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(1! + 2! + 3! + 4! + ... + 100!)  / 36  ; What is the remainder of this division?

I found 9 via the calculator, but how can i solve this problem without being too harsh on it... :( I can't believe i just tried to calculate it on the calculator but if there's a formula or something it will really help me. :) 

Mmm,     36=1*2*3*  6

so from 6! up to 100! there will be no remainders so I am only going to look at

(1!+2!+3!+4!+5!)/36 = (1+2+6+24+120 )/36  =  153/36  =  (144+9)/36

The remainder will be 9.

Can you understand my logic?

Hi Eloise,

These questions are really awful because they can be interpreted in different ways.

Your interpretation of the first one sound ok.  Although, there is no reason to think that he does work 7 days a week.  Mind you, he is working VERY long hours.  Also 69/7=9.857.... which is closer to 9.9 then it is to your 9.8hours.

The second one is also very badly worded. We do not know if it is 1/5 before the tax is taken out of afterwards.  

 But again, your interpretation is reasonable and the maths you have done appears to be corrrect:)

The last one looks reasonable too :))

Okay, 1st off, Happy Birthday!

2ndly, 10 cakes - 6 cakes = 4 cakes

Alice has 4 cakes left.

Oh and, Chocolate cake is the best!!!!!!!! You should have chocolate cake. And save some for me! 

if base is 10 answers is x1~ -0.58 and x2~ 1.97

HELP ME 

Hi Genys,

A manufacturer produces soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 8% of the cans are defective. What is the probability that the two selected cans are defective if the quality control worker selects the two cans from a batch of 50 cans.

0.08 * 0.08 = 0.0064

Sorry CPhill, your answer was right if the guest is to find the y-intercept but he was actually requesting us to find the x-intercept.

y = (-4/5)x + 36/5 Copying CPhill's last step. That's is the equation for slope-intercept form.

Set y to 0

0 = -4x / 5 + 36 / 5

Multiply by 5,

-4x + 36 = 0

-4x = -36

x = 9

The x-intercept is 9.  Which is at the point (9 , 0)

What's the function for f(x)? We can't calculate if we don't even know what f(x) is.

Red = f(x), Blue = g(x)

Using Desmos Online Graphing Calculator.

(x-4)² > x(x+12)

x²-8x+16 > x² + 12x

-8x+16 > 12x

20x < 16

x < 0.8

:D

42 = -2(m+6)+6

42 = -2m - 12 + 6

42 = -2m - 6

-2m = 48

m = -24

Same as Guest #2's answer.

Question: 3 over 9 =?

3 over 9

= 3/9 

= 1/3

143.3336

Use the calculator on this site! :D

\(\log_4(64\times 16)\\ = \log_4\space 64 + \log_4\space 16\\ = 3 + 2\\=5\)

\(45^2+56^2\\ = 2025 + 3136\\ = 5161\)

\(72^2\\=5184\\\neq5161\)

45²+56² does not equal to 72²

\(-|a-b|+c\\ = -|-3-4|+(-5)\\ = -|-7|-5\\ = -7-5\\ =-12\)

Length of each side of base = \(+\sqrt{64}= 8\)

Using Pyth. Thm., Slant height = \(\sqrt{15^2-(\dfrac{8}{2})^2}=\sqrt{209}\)

Using Pyth. Thm. again, Height = \(\sqrt{(\sqrt{209})^2-(4)^2}=\sqrt{193}\)

Volume = \(\dfrac{1}{3}(8)^2(\sqrt{193})\)

=\(\dfrac{64\sqrt{193}}{3}\text{cm}^3\)

You can work out big numbers using this website's calculator. However if you ask, I am willing to do it for you.

17 600 000 000 ÷ 285 000 = 61 754.3859649122 807018

Or......

\(\dfrac{17600000000}{285000}\\=\dfrac{17600000}{285}\\ =\dfrac{3520000}{57}\)

\(-\dfrac{3}{2}+\dfrac{3}{-5}\)

=\(-\dfrac{15}{10}-\dfrac{6}{10}\)

=\(\dfrac{(-15-6)}{10}\)

=\(-\dfrac{21}{10}\)

pi is irrational and have infinite decimal places, also cannot be represented by a fraction. That's good you have an estimation. But I have a better one.

3.1415926535897932384626433........

\(10^{-4}\times 10^{-x}\)

= \(\dfrac{1}{10^4}\times \dfrac{1}{10^x}\)

=\(\dfrac{1}{10^4\times10^x}\)

=\(\dfrac{1}{10^{x+4}}\)

-|a-b|=-|-7|=-7

-7+(-5)=-12

M U C= 1/2 

C=3/7 

m=M U C - C = 7/14-6/14 = 1/14 

"In a given city, the probability that a given person is taller than 180 cm is 0.26
 If 18 people are chosen, what is the probability that at least 3 are taller than 180 cm?"

.

Solving Longarithmic Equations

log₇ 4 - log₇ (x-4) = log₇ 41

\(\begin{array}{|rcll|} \hline \log_7{(4)} - log_7{(x-4)} &=& log_7{(41)} \qquad | \qquad + log_7{(x-4)} \\ \log_7{(4)} &=& log_7{(41)} + log_7{(x-4)} \\ && \begin{array}{|rcll|} \hline \qquad \log(a) + \log(b) &=& \log(a\cdot b) \\ \hline \end{array} \\ \log_7{(4)} &=& log_7{(~41\cdot (x-4)~)} \\ 4 &=& 41\cdot (x-4) \\ 4 &=& 41x-4\cdot 41 \\ 41x &=& 4 + 4\cdot 41 \\ 41x &=& 4\cdot (1 + 41) \\ 41x &=& 4\cdot 42 \qquad | \qquad :41 \\ x &=& 4\cdot \frac{42}{41} \\ x &=& 4\cdot 1.02439024390 \\ \mathbf{x} &\mathbf{=} & \mathbf{4.09756097561} \\ \hline \end{array}\)