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3 years ago

Find the domain and range of the graph below.

Mathematics

1 answer:

8_murik_8 [283]3 years ago

7 0

Hello! My name is Chris and I’ll be helping you with this problem.

Date: 9/28/20 Time: 10:53 am CST

Answer:

D: {-4,-2, 1, 3}

R: {-2,-1, 2, 3}

I hope this helped answer your question! Have a great rest of your day!

Furthermore,

Chris

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Point B represents the greater number because it is farther to the right.

Step-by-step explanation:

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How do i find the estimate of 92×68 please help!!!!!!!

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3 years ago

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

In a class of 18 students, 5 are math majors. A group of four students is chosen at random. (Round your answers to four decimal

ss7ja [257]

Answer:

(a) 0.2721

(b) 0.7279

Step-by-step explanation:

(a) If we choose only one student, the probability of being a math major is $\frac{5}{18}$ (because there are 5 math majors in a class of 18 students). So, the probability of not being a math major is $\frac{18}{18} - \frac{5}{18} = \frac{13}{18}$ (we subtract the math majors of the total of students).

But there are 4 students in the group and we need them all to be not math majors. The probability for each one of not being a math major is $\frac{13}{18}$ and we have to multiply them because it happens all at the same time.

P (no math majors in the group) = $\frac{13}{18} *\frac{13}{18}*\frac{13}{18}*\frac{13}{18} = (\frac{13}{18}) ^4$ = 0.2721

(b) If the group has at least one math major, it has one, two, three or four. That's the complement (exactly the opposite) of having no math majors in the group. That means 1 = P (at least one math major) + P (no math major). We calculated this last probability in (a).

So, P (at least one math major) = 1 - P(no math major) = 1 - 0.2721 = 0.7279

(c) In the group of 4, we need exactly 2 math majors and 2 not math majors. As we saw in (a), the probability of having a math major in the group is 5/18 and having a not math major is $\frac{13}{18}$ . We need two of both, that's $\frac{5}{18}*\frac{5}{18}*\frac{13}{18}*\frac{13}{18}$ . But we also need to multiply this by the combinations of getting 2 of 4, that is given by the binomial coefficient $\binom{4}{2}$ .

So, P (exactly 2 math majors) = $\binom{4}{2}*(\frac{5}{18} )^2*(\frac{13}{18})^2$ = $\frac{4!}{2!2!}*\frac{25}{324}*\frac{169}{324}$ = 0.2415

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4 years ago

The diagonal of a rectangle is 40 and its base is 32. Find the altitude of the rectangle.

Nutka1998 [239]

The altitude of the rectangle ?

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4 years ago

Find the domain and range of the graph below. ​

Find the domain and range of the graph below.