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A probability distribution must have each number in the range:  0.00 <= x <= 1.00.

It also must have a sum of 1.00.

Which answer meets both criteria?

The probability is the area under the curve.

This area is a triangle whose base is 4 and whose height is 0.10

The area is ½·base·height  =  ½·(4)·(0.10)  =   

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Hi there...

If "(1/4)" is half way between "0" and "(1/2)".

Then logically half way between "(1/2)" and "1" would equal "?".

I hope that helped a bit?

Kind regards

BizzyX

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0.35A + 0.25B =0.29*21...................(1)

A  +  B = 21........................................(2), solve for A, B

Use substitution from (2) into (1) and should get:

A =42 / 5 =8.4 ounces of Brand A

B =63 / 5 =12.6 ounces of Brand B

find the net HORIZONTAL forces acting on the box     4.20 cos 50      +     2.25 cos 122

then   f   = ma      to find   'a' 

After drawing the picture, note that the complementary angle (at the point 80 ft above the surface of the water) is 89.3°.

Let x represent the distance from the ship to the point on the water directly below the observer.

In the right triangle from the ship to the point on the water directly below the observer to the observer:

tan(89.3°)  =  x / 80     --->     x  =  80·tan(89.3°) 

Take this answer, which is in feet, and convert it to miles.

r must be a number in the range  -1 <= r <= +1

1.6 is impossible

R = cost of one rose bush

S = cost of one shrub

6·R + 18·S  =  228     --->                                         6·R + 18·S  =  228

8·R + 9·S  =  139       --->   multiply by -2   --->     -16·R  - 18·S  =  -278

Adding down the columns:                                     -10·R              =  -50

                                                                                                  R  =  5

Since     8·R + 9·S  =  139      --->     8·5 + 9·S  =  139      --->     40 + 9·S  =  139     --->     9·S  =  99     --->     S  =  11

To get at least one paperback book:

Either two paperback books and four hadrback books:  ₂C₂ · ₆C₄  =  15

Or one paperback book and five hardback books:         ₂C₁ · ₆C5  =  12

Since these are mutually exclusive, adding them together = 27 ways.

How did you get your answer?

To make the equations easier to solve, I let

QU = a

UT = b

QR = c.

Then:  area(PQRS) = b·c = 6

           area(PQUT) = a·b = 15

           area(QUVR) = a·c = 40

Since b·c = 6     --->   c = 6/b

Since a·c = 40   --->   a = 40/c   --->   a = 40/(6/b)   --->   a = 40·b/6         [substituting]

Since a·b = 15   --->   (40·b/6)·b = 15   --->   40·b² = 90   --->   b² = 9/4   --->   b = 3/2

Since b = 3/2   --->   b·c = 6   --->   (3/2)·c = 6   --->   c = 4

Since a·c = 40   --->   a·(4) = 40   --->   a = 10

The volume of the object = length·width·height = a·b·c  =  (10)·(3/2)·(4)  =  your answer

After turning over 10 cards, there are 42 cards remaining.

The 10th card is a king and the first face card to appear.; but we don't know which king.

If it's the king of spades, the probability that the next card is the king of spades is 0.

If it's not the king of spades, the probability that the next card is the king of spades is 1/42.

(The probability that the next card is a king is 3/42.)

The probability that the next card is the queen of spades is 1/42.

(The probability that the next card is a queen is 4/42.)

a = 2      c = 6

Side   b = sqrt ( 6² - 2² )               b = 5.656854249 in       

Area    A = b * 1                      A = 5.656854249 sq. in  

Pythagorean Theorem:  c²  =  a² + b²     [c must be the hypotenuse; a and b are the other sides]

For this problem, c = 6.

We can let either a or b = 2; let's say that b = 2.

Place these values into the equation:  c²  =  a² + b²    --->   6²  =  a² + 2²    --->   36  =  a² + 4 

                                                                                      --->   32  =  a²

So:  a = sqrt(32)

Area  =  ½·base·height   --->   Area  =  ½·sqrt(32)·2   --->   Area  =  sqrt(32)

The length of the diagonals is 4*sqrt(7).

This is what happened when I graphed them on Desmos, I'm not sure how to describe exactly? They overlap each other, yes, but is there something more, in particular, I should be looking at about them? 

Well, what I did while checking your answer was

x*y=6

x*z=15

y*z=40

x*y*z=48

48/6=8=z

15/8=1.875

6/1.875= 3.2

3.2*8=25.6, which is wrong.

You can assign variables to the side lengths, and then solve the equations.

sorry, could you explain how you got the answer? I'd like to be sure i understand how to solve the problem.

Sum of the digits from 1 to 999 inclusive =13,500

The volume is 48.

13 P 5 = 154440       

13!/8! = 154440

Thank you, DragonLord !

Thank you Guest,

Bill has 300 ft to cover

   the people 120 ft in front of him have 180 feet to cover  at conveyor speed = 180 feet/3 ft/sec = 60 seconds

   and everyone finishes at the same time     Bill has covered the 300 ft in 60 seconds      300ft/60s = 5 ft/sec