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3 years ago

Hi!

Mathematics

2 answers:

Radda [10]3 years ago

7 0

Answer:

90 men

Step-by-step explanation:

Ratio of men to women = 3:7

Sum of ratio= 3+7 = 10

Number of men= 3/10 * 100

= 3*30

= 90

Hope this helps!!!

Dima020 [189]3 years ago

5 0

Answer:

90 men

Step-by-step explanation:

just keep the ratio constant

3:7

equals 10 parts

300/10=30

3*30:7*30

90 men and 210 women

hope this helps!!! :)

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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.

5 0

3 years ago

anna has a 10 foot long ladder that she is going to rest against a vertical wall along the bottom of a window still that is 8.5

Semmy [17]

As you can see in the picture, the ladder leaning against the wall makes a right triangle with the sides being the wall, the ground and the ladder. The ladder is opposite the right angle and so is the hypotenuse (the longest side of the triangle). The angle between the ladder and the ground is labeled a.

We know the height of the ladder (10 feet) and also the height off the ground of the windowsill (8.5 feet). That second side is opposite the angle a. So, when we consider angle a we know the length of the side opposite and of the hypotenuse.

Recall the sin of an angle can be found by using (opposite/hypotenuse).

So we have: sin a = 8.5 / 10. That is, sin a = .85
We are looking for the angle whose sin is .85 and can find this using the inverse sin function.

$sin^{-1}.85=a$
a is approximately 58.211669 degrees which is less than the 65 degrees and so safe.

Just to be on the safe side, I remind you that your calculator must be in degrees (not radians) to do this problem.