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Semmy [17]
3 years ago
8

The surface area of a cube is 96 square feet. Find the volume of the cube.

Mathematics
1 answer:
Tamiku [17]3 years ago
4 0
<span>cube has six identical walls

96ft</span>²<span> : 6 = 6 ft</span>²<span>  - </span>one wall surface

<span>pattern on the surface of the cube
</span>A = a²
a - <span>the edge of the cube

A = a</span>²    ⇔ a=√A
                  a = √(16ft)² = 4ft
V = volume
V = a³
V = (4ft)³ = 64 ft³


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Troyanec [42]

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(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c) Because the variance of each variable is dependent on the other.

Step-by-step explanation:

The random variable <em>X</em> and <em>Y</em> are defined as follows:

<em>X</em> = amount of ice cream in the box

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The information provided is:

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The total amount of ice-cream served at the party can be expressed as:

<em>X</em> + 3<em>Y</em>.

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E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54

Compute the variance of (<em>X</em> + 3<em>Y</em>) as follows:

V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625

Then the standard deviation of (<em>X</em> + 3<em>Y</em>) is:

SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

<em>X</em> - <em>Y</em>.

Compute the expected value of (<em>X</em> - <em>Y</em>) as follows:

E(X-Y)=E(X)-E(Y)\\=48-2\\=46

Compute the variance of (<em>X</em> - <em>Y</em>) as follows:

V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625

Then the standard deviation of (<em>X</em> - <em>Y</em>) is:

SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031

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(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

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