find the remainder when 1!+2!+3!...100! Is divided by 15

Answers

Answer 1

Answer: 33

======================================================

Explanation:

The exclamation mark means factorial.

Factorial's are operations in which we start with the given number, then count our way down to 1, multiplying along the way.

Examples:

7! = 7*6*5*4*3*2*14! = 4*3*2*1

The original number must be a positive whole number (side note: other inputs are possible but we have to involve more complicated math which I'll ignore for this solution).

Let's expand out the first few terms. I'll leave them in factored form and not multiply out the values

1! = 1

2! = 2*1

3! = 3*2*1

4! = 4*3*2*1

5! = 5*4*3*2*1 ... note the 3 and 5 in bold

6! = 6*5*4*3*2*1

7! = 7*6*5*4*3*2*1

This keeps going until we reach 100!

As you can see in the factors above, we have 3 and 5 show up as soon as we reach 5! which means we'll have 3*5 = 15 as a factor of the following items: {5!, 6!, 7!, 8!, ..., 99!, 100!}

Each higher factorial just builds in the last factorial so to speak.

So what this means is that we can write this

15q = 5!+6!+7!+...+99!+100!

where q is some integer. We don't need to worry about what q is

--------------

Therefore,

1!+2!+3!+4!+5!+6!+7!+...+99!+100!

1!+2!+3!+4!+( 5!+6!+7!+...+99!+100! )

1!+2!+3!+4! + 15q

1+2+6+24 + 15q

33+15q

15q+33

--------------

Recall that if we divide integers x and y, then

x/y = q remainder r

x/y = q + r/y

x = yq+r

Where q and r are the quotient and remainder.

Since 1!+2!+3!...100! = 15q+33, we're in the form yq+r showing that r = 33 is the remainder.


Related Questions

Write the equivalent fraction with a denominator of 100.
9/10 = ?/100.

Answers

Answer:

90

Step-by-step explanation:

Find common denominators. Note that what you multiply to the denominator (bottom number of the fraction), you must also multiply to the numerator (top number of the fraction).

In this case, you are multiply 10 to both the numerator and denominator, as:

100/10 =10

Multiply 10 to the numerator:

? = 9 * 10

? = 90

90 is your answer.

~

Since the fractions are equivalent to each other, they must have the same simplified value. It means they can be multiple or divisor of each other.

Here, we have to find the numerator of the second fraction for which we have to multiply with the same number with which we multiplied the denominator.

➝ 10 × 10 = 100

The denominator was multiplied with 10, So the numerator will be multiplied with 10 too.

➝ 9 × 10 = 90

➝ [tex] \dfrac{9 \times 10}{10 \times 10} = \dfrac{90}{100} [/tex]

Thus, the required numerator is 90

Carry On Learning !

mr peters drives 266 miles in 3.5 hours what is the rate mr peters travels

Answers

Answer:

The answer is 76

Step-by-step explanation:

I just divided 266 by 3.5  - *I used a calculator*

Anyone, can help me with this question?

25)

Answers

9514 1404 393

Answer:

  A)  Positive (4, 2, 0), negative (0)

Step-by-step explanation:

Descartes' rule of signs tells you the number of positive real roots is equal to the number of sign changes in the coefficients (with allowance for an even number of roots possibly being complex).

The signs of the coefficients are ...

  - + - + -

so there are 4 sign changes. The number of positive real roots will be 4, 2, or 0.

__

Changing the signs of odd-degree terms, you can use the same method to determine the number of negative real roots. With those signs changed, the signs of the coefficients are ...

  - - - - -

so there are 0 sign changes. The number of negative real roots is 0.

_____

The graph shows there are no real roots of either sign. All the roots are complex.

What is the slope of the linear equation Y-5=3/7(x+2)

Answers

Answer:

[tex]y=\frac{3}{7} x+\frac{41}{7}[/tex]

Slope is 3/7

Step-by-step explanation:

y-5+5=3/7x+6/7+5

y=3/7x+41/7

Which numbers have been rounded correctly to the nearest ten thousand? Choose a the correct answers.
A. 13,500 ➡️ 10,000
B. 78, 210 ➡️ 78,000
C. 620,499 ➡️ 600,000
D. 456,234 ➡️ 460,000
E. 129,302 ➡️ 129,000
F. 324,985 ➡️ 320,000

Answers

D is the answer ten thousands is 5 digits over

|4x-1|=2x+13
what does x equal

Answers

The variable x equals x=7

Answer:

2x+13=4x-1

2x=14

x=7

another solution

2x+13=-(4x-1)

2x+13 =-4x+1

6x=-12

x =-2

so solutions are 7,-2

Find the interest on the following loan.
$5350 at 9%; loan made on August 15 and due December 18
The simple interest for this loan is $
(Round to the nearest cent as needed.)

