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convert 1 hour 40 mins and 1 hr 20 mins into minutes (100 minutes and 80 minutes)

100+80+90+80+110

460 minutes.

Convert to hours.

460/60

7.666666.... hours

7 hours = ? minutes (7*60 = 420 minutes)

(460 - 420 = 40) 40 is the minutes left over.

So it's 7 hours and 40 minutes.

h(t) = -20 + 11t at the specified input. h(11)

This  just means that we want to substitute 11 for "t"  and evaluate......so we have

h(11)  = -20 + 11(11)   =   -20 + 121   =     101

The divisors of 2012  are  1, 2, 4, 503, 1006, 2012

Assuming that x, y and z don't have to be unique [ all different], we have

x      y         z

1     1       2012

1     2       1006

1     4         503

2     2         503

4 triplets  ???

I think that's it   [ could you check this, heureka???.....your always way better at this than I am....!!!]

Two Times Ten is 2*10=20 

What is the missing digit in the problem:  5 1/8 - 3 ?/8  =  1 3/8?

Let's change the problem slightly to this:  5 1/8 - x  =  1 3/8

To find the unknown x:                              5 1/8 - 1 3/8  =  x

--->     5 1/8 - 1 3/8  =  5 + 1/8 - 1 - 3/8  =  (4 + 1) + 1/8 - 1 - 3/8   =  (4 + 8/8) + 1/8 - 1 - 3/8  

                                =  4 + (8/8 + 18) - 1 - 3/8  =  4 + 9/8 - 1 - 3/8  =  (4 - 1) + (9/8 - 3/8)  =  3 + 6/8

--->  the missing digit is 6 

The trick is to remember that after the last jump it will be out of the well and won't be slipping back 2 metres.

So, after the first 22 jumps, it will be up 22 metres from the bottom of the bell and only 3 metres from the top. On the 23rd jump it will be at the top of the wall and so can leave the well.

(1 hr 40 min) + (80min) + (90 min) + (1 hr 20 min) + (110 min)  =  ?

Rearrange, placing the hours together and the minutes together:

=  (1 hr + 1 hr) + (40 min + 80 min + 90 min + 20 min + 110 min)

=  (2 hr) + (340 min)

Change minutes into hours by finding the number of full hours in 340 minutes. Divide the number of minutes by 60:  

340 / 60  =  5.6666...

This means that there are 5 full hours in 340 minutes.  Multiplying 5 x 60  =  300 minutes.

Subtracting 300 minutes from 340 minutes leaves 40 minutes.

So 340 minutes is 5 hours and 40 minutes.

(2 hr) + (340 min)  =  (2 hr) + (5 hr 40 min)  =  (2hr + 5 hr) + (40 min)  =  7 hr 40 min

very, VERY good job!

It means you have to find 

sin(Q),  cos(Q),  tan(Q),  cosec(Q),  sec(Q),  cot(Q)

I interpret this question as:

What is the minimum number of pens that must be selected (blindly) such that Lucy is guaranteed to have 16 pens of the same colour in the selection?

It is possible (though perhaps unlikely) that she selects in the following order:

5 black pens

15 white pens

15 blue pens

16 red pens (or possibly 15 red pens followed by 1 blue pen for these last 16)

The total number she has to select in order to guarantee getting 16 of one colour is therefore 51.

.

Thanks Alan,

I stand corrected :))

division with decimals

\(0.8 \div 0.002\)

write it like a fraction

\(\frac{0.8}{0.002}\)

Now multiply the bottom by the smallest power of 10 to make it a whole number.  

You will need to mult by 1000. That is the same as moving the dec point 3 places

Since you have to multiply the bottom by 1000 your will need to multiply the top by 1000 also!

\(\frac{0.8}{0.002}\times \frac{1000}{1000}= \frac{0800.}{0002.}=\frac{800}{2}=400\)

"4.5!  is the gamma function of 4.5"

Not quite.   Gamma(n) = (n-1)!

.

Gamma(4.5) = 11.632   which is between 3! = 6 and 4! = 24

Oh ok  :)

I was wondering where all these different questions of yours were comeng from :)

Do you actually have the questions or are you just trying to remember what they are?

This one does not make sense :)

In how many permutations can I place flags (red or blue) on the sandbox such that there are 9 flags on the sand box, and there are at least 2 blue flags? Show solution.

2blue 7red      

 **R*RRRRRR           9C7     

3blue 6red    

***RRRRRR                9C6                     

4blue 5red

****RRRRR                  9C5

5blue 4red

*****RRRR                    9C4

6blue 3red

******RRR                   9C3

7blue 2red

*******RR                       9C2

8blue 1red

********R                        9C1

9blue                               1

nCr(9,7)+nCr(9,6)+nCr(9,5)+nCr(9,4)+nCr(9,3)+nCr(9,2)+nCr(9,1)+1

nCr(9,7)+nCr(9,6)+nCr(9,5)+nCr(9,4)+nCr(9,3)+nCr(9,2)+nCr(9,1)+1 = 502

So I get 502 ways.                                    

For a linearised (i.e. small amplitude), unforced pendulum the following is a state-space representation, where the state space is represented by angle and angular velocity:

.

11 hours

Y=1519.556

25 sheep and 15 chickens

Because it is the gamma funtion.

4! that is 4 factorial = 24

5! that is 5 factorial = 120

Now 4.5 factorial does not makes sense but it you have a curve where (4,24) is one point and (5,120) is the next point, you could join this up to get a smooth curve and that curve is the gamma function,   :)

4.5!  is the gamma function of 4.5

Because with decimals we use the gamma function:

https://www.wikiwand.com/en/Gamma_function

What is the answer to Q if  Q=a+bP
If P=a+b[(a-c)/(d-b)]
Please explain working out.

\(Q=a+b[a+b\frac{(a-c)}{(d-b)}]\\ Q=a+b[\frac{a(d-b)+b(a-c)}{(d-b)}]\\ Q=a+b[\frac{ad-ab+ba-bc}{(d-b)}]\\ Q=a+b[\frac{ad-bc}{(d-b)}]\\ Q=a+\frac{abd-b^2c}{(d-b)}\\ Q=\frac{ad-ab+abd-b^2c}{d-b}\\\)

That is it I think      

I'm also not sure what I was saying... I had that question in my Mathematics Olympiad contest.

I still do not think I understand what you are asking.

If she takes out 16 pens all of the same colour then that meets this requirement. So the answer is 16