I need help figuring which of the answers are it I need to pick 3 please help

What is the value of the expression below? 8 + 24 / 2 X 6 - 4

umka21 [38]

8 + 24 / 2 X 6 - 4

following order of operations divide 24 by 2:

8 + 12 x 6 -4

Multiply 12 by 6:

8 + 72 -4

Add 8 and 72:

80-4

Subtract to get 76

6 0

3 years ago

Read 2 more answers

The average Act score follows a normal distribution, with a mean of 21.1 and a standard deviation of 5.1. What is the probabilit

ohaa [14]

Answer:

0.43% probability that the mean IQ score of 50 randomly selected people will be more than 23

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 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 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.

In this question:

$\mu = 21.1, \sigma = 5.1, n = 50, s = \frac{5.1}{\sqrt{50}} = 0.7212$

What is the probability that the mean IQ score of 50 randomly selected people will be more than 23

This is 1 subtracted by the pvalue of Z when X = 23. So

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

By the Central Limit Theorem

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

$Z = \frac{23 - 21.1}{0.7212}$

$Z = 2.63$

$Z = 2.63$ has a pvalue of 0.9957

1 - 0.9957 = 0.0043

0.43% probability that the mean IQ score of 50 randomly selected people will be more than 23

5 0

3 years ago

Identify the three similar right triangles in the given diagram.

irga5000 [103]

Answer:

B. ΔABD, ΔADC, ΔDBC

Step-by-step explanation

Step -1 In ΔABD and ΔADC (from figure).

∠DAB=∠CAD (common in both triangles) ,

∠DBA=∠CDA =90 degree, and

∠BDA=∠DCA (rest angle of the two triangles).

therefore ΔABD similar to ΔADC (by AAA similarity theorem).

Step -2 In ΔDBC and ΔADC (from figure).

∠DCB=∠ACD (common in both triangles) ,

∠DBC=∠ADC =90 degree, and

∠CDB=∠CAD (rest angle of the two triangles).

therefore ΔDBC similar to ΔADC (by AAA similarity theorem).

Step -3 In ΔABD and ΔDBC (from figure).

∠BDA=∠BCD (because , ∠ACD=ADB from stap-1 and ∠ACD=∠BCD from figure) ,

∠DBA=∠CBD =90 degree, and

∠BAC=∠BDC (rest angle of the two triangles).

therefore ΔABD similar to ΔDBC (by AAA similarity theorem).

In the above step- ΔABD similar to ΔADC, ΔDBC similar to ΔADC and ΔABD similar to ΔDBC.

Hence ΔABD, ΔADC, ΔDBC similar to each other in the given figure.

4 0

3 years ago

Find the mean and standard deviation for the set of data.

dem82 [27]

The mean and standard deviation for the set of data will be 16 and 5.87. Then the correct option is A.

<h3>What is a standard deviation?</h3>

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

The set of data is given below.

16, 22, 8, 5, 20, 18, 14, 17, 24

The mean of the data set will be

μ = (16 + 22 + 8 + 5 + 20 + 18 + 14 + 17 + 24) / 9

μ = 144 / 9

μ = 16

Then the standard deviation of the data set will be

$\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}} \\\sigma = \sqrt{\dfrac{(16 - 16)^2 +(22 - 16)^2 + (8-16)^2 + ......+(24-16)^2 }{9}} \\\sigma = \sqrt{\dfrac{310}{9}}\\$