Answer:
H0: p ≥ 0.03 Ha: p < 0.03
Step-by-step explanation:
1) Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
2) Solution to the problem
On this case we want to test is 
, where:
represent the true proportion for the population of broken pieces
What we want to proof need's to be on the alternative hypothesis and the complement on the null hypothesis.
So the correct system of hypothesis for this case would be:
Null hypothesis: 
Alternative hypothesis: 
H0: p ≥ 0.03 Ha: p < 0.03
The residual value comes out to be 2.94 cm and height is 157.06 cm
<u>Explanation:</u>
The regression equation is calculated at the first step.
height = 105.08 plus 2.599 multiply foot length
At foot length = 20cm, height = 105.08 plus 2.599 multiply 20
= 157.06 cm
Residual = Actual minus predicted value = 160 minus 157.06
=2.94 cm
B) The residual standard deviation generally gives a sense of the goodness of fit of goodness of regression equation on our data. The magnitude tells us that how much will be predicted values from model will vary from actual values. the linear model is justified.
The volume of the removed portion is 35 cm³.
Step-by-step explanation:
Given,
The length× width× height (L×B×H) of the outer part = 3 cm×3 cm×7 cm
The length× width× height (l×b×h) of the inner part = 2 cm×2 cm×7 cm
To find the volume of the removed portion.
Formula
The volume of the removed portion = volume of outer part - volume of inner part
Volume of rectangular prism = l×b×h
Now,
Volume of outer part = 3×3×7 cm³ = 63 cm³
Volume of inner part = 2×2×7 cm³ = 28 cm³
Hence,
The volume of the removed portion = 63-28 cm³ = 35 cm³
Devin borrowed $1,058 at 13 percent for nine months.
We have to calculate the interest paid.
Interest = 
Substituting the values of
Principal = $1058
Rate = 13%
Time = 9 months = 
year
Interest = 
Interest = 103.155
= 103.16
So, Devin will pay 103.16 as the interest.
Therefore, Option A is the correct answer.
Width = x
Length = x+18
Assuming the table is rectangular:
Area = x(x + 18)
Therefore:
x(x + 18) <span>≤ 175
x^2 + 18x </span><span>≤ 175
Using completing the square method:
x^2 + 18x + 81 </span><span>≤ 175 + 81
(x + 9)^2 </span><span>≤ 256
|x + 9| </span><span>≤ sqrt(256)
|x + 9| </span><span>≤ +-16
-16 </span>≤ x + 9 <span>≤ 16
</span>-16 - 9 ≤ x <span>≤ 16 - 9
</span>-25 ≤ x <span>≤ 7
</span><span>
But x > 0 (there are no negative measurements):
</span><span>
Therefore, the interval 0 < x </span><span>≤ 7 represents the possible widths.</span><span>
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