M < 2 and m < 3 are supplementary angles which add up to 180 degrees.
< 2 + < 3 = 180
3x + 17 + 5x - 21 = 180
8x - 4 = 180
8x = 180 + 4
8x = 184
x = 184/8
x = 23
m < 2 = 3x + 17 = 3(23) + 17 = 69 + 17 = 86 degrees
m < 3 = 5x - 21 = 5(23) - 21 = 115 - 21 = 94 degrees
m < 1 and m < 2 are corresponding angles....they are equal.
so m < 1 = 86 degrees <===
Answer: Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Step-by-step explanation:
Given that;
U = 75
X = 78
standard deviation α = 10
sample size n = 20
population is normally distributed
PROBLEM is to test
H₀ : U = 75
H₁ : U ≠ 75
TEST STATISTIC
since we know the standard deviation
Z = (X - U) / ( α /√n)
Z = ( 78 - 75 ) / ( 10 / √20)
Z = 1.3416 ≈ 1.342
Now suppose we need to test at ∝ = 0.05 level of significance,
Then Rejection region for the two tailed test is Zc = 1.96
∴ Reject H₀ if Z > Zc
and we know that Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
The point
on the plane
determines the volume of the box, since
. Restricting the box to lie within the first octant is to say that
.
Let's do it via Lagrange multipliers. The Lagrangian is
with partial derivatives (set equal to 0)
We have
We already assume
, so we can ignore those options, leaving us with
,
, and
. Substituting into the plane equation, we get
So the box with largest volume has its vertex (the one opposite the vertex at the origin) in the plane at
, giving a volume of
.