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KATRIN_1 [288]
2 years ago
5

Eight people attend the theater "together and sit in a row with exactly eight seats. Suppose the eight people consist of three m

arried couples and each couple wants to sit together with the husband on the left. How many ways can the eight be seated together in the row"
Mathematics
1 answer:
Nata [24]2 years ago
8 0

Answer:

They can be seated in 120 differents ways.

Step-by-step explanation:

Taking into account that there are 3 couples and every couple has an specific way to sit, for simplify the exercise, every couple is going to act like 1 option and it's going to occupy 1 Place. If this happens we just need to organize 5 options (3 couples and 2 singles) in 5 Places (3 for a couple and 2 for the singles)

It means that now there are just 5 Places in the row and 5 options to organized. So the number of ways can be calculated using a rule of multiplication as:

<u>      5         </u>*<u>        4          </u>* <u>       3           </u> *  <u>        2     </u>  * <u>         1         </u> = 120

 1st place    2nd Place    3rd place        4th Place    5th Place

Because we have 5 options for the 1st Place, the three couples and the 2 singles. Then, 4 options for the second Place, 3 options for the third place, 2 for the fourth place and 1 option for the 5th place.

Finally, they can be seated in 120 differents ways.

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Step-by-step explanation:

"However" expresses disappointment of what is mentioned in the previous paragraph to that of now.

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In kite WXYZ, the measure of Measure of angle X = measure of angle Z = 86 degrees, and the Measure of angle Y = 72 degrees.
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2 years ago
A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set w
VashaNatasha [74]

Complete Question

A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set was split into 5 segments (each 6.4 seconds long), what is the resulting:

a)F minimum

b) F maximum

c) Frequency resolution

Answer:

a) Fmax=100Hz

b) Fmin=0Hz

c) F_r=0.0313

Step-by-step explanation:

From the question we are told that:

Time t=32sec

FrequencyF=200Hz

Segments \mu=5

Generally the equation for Frequency Range is mathematically given by

Fmax=\frac{F}{2}

Fmax=100Hz

Therefore

a) Fmax=100Hz

b) Fmin=0Hz

c)

Generally the equation for Frequency Resolution is mathematically given by

F_r=\frac{F}{N}

Where

N=The Total dat points

N=Sampling Frequency *Time

N=200*32

N=6400

Therefore

F_r=\frac{200}{6400}

F_r=0.0313

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Read 2 more answers
You multiply two integers. You increase one of them by 1 and decrease the other
snow_tiger [21]

Integers are numbers without decimals

The integers could you have multiplied are 9 and 2

Let the numbers be x and y

So, we have:

\mathbf{x \times y}

Increase x by 1 and reduce y by 1.

So, we have

\mathbf{(x +1) \times (y -1) = 6 + xy }

Open brackets

\mathbf{xy -x + y - 1 = 6 + xy}

Subtract xy from both sides

\mathbf{ -x + y - 1 = 6}

Collect like terms

\mathbf{ -x + y = 6 + 1}

\mathbf{ -x + y = 7}

Rewrite as:

\mathbf{ y -x= 7}

The above means that, the difference between the integers is 7.

There are several integers that fit the above <em>description</em>;

One possibility is: 9 and 2

Read more about products at:

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6 0
2 years ago
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