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d/8km/hr  + d/4km/hr =   27/60  hr

d+2d = 8 * 27/60

3d = 3.6 km

 d =1.2 km

The integers between -12.1 and 3.3 are -12 to 3.

We can add the negatives and the positives separately.

1+2+3 is 6.

1+2+3+4+5+6+7+8+9+10+11+12 is 78, so the negatives would equal -78.

-78+6 is -72.

The problem specifies that there are 10 integers in the list.  This is nice reasoning, though. 

_.

LCM of 1/2  2  7   10 = 70 seconds

Suppose ten distinct, positive integers have a median of 10. ("Distinct integers" means that no two integers are the same.)

What is the smallest the average of those ten integers could be?

P.S. When you are answering, please include equations. Not just the answer.  

I don't have an equation, but I'll include my reasoning.  Maybe you can make the equations. 

The median is the integer that the number of integers smaller than it is equal to the number of intergers larger than it.  To get the smallest average, we'll need the smallest integers.  Since there's an even number of integers in the list, the median has to fall between two integers.  9 and 11 are the smallest that will give us 10. 

Now you just use the smallest numbers that include those two.   I get 1, 2, 3, 4, 9, 11, 12, 13, 14, 15. 

The integers in that list total 84 so the average of them is 8.4.  

_.

If the median of an even number of distinct integers is ten, then the two middle numbers have to sum to 20.

Making them 9 and 11 would be ideal so we can use the rest of the small one-digit numbers for the below numbers and the small two-digit numbers directly above 11(what I'm saying is using these numbers will minimize the other numbers)

To minimize the others, we make them 1, 2, 3, 4, 9, 11, 12, 13, 14, and 15.

The average of those numbers is 84/10 or 8.4.

4 miles / (20 + 55 m/hr) = .053333 hr = 192 seconds

_ _ _ 10 _ _ _          three integers below 10    three above 10    choose the smallest possible to make the average as small as possib;e

123 10 11 12 13    av =7.42

Have you proofread your question?  5 4 x    What is that supposed to be?

Have you drawn the pic for yourself?

Have you tried to solve it?  What have you tried?

Trapezoid means different things in different countries.  I assume you mean a trapezium. (Australia).

A quadrilateral with 4 sides, one pair is parallel.

k = 12.

-8.8

what are the amount and compound interest for $720 for 3 years at 5% per annum 

wouldn't  (0,0)   work?

Jennifer has biked 12 * 4 = 48 miles   while Thomas has walked 4 x 4 = 16 miles

   it will take him 8 more hours to get to the bike  at which time Jennifer will have walked  8 x 2= 16miles

their closing speed once T starts biking is  12 -2 = 10 m/hr       16miles will take   1.6 more hours

4 hours + 8 hours + 1.6 hours =13.6 hours from their start they will meet .

Oh I did make a mistake. Its a good thing everyone is checking its easy to get wrong!!!

There is probably a way to do this without first converting to base 10, but I'm not super sure how to do it.

Anyway, first convert 45 from base 6 to base 10, which is \(5+4\cdot6=29\). 

The sum of the integers 1 to 29 base 10 is \(\frac{(29)(30)}{2}=435\). In base 6 that would be equal to \(\boxed{2003}\), which is our answer.

I'm not sure how to code a diagram using $LaTex.$ 

You made a mistake its 18 minutes I just rechecked my work. Its .3 hours that is 18 minutes.

Close!   Haha    60 / .3 = 200

60 X .3  = 18

Wait I get 9 minutes Why am I getting 9 minutes when everyone else is getting 18 minutes

 I must have made a mistake

60/.3 = 18 so its 18 minutes

I get 18 mins too

Yep. I get .3 hours that’s 18 minutes.

Thanks Alan,

How did you get this step?

\(|\frac{e^{i\theta}-1}{1-e^{-i\theta}}|=|e^{i\theta}|\)