First of all we need to find a representation of C, so this is shown in the figure below.
So the integral we need to compute is this:

So, as shown in the figure, C = C1 + C2, so:
Computing first integral:
Applying derivative:

Substituting this value into

Computing second integral:
Applying derivative:

Substituting this differential into


We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:
![I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%20-8%5Cint_%7B4%7D%5E%7B8%7D%7Ddx%3D-8%5Bx%5D%5Cright%7C_4%20%5E%7B8%7D%3D-8%288-4%29%20%5Crightarrow%20%5Cboxed%7BI_%7B2%7D%3D-32%7D)
Finally:
To find this answer, we must first find the percentage of batteries that are defective. We can do this by dividing 3 by 500.
3 / 500 = 0.006
So our percentage of defective batteries is 0.6%.
Now, to find out how many defective batteries would be in a batch of 12000, we just need to multiply the constant (percentage of defective batteries) by the amount in the new batch.
12000 * 0.006 = 72
In a shipment of 12,000 batteries, 72 will be defective, so the correct answer choice would be B.
Hope that helped =)
Answer:
129
Step-by-step explanation:
Considering the survey to be representative, you can simply multiply the share of students <em>p</em> preferring “Track & Field” with the whole school population at the same time to estimate the number of such students in the whole school.
First we need to find the relative share <em>p</em> of such answers in the study by dividing it by the sum of answers, assuming that the table is complete for that random sample:
<em>p</em> = 4/(8 + 5 + 4) = 4/17
Then for the whole school we get 550 <em>p</em> ≈ 129.4
The resulting equation will represent a line whose slope is 1/2 times the slope of the line
<h3>How to determine the slope of the new line?</h3>
The equation of the line is given as:
y = 3x/a + 5
The constant a is a positive constant.
So, when the value of a in the equation is doubled, we have:
y = 3x/2a + 5
A linear equation is represented as
y = mx + b
Where m represents the slope.
So, we have:
m1 = 3/a
m2 = 3/2a
Substitute m1 = 3/a in m2 = 3/2a
m2 = 1/2 * m1
Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line
Read more about linear equation at:
brainly.com/question/14323743
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