.

Colin can type 1500 in 30 minutes.

Brian can type 2200 words in 40 minutes.

To find:

The person who types at the fastest rate of words per minute.

Solution:

We know that,

$\text{Rate of words per minute}=\dfrac{\text{Number of words}}{\text{Number of minutes}}$

Using this formula, we get

$\text{Henry's rate of words per minute}=\dfrac{3500}{70}=50$

$\text{Colin's rate of words per minute}=\dfrac{1500}{30}=50$

$\text{Brian's rate of words per minute}=\dfrac{2200}{40}=55$

Since 55>50, therefore Brian's types at the fastest rate of words per minute.

6 0

2 years ago

What is 0.15% of 43 i suck at math it will help me so much

butalik [34]

.15% translates to
.0015, and "of" means to multiply. so .0015 multiplied with 43 is
.0645

7 0

3 years ago