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tester [92]
3 years ago
10

Two married couples have purchased theater tickets and are seated in a row consisting of just 4 seats. If they take their seats

in a completely random order, what is the probability that at least one of the wives ends up sitting next to her husband? Hint: Use probability of a complement event. That is, P(A) = 1 − P(A′), where A′ is the complement of an event A.
Mathematics
1 answer:
Licemer1 [7]3 years ago
7 0

Answer:

The answer is 0.75.

Step-by-step explanation:

To use probability of a complement event, we need to find the situation where none of the couples are sitting next to each other which can happen either two husbands are sitting in the seats 2 and 3 or two wives are sitting in the seats 2 and 3. Also in the first scenario, the wives would need to be sitting at the opposite ends to their husbands and vice versa for the second scenario.

So there are in total 4 scenarios where no couple is sitting next to each other.

There are a total of 16 different ways that they can be seated so the probability of compelement is 16 - 4 = 12, which is 3/4 of the total, meaning that the probability of at least one of the wives sittting next to her husband is 0.75 or 75%.

I hope this answer helps.

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How many solutions are there to the equation below?
Elza [17]

Answer:

no solution

Step-by-step explanation:

heres why:

Let's solve your equation step-by-step.

4x−9(x+1)=20−5x

Step 1: Simplify both sides of the equation.

4x−9(x+1)=20−5x

4x+(−9)(x)+(−9)(1)=20+−5x(Distribute)

4x+−9x+−9=20+−5x

(4x+−9x)+(−9)=−5x+20(Combine Like Terms)

−5x+−9=−5x+20

−5x−9=−5x+20

Step 2: Add 5x to both sides.

−5x−9+5x=−5x+20+5x

−9=20

Step 3: Add 9 to both sides.

−9+9=20+9

0=29

so there are no solution

4 0
3 years ago
Let log P/N=8 and log M/N=5<br><br> What is the relationship between P and M?
Radda [10]
Want to use some of the algebra rules of log's:

log(a)-log(b)= log(a/b),

so log(P/N) - log(M/N) = log( P/N:M/N) = log(P/M),

Then: 8-5 = log(P/M), log(P/M)=3.

If log here means natural logarithm (base e), then P/M = e^3,

If log here means basis 10, decimal logarithm, then P/M = 10^3 = 1000.
8 0
3 years ago
Energy &amp; Motion in the Ocean &amp; Atmosphere
gtnhenbr [62]
I really don’t understand
3 0
3 years ago
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What is the answer of 8(3v+3w-2)
stepan [7]

Answer:24v+24w-16

Step-by-step explanation:

8(3v+3w-2)

8 times 3 =24

So 24v+24w

Then 8 times 2=16

So the answer would be 24v+24w-16

5 0
3 years ago
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A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric f
likoan [24]

Step-by-step explanation:

Let x be the length and y be the width of the rectangular plot.

The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,

x+2y = 1500

x = 1500 - 2y ....(1)

We know that the area of a rectangular plot is given by :

A = xy ....(2)

Put the value of x from equation (1) in (2)

A=(1500-2y)y\\\\A=1500y-2y^2 .....(3)

For largest area, differentiate above area equation wrt y.

\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375

Put the value of y in equation (1).

x = 1500-2(375)

= 750 m

Put the value of y in equation (3).

A =1500(375)-2(375)^2\\A=281250\ m^2

Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.

3 0
3 years ago
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