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2 years ago

What is the Volume of the square pyramid? (Round to the nearest tenth as needed)

Mathematics

2 answers:

ValentinkaMS [17]2 years ago

6 0

<h3>given:</h3>

base= 25 mm

height= 28 mm

the area of the square pyramid.

<h3>solution:</h3>

$volume = {a}^{2} \frac{h}{3}$

$v = {25}^{2} \times \frac{28}{3}$

$v = 5833.33333$

$v = 5833.3$

goldenfox [79]2 years ago

3 0

Answer:

5229 mm³

Step-by-step explanation:

Volume of square pyramid

$\sf \boxed{Volume \ of \ the \ square \ pyramid = \dfrac{1}{3}*b^2*H}$

b = base length = 25 mm

H = height

We have to find 'H' using Pythagorean theorem,

slant height (hypotenuse) = 28 mm

leg₁ = base length ÷ 2 = 25÷2 = 12.5

leg₂ = H

H² + (12.5)² = 28²

H² = 784 - 156.25

= 627.75

$\sf H = \sqrt{627.75}$

H = 25.01 mm

$\sf \text{Volume of square pyramid =$\dfrac{1}{3}*25*25*25.1$ }$

= 5229 mm³

$\sf \boxed{\text{Volume of square pyramid = \dfrac{1}{3}*25*25*28}}$

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Answer:

(a) Null Hypothesis, $H_0$ : $\mu$ = $1,150

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $1,150

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Step-by-step explanation:

We are given that a sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126.

We have test the hypothesis to determine whether the mean of all account balances is significantly different from $1,150.

Let $\mu$ = mean of all account balances

(a)So, Null Hypothesis, $H_0$ : $\mu$ = $1,150 {means that the mean of all account balances is equal to $1,150}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $1,150 {means that the mean of all account balances is significantly different from $1,150}

The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average balance = $1,200

s = sample standard deviation = $126

n = sample of account balances = 81

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P-value = P( $t_8_0$ > 3.571) = Less than 0.05%

Because in the t table the highest critical value for t at 80 degree of freedom is given between 3.460 and 3.373 at 0.05% level.

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