Answers

Answer     for 2020:  loan maturity in days 125

                                   Actual Interest is $164.90

Step-by-step explanation:

loan x Interest x Time (in days =Total interest

the simple interest on the loan is approximately $161.28.

To calculate the interest on the loan, we need to determine the time period in years and multiply it by the principal amount and the interest rate.

The loan period runs from August 15 to December 18, which is a total of 4 months. To convert this into years, we divide 4 by 12 (since there are 12 months in a year), resulting in 1/3 or approximately 0.3333 years.

The principal amount is $5350, and the interest rate is 9% or 0.09 as a decimal.

Using the formula for simple interest: Interest = Principal x Rate x Time

Interest = $5350 x 0.09 x 0.3333 ≈ $161.28

Therefore, the simple interest on the loan is approximately $161.28.

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Please help me out fast.

Answers

your answer 17 is correct

Find the value of x
X + 90
100°

Answers

10 is the answer sorry don’t know how to explain jus trust me

Convert 4 to a percent.

Answers

Well, 100% = 1, 400% = 4.

Step-by-step explanation:

0.04 is ur answer ..........

What is 22.5 subtract by 2.5

Answers

Answer:

The answer is 20 hope this helps

Step-by-step explanation:

22.5 divided by 2.5 = 20

Susie filled up at the gas station where it costs $3.14 per gallon. She put 22.5 gallons of gas in her vehicle. She also bought a fountain drink for $0.99. How much did she spend at the gas station?
A. $66.00
B. $70.65
C. $71.64
D. $141.30

Answers

the answer is 71.64

you multiply the price per gallon times the total amount of gallons put in her car then add the fountain drink

Where’s my smart friends??

I had $3.00.
My Mom gave me $10.00.
My Dad Gave me $30.00.
My Aunt & Uncle gave me $100.00.
I had another $7.00.
How much did I have?

Answers

Answer:

$10 Its asking how much you had not how much was given to you. So the answer is you had 10

I have $150

In order to determine the amount you have, add the amounts you are given to the original amount. This is because the money you have increases by the amounts you are given

Total sum of money = amount you have + amount given by mum +  amount given by dad +  amount given by uncle and aunt

$3 + $10 + $30 + $100 + $7 = $150

A similar question was solved here: https://brainly.com/question/24101822?referrer=searchResults

Help please !! I need to find x

Answers

Answer:

6

Step-by-step explanation:

12x + 3 = 11x + 9 because these two angles are corresponding angles

12x - 11x = 9 - 3

x = 6

1. Five more than twice a number is 7.

Answers

Answer:

5+2n=7

Step-by-step explanation:

5+2n=7

7-5=2n

2=2n

2÷2=1

n=1

Let’s say the number is “n”

First it’s telling u twice a number meaning the number is going to multiply by 2 so

2 X n (X means multiplication) or 2n

Then it states five more than which means to add 5 to what follows so

2n + 5

It’s saying it’s 7 so

2n+5=7
2n= 7-5
2n=2
2n/2=2/2
N=1

The final answer is 1 meaning the number is 1

What is 7 7//8 + 2 1/4=

Answers

Answer:

14.875

Step-by-step explanation:

77/8 = 9.625 and 21/4 = 5.25

So, 9.625+5.25 =14.875

Answer: 10  1/8

............................

the cost of old boiler is £775 per year,the new one is £1850 ,the cost of using a new boiler will be 1/5 less than the cost of using the opd boiler. how many years will it take for the savings feom cost of using nthe new boiler to total £1850​

Answers

Answer:

I think its 12.3 years

Step-by-step explanation:

a fifth of 775 is 155 and 155 x 12.3 = 1850

How man ten thousand are in 440000

Answers

44 ten thousands because 44x10000= 440000

Fill in the blanks from the attachment.

Answers

Answer: why was 8 scard of 7

Step-by-step explanation: becues

789

What is the zero of the function that is graphed below?

Answers

Answer:

a which is -2

Step-by-step explanation:

that's the answer

Multiply.

