In a standard deck of 52 playing cards, 13 cards are clubs, and 3 of the clubs are "face" cards (K, Q, J). What is the probability of drawing one card that is:


A) A club or a face card? Is this event a union or an intersection?


B) A club and a face card? Is this event a union or an intersection?


C) Not a club and not a face card?

Answers

Answer 1

A) This event is a union. If a card is of the suit of clubs or a face card or both, then it belongs to the set of "cards with clubs or a face".

For the probability in question, we use the inclusion/exclusion principle:

P(club or face) = P(club) + P(face) - P(club and face)

That is, we add the probabilities of drawing a club and of drawing a face card, and subtract the probability of both conditions being met because, in a certain sense, we've double-counted the event of the card being both of clubs and a face. The sets "club" and "face" are not disjoint; there is overlap between them.

Then we have

P(club) = 13/52

P(face) = 12/52

P(club and face) = 3/52

so that

P(club or face) = 13/52 + 12/52 - 3/52 = 22/52 = 11/26

B) This event is an intersection. If a card is of the suit of clubs and a face card, then it belongs to both the set of clubs and the set of face cards.

We already found the probability of the intersection above:

P(club and face) = 3/52

C) If a given card is not a club and not a face card, this is the same as saying the card is neither a club nor a face card. In other words,

P(not club and not face) = P(not(club or face))

and this probability is complementary to the probability that a card is either a club or face, which is to say

P(not(club or face)) = 1 - P(club or face)

Using the result from part (A), we have

P(not club and not face) = 1 - 11/26 = (26 - 11)/26 = 15/26


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Answer:

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=> 36 ÷ (3 + 9)

=> 36 ÷ 12

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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they would be confirmation

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Step-by-step explanation:

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Answers

The maximum value of the objective function is 3080

The vertices of a feasible region are given as

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The objective function is given as:

[tex]\mathbf{P = 180x + 250y}[/tex]

Substitute the ordered pairs in the objective function

Point (14,2)

[tex]\mathbf{P = 180 \times 14 + 250 \times 2}[/tex]

[tex]\mathbf{P = 3020}[/tex]

Point (0,9)

[tex]\mathbf{P = 180 \times 0 + 250 \times 9}[/tex]

[tex]\mathbf{P = 2250}[/tex]

Point (6,8)

[tex]\mathbf{P = 180 \times 6 + 250 \times 8}[/tex]

[tex]\mathbf{P = 3080}[/tex]

Lastly, we have point (10,3)

[tex]\mathbf{P = 180 \times 10 + 250 \times 3}[/tex]

[tex]\mathbf{P = 2550}[/tex]

The maximum value of P is calculated to be 3080.

Hence, the maximum value of the objective function is 3080

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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then you will find the y or k then make a table of values and put the vertex of the x and y that you found.

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Step-by-step explanation:

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[tex]2 \times + 3y = 5x - y[/tex]

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Answers

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Step-by-step explanation:

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Answers

Answer:

Solve the equation for y. See example.

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

The value of p that makes the given equation true is equal to: B. p = -5

Given the following equation:

[tex]3p - 8 = -23[/tex]

To find a value of p that makes the given equation true:

In this exercise, you're required to determine a value of p that satisfies the given equation true such that when substituted into the equation, it has a true result or outcome.

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Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I'll help you with your problem today. I hope you are having a nice day!

The Function

First of all, to figure out the function and how it will work, with that, we can see that it is a parabola, a parabola is a function which looks like a curve in which the multiplication of the [tex]x[/tex] cation, when more smaller, is more wider.

Parabola's also have two ways they go, them being upwards and downwards which in the quadratic formula are figured out by the a catition.

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Solving

So, we know to find for [tex]f(1)[/tex] we have to find what is y when x is 1. To solve for that, we can look at the function's graph and see that when x is one, y is 5.

Solution

To solve for this, we can usually just look at the graph to see where the point where we need to find is, but, we also might have to graph the equation if the graph is not already given.

So our answer would be [tex]y=5[/tex] and/or [tex](1,5)[/tex]

Cheers!

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Step-by-step explanation:

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I tried

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Answers

the answer is the first one 25
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