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The rope should be cut according to this ratio:       1 : 5 : 10

Therefore, the length of the 3rd rope is:            48 / 16 = 3 ft    

Thanks for the A2A.

The answer is 5 tasks.

Cheers!

Yeah....look at the graph I cited in my answer

When   t  = 4.5   the  graph is at its minimum =  -56.25

So....t =4.5  produces the minimum value of the quadratic

The volume of the  4 largest samples  =

4 (3 + 1/2)   =

4 ( 7/2)  =

14 oz

found this on the internet hopefully it is right and helps you

In order to compute the probability, we need to count the total number of ways six numbers can be drawn, and the number of ways the six numbers on the player’s ticket could match the six numbers drawn from the machine. Since there is no stipulation that the numbers be in any particular order, the number of possible outcomes of the lottery drawing is 48C6 = 12,271,512. Of these possible outcomes, only one would match all six numbers on the player’s ticket, so the probability of winning the grand prize is:

c6c/48c6=1/12271512≈=0.0000000815

@CPhill, are you sure it is 4.5?

The  "t"  that produces the smallest value is at the vertex of this parabola.....this is

- (-9) / [ -2 *1 ]  =  9/2  = 4.5

See the graph here :  (I've used x instead of t....but....same idea) :

https://www.desmos.com/calculator/jzlppgwsly

No problem!

Hey @pinklemonade!

Use the factoring method to get -3 as the answer for t.

Cheers!

We know an angle and the hypotenuse....we are looking for the opposite side to the angle.....we need the sine, here

So

sin(58)  = BC  / 14

14 * sin (58) = BC ≈  11.9

Thanks for the A2A.
 

Each friend recieves 2 slices and 4 slices remain.

Cheers!

See the following diagram :

Let AC = 9.3

Let CE  =  AC  - BD  =  9.3 - 2.4  =  6.9

Let AB  = 26.5  = ED

So.....we have right triangle DEC  with legs ED and EC

And the hypotenuse (CD) is the distance we are looking for  = sqrt ( ED^2 + EC^2)   =

sqrt (26.5^2 + 6.9^2) ≈ 27.38 in

Thanks for the A2A.

The answer is 11.9 cm.

Cheers!

Thanks for the A2A.

36/9 = 4.

4*5 = 20/2 = 10

10+36 = 46 \({cm}^{2}\)

Cheers!

thank you a lot

Thanks for the A2A.

23-5 = 18 meters without the gaps.

18/4  =  4.5 meters is the width

17 - 1(2) = 15 meters is the length.

Cheers!

Hi Guest, your answer is correct!  

Use the identity a^3+b^3=(a+b)^3 - 3ab(a+b) to determine the product of the two numbers if the sum of the cubes of the two numbers is 152 and the sum of the two numbers is 8.

Since these are similar....then

DE  / YZ  = BC  /WX

5  / 8  =  BC  /  6       multiply both sides by 6

30  / 8  =  BC  =   15 / 4  =  3 .75

Correct. The solutions are irrational, the coefficients of the cubic polynomial are rational. 

At least  2 women means that the committee  contains 2, 3, 4  or 5 women

P(2 women)  = C(16,3) * C(12, 2)  / C(28,5)

P(3 women)  = C(16,2) * C(12,3) / C(28,5)

P(4 women) =  C(16,1) * C(12,4) / C(28,5)

P(5 women ) =  C(12,5) / C ( 28,5)

So....the total probability  is

 [ C(16,3)* C(12,2)  + C(16,2)*C(12,3)  + C(16,1) * C(12,4)  + C(12,5) ] / C(28,5)    = 

 11  / 15  

We have that

a^3 + b^3  =  152      and       a + b   = 8

So  we have that

152  =  (a + b)^3 - 3ab ( a + b)

152  =   (8)^3  - 3ab (8)

152  =  512  - 24ab     rearrange as

24ab  = 512  - 152

24ab  = 360     divide both sides by  24

ab  = 15   →   (the product of the two numbers )

BTW.....the numbers are 3 and 5  ....

We can use the Law of Sines here

The remaining angle in the triangle  (at the site of the fire) =   180 - 42  - 64  =  74°

Let D  be the distance  from tower B to  the fire....so....we  have

D / sin (42)  =  10 / sin (74)      rearrange as

D  =  10* sin (42) / sin (74)  ≈  6.96 miles  =  7 miles  (to the nearest  10th )

OK thanks

Basically, it's undefined.