Five pieces can be selected in 1287 ways
Step-by-step explanation:
When the selection has to be made without considering the order of selection, combinations are used.
The formula for combination is:
Here
Total candies = n = 13
Candies to be selected = r = 5
Putting the values in the formula
Five pieces can be selected in 1287 ways
Keywords: Combinations, selection
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Answer:
Step-by-step explanation:
<u>Maximization With Derivatives</u>
Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.
We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.
The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.
The amount of fence needed to enclose the external and the internal divisions is
We know the total fencing is 1/2 miles long, thus
Solving for x
The total area of the pasture is
Substituting x
Differentiating with respect to y
Equate to 0
Solving for y
And also
Compute the second derivative
Since it's always negative, the point is a maximum
Thus, the maximum area is
The new height of the water is = 9.34 inches (approx)
Step-by-step explanation:
Given, a rectangular container measuring 20 inches long by 16 inches wide by 12 inches tall is filled to its brim with water.
Let the new height of water level be x inches.
The volume of the container = (20×16×12) cubic inches
=3840 cubic inches
According to the problem,
3840 - (20×16×x) = 850
⇔3840 -320x = 850
⇔-320x =850-3840
⇔-320 x = -2990
⇔x = 9.34 inches
The new height of the water is = 9.34 inches (approx)
