Please help i’ll give brainliest if you help thanks
1 answer:
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Answer:
Step-by-step explanation:
If a watch has fewer than three defects, then either 1.) It has no defects, 2.) it has exactly 1 defect, or 3.) it has exactly 2 defects.
1.) The probability that the watch has no defects is , because for every chime there is a probability of
that there is no defect
2.) The probability that the watch has exactly 1 defect is times the number of ways you can choose 1 of 75 of the chimes to be defective, which is
, so the probability that the watch has exactly 1 defect is
.
3.) For the same reason as 2.), the probability that the watch has exactly two defects is
Since 1.), 2.), and 3.) are mutually exclusive events, the probability of their union is simply the probability of each of them added together, which is
Answer:
Each square should have 5 inches of side and area = 25 square inches.
Step-by-step explanation:
Candy box is made that measures 45 by 24 inches.
Let the squares of equal size x inches has been cut out of each corner.
The sides will then be folded up to form a rectangular box.
Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.
Now the box is with length = (45 - 2x) inches
and width = (24 - 2x) inches
and height = x inches
Volume of the candy box = Length × width × height
V = (45 - 2x)(24 - 2x)(x)
V = x(1080 - 48x -90x + 4x²)
= x(1080 - 138x + 4x²)
= 4x³ - 138x² + 1080x
Now we will find the derivative of volume and equate it to zero.
12(x² - 23x + 90) = 0
x² - 23x + 90 = 0
x² - 18x - 5x + 90 = 0
x(x - 18) - 5(x - 18) = 0
(x - 5)(x - 18)=0
x = 5, 18
Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12
Which is not possible.
Therefore, x = 5 will be the possible value.
Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.
