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Natali5045456 [20]

3 years ago

14

Find the absolute maximum and absolute minimum values of tghe function over the indicated interval, and indicate the x-values at

which they occur. f(x)=x^3-x^2-x+6; [-1,2]

1 answer:

Marina86 [1]3 years ago

4 0

A graph shows ...

... absolute minimum: 5, at x=-1 and x=1

... absolute maximum: 8, at x=2

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A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11. Use the TI-84 Plus calculator. (a) I

sukhopar [10]

Answer:

a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

b) There is a 15.97% probability that x will be between 54 and 55.

c) The 47th percentile of x is $X = 52.877$ .

Step-by-step explanation:

Problems of normally distributed samples can be 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

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

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.

This means that $\mu = 53$ .

We have to find the standard deviation of the sample, that is:

$\sigma = \frac{11}{\sqrt{45}} = 1.64$

(a) Is it appropriate to use the normal distribution to find probabilities for x?

We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

(b) Find the probability that x will be between 54 and 55.

This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.

X = 55

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

$Z = \frac{55 - 53}{1.64}$

$Z = 1.22$

$Z = 1.22$ has a pvalue of 0.88877.

X = 54

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

$Z = \frac{54 - 53}{1.64}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of 0.72907.

So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.

(c) Find the 47th percentile of x. Round the answer to at least two decimal places.

This is the value of X when Z has a pvalue of 0.47;

This is between $Z = -0.07$ and $Z = -0.08$ . So we use $Z = -0.075$ .

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

$-0.075 = \frac{X - 53}{1.64}$

$X = 52.877$

The 47th percentile of x is $X = 52.877$ .

8 0

3 years ago

Solve 1/8^-1/3<br> Write in fraction form plz.<br> :)

sladkih [1.3K]

Answer:

$\frac{1} {2^{-1}}$

Step-by-step explanation:

$\huge \frac{1}{ {8}^{ - \frac{1}{3} } } \\ \\ = \huge \frac{1}{ {( {2}^{3} )}^{ - \frac{1}{3} } } \\ \\ = \huge \frac{1}{ {{2} }^{ - 3 \times \frac{1}{3} } } \\ \\ = \huge \frac{1}{ {{2} }^{ - 1 } }$

7 0

3 years ago

8. The high school graduating class of 2000 was 260 students. Five years later, the graduating class was 320 students. By 2010,

olga nikolaevna [1]

Answer:

the question is confusing but the answer is 2010

Step-by-step explanation:

because in the year 2000 it was

260

then increased by

60

over 5 years making the next class

320

then in 2010 it was

400

and 320 + what is 400?

80

so the answer is:

2010

4 0

3 years ago

Rewrite the expression 14m-(5+8m) without parentheses

JulijaS [17]

Answer:

14m-5-8m

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Plzzzzzzzzzzzzzaaaaaa

son4ous [18]

Answer:

C

Step-by-step explanation:

$y^2+4y-32=0\\(y+8)(y-4)=0\\y=4,-8$

Therefore, the answer is C. Hope this helps!

5 0

3 years ago