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|a|.|b| = | 21 - 20i | = sqrt(21^2 + 20^2) = sqrt(441 + 400) =sqrt(841).

|b| = 29 = sqrt(841), so |a| = 1.

no, it was supposed to be ≤ 

"Given ab=21-20i  and |b|=29 , find |a|"

Let     \(a=u+iv\text{ , }b=x+iy\)

Then   \(ab=ux-vy+i(vx+uy)\)

so     \(ux-vy=21\\vx+uy=-20\)

Solve these equations to find u and v in terms of x and y.

Then, make use of    \(|b|=\sqrt{x^2+y^2}=29\\\)   to find \(|a|=\sqrt{u^2+v^2}\)

(You should find |a| = 1).

Solve the following system:
{3 + 10 d + 5 n = 168 | (equation 1)
5 + 10 d + 5 (n - 1) + p = 168 | (equation 2)
d + n + p = 24 | (equation 3)

Express the system in standard form:
{5 n + 10 d+0 p = 165 | (equation 1)
5 n + 10 d + p = 168 | (equation 2)
n + d + p = 24 | (equation 3)

Subtract equation 1 from equation 2:
{5 n + 10 d+0 p = 165 | (equation 1)
0 n+0 d+p = 3 | (equation 2)
n + d + p = 24 | (equation 3)

Divide equation 1 by 5:
{n + 2 d+0 p = 33 | (equation 1)
0 n+0 d+p = 3 | (equation 2)
n + d + p = 24 | (equation 3)

Subtract equation 1 from equation 3:
{n + 2 d+0 p = 33 | (equation 1)
0 n+0 d+p = 3 | (equation 2)
0 n - d + p = -9 | (equation 3)

Swap equation 2 with equation 3:
{n + 2 d+0 p = 33 | (equation 1)
0 n - d + p = -9 | (equation 2)
0 n+0 d+p = 3 | (equation 3)

Subtract equation 3 from equation 2:
{n + 2 d+0 p = 33 | (equation 1)
0 n - d+0 p = -12 | (equation 2)
0 n+0 d+p = 3 | (equation 3)

Multiply equation 2 by -1:
{n + 2 d+0 p = 33 | (equation 1)
0 n+d+0 p = 12 | (equation 2)
0 n+0 d+p = 3 | (equation 3)

Subtract 2 × (equation 2) from equation 1:
{n+0 d+0 p = 9 | (equation 1)
0 n+d+0 p = 12 | (equation 2)
0 n+0 d+p = 3 | (equation 3)

n = 9 Nickels
d = 12 Dimes
p = 3 Pennies

I feel Post views are decreasing, hopefully, it doesn't end the site, and make it unactive.

There are 7 nCr 2 = 21 outcomes for the 7 numbers in the set and they are as follows:

(8, 20, 24, 30, 40, 100, 40, 48, 60, 80, 200, 120, 150, 200, 500, 180, 240, 600, 300, 750, 1000) = 21

There are 7 multiples of 100 (including 100 itself). Therefore, the probability would be:

7 / 21 = 1/3

Wow! What a beautiful solution!! 

4 votes out of 13 would yield 30.76 % which rounds to 31%

13

Question was edited....

y<= 3    DOES include 3    it says y is less than or EQUAL to 3

PLease do not change your questions after an answer has been posted..... if you need to change it, re-post ...or make note of the changes....

check again

B: false.

The equation you will need is

FV = PV (1+i)ⁿ

^{FV = future value   (83200)}

^{PV = present (or starting value)}

^{i = periodic interest in decimal form . The periods are 1 month    18% / 12months = 1.5% per period  =  .015} 

^{n = mumber of periods (months) <===== this is what you are looking for in the Q}

^{Try it to see what YOU can compute.....}

First one says LESS than  -5     numbers LESS than -5   include   -6   -7  -8  -9  etc......so  what do yo think about +4?

Second one says GREATER than -2    numbers greater than -2 include -1  0  + 1  +2   etc.....what do YOU think about -3 in this case?

Yeah, it's right. Thanks!

False

  it does not say = to three, it only says LESS THAN three

I've thought of yet another way, or, rather, another four ways.  Start with a string of eight rooks in a diagonal direction.  Then take one half of it and rotate that line of four rooks 90^o.  Do this at each of the four corners, for an additional four solutions.  Now it's up to EIGHT ways. After all this, I wouldn't be suprised if there are even more ways to position the rooks, but I'm going to stop thinking about it. 

.

ok

Here is how I would present the answer.

\(y=4^{2012}\\ log_{10} \;y=log_{10} \;4^{2012}\\ log_2 \;y=2012\;log_2 \;4\\ log_2 \;y=2012*2\\ log_2 \;y=4024\\ \frac{log_{10}\;y}{log_{10}\;2}=4024\\ log_{10}\;y=4024*log_{10}2\\ log_{10}\;y\approx 1211.344703\\ y\approx 10^{1211.344703}\\ y\approx 10^{0.344703}*10^{1211}\\ y\approx 2.211581763*10^{1211}\\ \)

I didn't answer your question properly! You CAN use any ordinary calculator and calculate ANY very large number by using the "Log Key base 10". Example: 25^1E12. You simply take the exponent, or 1E12 and multiplied it by Log 25 base 10. You should get:1,397,940,008,672.037609572522210551. Then you would raise the fractional part to the power of 10 thus. 10^0.037609572522210551 =1.0904595806948112697717659697915 x 10^1,397,940,008,672.

Yes I know there are calculators online that can do it.

I do not think that this is how guest was expected to answer this question.

I asked you if you knew how to do it with a standard old fashioned calculator. (or with the web2.0 calc if you want)

With Windows 10 comes an HP calculator that can calculate up to 10^10,000 and it has a "mod" key on it as well.