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weqwewe [10]
2 years ago
9

A) what is average rate of change of f(x) over the interval from x=5 to x=9? (table shows values of f(x). graph shows function o

f g(x).)
table:
x: 4, 5, 6, 7, 8, 9, 10
F(x): -8, -4, 8, 10, 11, 14 ,18


b) Find the average rate of change of g(x) over the interval from x = 0.25 to x= 1. (Write answer as a simplified fraction. Show work)

c) if g(x) represents the height of a ball that was throw. up into the air, interpret your answer from part b) in terms of the real-world it represents.

Mathematics
1 answer:
SVETLANKA909090 [29]2 years ago
5 0

Answer:

See below for answers and explanations

Step-by-step explanation:

<u>Part A</u>

The average rate of change of a function over the interval [a,b] is equal to \frac{f(b)-f(a)}{b-a}, hence:

\frac{f(b)-f(a)}{b-a}\\\\\frac{f(9)-f(5)}{9-5}\\\\\frac{14-(-4)}{9-5}\\ \\\frac{14+4}{4}\\ \\\frac{18}{4}\\ \\\frac{9}{2}

Therefore, the average rate of change of f(x) over the interval [5,9] is \frac{9}{2}.

<u>Part B</u>

Do the same thing as in Part A:

\frac{f(b)-f(a)}{b-a}\\ \\\frac{f(1)-f(0.25)}{1-0.25}\\ \\\frac{2-5}{0.75}\\ \\\frac{-3}{0.75}\\ \\-4

Therefore, the average rate of change of g(x) over the interval [0.25,1] is -4.

<u>Part C</u>

To interpret our answer from Part B in terms of the real world it represents, we say that between 0.25 seconds and 1 second, the ball falls at a rate of 4 feet per second (since our average rate of change is negative).

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inna [77]

Answer:

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Step-by-step explanation:

First thing to do here is to calculate the z-score

Mathematically;

z-score = (x-mean)/SD

here, x = 130, mean = 120 and SD = 10

Substituting these values

z-score = (130-120)/10 = 10/10 = 1

So the probability we want to calculate is;

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Answer:

320128-1.96\frac{50324}{\sqrt{529}}=315839.52    

320128+1.96\frac{50324}{\sqrt{529}}=324416.48    

So on this case the 95% confidence interval would be given by (315839.52;324416.48)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

\bar X=320128 represent the sample mean

\mu population mean (variable of interest)

\sigma=50324 represent the population standard deviation

n=529 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

320128-1.96\frac{50324}{\sqrt{529}}=315839.52    

320128+1.96\frac{50324}{\sqrt{529}}=324416.48    

So on this case the 95% confidence interval would be given by (315839.52;324416.48)    

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