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3 years ago

Is −1 4 < −3 4 ? Use the number line to explain your answer.

Mathematics

1 answer:

alexira [117]3 years ago

6 0

Answer:

Step-by-step explanation:

I used the number line and the number that is closest to zero is the largest

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Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give t

Lapatulllka [165]

Answer:

$P(\bar X >80)=P(Z>2.143)=1-P(z$

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let X the random variable that represent the Student scores on exams given by a certain instructor, we know that X have the following distribution:

$X \sim N(\mu=74, \sigma=14)$

The sampling distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

The deduction is explained below we have this:

$E(\bar X)= E(\sum_{i=1}^{n}\frac{x_i}{n})= \sum_{i=1}^n \frac{E(x_i)}{n}= \frac{n\mu}{n}=\mu$

$Var(\bar X)=Var(\sum_{i=1}^{n}\frac{x_i}{n})= \frac{1}{n^2}\sum_{i=1}^n Var(x_i)$

Since the variance for each individual observation is $Var(x_i)=\sigma^2$ then:

$Var(\bar X)=\frac{n \sigma^2}{n^2}=\frac{\sigma}{n}$

And then for this special case:

$\bar X \sim N(74,\frac{14}{\sqrt{25}}=2.8)$

We are interested on this probability:

$P(\bar X >80)$

And we have already found the probability distribution for the sample mean on part a. So on this case we can use the z score formula given by:

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

Applying this we have the following result:

$P(\bar X >80)=P(Z>\frac{80-74}{\frac{14}{\sqrt{25}}})=P(Z>2.143)$

And using the normal standard distribution, Excel or a calculator we find this:

$P(Z>2.143)=1-P(z$

6 0

4 years ago

Help plz:)))I’ll mark u Brainliest

Mamont248 [21]

Answer:

4/5

Step-by-step explanation:

Given :

A right angled triangle with sides 24 , 3 and 40 .

And we need to find the value of sinZ .

We know that , sine is the ratio of perpendicular and Hypotenuse. So that ,

$:\implies$ sinZ = p/h

$:\implies$ sin Z = 32/40

$:\implies$ sin Z = 4/5

<u>Hence the renquired answer is 4/5.</u>

7 0

3 years ago

which of the following lines is parallel to the graph of 5x+2y=8? a) 2x+5y=3 b) 5x-2y=6 c) -10x-4y=7 d) -10x+4y=9

zaharov [31]

I hope this helps you

3 0

3 years ago

What is the slope of the line that passes through the points (-2,3) and (-14, -5)?

TEA [102]

Slope = 2/3 (positive 2/3)
You use the formula Y2-Y1/X2-X1 in order to get the slope

8 0

3 years ago

Please help!

Gemiola [76]

The derivative of $f(x) = 2\cdot x^{2}-9$ is $f'(x) = 4\cdot x$ .

In this exercise we must apply the definition of derivative, which is described below:

$f'(x) = \lim_{x \to 0} a_n \frac{f(x+h)-f(x)}{h}$ (1)

If we know that $f(x) = 2\cdot x^{2}-9$ , then the derivative of the expression is:

$f'(x) = \lim_{h \to 0} \frac{2\cdot (x+h)^{2}-9-2\cdot x^{2}+9}{h}$

$f'(x) = 2\cdot \lim_{h \to 0} \frac{x^{2}+2\cdot h\cdot x + h^{2}-2\cdot x^{2}}{h}$

$f'(x) = 2\cdot \lim_{h \to 0} 2\cdot x + h$

$f'(x) = 4\cdot x$

The derivative of $f(x) = 2\cdot x^{2}-9$ is $f'(x) = 4\cdot x$ .

We kindly invite to check this question on derivatives: brainly.com/question/23847661

4 0

3 years ago