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3 years ago

The area of the face of a cube is 9 square meters. what is the volume of the cuber

Mathematics

1 answer:

Helga [31]3 years ago

6 0

Answer:

Step-by-step explanation:

We know: All faces of a cube are squares.

The formula of an area of a square with a side s:

A = s²

We have A = 9m²

Substitute:

s² = 9 → s = √9 = 3 m.

The formula of a volume of a cube with an edge s:

V = s³

Substitute:

V = 3³ = 27 m³

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alexandr1967 [171]

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2 years ago

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A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with

vovikov84 [41]

Answer:

6.68 %.

Step-by-step explanation:

The standardised z-score = ( 10.95 - 10.5) / 0.3

= 1.5.

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2 years ago

You are planning a skating party at a rink that charges a basic fee of $6.00 and $6.50 per person for catered parties. You don’t

Alekssandra [29.7K]

Answer:

y = 6.50x + 6 or 71 = 6.50x + 6

10 people are the max you can invite

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We have the simple equation

y = 6.50x + 6

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6 because it is a flat one time charge

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3 years ago

4. A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean

Ede4ka [16]

Adding 2 to each value of the random variable $X$ makes a new random variable $X+2$ . Its mean would be

$E[X+2]=E[X]+E[2]=E[X]+2$

since expectation is linear, and the expected value of a constant is that constant. $E[X]$ is the mean of $X$ , so the new mean would be

$E[X+2]=10+2=12$

The variance of a random variable $X$ is

$V[X]=E[X^2]-E[X]^2$

so the variance of $X+2$ would be

$V[X+2]=E[(X+2)^2]-E[X+2]^2$

We already know $E[X+2]=12$ , so simplifying above, we get

$V[X+2]=E[X^2+4X+4]-12^2$

$V[X+2]=E[X^2]+4E[X]+4-12^2$

$V[X+2]=(V[X]+E[X]^2)+4E[X]-140$

Standard deviation is the square root of variance, so $V[X]=3^2=9$ .

$\implies V[X+2]=(9+10^2)+4(10)-140=9$

so the standard deviation remains unchanged at 3.

NB: More generally, the variance of $aX+b$ for $a,b\in\mathbb R$ is

$V[aX+b]=a^2V[X]+b^2V[1]$

but the variance of a constant is 0. In this case, $a=1$ , so we're left with $V[X+2]=V[X]$ , as expected.

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3 years ago

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pashok25 [27]

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2 years ago

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