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k0ka [10]
3 years ago
9

Square pyramid A and square pyramid B are similar. Their respective heights are 6 and 15 inches. The volume of pyramid B is 312.

5 cubic inches. What is the volume of pyramid A?
Mathematics
1 answer:
VikaD [51]3 years ago
3 0

Answer:

V_a=125 cubic\ inches

Step-by-step explanation:

From the question we are told that:

Height of pyramid A h_a=6

Height of pyramid B h_b=6

The volume of pyramid B  V_b= 312.5 cubic inches.

 

Generally the equation for volume for pyramid A is mathematically given by

Since they are similar

 \frac{l_a}{l_b}=\frac{V_a}{V_b}\\\\\frac{6}{15}=\frac{V_a}{312.5}\\\\V_a=\frac{6}{15}*312.5

 V_a=125 cubic\ inches

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Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ &lt; 55 A sample of 36 is used. Identify the p-value and state your con
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Answer:

Step-by-step explanation:

Given that:

H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55

(a) For x = 54 and s = 5.3

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Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }

Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }

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Z = -1.132

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= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-1.132,35,1) = 0.1326

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b

For x = 53 and s = 4.6

The test statistics can be computed as:

Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }

Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }

Z = \dfrac{-2}{\dfrac{4.6}{6} }

Z = -2.6087

degree of freedom = n - 1

= 36 - 1

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Using the Excel Formula:

P-Value = T.DIST(-2.6087,35,1) =0.0066

Decision: p-value is < significance level; we reject the null hypothesis.

Conclusion: \  There  \ is \  sufficient \  evidence  \  to \  conclude \  that \mu < 55

c)

For x = 56 and s = 5.0

The test statistics can be computed as:

Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }

Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }

Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }

Z = 1.2

degree of freedom = n - 1

= 36 - 1

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Using the Excel Formula:

P-Value = T.DIST(1.2,35,1) = 0.88009

Decision: p-value is greater than significance level; do not reject \mathbf{H_o}

Conclusion: \  There  \ is \  insufficient \  evidence  \  to \  conclude \  that \ \mu < 55

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Answer :

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