-X + 2y = 10<br> -3x+ 6y = 11

If a parallelogram has congruent

o-na [289]

Answer: A

Step-by-step explanation:

The contrapositive of a statement is logically equivalent to the original statement.

6 0

2 years ago

The mean per capita income is 16,127 dollars per annum with a variance of 682,276. What is the probability that the sample mean

MakcuM [25]

Answer:

0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

Step-by-step explanation:

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

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

The standard deviation is the square root of the variance. So

$\mu = 16127, \sigma = \sqrt{682276} = 826, n = 476, s = \frac{826}{\sqrt{476}} = 37.86$

What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

Either it differs by 104 or less dollars, or it differs by more than 104 dollars. The sum of the probabilities of these events is 100. I am going to find the probability that it differs by 104 or less dollars first.

Probability that it differs by 104 or less dollars first.

pvalue of Z when X = 16127 + 104 = 16231 subtracted by the pvalue of Z when X = 16127 - 104 = 16023. So

X = 16231

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

By the Central Limit Theorem

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

$Z = \frac{16231 - 16127}{37.86}$

$Z = 2.75$

$Z = 2.75$ has a pvalue of 0.9970

X = 16023

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

$Z = \frac{16023 - 16127}{37.86}$

$Z = -2.75$

$Z = -2.75$ has a pvalue of 0.0030

0.9970 - 0.0030 = 0.9940

99.40% probability that it differs by 104 or less.

What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

p + 99.40 = 100

p = 0.60

0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

7 0

3 years ago

How to know if the number is a perfect square

emmasim [6.3K]

Answer:

Step-by-step explanation:

Prime factorize the given number. All factors should have pair. If all factors have pair, then it is a perfect square

EG: 36 : Factors of 36 are 2,3,2,3. Here there are two 2's and two 3's. so 36 is a perfect square.

EG: 24: Factors of 12 are 2,2,3. Here 3 is without pair. so it is not a perfect square.

3 0

3 years ago

How do u combine like terms

velikii [3]

If the equation is let's say 3x+ 7 +4x to combine like terms, you would take 3x and 4x since they both have x. You wouldn't take the 7 since it doesn't have and x like the other numbers. 3x +4x = 7x so your new equation would be 7x + 7.

6 0

3 years ago

Read 2 more answers

What’s the sum of -30 and 29

Nuetrik [128]

Answer:

The answer of -1.

Step-by-step explanation:

You have to add both numbers together :

$- 30 + 29 \\ = - 1$