Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much o
1 answer:
Answer:
Step-by-step explanation:
Given that private colleges and universities rely on money contributed by individuals and corporations for their operating expenses
A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars)
Mean = 180.975 and std dev s = 143.042
Assuming a normal distribution we have 95% critical value is 1.96 and 99% critical value is 2.58
a) 95% Conf interval = Mean ±1.96* std error
=
Since sample size is very small confidence interval is wider.
b) 99% Conf interval = Mean ±2.58* std error
=
Since sample size is very small confidence interval is wider.
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Answer:
and
Step-by-step explanation:
We must solve the quadratic equation to find the values of x that satisfy equality
Subtract 24 on both sides of equality
Now we factor the quadratic equation
Identify two numbers that when you add them you get as a result 2 and when you multiply them you get as a result -24
The numbers sought are: 6 and -4
So the factors are:
Finally note that the solutions are:
and
Answer:
The square-based box with the greatest volume under the condition that the sum of length, width, and heigth does not exceed 174 in is a cube with each edge of 58 in and a volume of
Step-by-step explanation:
For this problem we have two constraints, that are as follows:
1) Sum of length, width, and heigth not exceeding 174 in
2) Lenght and width have the same measure (square-based box)
We know that volume is equal to the product of all three edges, and with the two conditions into account we have the next function:
The interval of interest of the objective function is [0, 87]
This problem requieres that we maximize the function that defines the volume. We start calculating the derivative of the function, wich is:
We need to remember that the derivative of a function represents the slope of said function at a given point. The maximum value of the function will have a slope equal to zero.
So we find the value in wich the derivative equals zero:
The first value () will leave us with a 'height-only box', so the answer must be
The value is between the interval of interest.
And, once we solve for the constraints, we have that:
Lenght = Width = Heigth = 58 in
Volume =
