Part 1
1 answer:
You might be interested in
Using the vertex of a quadratic function, it is found that:
a) The revenue is maximized with 336 units.
b) The maximum revenue is of $56,448.
<h3>What is the vertex of a quadratic equation?</h3>A quadratic equation is modeled by:
The vertex is given by:
In which:
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
The demand function is given by:
p(x) = 336 - 0.5x.
Hence, the revenue function is:
R(x) = xp(x)
R(x) = -0.5x² + 336x.
Which has coefficients a = -0.5, b = 336.
Hence, the value of x that maximizes the revenue, and the maximum revenue, are given, respectively, as follows:
More can be learned about the vertex of a quadratic function at brainly.com/question/24737967
#SPJ1
Answer:
The scores are significantly lower than those from the general population.
Step-by-step explanation:
Hello!
To make the test we need to first identify the hypothesis we want to test. In this case, the hypothesis statement is
<em>"Studying from a screen lowers the scores on the final exam"</em>
Should this happen, it would mean that the average scores on the final exam will be lowered too. If this statement is not true, the average scores on the final exam should not change whether the students use virtual or printed materials to study.
On the other hand, we will take the previously known information as population reference, so for this example, the population mean is 577 and the standard deviation 58
With this in mind, we can state the null and alternative hypothesis:
H₀: μ = 577
H₁: μ < 577
The text doesn't specify a significance level, so I'll use the most common one. α=0.05
For this text, since we have a large sample (n=516), the variable has a normal distribution and its parameters known, we'll use a Z-test.
Z= (x(bar)-μ)/(σ/√n) ≈ N(0;1)
Critical region.
The rejection region is one-tailed, this is depicted in the hypothesis since it says the scores "lower" when virtual materials are used to study. So we will reject the null hypothesis if the calculated Z-value is less than the critical value.
Our critical value bein a =
= -1.64
So we will reject the null hypothesis if the is ≤-1.64 or support the null hypothesis if the
is >-1.64
Next we calculate the Z-value
= (x(bar)-μ)/(σ/√n) = (572.5-577)/(58/√516)= -4.5/2.55 = -1.76
since = -1.76 ≤ -1.64 we will reject the null hypothesis.
In other words, we can assume that the average scores on the final exam decrease when the students use virtual materials to study.
I hope you have a SUPER day!