18) Solve for x. A) 42 B) 50 C) 63 D) 75

Your reading material states that many banks pay interest that is calculated

Step2247 [10]

Carry on... There is not sufficient information to answer

3 0

3 years ago

Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter

sweet [91]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

What is P(A and B)?

What is P(A | B)?

Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Solution:

The probability of the two events A and B are:

P(A) = 0.30 and P(B) =0.40

(a)

Compute the value of P (A ∩ B) as follows:

$P(A\cap B)=0$

This is because mutually exclusive events are those events that cannot occur together.

(b)

Compute the value of P (A | B) as follows:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0$

Thus, the value of P (A | B) is 0.

(c)

No, P (A | B) is not equal to the P (A).

(d)

As mentioned in part (a), mutually exclusive events are those events which cannot occur together.

That is, $P(A\cap B)=0$ .

Events A and B are independent if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is, $P(A\cap B)=P(A)\times P(B)$ .

The concepts of mutually exclusive events and independent events are not the same.

(e)

As the it is provided that A and B are mutually exclusive events, we know that $P(A\cap B)=0$ .

Now compute the value of $P(A)\times P(B)$ as follows:

$P(A)\times P(B)=0.30\times 0.40=0.12\neq 0$

Thus, the events A and B are not independent.

Thus, if two events are mutually exclusive events they cannot be independent.

4 0

3 years ago

12-(-19)= HELP ME OUT PLZ

Vikentia [17]

Answer:

31

Step-by-step explanation:

A negative negative is a positive

12- (-19)

12+19

31

6 0

3 years ago

Please help me. if you can help me answer multiple questions only 3. offering 30 points for it

lubasha [3.4K]

Answer:

(-9, -5)

Step-by-step explanation:

Ok, so when you move an image to the right, you are moving along the x-axis, and when you move up, you are moving up the y-axis. So if the altered image is (x,y) and the values are (-5, -1), you reverse what has been done to the image. In this case, since we moved to the right 4 units, we know that means we added 4 to x, so we subtract 4 to get -9. And then, for the y-value, because we added 4, we do the opposite, and subtract 4 to get -5. So the pre-image should be (-9, -5)

7 0

3 years ago

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per

HACTEHA [7]

Answer:

A) Revenue function = R(x) = (580x - 10x²)

Marginal Revenue function = (580 - 20x)

B) Fixed Cost = 900

Marginal Cost function = (300 + 50x)

C) Profit function = P(x) = (-35x² + 280x - 900)

D) The quantity that maximizes profit = 4

Step-by-step explanation:

Given,

The Price function for the cake = p = 580 - 10x

where x = number of cakes sold per day.

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

where x = number of cakes sold per day.

Please note that all the calculations and functions obtained are done on a per day basis.

A) Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Revenue = R(x) = price × quantity = p × x

= (580 - 10x) × x = (580x - 10x²)

Marginal Revenue = (dR/dx)

= (d/dx) (580x - 10x²)

= (580 - 20x)

B) Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

The total cost function is a sum of the fixed cost and the variable cost.

The fixed cost is the unchanging part of the total cost function with changing levels of production (quantity produced), which is the term independent of x.

C(x) = 900 + 300x + 25x²

The only term independent of x is 900.

Hence, the fixed cost = 900

Marginal Cost function = (dC/dx)

= (d/dx) (900 + 300x + 25x²)

= (300 + 50x)

C) Find the profit function [Hint: profit is revenue minus total cost]

Profit = Revenue - Total Cost

Revenue = (580x - 10x²)

Total Cost = (900 + 300x + 25x²)

Profit = P(x)

= (580x - 10x²) - (900 + 300x + 25x²)

= 580x - 10x² - 900 - 300x - 25x²

= 280x - 35x² - 900

= (-35x² + 280x - 900)

D) Find the quantity that maximizes profit

To obtain this, we use differentiation analysis to obtain the maximum point of the Profit function.

At maximum point, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = (-35x² + 280x - 900)

(dP/dx) = -70x + 280 = 0

70x = 280

x = (280/70) = 4

(d²P/dx²) = -70 < 0

Hence, the point obtained truly corresponds to a maximum point of the profit function, P(x).

This quantity demanded obtained, is the quantity demanded that maximises the Profit function.

Hope this Helps!!!

8 0

2 years ago