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Andreas93 [3]
2 years ago
15

The area of a rectangle is 42 square feet.

Mathematics
1 answer:
Alchen [17]2 years ago
3 0

Answer:

26 ft and 46 ft.

Step-by-step explanation:

The prime  factors of 42 are 2 * 3 * 7.

Possible lengths and widths  are:

L = 7, W = 6 giving a perimeter of  2*7 + 2*6 = 26 ft.

L = 14 , W = 3  giving perimeter = 34 ft.

L = 21, W = 2 giving perimeter = 46 ft.

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Step-by-step explanation:

Let's start writing the sample space for this experiment :

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

Let's also define the event E ⇒

E : '' The sum of the two dice is 5 ''

We can describe the event by listing all the favorables cases from S ⇒

E = { (4,1) , (3,2) , (2,3) , (1,4) }

In order to calculate P(E) we are going to divide all the cases favorables to E over the total cases from S. We can do this because all 36 of these possible outcomes from S are equally likely. ⇒

P(E)=\frac{4}{36}=\frac{1}{9} ⇒

P(E)=\frac{1}{9}

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F : '' The number of the first die is exactly 1 more than the number on the second die ''

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

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P ( A ∩ B ) = P(A,B)

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P(A|B)=\frac{P(A,B)}{P(B)} with P(B)>0

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Looking at the sets E and F we find that (3,2) is the unique result which is in both sets. Therefore is 1 result over the 36 possible results. ⇒

P(F,E)=\frac{1}{36}

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P(F|E)=\frac{P(F,E)}{P(E)}=\frac{\frac{1}{36}}{\frac{1}{9}}=\frac{1}{4}=0.25

We find out that P(F|E)=\frac{1}{4}=0.25

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