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Nastasia [14]
3 years ago
10

If m/n = 3, what does 2n/m equal?

Mathematics
2 answers:
IceJOKER [234]3 years ago
7 0

Answer:

That would be n\geq 1\\

Step-by-step explanation:

Rufina [12.5K]3 years ago
5 0

(Hard) A composite number n is called a Carmichael number bn−1 ≡ 1 (mod n) for every number b such ... Base case: When n = 2 the formula a + c ≡ b + d (mod m) was already given. ... The sequence goes 1, 3, 7, 15, 31,... guess that it is equal to 2n+1 − 1. ... Prove (now using induction on n) that fm|fmn for all n ≥ 1.

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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
The students in a science class spent 65% of the class period performing an experiment. how long is a class period if the time s
Kaylis [27]
We let x be the length (in minutes) of a certain science class. 65% of this period is spent with the experiment which lasted for about 52 minutes. Mathematically, this can be expressed as,
                                    52 = (0.65)(x)
The value of x from the generated equation is 80. Thus, the science class is 80 minutes long. 
7 0
3 years ago
Hi can you please help and do the ones in red i got them wrong copy and paste then add your answer :)
max2010maxim [7]

Answer:

1. 14

2. 10

3. 7:6

5. 21

6. 10:7

I cant see 7-10

3 0
3 years ago
jacob bought company stock when it was $62.51 a share. In one year the stock increased to $79.56 a share. how much did the stock
Ket [755]
$79.56- $62.51= $17.05.

The stock increased $17.05 in one year~
6 0
3 years ago
Read 2 more answers
What is the value of the the digit 2 in 0.025
olga55 [171]
The 2 is the hundredths value.
 Hope it helps!
5 0
2 years ago
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