3⋅3/5

Enter your answer as an improper fraction, in simplified form, by filling in the boxes.

Answers

Answer:

9/5

Step-by-step explanation:

3/1 x 3/5 = 9/5

:HOPE  THIS HELPS

Simplify the expression.

Exact Form:

9

_                   9 over 5

5

Decimal Form:

1.8

Mixed Number Form:

1  4/5

Describe the relationship between integers and rational numbers.

Answers

Answer:

Integers are a subset of Rational Numbers because all Integers are Rational Numbers.

Step-by-step explanation:

Hope this helped mark me as brainliest (:

Answer: Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers

Step-by-step explanation:

Write the following using algebraic notation, using the letter x for any
unknown numbers:
I think of a number, add seven, then divide by five.

Answers

Answer:

(x+7)÷5

Step-by-step explanation:

since the number is unknown, it becomes X. Because we first add 7 then divide by 5, the expression will be a bracketed (X+7), followed by the division by 5. This makes sense because of the BODMAS rule to which, in coherence with the BODMAS rule, we first solve the expression in the brackets then move on outside them.

write the first 4 terms of the arithmetic sequence With first term 37 and common difference 9

Answers

Answers:

first term = 37

second term = 46

third term = 55

fourth term = 64

==========================================

Explanation:

Start at 37. Add 9 to this term to get the second term. Add 9 to that result to get the next term, and so on.

first term = 37

second term = 37+9 = 46

third term = 46+9 = 55

fourth term = 55+9 = 64

-----------

The nth term formula is

a(n) = 9n+28

It can be found by plugging a = 37 and d = 9 into the general form

a(n) = a + d*(n-1)

The  four terms of the arithmetic sequence with a first term of 37 and a common difference of 9 are: 37, 46, 55, and 64.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant.

Given:

First term (a1) = 37

Common difference (d) = 9

The arithmetic sequence can be represented as follows:

[tex]a_1[/tex]= 37

[tex]a_2[/tex] = [tex]a_1[/tex] + d

    = 37 + 9 = 46

[tex]a_3[/tex] = [tex]a_2[/tex] + d

   = 46 + 9 = 55

[tex]a_4[/tex] = [tex]a_3[/tex]+ d

   = 55 + 9 = 64

So, the first four terms of the arithmetic sequence are: 37, 46, 55, and 64.

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HELP ASAP 15 POINTS

Look i know this isnt mathematics but its an easy 15 points if your good a rhyming or if you just know the basics.

I need a rap or song about the six main nutrients (water, protein, carbohydrates, fats, minerals, and vitamins)

Answers

Answer:

I hope this helps

Step-by-step explanation:

carbonhydrates protein water fats minerals and vitamins

Quadratic formula
x2 + 3x - 5 = 0

Answers

Answer:

2x +3x- 5= 0

5x-5=0

5x=0+5

5x=5

x=5÷5

x=1

Help please you will get 20 points

Answers

Answer:

Part B:

His measure is incorrect because the interior angles of every triangle result up to 180°. His measures (50+90+38) added up to 178; so his measures are false.

Joshua quick made a deposit to his checking and recieved $50 in cash. His deposit slip shows a total deposit of $90. If Joshua deposited checks worth six times the value of the coins he deposited, how much did he deposit in (a) coins and (b) checks?

Answers

Joshua deposited

(a). $12.85 in coins

(b). $77.14 in checks

Linear equation in one variable?

The linear equation in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

Joshua deposited checks worth six times the value of the coins he deposited.

Let Joshua deposit the value of coins be x. Then the value of x will be 6x

There is total deposit of $90.

⇒ x + 6x = 90

⇒ 7x = 90

⇒ [tex]x = \frac{90}{7}[/tex] =$12.85

Therefore,

[tex]6x = \frac{90(6)}{7} =\frac{540}{7}[/tex] = $77.14

Hence, he deposit total $12.85 in coins and $77.14 in checks.

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What is the value of y?
7-120
56"

Answers

7-2030 x g x 65 -=65 65 65 65

find the value of x

Answers

Answer:

[tex] \frac{28}{3x - 1} = \frac{24}{x + 7 } \\ 24(3x - 1) = 28(x + 7) \\ 72x - 24 = 28x + 196 \\ 72x - 28x = 24 + 196 \\ 44x = 220 \\ x = 5[/tex]

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