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Inessa [10]
3 years ago
7

A single card is drawn from a standard​ 52-card deck. Let D be the event that the card drawn is a black card​, and let F be the

event that the card drawn is a 10 card. Find the indicated probability.
P(DUF')

The probability P(DUF') is
Mathematics
1 answer:
Svetllana [295]3 years ago
8 0

Answer:

\dfrac{25}{26}

Step-by-step explanation:

Let

  • D be the event that the card drawn is a black card​
  • F be the event that the card drawn is a 10 card
  • F' be the event that the card drawn is not a 10 card

The probability

Pr(D\cup F')=Pr(D)+Pr(F')-Pr(D\cap F')\\

Note that

Pr(D)=\dfrac{26}{52}=\dfrac{1}{2}\\ \\Pr(F)=\dfrac{4}{52}=\dfrac{1}{13}\\ \\Pr(F')=1-\dfrac{1}{13}=\dfrac{12}{13}\\ \\Pr(D\cap F')=\dfrac{24}{52}=\dfrac{6}{13}

So,

Pr(D\cup F')=\dfrac{1}{2}+\dfrac{12}{13}-\dfrac{6}{13}=\dfrac{25}{26}

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Answer:

12.75w + 25 = 114.25

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Step-by-step explanation:

since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet)  we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.

to find out what w represents, we have to solve for it. solving for w means isolating it on one side. so, what we can do first is subtract 25 from both sides. that would then make the equation:

12.75w = 89.25

now, we have only one step left to isolating w, and that's to get 12.75 on the other side somehow. since we're multiplying 12.75 with w, and we're applying additive inverse properties, meaning the opposite of what is happening to cancel it out on the side it's in, we would divide 12.75 on both sides. in the left, 12.75 would cancel out, and in the right, we would divide 89.25 by 12.75. the quotient is 7.

now there's nothing left to take out to isolate w, so we have:

w = 7

sarah saved up for 7 weeks.


3 0
4 years ago
A regular hexagon is dilated by a scale factor of 43 to create a new hexagon. How does the perimeter of the new hexagon compare
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Answer:

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Step-by-step explanation:

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Dilated perimeter: 43*6x=258x

Therefore, the dilated perimeter is 258x while the og perimeter is 6x

I hope this helped and have a good rest of your day!

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Step-by-step explanation:

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