Answer:
The joint probability distribution of X and Y is shown below.
Step-by-step explanation:
The distributions of X and of Y are described as follows:
X : 0 1
P (X) : 0.23 0.77
Y : 1 2 3
P (Y) : 0.40 0.22 0.38
It is provided that X and Y are independent.
That is:
P (X ∩ Y) = P (X) × P (Y)
Compute the joint probability distribution of X and Y as follows:
X 0 1
<u>Y </u>
1 0.9200 0.3080
2 0.0506 0.1694
3 0.0874 0.2926
Answer:
100 sir
Step-by-step explanation:
10 times 5 is 50 and plus 50 is 100
According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.
By using this theorem we can set up the system of equations as follows:
x=y+1 ...(1)
2x+3= 3y + 3 ..(2)
By using equation (1) next step is to plug in y+1 for x in equation (2). So,
2 ( y + 1) + 3 = 3y + 3
2y + 2 + 3 = 3y + 3 By using distribution property.
2y + 5 = 3y + 3
2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.
2y = 3y - 2
2y - 3y = -2 Subtract 3y from each sides.
-y = -2
So, y=2
Next step is to plug in y=2 in equation (1) to get the value of x. Hence,
x= 2+1
=3
So, x=3 and y=2 make these triangles congruent.
So, the correct choice is 3. x = 3, y = 2.
Answer:
6
Step-by-step explanation:
Absolute value just means you make negatives into positives so it's just 6.
Answer:
y = 2(x + 3)² - 4
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square
y = 2x² + 12x + 14 ← factor out 2 from the first 2 terms
= 2(x² + 6x) + 14
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
y = 2(x² + 2(3)x + 9 - 9 ) + 14
= 2(x + 3)² - 18 + 14
= 2(x + 3)² - 4 ← in vertex form
