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irakobra [83]
4 years ago
11

Calculate the volume of the figure.

Mathematics
1 answer:
dimaraw [331]4 years ago
8 0

Answer: The volume is 33 cubic centimeters.

Step-by-step explanation:

First find the volume of the square pyramid on top of the cube. To find the volume of the square pyramid you use the volume  a^2*h/3 a is the side length of the base of the square pyramid and h is the height all divide by 3.

So we can say that the side length of the base of the square pyramid is 3 because it has the same side length base as the cube.

V= 3^2 * 2 /3

V= 9 * 2 /3

V= 18/3

v= 6  

So the volume of the square pyramid is 6 so now we need to find the volume of the cube and add them together.

Volume of the a cube uses the formula s^3 where s is the side length.

V= 3^3

v= 3*3*3

v= 27  

The volume of the cube is 27.

Add 6 and 27 to find the total volume.

6 +27 = 33

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A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is
seraphim [82]

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a) The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at  0.01% level of significance

<em>They score is above 24 on the math portion of the​ exam</em>

<em>b) </em>

<u><em>Null Hypothesis</em></u>: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

<u>Alternative Hypothesis: </u>H₁: μ ≠ 24

<u>Step-by-step explanation:</u>

<u><em>Step(i)</em></u>:-

Given random sample 'n' = 250

Given data sample mean x⁻ = 24.5

Standard deviation = 3.3

<u><em>Null Hypothesis</em></u>: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

<u>Alternative Hypothesis: </u>H₁: μ ≠ 24

test statistic

Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }

Z = \frac{24.5 - 24}{\frac{3.3}{\sqrt{250} } } = \frac{0.5}{0.2087} = 2.397

a) 99% or 0.01% level of significance

Level of significance ∝ = 0.01

Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} =2.576

The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at  0.01% level of significance

<em>They score is above 24 on the math portion of the​ exam</em>

b) 95% or 0.05% level of significance

Level of significance ∝ = 0.05

Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96

The Z -value 2.397 > 1.96 at 95% or 0.05% level of significance

Null hypothesis is Rejected at  0.05% level of significance

<em>They score is below 24 on the math portion of the​ exam</em>

6 0
3 years ago
Solve for x.
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Begin by subtracting 2b from both sides. This will give us

-ax > -2b +8

Then we will divide by -a. This division by a negative number changes the direction of the inequality sign. When we divide by -a:

x

6 0
3 years ago
Read 2 more answers
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