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iragen [17]
3 years ago
15

Three boys and six girls are being seated in a row of nine chairs on a stage which are numbered from left to right. How many sea

ting arrangements are there if: A. There are no restrictions as to how they are seated? B. The boys sit in the middle three seats? C. Girls sit in the first two seats as well as the last seat? D. The first four seats alternate girl, boy,
Mathematics
1 answer:
OLga [1]3 years ago
3 0

Answer:

A. 362,880

B. 4,320

C. 14,400

D. 21,600

Step-by-step explanation:

A.

If there are no restrictions as to how they are seated, then we have permutations of 9 elements and there are 9! (factorial of 9) = 362,880 different seating arrangements.

B.  

If the boys sit in the middle three seats, they can sit in 3!=6 different ways, the girls can sit then in 6!=720 different ways. By the fundamental rule of counting, there are 6*720 = 4,320 different seating arrangements.

C.

We now have arrangements of the type

g, g, x, x, x, x, x, x, g  

The three girls at the ends can be chosen in C(6;3) (combinations of 6 taken 3 at a time) =  

\large \frac{6!}{3!(6-3)!}=\frac{6!}{3!3!}=20

different ways. The 6 in the middle can be sit in 6!=720 different ways.

By the fundamental rule of counting, there are 20*720 = 14,400 different seating arrangements.

D.

Now we have arrangements

g,b,g,b,x,x,x,x,x

For the 1st position we have 6 possibilities, for the 2nd we have 3 possibilities, for the 3rd we have 5 possibilities and for the 4th we have 2 possibilities. For the last 5 we have 5!=120 possibilities.

By the fundamental rule of counting, there are 6*3*5*2*120 = 21,600 different seating arrangements.

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Idk wat to do.....<br>........​
oksano4ka [1.4K]

Answer:

Mean : 95

Median : 85

Mode : 90

Part B : Impossible

Step-by-step explanation:

We can make an equation to find the mean using the first 5 history test scores.

85=\frac{80+75+90+75+95+n}{6} \\ \\ 85=\frac{415+n}{6} \\ \\ 510=415+n \\ \\ n=95

So a 95 would be needed to have a mean of 85.

Next, the median.

First, we sort the first 5 history scores from least to greatest.

We get 75, 75, 80, 90, 95.

Since, 80 is the middle value, it will be used in the calculation of the median.

We can make an equation with this.

82.5=\frac{80+n}{2} \\ \\ 165=80+n \\ \\ n=85

So a score a 85 would be needed to have a median of 82.5

Thirdly, the mode.

Since 90 is already in the set once, we can just have Maliah score another 90 to make 90 the mode (with the exception of 75 of course).

Finally, Part B.

We can use the equation we had for the first mean calculation but change 85 to 90.

90=\frac{80+75+90+75+95+n}{6} \\ \\ 90=\frac{415+n}{6} \\ \\ 540=415+n \\ \\ n=125

So Maliah would need a score of 125 to make her mean score 90, but since the range is only from 0-100, it is impossible.

8 0
3 years ago
How far can a caterpillar; traveling at 0.06m/s, move in 60 seconds?
nignag [31]

Answer:

3.6 meters in 60 seconds

4 0
3 years ago
What is the value of y?
Inessa [10]
I think it’s b but I’m not sure
3 0
3 years ago
Read 2 more answers
can some one explain to me how fractions work who ever explains it well gets brainliest, adding, subtracting, multiplying, divid
Ludmilka [50]
Adding: When adding fractions, you want to make sure that the denominator is the same for both fractions. If they are already the same, just add both the numerators to get the answer. For example,
\frac{3 }{5}  +  \frac{1}{5}  =  \frac{4}{5}
If the denominator is different in both fractions, you have to find the least common denominator, or LCD. The LCD is the smallest number that both denominators can multiply into. For example, say you need to find
\frac{1}{6}  +  \frac{1}{3}

Multiply both the numerator and the denominator of (1/3) by 2 to get (2/6). This way, the denominators are the same and you can find the answer.
\frac{1}{6}  +  \frac{2}{6}  =  \frac{3}{6}
In the case that one denominator does not go into the other, find the smallest number they both multiply into. For example,
\frac{1}{3 }  +  \frac{1}{4}
Here, the smallest number that both 4 and 3 multiply into is 12. Multiply both fractions by the correct amount to make both denominators 12. It would then become
\frac{4}{12}  +  \frac{3}{12}  =  \frac{7}{12}
Subtraction: follow the same rules as addition, except subtract the numerators instead of adding them.

Multiplication: multiply both numerators and both denominators.
\frac{2}{3}  \times  \frac{4}{5}  =  \frac{8}{15}
Division: Flip one of the fractions and multiply.
\frac{2}{3}   \div   \frac{4}{5}
Becomes
\frac{2}{3}  \times  \frac{5}{4}  =  \frac{10}{12}  =  \frac{5}{6}
Hope this explains it all. Let me know if you have any questions :)
4 0
3 years ago
A store buys 12 sweaters for $96 and sells them for $264. How much profit does the store make per sweater?​
Nata [24]

Answer:

14$ per sweater

Step-by-step explanation:

264 - 96 = 168

168 / 12 = 14

6 0
3 years ago
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