Given:
10 blue marbles ; 15 yellow marbles, 5 green marbles, 6 red marbles
A total of 36 marbles.
Probabilities:
1st marble: red = 6/36
2nd marble: yellow = 15/35
6/36 * 15/35 = 6*15 / 36*35 = 90/1260 = 1/14
The probability that Kendra will draw a red marble and then a yellow marble is 1/14.
Answer:
see below
Step-by-step explanation:
12.5x − 10.2 = 3(2.5x + 4.2) - 6
Use the distributive property to distribute the 3
12.5x − 10.2 = 7.5x + 12.6 − 6
Combine like terms
12.5x − 10.2 = 7.5x + 6.6
Add 10.2 to each side of the equation by using the addition property of equality
12.5x = 7.5x + 16.8
Subtraction 7.5x from each side of the equation by using the subtraction property of equality
5x = 16.8
Divide by 5 on each side by using the division property of equality
x = 3.36
Answer:
D
Step-by-step explanation:
You can plug in the given x and y values into the equations and see which one works for both of them.
D works for both of them:
5 = 5/4(4)
0 = 5/4(0)
From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
Answer:
Change = -(1/2) * 30 = -15 inches
Step-by-step explanation:
If the water level decreases by 1/2 inch each day, the change in the water level in one day is -1/2 inch.
So, after t days, the total change in the water level can be calculated as:
Total change = -(1/2) * t inches
So, after 30 summer days, the total change is:
Change = -(1/2) * 30 = -15 inches
So the water level of the pool after 30 summer days has decreased by 15 inches.
