Answer:
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- <u>The correct answer is the first choice: Hinge Theorem.</u>
Explanation:
The <em>Hinge Theorem</em> compares the lengths of two sides of two triangles, given that the other two pairs of sides are congruent and the included angles are different.
The theorem states that if two sides of a triangle are congruent to two sides of another triangle and the included angle of one triangle is greater than the included angle of the other triangle, then length of the third side of the first triangle is greater than the length of the third side of the second triangle.
The figures shows triangles UVT and STV
The angle UVT is greater than the angle STV.
The sides ST and VU are congruent, as the small vertical marks indicate.
The side TV is a common side of both triangles.
Then, you already have that two sides of the triangle STV are congruent to two sides of triangle UVT and the angle UVT is greater than the angle STV.
Hence, by the HInge Theorem the side TU is greater than side SV.
To solve this you would use the pythagorean theorem since the brace is making the frame look like two right triangles. The theorem states that for a triangle with a right angle, A^2+B^2=C^2. A and B are the sides of the frame and C is the brace which is like the hypotenuse of the triangle. It doesn't matter which side is A or B so you can put 6 or 8 in place of either in the equation. 6^2+8^2=C^2. If you simplify this it equals 36+64=C^2, which then simplifies to 100=C^2. Then you take the square root of both sides (what number multiplied by itself = the number you are trying to get, in this case, 100). So then you get C=10 because 10x10=100. So the length of the diagonal brace is 10ft.
Given Information:
Population mean = p = 60% = 0.60
Population size = N = 7400
Sample size = n = 50
Required Information:
Sample mean = μ = ?
standard deviation = σ = ?
Answer:
Sample mean = μ = 0.60
standard deviation = σ = 0.069
Step-by-step explanation:
We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10
np ≥ 10
50*0.60 ≥ 10
30 ≥ 10 (satisfied)
n(1 - p) ≥ 10
50(1 - 0.60) ≥ 10
50(0.40) ≥ 10
20 ≥ 10 (satisfied)
The mean of the sampling distribution will be same as population mean that is
Sample mean = p = μ = 0.60
The standard deviation for this sampling distribution is given by
Where p is the population mean that is proportion of female students and n is the sample size.
Therefore, the standard deviation of the sampling distribution is 0.069.
