Find two consecutive positive even integers such that the sum of their squares is 452 please show work

Maria mixes \frac{1}{4} cup white sugar and \frac{2}{3} cup brown sugar to make a topping for some muffins. She uses \frac{1}{12

Hoochie [10]

Answer: 11 muffins

Step-by-step explanation:

Since Maria mixes 1/4 cup white sugar with 2/3 cup brown sugar, this will give us a mixture of:

= 1/4 + 2/3

= 3/12 + 8/12

= 11/12

Ww are then told that she uses 1/12 cup of the mixture to top each muffin. Therefore, the number of muffins that she can top will be:

= 11/12 ÷ 1/12

= 11/12 × 12/1

= 12

She can top 11 muffins.

3 0

3 years ago

Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years an

Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean $\mu$ , standard deviation $\sigma$ .

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

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

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

8 0

2 years ago

Calculate the distance between the points )=(-2, 4) and G = (5,-2) in the coordinate plane.

Alika [10]

Answer:

Somewhere around 6 or 9

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Write the sentence as an equation.<br> 62 more than the product of 150 and r is 40

aleksandrvk [35]