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brilliants [131]
3 years ago
9

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She wil

l list the books in the order in which they are chosen. How many different lists are possible?A. 6B. 40C. 210D. 5,040E. 151,200
Mathematics
1 answer:
EastWind [94]3 years ago
8 0

Answer: D. 5040

Step-by-step explanation:

Given : The total number of books = 10

The number of books required by Clarissa = 4

Now , when we select r things from n things and order in which they are chosen matters then we use permutations to calculate the number of  different lists are formed to choose them.

The number of permutations of n things taking r at a time is given by :-

^nP_r=\dfrac{n!}{(n-r)!}

For r= 4  and n= 10 , we have

^{10}P_{4}=\dfrac{10!}{(10-4)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!}=10\times9\times8\times7=5040

Hence, the number of different lists are possible = 5040

Therefore , the correct answer = D. 5040

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Answer:

45 km/h

Step-by-step explanation:

In the first part of the trip, he already covered 30 km so we can subtract that from the total distance

45 - 30 = 15

This means he has 15 km to go

He also took an hour, or 60 minutes, to get to school. We subtract the time spent of the first part and time spent talking to a friend from the 60 minutes

60 - 35 = 25

25 - 5 = 20

He took 20 minutes to cover the second part of the journey

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15/20 = 0.75

He covered 0.75 km per MINUTE

to find it in km/h, we just multiply the number by 60

0.75 x 60 = 45

6 0
3 years ago
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vredina [299]
12/60 students chose science fiction

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x = 30

30/150 students are assumed to prefer sf

30/150 = x/100

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20/100 students are likely to prefer sf

Mr. Rodriguez made a reasonable estimate for the approximate percentage of students that prefer science fiction, because if 12/60 is equivalent to 30/150 which refers to the number of students who can be assumed to prefer science Fiction out of the whole school. Considering we need to identify what 30/150 as a percentage is, we can reduce it down to 1/5 to make I easier, then divide 1 by 5 to get .2
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Step-by-step explanation:

From the given figure,

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RT ≅ RT [Reflexive property]

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