Your literature class will read 4 novels this year, chosen by class vote from a list of 7 possible books offered by the teacher.a) How many different ways could the course unfold, given that it probably matters what order you read the books in?
b) How many different choices of books could the class make?
a) The number of different ways the course could unfold is
Answers
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
Final answer:
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.
Explanation:
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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Answers
The three consecutive integers that add up to 450 are 149, 150, and 151.
What are the consecutive numbers?
The consecutive numbers are those numbers that follow each other continuously in the order from smallest to largest numbers.
Given that the sum of three consecutive even numbers is 450
We need to find the 3rd number of the integers.
Now assume the 3 consecutive integers are x, (x+1) and (x+2)
Therefore, x+(x+1)+(x+2)= 450
Combine the like terms;
3x+3= 450
X=149
Thus the second number is 149 + 1 and the third number is 149 + 2.
Hence, the 3rd number of the integers would be 151.
Learn more about the consecutive whole numbers;
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Step-by-step explanation:
Which means that the first number is 149, the second number is 149 + 1 and the third number is 149 + 2. Therefore, three consecutive integers that add up to 450 are 149, 150, and 151. We know our answer is correct because 149 + 150 + 151 equals 450 as displayed above.
PLEASEMARKMEASBRAINLIESTANSWER
HOPEITHELPSYOU
b. 4x+3
c. x-5
d. x+3
Answers
4x^4 -21x^3 -46x^2 + 219x+180
Factor
= (x+3)(4x+3)(x-4 )(x-5)
Answer : A .
x+4 is not a factor of 4x^4-21x^3-46x^2+219x+180
following system of equations.
-3x + 2y = 5 AND x = 2y - 3
Answers
Step-by-step explanation:
everything can be found in the picture
Answers
C = πd
C = π × 2
C = 6.28318530718
C = 6 feet
If 1km is 3280 feet, 2km is 6560 feet
6560 ÷ 6 = 1093.33333333 (recurring)
= 1093
Therefore the bike wheels rolls (approximately) 1093 times to cover 2km.