Revenue: R(x) = 100x
Profit: P(x)= 3100 + 9x + 0.1x2 <span>(0 ≤ x ≤ 500)
</span><span>equalize the two equations
</span>100x=3100 + 9x + 0.1x2
0.1x2-91x+3100=0
<span>using graphic tools
x1=35.447----35
x2=874
the domain is </span>(0 ≤ x ≤ 500)
the value from which there are profits is 35 <span>pairs of cleats
</span>
Revenue: R(x) = 100x --------100*35=$3500
Profit: P(x)= 3100 + 9x + 0.1x2 -------3100+9*35+0.1*(35)2=$3537.5
Profit > Revenue up to the amount of 35 pairs of cleats
The answer is: 0.6 .
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Explanation:
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Given:
y = (0.2)x ;
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Plug in: "(3)" for "x"; to solve for "y" ;
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y = (0.2) * 3 = 0.6 ; which is the solution.
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y = 0.6 . The answer is: 0.6 .
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Answer: 0.8461
Step-by-step explanation:
Let p be the proportion of residents are against the increase of taxes to fund alternatives to drug addiction treatment.
As per given , we have p=0.40
A random sample is taken with size : n= 400
Expecting sample proportion : 
Now , the probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed will be :

![=P(z>\dfrac{0.375-0.40}{\sqrt{\dfrac{0.40(0.60)}{400}}})\ \ [\because\ z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]](https://tex.z-dn.net/?f=%3DP%28z%3E%5Cdfrac%7B0.375-0.40%7D%7B%5Csqrt%7B%5Cdfrac%7B0.40%280.60%29%7D%7B400%7D%7D%7D%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D)

[By z-table]
Hence, the approximate probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed is 0.8461 .
Answer:
y = (x - 3)² - 4 Vertex form
(3, -4) Vertex
Step-by-step explanation:
f(x) = x² - 6x + 5
Complete the square
y = (x - 3)² + 5 - (-3)²
y = (x - 3)² + 5 - 9
y = (x - 3)² - 4 Vertex form
(3, -4) Vertex
The answer is 1 and 7/8, all you have to do is turn the 3/4 into eighths.