All Answers 358087 Answers

Thanks. This question is kinda weird because I was thinking like "why would the past gas prices matter if I'm trying to get gas right now? Obviously, I'm gonna go for the cheapest today". Your take on it is very interesting though. I haven't thought about it that way.

Day 1-4    go to station A        Day 5-7 go to station B        Day 8 could be anything, but I would likely go to B

(x - 1)^2 = -4 + 4x.          expand L side

x^2 -2x +1 = -4 + 4x        simplify

x^2 -6x +5 = 0                factor

(x-1)(x-5) = 0

x = 1 and 5

We can help you if you help us. Enter the problem in a way that it is readable.

In a function, every input must have exactly 1 output. For example,f(x) = x + 1 is a function, because every value of x has exactly 1 value of y. Using this, you can find which ones qualify. 

8 options for the first, 8 for the second, 8 for the third, 8 for the fourth, and 4 for the fifth because it has to be odd. 

So, there are 8 x 8 x 8 x 8 x 4 options. 

**** edit *****     corrected !

36 possible rolls

 1   x

 4   x

  x  1

 x   4         where x = 1-6      less  the  1-1  4-4 counted twice     AND the  1-4   4-1   counted twice   =    20 rolls out of 36         (Thanx, Alan !)

I cannot find "Three consecutive positive ODD integers", where the difference between their squares==348 !!

However, there are "consecutive EVEN integers" that satisfy your condtions: 86, 88 and 90.

If the difference between their squares is 384, then there are 3 consecutive ODD integers: 95, 97 and 99.

Check your numbers carefully.

You have 2 choices for the first digit [1 and 2] ==2

You have 5 choices for the 2nd digit [1, 2, 3, 4, 5]==5

You have 2 choices for the 3rd digit [2 and 4]==2

Total number of 3-digit permutations under 300 and all EVEN ==2  x  5  x  2 ==20 such permutations.

Yep, I believe you are correct..... there is a problem with the Q   AND my solution had a math error !   D'Oh !        ~ EP

Let's use the correct numbers (thanx , Guest !)

a = arthur now

(a-4) = 11 (j-4)      and     (a+4) = 4 (j+ 4) 

a = 11j -40                         11j-40 + 4 = 4j+ 16        shows j = 52/7      then a = 292/7 

                                                           check:    4 years ago   j = 24/7      a = 264/7         CHECK !

                                                           check     4 years from now   j = 80/7      a = 320/70     CHECK !

Now find when a is twice as old

11j-40 + x    =   2 ( j+x)

11(52/7) - 40   + x   = 104/7 + 2x

188/7 = x                  188/7 years from now   a   will be twice as old as   j        CHECK !

EP: Your 2 equations: (a-4) = 11 (j-4),   (a+4) = 4 (j+ 4), solve for a, j  give the following fractional results:

a = 292/7 and j = 52/7  [I think there is a mistake in the question] !!

Nicely done Melody.  Here are the answers found by Mathcad (I should have said 6, not 9):

 2/3*3/4*4/5* ... * n/(n+1) = 1/500

Solve for n:
2/(n + 1) = 1/500

Take the reciprocal of both sides:
(n + 1)/2 = 500

Multiply both sides by 2:
n + 1 = 1000

Subtract 1 from both sides:

n = 999   and (n +1) ==1,000

cringe

what do you need help with?

a = arthur now

(a-4) = 11 (j-4)      and     (a+4) = 4 (j+ 4) 

a = 11j -40                         11j-40 + 4 = 4j+ 16        shows j = 8          then a = 48

now find when he is twice as old as j

a + x   = 2 ( j+x)

48 + x = 2(8) + 2x

32 = x                                     32 years from now    arthur = 80   j = 40 y/o

I see! Thank you!

I think you have to have even numbered exponents of all of the prime factors to get a perfect square....

   so you would need to multiply by   3 *5 * 7             ( the 9^9  = 3^18 )

Originally

r / y = 3/7      or    r = 3/7 y       and    y+r = 4          

                                                          y + 3/7 y = 4      shows   y = 4 * 7/10 = 2.8 gal      and red = 1.2 gal    

now add yellow to get  2/15

r / ( y+x)  = 2 /15  

1.2 / (2.8+ x )  = 2/15

1.2 (15/2) = 2.8 + x                    x =    6.2   gal of yellow to add

LCM of 3 and 5 is 15      multiiply through by 15 to get

10 x - 45 = 6     

9   *  5 C 2 = 90

36 possible rolls

 1   x

 4   x

  x  1

 x   4         where x = 1-6      less  the  1-1  4-4 counted twice    =    22 rolls out of 36