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Lena [83]
3 years ago
15

What is the relationship between turning points of a graph and its derivative function​

Mathematics
1 answer:
shutvik [7]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

Given a function f(x)

Then at the turning points the derivative of f(x) equals zero, that is

f'(x) = 0 at the turning points

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A popular soft drink is sold in 2-liter (2000 milliliter) bottles. Because of variation in the filling process, bottles have a m
andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important 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 s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 2000, \sigma = 18

A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?

So n = 100, s = \frac{18}{\sqrt{100}} = 1.8

This probability is the pvalue of Z when X = 1995. So

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

By the Central Limit Theorem

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

Z = \frac{1995 - 2000}{1.8}

Z = -2.78

Z = -2.78 has a pvalue of 0.0027

So 0.27% probability that the mean is less than 1995 milliliters.

B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9.

So it is X when Z = 1.28

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

1.28 = \frac{X - 2000}{1.8}

X - 2000 = 1.8*1.28

X = 2002.3

2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

3 0
3 years ago
The ratio of ebooks to novels is 4:5. if there are 32 ebooks how many novels are there?
12345 [234]
<h3>Answer:  40 novels</h3>

================================================

Work Shown:

n = number of novels

(32 ebooks)/(n novels) = 4/5

32/n = 4/5

32*5 = n*4 ............ cross multiply

160 = 4n

4n = 160

n = 160/4 .............. dividing both sides by 4

n = 40

There are 40 novels.

4 0
3 years ago
If g(x) = 1 - ¾ x <br> find: -5g(4) - 1
cricket20 [7]

Answer:

<u>-</u><u>5</u><u>g</u><u>(</u><u>4</u><u>)</u><u> </u><u>-</u><u> </u><u>1</u><u> </u><u>is</u><u> </u><u>9</u>

Step-by-step explanation:

g(x) = 1 -  \frac{3}{4} x

when x is 4:

g(4) = 1 -  \frac{3}{4}  \times 4 \\  = 1 - 3 \\  =  - 2

therefore:

- 5g(4) - 1 =  - 5( - 2) - 1 \\  = 10 - 1 \\  = 9

5 0
3 years ago
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Find the value of b.
Naya [18.7K]

Step-by-step explanation:

The value of b will be 43° as it is vertically opposite angle.. !!

6 0
2 years ago
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Give me answer, i will mark best brainliest
Marta_Voda [28]

Answer:

<u>Shape representation</u>

Yellow = 1 whole unit

Blue = 1/3

Red = 1/2

Green = 1/6

1)  see attachment

2) 7  1/2s in 3 1/2

   8  1/3s in 2 2/3

   4  1/6ths in 2/3

5 0
2 years ago
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