Answer:
The 95% confidence interval for the population variance is (8.80, 32.45).
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for the population variance is given as follows:
It is provided that:
<em>n</em> = 20
<em>s</em> = 3.9
Confidence level = 95%
⇒ <em>α</em> = 0.05
Compute the critical values of Chi-square:
*Use a Chi-square table.
Compute the 95% confidence interval for the population variance as follows:
Thus, the 95% confidence interval for the population variance is (8.80, 32.45).
Answer: 7 x 80 i think
Step-by-step explanation:\
nothing
The figure consists of three objects, a rectangle, a trapezoid, a triangle
Find the area of the rectangle
The rectangle is 16 in long and 9 in wide
a₁ = l × w
a₁ = 16 × 9
a₁ = 144 in²
Find the area of the trapezoid
The base of trapezoid is 31 in and 16 in, and the height is 35 - 20 = 15 in.
a₂ = 1/2 × (a + b) × h
a₂ = 1/2 × (31 + 16) × 15
a₂ = 1/2 × 47 × 15
a₂ = 352.5 in²
Find the area of the triangle
The base of the triangle is 31 in, the height is 20 in
a₃ = 1/2 × b × h
a₃ = 1/2 × 31 × 20
a₃ = 310 in²
Add the area together
a = a₁ + a₂ + a₃
a = 144 + 352.5 + 310
a = 806.5
The answer is 806.5 in²
Answer: The two roots are x = 3/2 and x = -2
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Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
- 2x-3 = 0 solves to x = 3/2 = 1.5
- -x-2 = 0 solves to x = -2
The two roots are x = 3/2 and x = -2
