MATHEMATICS COLLEGE

Find cardinality of set B

B = {∅, {1}, {1, 2}, {1, 2,3}, · · · , {1, 2, · · · , m}}

Answers

Answer 1

Answer:

Answer:

m + 1

Step-by-step explanation:

Given set,

B = {∅, {1}, {1, 2}, {1, 2,3}, · · · , {1, 2, · · · , m}},

Since, the elements of S are,

{} , {1}, {1, 2}, {1, 2, 3}....... {1, 2,.....m }

Thus, every next set contains one more succeeding natural number than the previous set.

So, if the last set contains m natural numbers.

Then there are 'm + 1' sets in B ( m sets included ∅ )

Hence, the number of elements in B is 'm+1'

I.e. Cardinality of B is m + 1.

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Answers

Answer:

0.67184

16.4

2738.575

797.458

Answer:

0.67184

16.4

2738.575

847.458

Connor works in a department store selling clothing. He makes a guaranteed salary of $300 per week, but is paid a commision on top of his base salary equal to 5% of his total sales for the week. How much would Connor make in a week in which he made $2175 in sales? How much would Connor make in a week if he made xx dollars in sales?

Answers

Answer:

If Connor makes x dollars in sales, he will make 0.05x + 300 that week.

He makes $408.75 in a week if he makes $2175 in sales.

Step-by-step explanation:

y = 0.05x + 300

y = 0.05(2175) + 300

y = 408.75

During the period of time that a local university takes phone-in registrations, calls come inat the rate of one every two minutes.
a. What is the expected number of calls in one hour?
b. What is the probability of three calls in five minutes?
c. What is the probability of no calls in a five-minute period?

Answers

Answer:

a) The expected number of calls in one hour is 30.

b) There is a 21.38% probability of three calls in five minutes.

c) There is an 8.2% probability of no calls in a five minute period.

Step-by-step explanation:

In problems that we only have the mean during a time period can be solved by the Poisson probability distribution.

Poisson probability distribution

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

a. What is the expected number of calls in one hour?

Calls come in at the rate of one each two minutes. There are 60 minutes in one hour. This means that the expected number of calls in one hour is 30.

b. What is the probability of three calls in five minutes?

Calls come in at the rate of one each two minutes. So in five minutes, 2.5 calls are expected, which means that $\mu = 2.5$ . We want to find P(X = 3).

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 3) = (e^(-2.5)*(2.5)^(3))/((3)!) = 0.2138$

There is a 21.38% probability of three calls in five minutes.

c. What is the probability of no calls in a five-minute period?

This is P(X = 0) with $\mu = 2.5$ .

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 0) = (e^(-2.5)*(2.5)^(0))/((0)!) = 0.0820$

There is an 8.2% probability of no calls in a five minute period.

Once again im still struggling with this

Answers

Answer:

In bold below.

Step-by-step explanation:

There are 2 whole circles shaded and the other has 3 parts out of 5 shaded.

Mixed number = 2 3/5.

Improper fraction = 13/5.

Find an equation for the tangent to the curve at P and the horizontal tangent to the curve at Q. y = 5 + cot x - 2 csc x 0 1 2 3 0 2 4 x y Upper QUpper P left parenthesis StartFraction pi Over 2 EndFraction comma 3 right parenthesis

Answers

Answer with explanation:

The given function in x and y is,

y= 5 +cot x-2 Cosec x

To find the equation of tangent, we will differentiate the function with respect to x

$y'= -\csc^2 x+2 \csc x* \cot x$

Slope of tangent at (π/2,3)

$y'_{((\pi)/(2),3)}= -\csc^2(\pi)/(2) +2 \csc (\pi)/(2)* \cot (\pi)/(2)\n\n=-1+2* 1 * 0\n\n= -1$

Equation of tangent passing through (π/2,3) can be obtained by

$\rightarrow (y-y_(1))/(x-x_(1))=m(\text{Slope})\n\n \rightarrow (y-3)/(x-(\pi)/(2))=-1\n\n\rightarrow 3-y=x-(\pi)/(2)\n\n\rightarrow x+y-3-(\pi)/(2)=0$