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Distance Formula:  Distance  =  sqrt[ (x₂ - x₁)² + (y₂ - y₁)² ]

Let  (x₁, y₁)  =  (a, 21)     and   (x₂, y₂)  =  (4,7)

Distance  =  sqrt[ (x₂ - x₁)² + (y₂ - y₁)² ]     

                    --->     10·sqrt(2)  =  sqrt[ (4 - a)² + (7 - 21)² ] 

                    --->     10·sqrt(2)  =  sqrt[ (4 - a)² + (-14)² ] 

                    --->     10·sqrt(2)  =  sqrt[ (4 - a)² + 196 ] 

square both sides:

                    --->     100·2  =  (4 - a)² + 196 

                    --->        200  =  (4 - a)² + 196 

                    --->            4  =  (4 - a)² 

take the square root of both sides:

                    --->     Either  4 - a  =  2     or     4 - a  =  -2

                    --->     Either       a  =  2     or          a  =  6

Summing the two answers:  2 + 6  =  8                     

I don't think it is possible to delete a question after it has been posted, however, I'm pretty sure you can always come back to edit it.

It is impossible to draw 12 yellow balls, but you could draw 11 red, 11 green, and 9 yellow without getting 12 of the same color; however, the next ball is guaranteed to give you 12 of the same color.

11 + 11 + 9 + 1  =  32

Lateral surface area of a cylinder  =  pi x diameter x height

                                              LSA  =  pi x 6 x 4  ft² 

                                             LSA  =  24pi   =  75.36 ft²  (approximately)

THANK YOU!

(percent x amount) + (percent x amount)  =  final percent x final amount

                                  0.40 · x  +  0.50 · 6  =  0.46 · (x + 6)      [x is the unknown number of liters of the 40% solution]

                                             0.40x + 3.00  =  0.46x + 2.76

subtract 0.40x from both sides:         3.00  =  0.06x + 2.76

subtract 2.76 from both sides:           0.24  =  0.06x

divide both sides by 0.06:                       4  =  x

I've come up with 2,176 u²    

Since the slope is -3/7, every time the y-value decreases by three, the x-value will increase by 7

If the start with a y-value of 18, you can make 6 decreases (of three each time) to get to the x-axis.

So, increase the original x-value (zero) 6 times:  6 x 7  =  42.

Therefore, the x-intercept will be (42,0)

Sorry... but that is not right...

The x-intercept is (-18*3/7,0) = (-54/7,0).

There are 6*5*4 = 120 ways to choose the positions of the 3's.  Then there are 3 ways to choose the position of the 1, and the remaining rolls must be 2, so there are 120*3 = 360 possible sequences.

There are C(6,3)*C(7,2) = 420 ways to get from P to Q.

Since there are 2*3*5 = 30 possible combinations of the above properties, each possible type of car is represented exactly once. Once we choose the first car, the second car has 2-1=1 possibility for the transmission to be different, 3-1 = 2 possibilities for the color to be different, and  possibilities for the brand to be different. Thus there are 1*2*4 cars that have no properties in common with the first car. We could have chosen this second car in 29 equally-likely ways, and hence our answer is 8/29.

However, thank you for the effort... I really appreciate it... thanks!!

tan( pi / 3 )  =  sqrt( 3 )

So, the answer is "no."

There are six different ways the cars can finish (turquoise = a; teal = b, aquamarine = c):

a-b-c     a-c-b     b-a-c     b-c-a     c-a-b     c-b-a

Since it's completely random, 1/3^rd of the time the turquoise car will finish ahead of the other two cars.

Probability = 0.333

C) Tapeworms :)

A proglottid is an individual segment of the strobila of a tapeworm.

As an aside

6! means 1*2*3*4*5*6

2! means 1*2

Is you look on any proper calculator you will find a  ! .  It is called 'factorial'

Fair enough,

I do not know what you know unless you tell me, which you now have. 

If you have not studied any probability formally then you will have to just set out all the possibilities in an organized way.

Barry has 4 wooden blocks, 2 are blue, 1 is red and 1 is green. How many ways can he arrange the 4 blocks in a line?

BBRG

BBGR

GBBR

RBBG

RGBB

GRBB

BRBG

BGBR

BRGB

BGRB

RBGB

GBRB

THERE IS YOUR 12.

Barry's friend Billie is colour blind and cannot distinguish between red and green. How many ways can the blocks be arranged so that Billie can see different looks?

Now copy out those 12 choices.  Bille sees red and green as the same so Chang all the R's and Gs to S (for same)

Now see how many of them are distinguishable. There should be 6.

We know that the two numbers add to 51, let's call them x and y

x+y=51

y=51-x

And we know one number is 5 less than the other

y=x+5

We can equate these two eqations

x+5=51-x

2x=46

x=23

Now we know x is 23, we can find y.

y=23+5

y=28

So the numbers are 28 and 23.

Hope this helps!

-C

Thankyou! That is what I meant :)

There are 1*2*4 = 8 ways of choose the second car so that it is completely different, so the probability is 8/30 = 4/15.

Thank you so much!

Let's suppose the number of large candies sold is x, and the number of small candies sold is y. 
 

Here are your two equations: 

x + y = 28

4y + 6x = 144

From the first equation, we get:

x = 28 - y

Plugging that into the second equation, we get:

4y + 6 ( 28 - y ) = 144

All you have to do next is expand 6 ( 28 - y ) , add them ( the two y expressions ) together, and then divide by the constant of y on both sides to get y ( the number of small candies sold )

To get x ( the number of large candies sold ), just plug y into the equation x + y = 28 and isolate the x ( you can do that by subtracting the value of y on both sides ).

I hope this helped! If I made a mistake somewhere please lmk .