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mihalych1998 [28]
3 years ago
11

Use each of the digits 2, 3, 4, 6, 7, 8 exactly once to

Mathematics
1 answer:
goblinko [34]3 years ago
4 0
2,3,4
6,7,8


I think this is what u wanted???
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Steve, 18 years old, is three times as old as his brother Daniel. How old will Steve be when he will be twice as old as Daniel?
gtnhenbr [62]
18 ÷ 3 is 6, which means that Daniel is 6, and there is a 12 year gap between Steve and Daniel.

12 x 2 is 24, so therefore when Steve is 24, Daniel will be 12, so Steve is twice as old as Daniel:)
4 0
2 years ago
What is -3x+13=16 help me with each step.
hoa [83]

-3x+13=16

Move +13 to the other side. Sign changes from +13 to -13.

-3x+13-13=16-13

-3x=16-13

-3x=3

Divide by -3 for both sides.

-3/-3x=3/-3

Cross out -3 and -3, divide by -3, then becomes 1*1*x=x

x=-1

Answer: x=-1

6 0
3 years ago
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
Can someone help me with this
Alborosie
✌HEYA!!!
HERE IS YOUR ANSWER=
THERE ARE ONLY TWO CASES WHEN COMPUTER PICKED A 1 AND A 2 OUT OF 25..
CASES= (1,2);(2,1)

P (E)=2/25
O.O8
WHICH IS OPTION D.

HOPE IT HELPS YOU '_'
7 0
3 years ago
15 points! What is the scale factor of the dilation?
maw [93]

Answer: \frac{1}{2}

Step-by-step explanation:

Use the formula for calculate the distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Calculate the distance AB. Substitute the coordinates into the formula. Then:

d_{AB}=\sqrt{(8-0)^2+(8-(-7))^2}

d_{AB}=17

Calculate the distance A'B'. Substitute the coordinates into the formula. Then:

d_{A'B'}=\sqrt{(2-6)^2+(1-5-(-6))^2}

d_{A'B'}=\frac{17}{2}

As you can see, the distance A'B' is the distance AB multiplied by 1/2. Therefore, this is the scale factor.

5 0
3 years ago
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