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zaharov [31]
3 years ago
12

A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inces. How far to the ne

arest hundredth of an inch, does each corner of the burger stick ourt from the bun.
Mathematics
1 answer:
Korolek [52]3 years ago
4 0

-- For the bread . . .

                 Area = π R²
 
                16 in² = π R²

                R² = 16 in² / π

                Bunradius = √(16 in² / π)  =  2.257 inches

-- For the meat . . .

               Area = side²

               16 in² = side²

               Side =  √16 in²  =  4 inches

               Diagonal of the square = 4 √2  =  5.657 inches

               1/2 of the burgerdiagonal = 2.828 inches .

If the meat is centered on the bun, then the corner of the burger
extends

           (2.828 - 2.257)  =  0.57 inch

rounded to the nearest hundredth inch.

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7/8-1/5  

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There are 7 acts in a talent show.
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Answer:

<u><em></em></u>

  • <u><em>Event A: 1/35</em></u>
  • <u><em>Event B: 1/840</em></u>

<u><em></em></u>

Explanation:

<u>Event A</u>

For the event A, the order of the first 4 acts does not matter.

The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.

Thus, the number of ways that the first <em>four acts</em> can be scheduled is:

          C(m,n)=\dfrac{m!}{n!(m-n)!}

         C(7,4)=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!(3)!}=35

And<em> the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order</em>, is 1: C(4,4).

Therefore the<em> probability of Event A</em> is:

           P(A)=1/35

Event B

Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.

The number of ways in which <em>four acts </em>can be scheculed when the order matters is:

           P(m,n)=\dfrac{m!}{(m-n)!}

         P(m,n)=\dfrac{7!}{(7-4)!}=P(m,n)=\dfrac{7!}{4!}=840

The number of ways <em>the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth</em> is 1: P(4,4)

Therefore, <em>the probability of Event B</em> is:

            P(B)=1/840

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