Answer:
Step-by-step explanation:
The quadratic formula is as follows:
It is used for factoring second degree polynomials ONLY!!! That's why it's called the quadratic formula...quadratics are second degree polynomials. The a, b and c are found in the standard form of a quadratic equation:
Just plug them into the formula, but be careful with the "-4ac". Sometimes that mistakenly leads to an unwanted negative sign under you radical. Unless you are dealing with imaginary numbers, your solutions should be real.
Given
The demand function
To determine:
a) The revenue function.
b) The marginal revenue.
c) The marginal revenue when x=200.
d) The equation of tangent, and its derivation.
Explanation:
It is given that,
a) The revenue function is given by,
b) The marginal revenue function is,
c) The marginal revenue when x=200 is,
Hence, the marginal revenue is 3.84.
d) Let y=mx+c is the tangent.
Then,
That implies, for y=12.68, and x=200,
Hence, the equation of tangent is,
Answer:
(a) Null Hypothesis, :
3.50 mg
Alternate Hypothesis, :
> 3.50 mg
(b) The value of z test statistics is 2.50.
(c) We conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.
(d) The p-value is 0.0062.
Step-by-step explanation:
We are given that Green Beam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. Assuming a known standard deviation of 0.18 mg.
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<u><em>Let </em></u><u><em> = average mg of mercury in compact fluorescent bulbs.</em></u>
So, Null Hypothesis, :
3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is no more than 3.50 mg}
Alternate Hypothesis, :
> 3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg}
The test statistics that would be used here <u>One-sample z test</u> <u>statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean mg of mercury = 3.59
= population standard deviation = 0.18 mg
n = sample of bulbs = 25
So, <em><u>test statistics</u></em> =
= 2.50
The value of z test statistics is 2.50.
<u>Now, P-value of the test statistics is given by;</u>
P-value = P(Z > 2.50) = 1 - P(Z 2.50)
= 1 - 0.9938 = 0.0062
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<em>Now, at 0.01 significance level the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.