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Alja [10]
3 years ago
7

Solve for x: 30 > 6x

Mathematics
2 answers:
Eddi Din [679]3 years ago
7 0

Answer:

If it has the little line under the > sign then x = 5

Step-by-step explanation:

Pani-rosa [81]3 years ago
4 0

here is the answer to solve for x x<5

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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
On a certain​ route, an airline carries 8000 passengers per​ month, each paying ​$70.A market survey indicates that for each​ $1
son4ous [18]

Answer:

The maximum revenue is $661,250.

Step-by-step explanation:

The total revenue (R) is the product between the number of passengers (N) and the price of each ticket (P), so the inicial revenue is:

R = N * P = 8000 * 70 = $560,000

For each 1$ increase in the ticket, the airline loses 50 passengers, so if we call "x" the increase in the ticket price, we have that the revenue equation will be:

R = (8000-50*x) * (70+x) = 560000 + 8000*x - 50*70*x -50x2

R = -50*x2 + 4500*x + 560000

The value of x that gives the maximum value of a quadratic function is found using the formula:

x = -b/2a

where a and b are coefficients of the quadratic equation (in our case, a = -50 and b = 4500)

So the value of x that gives the maximum revenue is:

x = -4500 / (-100) = 45

Using this value in the revenue equation, we have that the maximum R is:

R = -50*45^2 + 4500*45 + 560000 = $661,250

(To get this revenue, the ticket will cost 70+45 = $115 and there will be 8000-50*45 = 5750 passengers)

3 0
3 years ago
A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?
mamaluj [8]

Answer:

Option C. y=(3/4)x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

Find the value of the constant k

For the point (-8,-6)

k=y/x=(-6/-8)=3/4

For the point (12,9)

k=y/x=(9/12)=3/4

<u><em>Note</em></u> A single point was required to find the constant k (because the line passes through the origin)

The equation is equal to

y=(3/4)x

7 0
3 years ago
Read 2 more answers
“The 7th grade class is planning a pancake breakfast. All materials are donated except the pancake mix. Based on the given infor
ArbitrLikvidat [17]

Answer:

a) 720

b) 60$

Step-by-step explanation:

a) each person is served 3 pancakes and there are 240 people, 240 x 3 = 720.

b) Each bag of mix costs 10$ and can make 120 pancakes, but we need 720 pancakes, which means six bags of mix (since 120x6 = 720). Since each cost 10$, 10 x 6 = 60$

6 0
3 years ago
The diagram shows 28 lattice points, each one unit from its nearest neighbors. Segment AB meets segment CD at E. Find the length
IrinaVladis [17]

Answer:

\frac{5\sqrt{5} }{3}

4 0
3 years ago
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