Show that a∧6 can be written as a perfect square and as a perfect cube.

Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t

NeTakaya

Answer:

$\mu = 11$

$\sigma = 2.08$

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.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when $Z = -1.44, X = 8$ . So

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

$-1.44 = \frac{8 - \mu}{\sigma}$

$8 - \mu = -1.44\sigma$

$\mu = 8 + 1.44\sigma$

Also, when X = 14, Z has a pvalue of 0.925, so when $X = 8, Z = 1.44$

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

$1.44 = \frac{14 - \mu}{\sigma}$

$14 - \mu = 1.44\sigma$

$1.44\sigma = 14 - \mu$

Replacing in the first equation

$\mu = 8 + 1.44\sigma$

$\mu = 8 + 14 - \mu$

$2\mu = 22$

$\mu = \frac{22}{2}$

$\mu = 11$

Standard deviation:

$1.44\sigma = 14 - \mu$

$1.44\sigma = 14 - 11$

$\sigma = \frac{3}{1.44}$

$\sigma = 2.08$

7 0

3 years ago

90 percent as a fraction in simplest form

inysia [295]

Whenever a number is followed by percent, you can turn it into a fraction by simply moving the decimal places two places to the left:

90.0 % becomes .90

As a fraction, this is 90 over 100. To reduce it to its simplest form, divide by 10:

9/10

6 0

3 years ago

Solve the blank: This equation for this graph is y=____x + _______

Marysya12 [62]

Answer:

y=3x+2

Step-by-step explanation:

3 0

3 years ago

Find the perimeter.<br> Perimeter = [?]<br> Simplify your answer completely.

viktelen [127]

The answer would be 119 and 4/7