2/3 of the 4/5 of the class has a dog and a cat. Just multiply
(2/3)(4/5)=8/15
45*(8/15)=24
<em>Y</em>₁ and <em>Y</em>₂ are independent, so their joint density is
By definition of conditional probability,
P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = P((<em>Y</em>₁ > <em>Y</em>₂) and (<em>Y</em>₁ < 2 <em>Y</em>₂)) / P(<em>Y</em>₁ < 2 <em>Y</em>₂)
Use the joint density to compute the component probabilities:
• numerator:
• denominator:
(I leave the details of the second integral to you)
Then you should end up with
P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = (1/6) / (2/3) = 1/4
Answer:
YES
Step-by-step explanation:
Explanation:
If this is a right triangle we can then substitute the sides of the triangle (12 and 35) and the hypotenuse (37) into the Pythagoras Theorem and the two sides of the equation will be equal. If this is not a right triangle the two sides of the equation will not be equal.
The Pythagoras Theorem is
a
2
+
b
2
=
c
2
Substituting we get:
12
2
+
35
2
=
37
2
12
⋅
12
+
35
⋅
35
=
37
⋅
37
144
+
1225
=
1369
1369
=
1369
Because these are equal this is a right triangle.
Answer:
The value of x = 6
Step-by-step explanation:
Given
To determine
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
here:
so substitute (x₁, y₁) = (x, -4)
, (x₂, y₂) = (2, 8) and m = -3
m = [y₂ - y₁] / [x₂ - x₁]
-3 = [8 - (-4)] / [2 - x]
-3 = [12] / [2-x]
-3 (2-x) = 12
-6+3x = 12
3x = 12+6
3x = 18
divide both sides by 3
3x/3 = 18/3
x = 6
Therefore, the value of x = 6
