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Goryan [66]
3 years ago
13

**IMPORTANT**

Mathematics
1 answer:
koban [17]3 years ago
8 0

Answer:

11/18

5/9

Step-by-step explanation:

we will make punnette square

         dice1

    +

dice2   1       2        3       4        5       6

1            2      3        4       5        6       7

2           3      4         5       6       7        8

3           4      5         6       7       8        9

4           5      6         7       8       9        10

5           6      7         8       9      10       11

6          7       8         9       10     11        12

1)

The probability that the sum of the numbers rolled is either even or a multiple of 5

even number = 18

{(1,1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4,2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)},

and

multiple of 5 = 4

{(1,4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)}

<em>(we will skip the repeating)</em>

<em />

18 + 4 = 22

probability = 22/36

                  = 11/18

               

2)

The probability that the sum of the numbers rolled is either a multiple of 3 or 4

multiple of 3 = 12

{(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (3, 6), (4, 2), (4, 5), (5, 1), (5, 4), (6, 3), (6, 6)}

and

multiple of 4 = 8

D = {(1, 3), (2, 2), (2, 6), (3, 1), (3, 5), (4, 4), (5, 3), (6, 2), (6, 6)}

<em>(we will skip the repeating)</em>

<em />

12 + 8 = 20

probability = 20/36

                  = 5/9

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A community theater uses the function p (d) = (-4d+40) (d−40) to model the profit (in dollars) expected in a weekend when the ti
fomenos

The theater make the maximum profit at d = $25. Then the maximum profit of the theatre is $ 900.

<h3>What is differentiation?</h3>

The rate of change of a function with respect to the variable is called differentiation. It may be increasing or decreasing.

A community theater uses the function P(d) = (− 4d + 40) (d − 40) to model the profit (in dollars) expected on a weekend when the tickets to a comedy show are priced at d dollars each.

Then the maximum profit of the theatre will be

The function is P(d) = (− 4d + 40) (d − 40)

Differentiate the function with respect to d and put it equal to zero for maximum or minimum profit.

\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= 0\\\\\dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) &= 0\\\\(-4d+40) -4 (d-40) &= 0\\\\-8d + 200 &= 0\\\\d &= 25 \end{aligned}

Then the checking for maximum or minimum, again differentiate, we have

\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(-8d + 200) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= -8\\\\ \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) & < 0\end{aligned}

The value is less than zero hence maximum value will occur at d = 25.

Then maximum profit will be

P(d) = (− 4×25 + 40) (25 − 40)

P(d) = (− 100 + 40) (−15)

P(d) = (− 60) (− 15)

P(d) = $ 900

More about the differentiation link is given below.

brainly.com/question/24062595

#SPJ1

7 0
1 year ago
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