Answer:
The p-value for the test is 0.0459.
Explanation:
The question involves a chi-squared test whose p-value is to be determined.
H₀: σ² ≤ 0.027 (null hypothesis)
H₁: σ² > 0.027 (alternative hypothesis)
Standard deviation = s = 0.2
Hence, s² = (0.2)² = 0.04
Sample size = n = 30
Degree of freedom = n - 1 = 30 - 1 = 29
Significance level = 0.05
Test statistic: X² = (n - 1)s² / σ²
= (30 - 1) x 0.04 / 0.027
= 42.9629
The p-value can now be determined using the Excel function:
CHISQ.DIST.RT(42.9629,29) = 0.0459
Hence, the p-value for the test is 0.0459.
Answer:
The correct answer is the first set {(-1, 8), (0, 5), (2, -1), (3, -4)}
Step-by-step explanation:
In order to determine if the set works, input each ordered pair to see if the statement ends up true. The first two ordered pairs are done below.
(-1, 8)
f(x) = -3x + 5
8 = -3(-1) + 5
8 = 3 + 5
8 = 8 (TRUE)
(0, 5)
f(x) = -3x + 5
5 = -3(0) + 5
5 = 0 + 5
5 = 5 (TRUE)
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
4 - 1/x (16)-1/x 2
4x-18/x
Answer: x=8
Step-by-step explanation:
Since we are given that ∠ABC and ∠DBC are complementary angles, we know that adding them together should give us 90°. We can use this to solve for x.
6x+13+4x-3=90 [combine like terms]
10x+10=90 [subtract both sides by 10]
10x=80 [divide both sides by 10]
x=8
Now, we know that x=8.
