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2 years ago

A whole number from 1 to 15 inclusive is picked at random.

Mathematics

1 answer:

Helen [10]2 years ago

8 0

Answer:

a) 3/7

b) 3/5

Explanation:

The figure attached shows the Venn diagram for the given sets.

a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?

From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.

There are a total of 7 multiples of 24, from 1 to 15.

Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:

b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?

The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.

The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.

Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:

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Answer:

Step-by-step explanation:

Alright, lets gets started.

First day, she saves nickels = 2

As we know, she doubles the number of nickels she saves each day.

Means second day she saves nickels = $2*2 = 4$

Third day she saves nickels = $2*4 = 8$

Fourth day she saves nickels = $2*8=16$

Hence we have $2 + 4 + 8 + 16...$

It is like a geometric series, the sum of nickels she needs more than 500.

So, lets see how many days she will take to save 500 nickels first

Using the sum formula for geometric series

$s=\frac{a(1-r^n)}{(1-r)}$

where s is sum, r is multiplication factor, that is 2 in this case and a is first term of series that is 2 also

$500=\frac{2(1-2^n)}{(1-2)}$

Simplifying, dividing 2 in both sides

$250=\frac{(1-2^n)}{(1-2)}$

$250=\frac{(1-2^n)}{-1}$

Cross multiplying

$-250=1-2^n$

$2^n-1=250$

$2^n=251$

Taking log on both sides

$nlog2=log251$

$n=\frac{log251}{log2}=7.971$

It means it will take 8 days to save mmore than 500 nickels. : Answer

Hope it will help :)

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2 years ago