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)!}](https://tex.z-dn.net/?f=%5EnP_r%3D%5Cdfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
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](https://tex.z-dn.net/?f=%5E%7B10%7DP_%7B4%7D%3D%5Cdfrac%7B10%21%7D%7B%2810-4%29%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B10%5Ctimes9%5Ctimes8%5Ctimes7%5Ctimes6%21%7D%7B6%21%7D%3D10%5Ctimes9%5Ctimes8%5Ctimes7%3D5040)
Hence, the number of different lists are possible = 5040
Therefore , the correct answer = D. 5040
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
Answer:
Step-by-step explanation:
4x − 1 = 19
solving for x, x = 5
2x − 4 = 10
x=7
2x + 2y = 48
x=24-7
y=24-x
5x + 2y = 90
x=18-2y/5
y=45-5x/2
all the situations I could find hope this helps for each equation.
Answer:
1) 144 seconds
2) 12
3) 24
Step-by-step explanation:
1) First off how many times can 15 dived into 90? 6! So we know it <em>can</em> go into 90 and that it's by 6. Next is to add 24 (seconds) 6 times. This will lead you too 144. So 144 seconds is your awnser
2) All you have to do is dived 72÷6. Which gives you the amount of each pack .
3) You take the total of step number two and 288 earsers and dived. so 288÷12=24
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Answer:
Step-by-step explanation:
look at the image