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oee [108]
3 years ago
7

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must

be 1.5 times the height, what should each dimension be?
Hint: Let x represent one of the dimensions, then define the other dimensions in terms of x.
Mathematics
1 answer:
love history [14]3 years ago
4 0
H = x, L = 1.5 x;  
L + W + H = 6
x + 1.5 x + W = 6
W = 6 - 2.5 x
Dimensions of the camera in terms of x:
x,  1.5 x,  6 - 2.5 x.
V = L x W x H
V = x * 1.5 x * ( 6 - 2.5 x ) = 9 x² - 3.75 x³
V ` = 18 x - 11.25 x² ( V max is when V` = 0 )
18 x - 11.25 x² = 0
x ( 18 - 11.25 x ) = 0
11.25 x = 18
x = 18 : 11.25
x = 1.6
The dimensions are:
L = 2.4
W = 2.0
H = 1.6
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Step-by-step explanation:

This is a hypothesis test for a proportion.

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We use the women's part for sample and population proportions.

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The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that female employees were passed over for management training in favor of their male colleagues.

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The sample proportion is p=0.3.

The standard error of the proportion is:

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The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_p=1.96 \cdot 0.0648=0.127

Then, the lower and upper bounds of the confidence interval are:

LL=p-z \cdot \sigma_p = 0.3-0.127=0.173\\\\UL=p+z \cdot \sigma_p = 0.3+0.127=0.427

The 95% confidence interval for the population proportion is (0.173, 0.427).

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<h2>\red{Solution} \blue \longrightarrow</h2>

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