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3 years ago

5

Lia dropped a coin from a certain height above the ground. She measured and represented its displacements x1, x2, and x3 in the

first, second, and third seconds of its fall. What is the ratio of x1, x2, and x3?
1:1:1
1:2:3
1:3:5
1:4:9

1 answer:

My name is Ann [436]3 years ago

3 0

Answer:

D

Step-by-step explanation:

S is directly proportional to t^2. So the ratio is 1^2:2^2:3^2

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Answer: The required number of ways is 46200.

Step-by-step explanation: Given that a catering service offers 8 appetizers, 11 main courses, and 7 desserts.

A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts.

We are to find the number of ways in which this can be done.

We know that

From n different things, we can choose r things at a time in $^nC_r$ ways.

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the number of ways in which 7 appetizers can be chosen from 8 appetizers is

$n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,$

the number of ways in which 8 main courses can be chosen from 11 main courses is

$n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165$

and the number of ways in which 4 desserts can be chosen from 7 desserts is

$n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.$

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$n=n_1\times n_2\times n_3=8\times165\times35=46200.$

Thus, the required number of ways is 46200.

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