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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.

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The blue are the two boards that you need to use.
ad-work [718]

Answer:

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Step-by-step explanation:

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3 years ago
Write a quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, −17).
Brilliant_brown [7]

Answer:

x^4 +y+1

Step-by-step explanation:

6 0
3 years ago
The denominator of a rational number is greater than its numerator by 5. If 5 is subtracted from the numerator and 4 is added to
nasty-shy [4]

Answer:

7/12.

Step-by-step explanation:

=x/x+5.

x-5/x+5+4=⅛

x-5/x+9=⅛

x-5=⅛(x+9)

x-5=⅛x+1⅛

x-⅛x=1⅛+5

⅞x=49/8

7x=49

x=7

thus the initial fraction is x/x+5= <u>7</u><u>/</u><u>1</u><u>2</u>

A rational number is a fraction

4 0
3 years ago
Solve for x.<br><br> 6x2−2=13
makkiz [27]

Answer:

x = ±sqrt(5/2)

Step-by-step explanation:

6x^2−2=13

Add 2 to each side

6x^2−2+2=13+2

6x^2 = 15

Divide each side by 6

6/6x^2 = 15/6

x^2 = 5/2

Take the square root of each side

sqrt(x^2) = ±sqrt(5/2)

x = ±sqrt(5/2)

5 0
2 years ago
Read 2 more answers
Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00
Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

A = P(1 + \frac{r}{n})^{nt}

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88

So, <em>the principal must be = $8991.88</em>

4 0
2 years ago
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