ElectricPavlov

4/21 * 77 =  14 2/3 ~~ 15 dogs chosen

3465

a_n = 5 + (n-1)   Arithnetic Sequence

   sum₁₀ = n/2 ( a₁+a₁₀)= 10/2 ( 5 + 14) = 190/2 = 95 coins saved in 10 weeks

Here ya go :

15 (r+10) = 18 (r)      r = price of orange

150 = 3r

r = 50       so 18 oranges is   9 dollars   ( the same price as 15 pears)

f = 5 bills                          value =  5f

t = 10 bills = 20-f              value =  10(20-f)                    summed = 125

5f         +       10(20-f)         = 125

-5f  = -75          You can take it from here .....

Are you sure you posted the correct numbers?

ABCD + BCD + CD + D + 377 = 2012.

  I fail to see how  4D + 7    can result in a '2' in the units digit ...

Related rates and the pythagorean theorem

x = car 1 = 2 hrs * 10 m/hr = 20 miles     and      dx/dt = 10  m/hr

y = car 2 = 2hrs * 20 m/hr = 40 miles      and      py/dt = 20 m/hr

Pythagorean theorem for the distance between the two cars :

x^2 + y^2 = s^2                        s^2 = 2000      now differentiate with respect to time (using chain rule)

2x dx/dt     +    2y dy/dy   =   2s ds/dt           We have all of these variables except   ds/dt (which we are looking for) ...so plug in

2(20)  * 10          + 2 (40)  *20  =   2 (sqrt(2000)  * ds/dt

ds/dt = 2000/(2 sqrt(2000))  = 1000/sqrt(2000) = 22.36 m/hr

4) 180 degrees

5)  72 degrees

6 )  Three

.....well. yah     and    2pi n  + 5pi/4