Probability is defined as the <u>likelihood or the certainty</u> that an event is going to<u> occur or happen.</u>
The probability of randomly choosing a red and then a green marble is
.
The total number of marbles = 20
The number of green marbles= 3
The number of blue marbles = 12
The number of red marbles = 5
<u>The probability of choosing a red marble</u> = Number of red marbles / Total number of marbles
= 5/20
<u>In simplest fraction form</u> = 
We are told in the question that you keep the red marble you choose, So this means the <u>total number of marbles</u> left reduces to 19
<u>The probability of choosing a green marble is</u> = Number of green marbles / New total number of marbles
= 3/19
Therefore, <u><em>the probability of randomly choosing a red and then a green marble is </em></u>
P (Red) x P(Green)
= 1/4 x 3/19
= 
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Hi there!
To solve is pretty easy. First, simplify.
21/4=(1/2x+3x) -> Combine Like Terms
21/4=7/2x
FLIP
7/2x=21/4
Multiply both sides by 2/7.
(2/7)*(7/2x)=(2/7)*(21/4)
x = 2/3
Hope this helps!
Complete Question
The complete question is shown on the first uploaded image
Answer:
the null hypothesis is 
the alternative hypothesis is 
The test statistics is 
The p-value is 
so

Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is n= 38
The sample mean is 
The standard deviation is 
Generally the null hypothesis is 
the alternative hypothesis is 
Generally the test statistics is mathematically evaluated as

substituting values


The p-value is mathematically represented as

From the z- table

So

Hi there!
Let x=1
X-3y=6
1-3y=6
-3y=6-1
-3y=5
Y=-5/3
Therefore a point would be (1, -5/3)
Hope this helps!