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BARSIC [14]
3 years ago
14

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]3 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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s2008m [1.1K]

Answer:

A

Step-by-step explanation:

I believe it is A If I remember correctly

8 0
3 years ago
For the inverse variation equation xy=k what is the constant of variation k when x=-3 And y=-2
ELEN [110]

ANSWER

The constant of variation is 6.

EXPLANATION

The inverse variation equation is:

xy = k

We want to find the constant of variation, when x=-3 and y=-2.

We substitute the values for x and y to get,

- 3 \times  - 2 = k

Multiply out the left hand keeping in mind that negative times negative yields a positive result.

This implies that;

k= 6

Hence the constant of variation is 6.

8 0
2 years ago
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viktelen [127]
Not a function because input has two outputs. 9 goes to two different numbers which make it not a function
4 0
3 years ago
The excursion boat on the river takes 2½ hours to make the trip to a point 12 miles upstream and to return. If the rate at which
Orlov [11]

Answer:

2 mph

Step-by-step explanation:

time = distance / speed

Let c represent the rate of the current. Then the upstream rate of the boat relative to the shore is (5c -c) = 4c, and the <em>upstream time</em> is ...

... 12/(4c) = 3/c.

Likewise, the downstream rate is (5c +c) = 6c, and the <em>downstream time</em> is ...

... 12/(6c) = 2/c.

The <em>total time</em> is the sum of upstream and downstream times:

... 3/c +2/c = 2.5

... 5/c = 2.5 . . . . . . combine terms

... 5/2.5 = c = 2 . . . multiply by c/2.5

6 0
3 years ago
plz help me The temperature at noon was 22°. From 6 AM until noon, the temperature changed by an average of 5° per hour. What WA
nevsk [136]

Answer:

-8° OR 52°

Step-by-step explanation:

Remember 22.

Now, you'll need to take 12 PM and see how many hours it is from 6 AM to 12 PM noon: 6-7, 7-8, 8-9, 9-10, 10-11, 11-12. We have 6 hours from 6 AM to 12 PM.

The problem gives us the average number of degrees it changed: 5. Since it doesn't specify HOW it changed, there are 2 answers.

In order to find the number of degrees it changed, we have to take the hours times the amount given, or in this case, 6 x 5 which equals 30.

Now that we know the fluxation number, we can either add or subtract 30 from the degrees given at noon.

So, 22 - 30 = <em>-8</em> AND 22 + 30 = <em>50</em>.

I hope that helps! :)

4 0
2 years ago
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