Answer:
k = 2/-3
Step-by-step explanation:
y = kx
Point: (-3, 2)
2 = k(-3)
k = 2/-3
k = -0.6
<h3>
Answer: A. 18*sqrt(3)</h3>
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
Answer: $69811
Step-by-step explanation:
Given : A survey organization, as part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants.
One of these surveys estimates with 90% confidence that the mean household income in the U.S. falls between $69,702 and $69,920. (1)
We know that the confidence interval is given by :-
Point estimate of mean ± Margin of error
From (1) , we have
Point estimate for mean -Margin of error = $69,702 (2)
Point estimate for mean +Margin of error = $69,920 (3)
Add (2) and (3), we get
2 (Point estimate for mean) = $139622
Divide both sides by 2, we get
Point estimate for mean=$ 69811
Therefore , the point estimate for mean U.S. household income. = $ 69811
