There is a bag filled with 2 blue, 4 red and 5 green marbles.

Mathematics

1 answer:

Vinil7 [7]3 years ago

6 0

<h3>Answer: 45/121</h3>

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Work Shown:

2 blue, 4 red, 5 green

2+4+5 = 11 total

P(blue) = probability of getting one blue marble

P(blue) = (number of blue)/(number total)

P(blue) = 2/11

A = P(2 blue) = (2/11)*(2/11) = 4/121

P(red) = 4/11

B = P(2 red) = (4/11)*(4/11) = 16/121

P(green) = 5/11

C = P(2 green) = (5/11)*(5/11) = 25/121

Add the values of A,B, and C to get the probability of getting two of the same color

A+B+C = 4/121+16/121+25/121 = 45/121

This is approximately equal to 0.3719 which is roughly a 37.19% chance of happening

Side note: we can add A,B, and C because they are mutually exclusive events.

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Geometric Series assistance

Levart [38]

we have been asked to find the sum of the series

$\sum _{n=1}^5\left(\frac{1}{3}\right)^{n-1}$

As we know that a geometric series has a constant ratio "r" and it is defined as

$r=\frac{a_{n+1}}{a_n}=\frac{\left(\frac{1}{3}\right)^{\left(n+1\right)-1}}{\left(\frac{1}{3}\right)^{n-1}}=\frac{1}{3}$

The first term of the series is $a_1=\left(\frac{1}{3}\right)^{1-1}=1$

Geometric series sum formula is

$S_n=a_1\frac{1-r^n}{1-r}$

Plugin the values we get

$S_5=1\cdot \frac{1-\left(\frac{1}{3}\right)^5}{1-\frac{1}{3}}$

On simplification we get

$S_5=\frac{121}{81}$

Hence the sum of the given series is $\frac{121}{81}$

5 0

2 years ago

The equation $y=-4.9t^2+3.5t+5$ describes the height (in meters) of a ball thrown upward at $3.5$ meters per second from $5$ met

Georgia [21]

Answer:

Step-by-step explanation:

The position function is

$s(t)=-4.9t^2+3.5t+5$ and if we are looking for the time t it takes for the ball to hit the ground, we are looking for the height of the ball when it is on the ground. Of course the height of anything on the ground is 0, so if we set s(t) = 0 and solve for t, we will find our answer.