WHICH POINT IS NOT ON THE GRAPH OF THE FUNCTION y = x -2?

Calculating conditional probabilities - random permutations. About The letters (a, b, c, d, e, f, g) are put in a random order.

Evgesh-ka [11]

A="b is in the middle"

B="c is to the right of b"

C="The letter def occur together in that order"

a) b can be in 7 places, but only one is the middle. So, P(A)=1/7

b) X=i, "b is in the i-th position"

Y=j, "c is in the j-th position"

$P(B)=\displaystyle\sum_{i=1}^{6}(P(X=i)\displaystyle\sum_{j=i+1}^{7}P(Y=j))=\displaystyle\sum_{i=1}^{6}\frac{1}{7}(\displaystyle\sum_{j=i+1}^{7}\frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}$

P(B)=1/2

c) X=i, "d is in the i-th position"

Y=j, "e is in the j-th position"

Z=k, "f is in the i-th position"

$P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}$

P(C)=1/42

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

$P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)=\displaystyle\sum_{i=1}^{3}\frac{1}{6}\frac{1}{7}\frac{1}{5}(\displaystyle\sum_{j=1+3}^{6}\frac{1}{4}\frac{1}{3})=1/420$

P(B∩A)=3*(1/7*1/6)=1/14

P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7

P(A∩B)=1/14

P(A)P(B)=(1/7)*(1/2)=1/14

A and B are independent

P(A∩C)=1/420

P(A)P(C)=(1/7)*(1/42)=1/294

A and C aren't independent

P(B∩C)=1/420

P(B)P(C)=(1/2)*(1/42)=1/84

B and C aren't independent

8 0

3 years ago

PLease tell me the inequalities and the answers also label which problems you d. I was out sick and I have no idea what to do lo

tatuchka [14]

Answer:

1) Amy can invite 17 people.

2) x > 76

3) 40 - 6 is greater than or equal to 3x

4) x is greater than or equal to 98

Step-by-step explanation:

1) 50 + 8x = 200

2) 200 < 3x - 28

3) 40 = 6 +3x

4) (95 + 78 + 89 + x)/4 is greater than or equal to 90

3 0

3 years ago

Write as an algebraic expression: Five times

Alenkasestr [34]

Given:

The statement is "Five times the difference of the cube of y and the square of x".

To find:

The algebraic expression for the given statement.

Solution:

We know that,

Cube = Power 3

Square = Power 2

Difference = Minus (-)

Times = Multiplication (×)

Now,

Cube of y = $y^3$

Square of x = $x^2$

Difference of the cube of y and the square of x = $y^3-x^2$

Five times the difference of the cube of y and the square of x is:

Required expression = $5(y^3-x^2)$

Therefore, the correct option is C. The required algebraic expression for the given statement is $5(y^3-x^2)$ .

5 0

3 years ago

If 10% is deducted from a bill, $58.50 remains to be paid. How much is the original bill?

NARA [144]

Answer:

From the above we can roughly for an equation which is:

58.50 = Bill - (10% x Bill)

58.5 = Bill - (1/10 x Bill)

58.5 = 9/10 x Bill (Divide both sides by 9/10)

We get:

Bill = 58.5 / (9/10)

Bill = 65

Original bill is $65.

8 0

3 years ago

At the beach, 39% of people are on the boardwalk and 23% are on the sand. If the rest are in the water, what percentage of peopl

frozen [14]

100% - (39% + 23%) = 100% - 62% = 38% <== the percentage of ppl in the water

6 0

4 years ago