Answer: B
Step-by-step explanation:
It is one sided test of R-squared being zero versus being greater than zero.
These are the steps of the test.
1. State the null and alternative hypothesis: ...
2. Compute the test statistic: ...
3. Find a (1 - 0.05)×100% confidence interval for the test statistic. ...
4. Decide whether to accept or reject the null hypothesis: 5.991 ∉ [0, 2.28], so reject H 0 .
5. Determine the p-value.
Answer:
12
Step-by-step explanation:
First, you will have to use trigonometry. Since the side of the triangleis the opposite of the angle 53 and the hypotenuse, you will use sin.
Sin 53 degrees = opposite side / hypotenuse side.
The opposite side is x and the hypotenuse side equals 15.
sin53= x/15
15 ( sin 53 ) =x
x= 11.97953
Round
x=12
Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
D is correct. U is incenter of the triangle.
