7 with 13 over 125 this is the mixed number form.
Combine the terms by multiplying into a single fraction.
Find the common denominator.
Combine fractions with the lowest common denominator.
Multiply the numbers.
Combine the multiplied terms into a single fraction
Find the common denominator.
Combine fractions with the lowest common denominator.
Multiply the numbers.
Eliminate the denominators of the fractions.
Cancel the multiplied terms that are in the denominator.
To distribute.
Add 28 to both sides.
Simplify
Subtract 3x from both sides.
Simplify
Divide both sides by the same factor.
Simplify
↓
<h3>Verification</h3>
Let x=12.
Checked ✅
If 2 boxes remain empty, it means that we put all three balls in one single box.
Suppose the full box is box number 1. For each ball, we have three choices - we may put it in box number 1, 2 or 3. This means that each box has a 1/3 chance of receiving each ball.
So:
- we choose box 1 for ball 1 - that's a 1/3 chance
- we choose box 1 for ball 2 - that's a 1/3 chance
- we choose box 1 for ball 3 - that's a 1/3 chance
So, the probability of putting all balls in box 1 is
But this is the probability of putting all ballx in box 1, and you can repeat this logic for box 2 and 3.
So, the probability of putting all balls in one single box is 1/27 for each box, for a total of
Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
Answer:well the answer is 3,483 but i’m not sure how to do the long divison part try to go to khan acadamy they will explain better!
Step-by-step explanation: