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astraxan [27]
3 years ago
6

A collar of Styrofoam is made to insulate a pipe. Find its volume. The large radius R is to the outer rim. The small radius r is

to the edge of the insulation. Use pi almost equals 3.14 .
r =3 in.
R=5 in.
h =15 in.
Mathematics
1 answer:
vesna_86 [32]3 years ago
8 0

Answer:

the answer is 1  1/5

Step-by-step explanation:

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The ratio of dogs to cats being treated at a veterinarian's office this week is 5 : 2. Suppose there are 168 dogs and cats sched
Alexeev081 [22]

Answer:

48 cats

Step-by-step explanation:

Am interesting factoid about ratios:

The ratio a:b can be separated into fractional parts of \frac{a}{a + b} and \frac{b}{a + b}. We need to know the cat part. \frac{2}{5 + 2} = \frac{2}{7}, so that is the fraction part. Then, we multiply this fraction by 168 to get the total number of cats. This number is 48.

4 0
3 years ago
At a local print shop, 4 copies can be made for $2. At this rate, how how many copies could be made for $12?
san4es73 [151]

Answer:

24

Step-by-step explanation:

$2 divided by 4 equals 50 cents

50 cents per copy

$12 will get you 24 copies

5 0
3 years ago
Read 2 more answers
Let X and Y be discrete random variables. Let E[X] and var[X] be the expected value and variance, respectively, of a random vari
Ulleksa [173]

Answer:

(a)E[X+Y]=E[X]+E[Y]

(b)Var(X+Y)=Var(X)+Var(Y)

Step-by-step explanation:

Let X and Y be discrete random variables and E(X) and Var(X) are the Expected Values and Variance of X respectively.

(a)We want to show that E[X + Y ] = E[X] + E[Y ].

When we have two random variables instead of one, we consider their joint distribution function.

For a function f(X,Y) of discrete variables X and Y, we can define

E[f(X,Y)]=\sum_{x,y}f(x,y)\cdot P(X=x, Y=y).

Since f(X,Y)=X+Y

E[X+Y]=\sum_{x,y}(x+y)P(X=x,Y=y)\\=\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y).

Let us look at the first of these sums.

\sum_{x,y}xP(X=x,Y=y)\\=\sum_{x}x\sum_{y}P(X=x,Y=y)\\\text{Taking Marginal distribution of x}\\=\sum_{x}xP(X=x)=E[X].

Similarly,

\sum_{x,y}yP(X=x,Y=y)\\=\sum_{y}y\sum_{x}P(X=x,Y=y)\\\text{Taking Marginal distribution of y}\\=\sum_{y}yP(Y=y)=E[Y].

Combining these two gives the formula:

\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y) =E(X)+E(Y)

Therefore:

E[X+Y]=E[X]+E[Y] \text{  as required.}

(b)We  want to show that if X and Y are independent random variables, then:

Var(X+Y)=Var(X)+Var(Y)

By definition of Variance, we have that:

Var(X+Y)=E(X+Y-E[X+Y]^2)

=E[(X-\mu_X  +Y- \mu_Y)^2]\\=E[(X-\mu_X)^2  +(Y- \mu_Y)^2+2(X-\mu_X)(Y- \mu_Y)]\\$Since we have shown that expectation is linear$\\=E(X-\mu_X)^2  +E(Y- \mu_Y)^2+2E(X-\mu_X)(Y- \mu_Y)]\\=E[(X-E(X)]^2  +E[Y- E(Y)]^2+2Cov (X,Y)

Since X and Y are independent, Cov(X,Y)=0

=Var(X)+Var(Y)

Therefore as required:

Var(X+Y)=Var(X)+Var(Y)

7 0
3 years ago
Help me and ill give brainlist
Cerrena [4.2K]

3 X 10 = 30/2 = 15

area: 15yd^2

3 0
3 years ago
Read 2 more answers
3n + 19 = 28<br> How do I solve this
olga2289 [7]

Answer:

to solve this you need to find out what number n is to make it equal 28.

Step-by-step explanation:

19+3 =22 so 3 is not it

19+9=28

answer is 9

hopefully this is right and this gets to you on time

4 0
2 years ago
Read 2 more answers
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