Answer: B. one-third
Step-by-step explanation:
Probability of picking a red marble, P(R) = 1/6
Probability of picking a yellow marble, P(Y) = 1/2
Therefore, the probability of picking a blue marble will be:
= 1 - (P(R) + P(Y))
= 1 - (1/6 + 1/2)
= 1 - (4/6).
= 1 - 2/3
= 1/3
The probability of picking a blue marble will be one third
Answer:
Step-by-step explanation:
We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...
y = a(x -3)² +b
Filling in the values from the first two table points, we get
For (x, y) = (0, 6):
6 = a(0 -3)² + b ⇒ 9a +b = 6
For (x, y) = (2, 22):
22 = a(2-3)² +b ⇒ a +b = 22
Subtracting the second equation from the first gives ...
(9a +b) -(a +b) = (6) -(22)
8a = -16 . . . . . . collect terms
a = -2 . . . . . . . . divide by 8
The second equation above tells us ...
b = 22 -a = 22 -(-2) = 24
So, our equation for y is ...
y = -2(x -3)² +24
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The value of y for x=5 is ...
y = -2(5 -3)² +24 = 16
The height of the ball after 5 seconds is 16 feet.
The distance, s = 40t₁ where t₁ is the time to complete the outward journey.
The same distance = vt₂ where t₂ is the time to complete the return journey at speed v.
For the whole journey, 2s=60(t₁+t₂). Therefore s=30(t₁+t₂)=40t₁=vt₂.
30t₁+30t₂=40t₁, 10t₁=30t₂, t₁=3t₂, so s=120t₂=vt₂ and v=120kph.
draw an imaginary line down from the 1 dimension so you have a rectangle that is 1 by 24
area = L x w = 24 * 1 = 24 square units
now you have a triangle that is 7 at the bottom and 24 tall
area of triangle = 1/2 x base x height
so you have 1/2 * 7 * 24 which =84 square units
total area = 84 + 24 = 108 units^2
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