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3 years ago

Drag steps in the given order to evaluate this expression. (−3)(2)−7(−3)−10

2 answers:

8 0

Step 1:
Multiply the numbers in parentheses:
(-3 * 2) - (7 * (- 3)) - 10
-6 - (- 21) -10
Step 2:
Equal signs are added:
-6 + 21-10
Step 3:
Make the algebraic sum:
-6 + 21-10 = 5
Answer:
the final result is 5.

Ad libitum [116K]3 years ago

8 0

Answer:

$(-3)(2) - 7 ( -3) -10\\= (-6) - (-21) -10\\= -16 + 21 - 10\\= -5\\$

Step-by-step explanation:

We will follow the rule of BODMAS

B - Bracket Of

D - Division

M = Multiplication

A = Addition

S = Subtraction

On solving the give equation as per the order of BODMAS, we get -

$(-3)(2) - 7 ( -3) -10\\= (-6) - (-21) -10\\= -16 + 21 - 10\\= -5\\$

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The staff at the Arcola Country Club prepares tables for a wedding reception. They are able to prepare 6 tables in 45 minutes. H

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24

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3 years ago

How do you say 506,709 in expanded form?

lakkis [162]

Five hundred six thousand seven hundred nine.

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3 years ago

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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:

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

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3 years ago

What is 4(1 + 9x) simplified?

konstantin123 [22]

Answer:

4 + 36x is your expression

Step-by-step explanation:

4 x 1 = 4

4 x 9x = 36x

so 4 + 36x is your expression because you can't add numbers with different variables or if they don't even have one.

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3 years ago

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Find n so that the number sentence below is true:

adell [148]

Answer: n=6

Step-by-step explanation:

2^3 x 4^3 = 2^3 x 2^n = 2^9

(2×2×2) ×(4×4×4) = (2x2x2) ×2^n=(2x2x2x2x2x2x2x2x2)

8 x 64 = 8x 2^n = 512

512= 8x 2^n = 512

divide all through by 8 so that 2^n can stand alone

512/8 = (8x 2^n)/8 = 512/8

64 = 2^n = 64

express 64 as a base of 2

2^6 = 2^n = 2^6

since they all have same base, cancel out the base.

therefore,

6=n=6

n = 6

6 0

3 years ago