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kozerog [31]
1 year ago
12

Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval.

Mathematics
2 answers:
prisoha [69]1 year ago
8 0

Answer:

Increasing

−5<x<−1

−1<x<1

Decreasing

4<x<7

−8<x<−5

Neither Increasing nor Decreasing

1<x<4

Step-by-step explanation:

kenny6666 [7]1 year ago
5 0

Answer:

Increasing : -5  or -1

Decreasing : -8  or 4

Neither : 1

Step-by-step explanation:

Increasing function : In this function, the y-value increases as the x-value increases.

From the given graph it is clear that the function is increasing on  

-5

-1

Decreasing function : In this function, the y-value decreases as the x-value increases.

From the given graph it is clear that the function is decreasing on  

-8

4

Neither increasing nor decreasing function : In this function, the y-value remains constant as the x-value increases.

From the given graph it is clear that the function is neither increasing nor decreasing on  

1

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Marginal cost At a certain factory the marginal cost is 3(q-4)^2 dollars per unit when the level of production is q units.
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Answer:

a.) C(q) =  -(1/4)*q^3 +  3q^2  -  12q + OH          b.) $170

Step-by-step explanation:

(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:

Marginal cost (MC) = change in total cost/change in quantity

Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:

Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k

where k is a constant.

The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k

C(q) = -(1/4)*(q^3  - 12q^2  + 48q - 64) + k = -(1/4)*q^3 +  3q^2  -  12q  -16 + k

Thus:

C(q) =  -(1/4)*q^3 +  3q^2  -  12q + OH

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A grocery store is selling 90 fl. oz of detergent for $6.99. To the nearest cent, what is the unit price?
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Answer:

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Alternative hypothesis:p_{1} \neq p_{2}  

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Step-by-step explanation:

Data given and notation  

X_{1}=25 represent the number of homeowners who would buy the security system

X_{2}=9 represent the number of renters who would buy the security system

n_{1}=140 sample 1

n_{2}=60 sample 2

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z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the two proportions differs , the system of hypothesis would be:  

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{25+9}{140+60}=0.17  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500  

Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test.    

Since is a two sided test the p value would be:  

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So the p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.  

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