The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of functio
n g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply. The functions have the same range. The functions have the same domains. The only value that is in the domains of both functions is 0. There are no values that are in the ranges of both functions. The domain of g(x) is all values greater than or equal to 0. The range of g(x) is all values less than or equal to 0.'
2 answers:
Answer:
The true statements:
The only value that is in the domains of both functions is 0.
The range of g(x) is all values less than or equal to 0.
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Step-by-step explanation:
See the attached figure:
As shown: f(x) = √x with blue color
When f(x) is reflected across the x-axis the result will be (-√x) with red color.
Then the is reflected result across the y-axis to create the graph of function g(x) = -√(-x) with green color.
<u>Domain </u>of f(x) = [0,∞) & <u>Range</u> of f(x) = [0,∞)
<u>Domain </u>of g(x) = (-∞,0] & <u>Range </u>of g(x) = (-∞,0]
So, according to previous, we will check the statements:
1) The functions have the same range. <u>(Wrong)</u>
2) The functions have the same domains. <u>(Wrong)</u>
3) The only value that is in the domains of both functions is 0. <u>(True)</u>
4) There are no values that are in the ranges of both functions. <u>(Wrong)</u>
5) The domain of g(x) is all values greater than or equal to 0. <u>(Wrong)</u>
6) The range of g(x) is all values less than or equal to 0. <u>(True)</u>
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Answer:
We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.
Step-by-step explanation:
We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.
You select a sample of 100 light bulbs and find mean bulb life is 490 hours.
Let = <u><em>population mean light bulb life.</em></u>
So, Null Hypothesis, :
500 hours {means that the population mean light bulb life is at least 500 hours}
Alternate Hypothesis, :
< 500 hours {means that the population mean light bulb life is below 500 hours}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean bulb life = 490 hours
σ = population standard deviation = 50 hours
n = sample of light bulbs = 100
So, <u><em>the test statistics</em></u> =
= -2
The value of z test statistics is -2.
<u>Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.</u>
Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis.</u>
Therefore, we conclude that the population mean light bulb life is at least 500 hours.
Answer:
The sample size required is at least 171
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
What sample size is required?
A samle size of at least n is required, in which n is found when
So
Rouding up
The sample size required is at least 171