Answer:
Given:
- Total balls = 10
- Black balls = 3
- White balls = 7
⇒ P(black ball) = 3/10 = 0.3
⇒ P(white ball) = 7/10 = 0.7
If one ball is chosen at random and <u>replaced</u>, the probabilities do not change between the first and second ball.
Let event D = first ball is black
Let event S = second ball is black
P(D) = 0.3
P(S) = 0.3 (since the first ball is replaced)
⇒ P(D ∩ S) = P(D) × P(S)
= 0.3 × 0.3
= 0.09
For Independent Events we know that: P(A ∩ B) = P(A) × P(B)
Therefore, as P(D ∩ S) = P(D) × P(S) the events are independent.
Answer:
21 pencils for Nick and 63 pencils for Lance
Step-by-step explanation:
- Lance is said to have 3 times the pencils Nick has.
- Let's keep the number of pencils Nick has as x.
- If Nick has x pencils that means Lance has 3x pencils.
- The total number of pencils present is 84.
Now let's make an equation out of the information above:
3x + x = 84
Now solve for x.
3x + x = 84
4x = 84
x = 84/4
x = 21
So Nick has 21 pencils
Now for Lance:
3x
3 * (21) = 63
So Lance has 63 pencils
63 + 21 = 84 pencils
Answer:
40/100
Step-by-step explanation:
Answer:
The third graph.
Step-by-step explanation:
The equations for the lines will be
P(x) = 2x-4
l(x) = -2x-4
When x = 0 both of these functions equal -4. The only graph where this happens is the third one.
You can check this by looking at the slopes and plugging in points.
Answer:
A, B, C
Step-by-step explanation:
x is in the intersection of sets B and C, in set B, in set C, in the union of sets B and C, in the union of sets A and C
Answer: A, B, C
