Answer:
I think it is of the last option
Answer:
4
Step-by-step explanation:
The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)
If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0
However, I will assume you meant the angle to be
rather than 0 which makes sense and proceed accordingly
We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0
The original function is

Taking the first derivative of this with respect to
and setting it equal to 0 lets us solve for the maximum (or minimum) value
The first derivative of
w.r.t
is

And setting this = 0 gives

Eliminating
on both sides and solving for
gives us
Plugging this value of
into the original equation gives us

This is the maximum value that the function can acquire. The attached graph shows this as correct
The answer is no solution
Step-by-step explanation:
The equation is
and 
Subtracting these two equations, we get,

Thus,
is not possible.
Hence, the system of equations have no solutions.
Answer:
The 99% confidence interval for the mean sodium content in Oriental Spice Sauce is between 454.67 milligrams and 1722.61 milligrams
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 40 - 1 = 39
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.7079
The margin of error is:
M = T*s = 2.7079*234.12 = 633.97
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1088.64 - 633.97 = 454.67 milligrams
The upper end of the interval is the sample mean added to M. So it is 1088.64 + 633.97 = 1722.61 milligrams
The 99% confidence interval for the mean sodium content in Oriental Spice Sauce is between 454.67 milligrams and 1722.61 milligrams