Number 3 and 4 please ASAP
1 answer:
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Using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.
According to the question,
The average household income for a recent year (x₁⁻) = $30,000
The average household income for a recent year (x₂⁻) = $24,500
sample sizes n₁ = n₂ = 34
standard deviation of both samples were $24,500. Thus, s₁ = s₂ = $5928.
Null hypothesis: There is no evidence to believe that the average household income has increased.
H₀ : μ₁ ≤ μ₂
Alternative hypothesis: There is evidence to believe that the average household income has increased.
H₁: μ₁ > μ₂
To check hypothesis we have the formula
Standard error=
=
= 1437.7512
Thus, standard error is $1437.7512.
Formula for test statistic = [(x₁⁻ - x₂⁻) - (μ₁ - μ₂)]/standard error
= [(30000 - 24500) - 0]/1437.7512
= 3.8254
The critical value of z at 5% level of significance is 1.6449.
Here, the calculated value is greater than the critical value so we reject H₀.
Hence using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.
Learn more about hypothesis test here
#SPJ2
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We need two points through which the line passes to find the slope:
We found the slope:
So, the equation is of the form:
We substitute a point to find "b":
Finally, the equation is:
Answer:
Option D
See the attached picture.
- Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
The resulting box has a volume
because the volume of a box is the product of its width , length
, and height
.
- find the zeroes
You know right away from the factored form of that the zeroes are
. (zero product property)
- sketch the graph of the function
Easy to plot by hand. You know the zeroes, and you can check the sign of for any values of
between these zeros to get an idea of what the graph of
looks like. See the second attached picture.
Here's what I mean by "check the sign" in case you don't follow. We know when
and
. So we pick some value of
between them, say
, and find that
which is positive, so will be positive for any other
between 0 and 8. Similarly we would find that
for
between 8 and 12, and so on.
- What is the size of the cutout he needs to make so that he can fit the most marbles in the box?
It's impossible to answer this without knowing the volume of each marble...
- If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?
Thomas wants , so you solve
While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions
but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.
- What would be the dimensions of this box?
The box's dimensions are ( in) x (
in) x (
in).
If , then
and
.
If , then
and
.
