All categories

3 years ago

If the sum of $1! + 2! + 3! + \cdots + 49! + 50!$ is divided by $15$, what is the remainder?

Mathematics

1 answer:

kompoz [17]3 years ago

3 0

Answer:

Step-by-step explanation:

All factorials 5 and above are evenly divisible by 15, so have no remainder. Thus, you are interested in ...

mod(1! +2! +3! +4!, 15) = mod(1 +2 +6 +24, 15)

= mod(33, 15) = 3

The remainder is 3.

You might be interested in

Solve for the indicated variable in the literal equation

ANTONII [103]

Answer:

$x = \frac{y}{3} - \frac{5}{3}$

Step-by-step explanation:

Given

$y = 5 + 3x$

Required

Solve for x

Subtract 5 from both sides

$y-5 = 5 -5+ 3x$

$y-5 = 3x$

Divide through by 3

$\frac{y}{3} - \frac{5}{3} = x$

$x = \frac{y}{3} - \frac{5}{3}$

8 0

3 years ago

LaTonda rolls two number cubes that are each numbered 1 through 6. What is the probability that the sum of the numbers on the to

ZanzabumX [31]

Answer:

1/4

Step-by-step explanation:

The maximum sum of the two cubes is 6 + 6 = 12

The multiples of 4 until 12 are: 4, 8 and 12.

each cube has 6 possible values, so two cubes have a total of 6 * 6 = 36 possible results

We can have a sum of 4 with the pairs (1,3), (2,2), (3,1).

We can have a sum of 8 with the pairs (2,6), (3,5), (4,4), (5,3), (6,2)

We can have a sum of 12 with the pair (6,6)

So we have a total of 9 pairs that satisfy our condition over a total of 36 possibilities, so the probability is 9 / 36 = 1/4

8 0

3 years ago

I will mark brainiest is my answer is correct?

Kruka [31]

Yes you have the correct one good job.

8 0

3 years ago

Determine if each scenario would produce more than one triangle, no triangle, or a unique triangle. Explain your reasoning for e

weqwewe [10]

Answer:

1. Right angle triangle, 2. One triangle, 3. No triangle

Step-by-step explanation:

1. Has a 90-degree angle which makes it a right-angle triangle.

2. 30 + 60 + 90 = 180 degrees. Hence it satisfies the angle sum property so it is a triangle, a right-angle triangle.

3. It does not form a triangle as it does not satisfy the triangle inequality property, which is the sum of the two smaller sides should be greater than the larger side. 2 + 4 = 6, which is smaller than 7.

7 0

2 years ago

Round answers to the place value shown.

Vinvika [58]

1. 30
2. 40
3. 70
4. 200
5. 220
6. 300
7. 8,100

8. 120
9.650
10. 2,200
11.6,000

12. 7,000
13. 1,560,000
14.1,000

8 0

3 years ago