The result of 155 divided by 5 is 31.
To calculate 155 divided by 5, we can perform long division to find the quotient.
Step 1: Set up the long division:
31
___________
5 | 155
Step 2: Determine how many times 5 can go into the first digit of 155 (which is 1). It goes 0 times, so we write 0 above the division bar.
31
___________
5 | 155
0
Step 3: Bring down the next digit (5) and place it next to the 0. Now we have 15.
31
___________
5 | 155
0
15
Step 4: Determine how many times 5 can go into 15. It goes 3 times (5 x 3 = 15). Write 3 above the division bar.
31
___________
5 | 155
0
-15
15
Step 5: Subtract 15 from 15 to get 0. Bring down the next digit (5).
31
___________
5 | 155
0
-15
15
-15
Step 6: Determine how many times 5 can go into 0. It goes 0 times, so we write 0 above the division bar.
31
__________
5 | 155
0
-15
15
-15
0
Step 7: Since there are no more digits to bring down and no remainder left, the division is complete. The quotient is 31.
Therefore, 155 divided by 5 equals 31.
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It would take 11.7 seconds for the sheepdog to catch up with the collie.
To determine the number of seconds after which the sheepdog would catch up with the collie, knowing that the distance of the relay race is 51 feet, and the collie starts the course 0.3 second before the sheepdog, and the collie is running 23.4 feet per second, while the sheepdog is running 24 feet per second, the following calculation must be performed:
Therefore, it would take 11.7 seconds for the sheepdog to catch up with the collie.
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b) How many different choices of books could the class make?
a) The number of different ways the course could unfold is
Answer:
a) 840 different ways
b) 35 different choices of books
Step-by-step explanation:
We know that our literature class will read a total of 4 novels this year.
All novels chosen by class vote from a list of 7 possible books offered by the teacher.
Wherever we have an experiment which is formed by sub - experiments that can occurred in
ways, the total number of ways in which the whole experiment
can be developed is :
x
x ... x
Then, for a) if it matters what order we read the books in, the total number of different ways could the course unfold is :
(I)
Because for the first book there are 7 different choices. Now, given that we choose the first book, we only have 6 different choices for the second one.
Continuing with the idea, we deduce the equation (I).
For item b) :
Wherever we have different objects and we want to find the ways that we can choose
objects from that group, we need to use the combinatorial number.
We define the combinatorial number as :
Then, if we apply this to the problem, the total different choices of books if we want 4 novels voting from a total of 7 possible books is :
a) 840 different ways
b) 35 different choices of books
The number of different ways the course could unfold is 210, and the number of different choices of books the class could make is 35.
The number of different ways the course could unfold is equal to the number of permutations of the 4 books chosen from the list of 7. This can be calculated using the formula for permutations: P(n, r) = n! / (n - r)!. In this case, n = 7 (the number of books) and r = 4 (the number of books chosen). Using the formula, we get P(7, 4) = 7! / (7 - 4)! = 7! / 3! = 7 imes 6 imes 5 = 210.
The number of different choices of books the class could make is equal to the number of combinations of the 4 books chosen from the list of 7. This can be calculated using the formula for combinations: C(n, r) = n! / (r! (n - r)!). In this case, n = 7 (the number of books) and r = 4 (the number of books chosen). Using the formula, we get C(7, 4) = 7! / (4! (7 - 4)!) = 7! / (4! imes 3!) = (7 imes 6 imes 5) / (4 imes 3 imes 2) = 35.
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