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Kelly drove  9 +12 miles =21 miles

This took this amount of time:

  21 miles/  42miles/hr = 1/2 hr = 30 minutes

Brenda drove  sqrt(9^2 + 12^2) = 15 miles

 This took this amount of time:

   15 miles / 45 miles/hr = 1/3 hr = 20 minutes

So Brenda arrived  30 -20 = 10 minutes before Kelly

there is 7/26 chance that it is 100,000 or higher at the start.

as you remove boxes, assuming they are all lower than 100,000

you would need to remove 12 cases to get the 7/14 chance to be half.

Melody: This answer was posted by either "Gavin" or by "ChowMein", because I saw one of their names on it originally, but later, for some reason, they changed it to "Guest". You may query them privately to confirm this fact. Thank you.

Anybody who is interested in this type of question can visit this page which gives very extensive details about the restrictions and a variety of formulas to solve them. Some of them are quite advanced, requiring knowledge of "partitions", "Stirling numbers of the second kind!"........etc.

https://www.careerbless.com/aptitude/qa/permutations_combinations_imp7.php

GCD[Greatest Common Divisor] of ANY four consecutive positive integers will always be a 1.

GCD[1, 2, 3, 4] =1, GCD[2, 3, 4, 5]=1, GCD[22, 23, 24, 25]=1, GCD[171, 172, 173, 174]=1.......and so on. 

CPhill used this formula three years ago on this post.

https://web2.0calc.com/questions/mack-the-bug-starts-at-0-0-at-noon-and-each-minute-moves-one-unit-right-or-one-unit-up-he-is-trying-to-get-to-the-point-5-7-howeve

Looks good to me :)

What is the greatest common divisor of all of the members of the set containing all numbers that are the product of four consecutive positive integers?

With any four consecutive numbers there will always be 2 even ones and one of those will be divisable by 4.

So that means that 8 will always be a factor of their product.

Also there will always be one that is divisable by 3 so there is another common factor.

So 24 will be a common factor.

Now the smallest member of the set is  1*2*3*4= 24

So 24 is the greatest common factor.

That is interesting Hectictar.

I know it is Heureka's formula but I don't remember seeing it before.  

The path from C to B must have two steps up and four steps right.

The possibilities are:

up, up, right, right, right, right

up, right, up, right, right, right

up, right, right, up, right, right

up, right, right, right, up, right

up, right, right, right, right, up

right, up, up, right, right, right

right, up, right, up, right, right

right, up, right, right, up, right

right, up, right, right, right, up

right, right, up, up, right, right

right, right, up, right, up, right

right, right, up, right, right, up

right, right, right, up, up, right

right, right, right, up, right, up

right, right, right, right, up, up

That is a total of  15  possibilities.

(x-3/2)^2 -5/4 

-3/2 + -5/4

-11/4

An archeologist found the remains of an ancient wheel,which she then placed on a grid, and an arc of the wheel passes through the A(-7,0),B(-3,-4) and C(7,0), locate the center of the wheel, and the standard equation of the circle defining its boundary.

.....or you use this way

The smallest 4 prime numbers are:

2 x 3 x 5 x 7 =210. Since you want the "smallest 4-digit number", then I think it is:

210 x 5 =1050.

2 3 5 7 go into 1050

t = number of tickets

70 - (t-60) = price of tickets

t (70-(t-60)) >4200

t(-t +130) > 4200

-t^2 + 130t -4200 > 0

t^2-130t+4200< 0          Use Quadratic formula to find zeroes at t = 60    70

When t = 60       Sales 4200  

    When t = 70    sales = 4200      The question asks for the greatest number to be MORE than 4200       that would be when  t = 69   Sales= 4209

Here is a graph:

The multiples of 25 are 25,50,75,100 etc

You forgot the 1 times multiples :)

Thanks for haveing a go and it is just a oversight error anyway. :)

Maybe it is, maybe it isn't,  but you have expressed yourself very rudely and unproductively.

If you believe it to be wrong you should be polite, thank the answerer for his/her efforts, and express why you think the answer is incorrect.

Hi guest,

You have chosen them in the order red blue white green. but they can be chosen in any order 

So I think you answer should be multiplied by  4!

Now that takes me back :))

If I understand your question, then there are:

33 - 25 + 1 = 9 different positive values of x:

25, 26, 27, 28, 29, 30, 31, 32, 33. Each one of these numbers has exactly 2 positive two-digit multiples:

Example: 25 has 50 and 75. 26 has 52 and 78. 27 has 54 and 81......and so on for all 9 of them.

X^2 + (Y-3)^2 = 9

Center at (0,3)

Look at solution #10 here:

https://web2.0calc.com/questions/how-many-ways-are-there-to-put-6-balls-in-3-boxes-if-the-balls-are-distinguishable-and-the-boxes-are-distinguishable

10 + 3 + 7 + 5 = 25 total number of marbles.

10/25 red marble x 3/24 blue marble x 7/23 white marble x 5/22 green marble =1,050/303,600 =0.0034585 x 100 =o.34585% - probability of  picking one of each colors on the first try.