Twice a number is less than or equal to the sum of a number and 15

A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

julsineya [31]

Answer:

a. $P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

b. $E(x) = 0.3$

c. $S(x)=0.5196$

d. $E=5,000$

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

$P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\$

For binomial distribution:

$E(x)=np\\S(x)=\sqrt{np(1-p)}$

Therefore, the company can expect to win 0.3 bids and it is calculated as:

$E(x) = np = 3*0.1 = 0.3$

Additionally, the standard deviation of the number of bids won is:

$S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196$

Finally, the probability to won 1, 2 or 3 bids is equal to:

$P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001$

So, the expected profit for the company is equal to:

$E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000$

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

5 0

3 years ago

1001112 = [ ? ]10<br> ?<br> what number belongs where the question mark is

EleoNora [17]

I suppose you're supposed to convert 100111 from base 2 to base 10. We have

$100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}$

so the missing number is 39.

4 0

3 years ago

Is it more difficult to run up a ramp with a slope of 1/5 or a ramp with a slope of 5? Explain.

VARVARA [1.3K]

It would be more difficult to run up a slope of 5 because it would be steeper. with a 1/5 slope you would have a rise over run but with a slope of 5 it would just be all rise

6 0

3 years ago

Read 2 more answers

Find the slope between the points (0,8) and (4,4)

Oxana [17]

Answer:

Slope=-1

Step-by-step explanation:

Slope=y1-y2/x1-x2

Where (X1,y1)(0,8) and (X2,y2) (4,4)

Slope=8-4/0-4

=4/-4

=-1

So slope is -1

5 0

2 years ago

A washer and a dryer cost $995 combined. The washer cost $45 more than the dryer. What is the cost of the dryer?

Talja [164]

When a washer and a dryer cost $995 combined. If the washer cost $45 more than the dryer, then the cost of the dryer is $475

The combined cost of a washer and a dryer = $995

Consider the cost of a dryer as x

The washer cost $45 more than the dryer.

The cost of the washer = x+45

Then the equation will be

x+x+45 = 995

2x+45 = 995

2x = 950

x = 950/2

x = 475

The cost of the dryer is $475

Hence, when a washer and a dryer cost $995 combined. If the washer cost $45 more than the dryer, then the cost of the dryer is $475

Learn more about equation here

brainly.com/question/1625308

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8 0

1 year ago