Answer:
θ = 60°
Step-by-step explanation:
The cross sectional area of the trapezoid shape will be that of a trapezoid with bases of 10 cm and (10 cm + 2·(10 cm)·cos(θ)) and height (10 cm)·sin(θ).
That area in cm² is ...
A = (1/2)(b1 +b2)h = (1/2)(10 + (10 +20cos(θ))(10sin(θ)
A = 100sin(θ)(1 +cos(θ))
A graphing calculator shows this area to be maximized when ...
θ = π/3 radians = 60°
_____
<em>A</em> will be maximized when its derivative with respect to θ is zero. That derivative can be found to be 2cos(θ)² +cos(θ) -1, so the solution reduces to ...
cos(θ) = 1/2
θ = arccos(1/2) = π/3
well, I think it's 60 because it prime factors are 2, 3, 5.
The distance between two points is calculated through the equation,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the known values from the given above,
d = √(4 - -4)² + (4 - -4)²
d = 8√2 = 11.31
The distance between the points is approximately equal to 11.31. The value that Jason presented is not the real distance because it does not account for the other set of coordinates.
x=12
x/16-1-4=1/2
multiply by both sides
x-4=8
move constant to the right side of and change its sign
x=8+4
add the numbers
x=12
Answer:
The minimum sample size required is 461.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
99% confidence level
So , z is the value of Z that has a pvalue of , so .
An interval estimate of the proportion p with a margin of error of 0.06. What is the minimum sample size required?
The minimum sample size required is n, which is found when M = 0.06.
We don't have an estimate for the true proportion, which means that we use . So
Rounding up
The minimum sample size required is 461.