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3 years ago

the sum of two numbers is 45. The difference between the numbers is 37. what is the value of the smallest number?

2 answers:

8 0

Sum and difference problem
--------------------------------------

We are given both the sum and difference of two unknown numbers.

S=sum of the two numbers=45, and
D=difference of the two numbers (larger minus the smaller) = 37
Then
larger number = (S+D)/2 = (45+37)/2 = 41
smaller number= (S-D)/2 = (45-37)/2 = 4

Rina8888 [55]3 years ago

6 0

The value of the smallest number is 25

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Assume that the business makes a profit with probability 0.8 in the first year. For each year thereafter, the business makes a p

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Answer:

The probability that the business makes a profit in exactly two of its first three years is 0.628.

Step-by-step explanation:

Given : Assume that the business makes a profit with probability 0.8 in the first year. For each year thereafter, the business makes a profit with probability 0.9 if it made a profit in the previous year, and with probability 0.2 if it did not make a profit in the previous year.

To find : What is the probability that the business makes a profit in exactly two of its first three years?

Solution :

Let X be the event that the business makes profit.

Y be the event that the business doesn't .

The business makes a profit with probability 0.8 in the first year.

For each year thereafter, the business makes a profit with probability 0.9.

It did not make a profit in the previous year is 0.2.

According to question,

The business makes a profit in exactly two of its first three years which is given by, XXY, XYX, YXX

So,

$P(XXY)=0.8\times 0.9\times (1-0.2)$

$P(XXY)=0.8\times 0.9\times 0.8$

$P(XXY)=0.576$

$P(XYX)=0.8\times (1-0.9)\times 0.2$

$P(XYX)=0.8\times 0.1\times 0.2$

$P(XYX)=0.016$

$P(YXX)=(1-0.8)\times 0.9\times 0.2$

$P(YXX)=0.2\times 0.9\times 0.2$

$P(YXX)=0.036$

The probability that the business makes a profit in exactly two of its first three years is given by,

P= P(XXY)+P(XYX)+P(YXX)

P= 0.576+0.016+0.036

P= 0.628

Therefore, The probability that the business makes a profit in exactly two of its first three years is 0.628.

= 0.272

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