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4 years ago

How many ways can we pick three distinct integers from {1, 2, ..., 15} such that their sum is divisible by 3?

Mathematics

1 answer:

gogolik [260]4 years ago

5 0

Answer:

Clearly from 1 to 15 we can only have the sum 6,9,12 and 15 to be divisible by 3.

Now meaning we have 4! ( 4 factorial) which implies 4x3x2x1= 24 .

We have 24 ways to pick distinct integers that are divisible by 3.

Step-by-step explanation:

The first thing you need to do is to look for numbers that are divisible by 3. Then you take its factorial

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5+x=12
Subtract 5 from both sides
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What is 3/8 inch converted to a decimal.

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A river has a normal depth of 10 feet. After a rain storm, the river is rising a 1.5 feet per hour. What is the river's depth af

Nadusha1986 [10]

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3 years ago

The radius of the large sphere is double the radius of the small sphere. How many times does the volume of the large sphere than

pshichka [43]

Answer:

8 times larger.

Step-by-step explanation:

The radius of the large sphere is double the radius of the small sphere.

Question asked:

How many times does the volume of the large sphere than the small sphere

Solution:

Let radius of the small sphere =  $x$ 

As the radius of the large sphere is double the radius of the small sphere:

Then, radius of the large sphere = $2x$

To find that how many times is the volume of the large sphere than the small sphere, we will divide the volume of large sphere by volume of small sphere:-

For smaller sphere: $Radius = x$

$Volume \ of \ sphere = \frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi x^{3}$

For larger sphere: $Radius = 2x$

$Volume \ of \ sphere = \frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi (2x)^{3}$

Now, we will divide volume of the larger by the smaller one:

$=\frac{4}{3} \pi (2x)^{3}\div\frac{4}{3} \times\frac{\pi }{1 } \times x^{3}\\ \\ =\frac{4}{3} \pi\times8x^{3} \times\frac{3}{4\pi }\ \times\frac{1}{x^{3} }$

$\frac{4}{3}\pi\ is \ canceled\ by\ \frac{3}{4\pi } \ and\ also\ x^{3} is\ canceled\ by \ \frac{1}{x^{3} }$

Now, we have

= $\frac{8}{1}$

Therefore, the volume of the large sphere is 8 times larger than the smaller sphere.

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4 years ago

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If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2f(1) + 3g(4). 1. 45 2. 43 3. 42

nordsb [41]

f(x) = x^2 + 1
f(1) = 1^2 + 1 = 2
so 2f(1) = 2(2) = 4

g(x) = 3x + 1
f(4) = 3(4) + 1 = 13
3g(4) = 3(13) = 39

 2f(1) + 3g(4) = 4 + 39 = 43

answer
2. 43

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4 years ago