Determining function values from a graph
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Answer:
Yes, the new equipment appear to be effective in reducing the variation of weights.
Step-by-step explanation:
We are given that Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065.
A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.047.
Let = <u><em>standard deviation of weights of new equipment.</em></u>
SO, Null Hypothesis, :
0.065 {means that the new equipment have weights with a standard deviation more than or equal to 0.065}
Alternate Hypothesis, :
< 0.065 {means that the new equipment have weights with a standard deviation less than 0.065}
The test statistics that would be used here <u>One-sample chi-square</u> test statistics;
T.S. = ~
where, s = sample standard deviation = 0.047
n = sample of quarters = 25
So, <u><em>the test statistics</em></u> = ~
= 12.55
The value of chi-square test statistics is 12.55.
Now, at 0.05 significance level the chi-square table gives critical value of 13.85 at 24 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of chi-square as 12.55 < 13.85, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.
Therefore, we conclude that the new equipment have weights with a standard deviation less than 0.065.
Using it's formula, the average rates of change are given as follows:
a) 30 meters per second.
b) -10 meters per second.
<h3>What is the average rate of change of a function?</h3>The average rate of change of a function is given by the <u>change in the output divided by the change in the input.</u> Hence, over an interval [a,b], the rate is given by the following equation:
For item a, taking the data from the table, we have that:
- f(0) = 0.
- f(4.6) = 138.
Hence the rate is given as follows:
r = (138 - 0)/(4.6 - 0) = 30 meters per second.
For item b, taking the data from the table, we have that:
- f(9.2) = 23.
- f(11.5) = 0.
Hence the rate is given as follows:
r = (0 - 23)/(11.5 - 9.2) = -10 meters per second.
More can be learned about the average rate of change of a function at brainly.com/question/11627203
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Answer:
Step-by-step explanation:
GIVEN: A car was sold standard washed in a day , which was
of their total sales for that day.
TO FIND: Total amount of washes that the car wash sold that day.
SOLUTION:
Let the total sales of car washes sold for that day
total number of standard car washes sold
As, total standard car washes sold are of total sales in a day
putting value in equation
Hence the total number of car washes sold that day are