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MAXImum [283]
3 years ago
6

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:

  3

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
Express the function graphed on the axes below as a piecewise function.
adoni [48]

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

  y = -3x +15 -1 = -3x +14

The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

3 0
3 years ago
What is 1/6x=4 in solving equations with rational coefficients
Debora [2.8K]
To solve an equation with a rational (fraction) coefficient you need to multiply both sides of the equation by the reciprocal (invert the fraction - flip it).

\frac{1}{6}x =4 The reciprocal of 1/6 is 6/1 or 6
6( \frac{1}{6} x)= 6(4)  The product of reciprocals equals 1 
1x = 24
x = 24


7 0
3 years ago
PLEASE HELP!! WILL MARK BRAINLIST ​
gayaneshka [121]

Answer:

3/50 7/50 40/50

Step-by-step explanation:

Ok. I'm not exactly a math wiz but I think you may be overthinking this. Experimental probability should be the probability from the experiment right. It's in the name. In chemistry if it's a well established value it's called a theoretical value or probability. So the answer should just be the probability from the said experiment. No other funky math terms are given here which clues me to the idea that it might just be this simple.

5 0
2 years ago
Read 2 more answers
Type the correct answer in each box. Use numerals instead of words. What is the y intercept of this quadratic function f(x)=-x*2
grandymaker [24]

Answer:

Y-intercept is (0, -22)

Step-by-step explanation:

4 0
4 years ago
Read 2 more answers
Determine the equation of the line given by the graph.
Lisa [10]

Answer:

Step-by-step explanation:

a) Y= 2/3X-1

5 0
2 years ago
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