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1/3  + 1/S = 1/2    Solve for 'S'     Sean's time to do the job alone

If it is equally likely that each passenger can stay at any of the three hotels:

--  the first passenger can stay at any hotel   --->   4/4  =  1

--  the probability that the second passenger stays at the same hotel   --->   1/4

--  the probability that the third passenger stays at the same hotel   --->   1/4

If these are independent choices:  the probability is 1 · ¼ · ¼  =  1/16.

[However, all three persons could be from the same family, which means that the choices are not independent.]

By A-A-A, triangle(ABC) is similar to triangle(EDC).

--->   AC / CE  =  BC / CD

--->         9 / 6  =  (24 - x) / x

--->           9·x  =  6·(24 - x)

--->            9x  =  144 - 6x

--->          15x  =  144

--->              x  =  9.6

Draw isosceles trapezoid TRAP with TR || AP.

TR = 32     PA = 8     area of the trapezoid = 100

Formula for the area of a trapezoid:  Area  =  ½·h·(b₁ + b₂)

--->     100  =  ½·h·(32 + 8)     --->     100  =  ½·h·(40)     --->     100  =  20·h     --->     h = 5

Drop a perpendicular from P to TR, call the point of intersection X.

Drop a perpendicular from A to TR, call the point of intersection Y.

XY = PA = 8

Since TX + XY + YR = 32  and  XY = 8, TX = YR = 12.

Triangle(TXP) is a right triangle with TX = 12 and XP = 5;

by the Pythagorean Theorem, PT = 13.

A-----------------------B

0 ---------------------- 180

The trip from A to B took him 3 hrs

The trip from B to A took 2hrs.

\(\frac52\) = 2.5

BTW, That's incorrect.

Label one vertex of the heptagon as any variable you choose.

The O's can't be next to the point N.

There are \(\binom42 = 6\) ways to choose the 2 spots. Since there are 4! ways to label the other vertices, we multiply 4! = 24 by 6 to get 144.

DO NOT COPY THIS SOLUTION WORD FOR WORD.

I know this is an AoPs problem but I also rlly needed help so.. Yeah.

Make sure to understand method used to solve this problem

Ok, This is very obsecure but there is a such thing as a cube difference rule.

This falls into the cube difference rule.

If we were to expand (x+y)^3 we would get: 

x^3+3x^2y+3xy^2+y^3

You can see the similarities...

Anyway, the answer is (x - 2)^3

Also, you can use the binomial theorem

Ok, 

Let's have Jane's age as "j" and Andrew's age as "a".

j = 4a

j+1 = 3(a+1)

We convert j into 4a

4a + 1 = 3a + 3

4a = 3a + 2

a = 2

If a = 2

j = 8

Andrew is 2 years old

Jane is 8 yrs old

(As of now)

I worked it out!  Angle AIB = 33 degrees.

Well, 0 is an imaginary number so.............

\(0i\)

:)

b

a = 1/2 b

c = .8 ( 1/2 b + b)    summed = 81

b + 1/2 b   + .8 (1/2b + b) = 81     solve for b

can anyone help

If the mean of his scores is 57 and there are 5 judges, then his total score was 57*5=285. If each judge gives out a score greater than 50, then the lowest score a judge can give is 51. To find the highest amount of points he could have earned from one judge, we can assume that the other four give him the lowest possible score, 51. x+51*4=285 simplifies to x=81, so the highest score he could have earned from one judge is 81.

centre and scale factor

 yeah

1 - sqrt(2) e^(-(i π)/24) ≈ 1.40211 -0.18459 i
2 - sqrt(2) e^((11 i π)/24) ≈ 0.18459 + 1.40211 i (principal root)
3 - sqrt(2) e^((23 i π)/24) ≈ -1.4021 + 0.18459 i
4 - sqrt(2) e^(-(13 i π)/24) ≈ -0.18459 -1.4021 i

Im not exactly sure how the question needs to be answered, but in order for the shapes to match the same size and rotation, B would need to be doubled in size and rotated 180. Shifting it to the location where A is should be trivial from that point.

we're not here to do your homework for you... the link doesn't work...

Calculate the probability of 5, 6, and 7 hits.

5 hits

(0.274)^5 * (1-0.274)^2 * 7 choose 5 = 0.017094

6 hits

(0.274)^6 * (1-0.274)^1 * 7 choose 6 = 0.002150

7 hits

(0.274)^7 = 0.000116, so adding up the probabilities gets us 2.036% as the probability.

You are very welcome!

:P

In what interval?

Draw a diagram, and get that DB=12 and CB=16 by Pythagoras.

Then we want to calculate the length of AC, which we can by observing right triangle ABC where AC is the hypotenuse.

16^2+13^2=425, so the answer is the sqrt of 425, or 5sqrt17.

You are very welcome!

:P

(4x51   + x)/5 = 57      solve for x

ah you guys.. im so sorry! i didn't realize someone already asked the same question. please don't worry about it anyore!! 

it's here: https://web2.0calc.com/questions/helllllppppp 

20 per cubic meter   /  3.28³    =.......