Kendra has a bowl containing 10 blue marbles, 15 yellow marbles, 5 green marbles, and red marbles of the same size. She will randomly put out a marble, keep it outside the bowl, then pull out another marble.What is the probability she will draw a red marble and then a yellow marble?
1/14
5/72
1/18
3/20
Answers
There are in total 36 marbles:
10 blue + 15 yellow + 5 green + 6 red.
The probability to put out a red marble in the first draw is 6 out of 36 marbles because there are 6 red marbles of total 36:
P(r) = 6/36 = 1/6.
After that 1 red marble is outside the bowl, there are now 35 marbles in total.
The probability to put out a yellow marble in the second draw is 15 out of 35 because there are 15 yellow marbles of total 35 marbles:
P(y) = 15/35 = 3/7.
If we want both these events to occur (1. to draw the red marble and 2. to draw the yellow marble), we will use a multiplication rule. The multiplication rule calculates the probability that both of two events will occur:
P(r) × P(y) = 1/6 × 3/7 = 3/42 = 1/14.
Therefore, the probability Kendra will draw a red marble and then a yellow marble is 1/14.
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Answer D
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Answer:
Range of f=R
Step-by-step explanation:
We are given that a function
We have to find the range of given function.
The given function is linear function because the degree of function is 1.
When the degree of function is 1 then the function is called the linear function.
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Answers
The system of equations can be used to determine whether the road intersects the boundary of the tower’s signal; y = 2( x - 4 )² + 2 and 5 x + 11 y = 62.
What is the vertex form of a quadratic equation?
If a quadratic equation is written in the form
y = a(x-h)^2 + k
then it is called to be in vertex form.
It is called so because when you plot this equation's graph, you will see the vertex point is on (h,k).
To determine a quadratic function in vertex form:
y = a ( x - 4 )² + 2
4 = a ( 5 - 4 )² + 2
4 = a + 2
a = 2
y = 2 ( x - 4 )² + 2
Then we will determine a linear function in standard form, that passes through the points ( -3, 7 ) and ( 8, 2 ).
7 = -3 m + b
2 = 8 m + b / ·(-1)
7 = - 3 m + b
- 2 = - 8 m - b
5 = - 11 m
m = -5/11,
2 = -5/11 · 8 + b,
b= 2 + 40/11,
b = 62/11
Substitue,
y = - 5/11 x + 62/11 / ·11
11 y = - 5 x + 62
5 x + 11 y = 62
Finally the system of equations is:
y = 2( x - 4 )² + 2
5 x + 11 y = 62
Learn more about vertex form of a quadratic equation here:
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