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21 + 55 = 76

\(3 \times 10^{-10}\\ = 0.0000000003\)

@Mellie

Are you taking AoPS online courses? You shouldn't cheat like this!

Real number units = 1

Imaginary number units = i = \(\sqrt{-1}\)

\(-2+-544343\\ = -2 - 544343\\ = -544345\)

Hope that helps.

\((-\dfrac{1}{3})(21)\\ =\dfrac{-21}{3}\\ =-7\)

5^1 mod 8 = 5

5^2 mod 8 = 1

5^3 mod 8 = 5

therefore 5^(2n+1) mod 8 = 5

therefore 5^137 mod 8 = 5.

Approximated to be 365.25      days/year

Subtract 5 from both sides of the equation to get:

2/3x = -12    then multiply both sides by 3/2 to get

x = -12 (3/2) = -18

5^137 =

573971 8509874450 7225035963 7315549647 3723952913 9262086011 1695169081 2584274681 2850236892 7001953125 / 8 =71746 4813734306 3403129495 4664443705 9215494114 2407760751 3961896135 1573034335 1606279611 5875244140.625

Since .625 x 8=5 Remainder.

What is the remainder when $5^{137}$ is divided by 8?

5^137 mod 8 =5 Remainder.

The formula for the standard error of estimate is:

    s_e  =  sqrt[ ( Sigma(y - y')² / (n - 2) ]

where y' is the predicted y-value.

If  f(x)  =  7x + 7  and  g(x)  =  6x²,

then  f(x) * g(x)  =  (7x + 7)(6x²)

                          =  (7x)(6x²) + (7)(6x²)

                          =  42x³ + 42x²

Since the product is 36, the possibilities are:

36, 1, 1  --->   sum = 38

18, 2, 1  --->   sum = 21

12, 3, 1   --->   sum = 16

9, 4, 1,   --->   sum = 14

9, 2, 2   --->   sum = 13

6, 6, 1   --->   sum = 13

6, 3, 2   --->   sum = 11

4, 3, 3   --->   sum = 10

Since the sum is the next door house's number, it does not give enough information only in the case that two answers have the same sum; thus, either 9, 2, 2 or 6, 6, 1.

Since there is an oldest child, the answer is 9, 2, 2.

I'm guessing that your maths is not at a very advanced stage,but here is a simple overview of imaginary numbers.

Imaginary numbers are parts of numbers which are called complex numbers.Complex numbers were developed to deal with problems where square roots of negative numbers are involved.   Complex numbers lie at the heart of mathematics.

A complex number has 2 parts,a real part ,that is a real number, like 2 for example,and an 'imaginary' part. The imaginary part is some multiple of  'i',which represents the square root of minus one.

So complex numbers look like this :    2+ i ,   17- 3i,  etc. We sometimes write Re (2+i) =2 and Im (2+i) = i  where Re means the real part of the complex number and Im means the imaginary part.

I don't think there's much point in me saying any more at this stage.   

M + 500 = 4732                    [minus 500 on both sides

M = 4732 - 500

M = 4232

20 people PER 5 x 5 = 25 sq ft

500 x 500 = 250,000 sq ft       250,000/25  sets of 20 people = 10,000 sets of 20 people   

10,000sets x 20 people = 200,000 people

5xyz=xyz, then x,y,z=0

500x+50y+5z=100z+10y+x

499x+40y-95z=0

x=-(40y-95z)/499

499x-(x/499)=0

249001x-x=0

249000x=0

x=0

40y-95z=0

z=40y/95

(z/95)-95z=0

z-9216z=0

9215z=0

z=0

40y=0

y=0

80 x 80 = 6400 sq ft       6400 sq ft / (4.5 sq ft/person) = only 1422.2 people will fit comfortably

20 x 20 = 400 sq ft

100 x 100 = 10,000 sq ft

10,000/400 = 25 times bigger of a room     25 times 50 = 1250 students in the larger room

                                                         10 x 80 = 800    first ten minutes

80 x .75 =60 each minute x 5                           300

60 x .50 = 30 each minute x5                           150

______________________________________________

                                                                       =1250 people

I'm going to assume that it's 1 billion gallons * 0.1341 miles/g

10^9*.1341=1.341*10⁸ mi

well the work is 37566578334*4665+775774(7+97457)-74476775

so the answer is 0.66644638476