Answer:
75%
Step-by-step explanation:
You pick a card at random. 6 7 8 9 What is P(not 9)? Write your answer as a percentage. %
Given the following
Total cards = 4 (6,7,8,9)
If the card is not 9, the required card will be (6,7,8)
Number of cards that are not 9 is 3
Probability = expected/total
Pr(not 9) = 3/4
express as percent
Pr(not 9) = 3/4×100
Pr(not 9) = 75%
Answer:
Sin(E) = 
Step-by-step explanation:
The full question is as follows :
To find - In the accompanying diagram, what is sin E?
Proof -
We know that,
Sin(theta) = (opposite side) / (hypotenuse)
From the diagram, we can see that,
Base = 3
Perpendicular = 5
Hypotenuse = 5
So,
For angle E,
Opposite side = 4
Hypotenuse = 4
∴ we get
Sin(E) =
Answer:
k = 8
Step-by-step explanation:
Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.
By the roots of an equation, ax² + bx + c , where its roots are x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.
Comparing both equations, a = 3 b = 2 and c = k.
So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3
x₁ + x₂ = -2/3 and x₁x₂ = k/3
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
3x₁ + (-2x₁) = -2 and x₁(3x₂) = k
3x₁ - 2x₁ = -2 and x₁(3x₂) = k
x₁ = -2 and x₁(-2x₁) = k
x₁ = -2 and -2x₁² = k
Substituting x₁ = -2 into -2x₁² = k, we have
-2x₁² = k
-2(-2)² = k
2(4) = k
8 = k
So, k = 8
