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vredina [299]
3 years ago
7

Find the average rate of change over the given interval f(x)=3^x,[1,4]

Mathematics
1 answer:
nexus9112 [7]3 years ago
7 0

Answer:

26

Step-by-step explanation:

Thus, f(b)−f(a)b−a=3(4)−(3(1))4−(1)=26.

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A recent survey describes the total sleep time per night among college students as approximately Normally distributed with mean
marin [14]

Answer:

a) \sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981

b) We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

c) z = \frac{6.9-6.72}{0.0981}= 1.835

And we can use the z normal table or excel and we got:

P(Z

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the total sleep time of a population, and for this case we know the distribution for X is given by:

X \sim N(6.72,1.26)  

Where \mu=6.72 and \sigma=1.26

(a)  What is the standard deviation for the average time in hours? (Round your answer to four decimal places.)

For this case the sample mean have the following distirbution

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

And the deviation is given by:

\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981

in minutes?= (Round your answer to three decimal places.)  

(b)  Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answer to four decimal places.)

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

(c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)

For this case we can use the z score formula given by:

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

And we can find the z score for 6.9 and we got:

z = \frac{6.9-6.72}{0.0981}= 1.835

And we can use the z normal table or excel and we got:

P(Z

4 0
2 years ago
Miranda is keeping track of how fast her dog is growing. Her dog was 20 inches long at birth and grew 10 inches during the first
Vladimir [108]

Answer: The one in the down right corner

Step-by-step explanation:

Hope this helps :)

6 0
3 years ago
Read 2 more answers
At 3pm the temperature was 9 degrees .By 11pm ,it had dropped 31 degrees .What was the temperature at 11pm
o-na [289]

Answer:

-22

Step-by-step explanation:

9-31=-22

5 0
3 years ago
On Monday, Jayla raised $30 and Carlos raised $50.
gayaneshka [121]

Answer:

84 days

Step-by-step explanation:

You would use the LCM to solve this.

12 and 7 don't share any common factors other than 1,

so you would multiply 12 x 7, which gets you 84.

After 84 days they would have raised the same amount.

8 0
3 years ago
A couch that regularly sells for $450<br> was discounted by 30% off.
vaieri [72.5K]

Answer:

The price after the discount would be $315.

8 0
2 years ago
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