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3 years ago

There are exactly 1,944 of the 12-, or 0.5-, cubes inside a rectangular prism.

Mathematics

1 answer:

drek231 [11]3 years ago

7 0

The volume of the rectangular prism is 3359232 cubic centimeters

<h3>How to determine the volume?</h3>

The length of the cube is given as:

Length, l = 12 cm

The volume of a cube is:

$V = l^3$

So, we have:

$V = 12^3$

Evaluate

V = 1728

The volume of 1944 cubes is then calculated as:

Volume = 1728 * 1944

Evaluate

Volume = 3359232

Hence, the volume of the rectangular prism is 3359232 cubic centimeters

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The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices o

likoan [24]

Answer:

Correct answer is option C.

Step-by-step explanation:

Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

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3 years ago

Read 2 more answers

68) Volume of a Bucket: Determine the volume of a cylindrical bucket in cubic inches if the bucket's radius is 5 in.

Natalija [7]

Answer:

V = 300 $\pi$ in³ or 942.48 in³

Step-by-step explanation:

Use the cylinder volume formula, V = $\pi$ r²h, where r is the radius and h is the height.

Plug in the values and solve:

V = $\pi$ (5²)(12)

V = 300 $\pi$ in³ or 942.48 in³

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3 years ago

The desired percentage of sio2 in a certain type of aluminous cement is 5.5. to test whether the true average percentage is 5.5

LekaFEV [45]

Given that the desired percentage of sio2 in a certain type of aluminous cement is 5.5. to test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. suppose that the percentage of sio2 in a sample is normally distributed with σ = 0.32 and that $\bar{x}=5.24$ .


To investigate whether this indicate conclusively that the true average percentage differs from 5.5.

Part A:

From the question, it is claimed that the desired average percentage of sio2 in a certain type of aluminous cement is 5.5 and we want to test whether the information from the random sample indicate conclusively that the true average percentage differs from 5.5.

Therefore, the null hypothesis and the alternative hypothesis is given by:

$H_0:\mu=5.5 \\ \\ H_a:\mu\neq5.5$

Part B:

The test statistics is given by:

$z= \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} \\ \\ =\frac{5.25-5.5}{0.32/\sqrt{16}} \\ \\ = \frac{-0.25}{0.32/4} = -\frac{0.25}{0.08} \\ \\ =-3.125$

Part C:

The p-value is given by

$P(z\ \textless \ -3.125)=1-P(z$

Part D:

Because the p-value is less than the significant level α, we reject the null hypothesis and conclude that "There is sufficient evidence to conclude that the true average percentage differs from the desired percentage."

Part E:

If the true average percentage is μ = 5.6 and a level α = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H0? (Round your answer to four decimal places.)

The probability of detecting the departure from $H_0$ is given by

$1-\phi\left(z_{1-\frac{\alpha}{2}}+ \frac{\mu_0-\mu_1}{\sigma/\sqrt{n}} \right)+\phi\left(-z_{1-\frac{\alpha}{2}}+ \frac{\mu_0-\mu_1}{\sigma/\sqrt{n}} \right) \\ \\ =1-\phi\left(z_{1-\frac{0.01}{2}}+ \frac{5.5-5.6}{0.32/\sqrt{16}} \right)+\phi\left(-z_{1-\frac{0.01}{2}}+ \frac{5.5-5.6}{0.32/\sqrt{16}} \right) \\ \\ =1-\phi\left(z_{1-0.005}+ \frac{-0.1}{0.32/4} \right)+\phi\left(-z_{1-0.005}+ \frac{-0.1}{0.32/4} \right)$

$=1-\phi\left(z_{0.995}+ \frac{-0.1}{0.08} \right)+\phi\left(-z_{0.995}+ \frac{-0.1}{0.08} \right) \\ \\ =1-\phi(2.576-1.25)+\phi(-2.576-1.25) \\ \\ =1-\phi(1.326)+\phi(-3.826) \\ \\ =1-0.90758+0.00007 \\ \\ =0.0925$

Part F:

What value of n is required to satisfy α = 0.01 and β(5.6) = 0.01? (Round your answer up to the next whole number.)

The value of n is required to satisfy α = 0.01 and β(5.6) = 0.01 is given by

$n=\left[ \frac{\sigma(z_{0.005}+z_{0.01})}{\mu_0-\mu} \right]^2 \\ \\ = \left[\frac{0.32(-2.576-2.326)}{5.5-5.6} \right]^2 \\ \\ =\left[\frac{0.32(-4.902)}{-0.1} \right]^2=\left[\frac{-1.56864}{-0.1} \right]^2 \\ \\ =(15.6864)^2=247$