QR questions

[Dental2000]

1)A container holds 8 red and 4 white balls. Two balls are drawn in sequence  without replacement  from the container. Which represents the probability that exactly one of these balls is red?


2)What is the length of each side of a regular hexagon inscribed in a circle with a diameter of 12?


3)A soup can has a base diameter of 6 cm and a height of 8 cm. If the label on the can covers the sides, what is the area of the label in cm2, neglecting overlap


any help is appreciated

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[Dental2000]

anybody??

 

[AlbinoPolarBear]

1)A container holds 8 red and 4 white balls. Two balls are drawn in sequence  without replacement  from the container. Which represents the probability that exactly one of these balls is red?
any help is appreciated

If only one ball is red, there will be 2 cases.
1) First one is red, second one is white.

P(1red) = 8/12 * 4/11
= 8/33

2) First one is white, second one is red.

P(2red) = 4/12 * 8/11
= 8/33

Add the probabilities..

16/33

 

[Demps]

I will give a shot at #1

it has to be EXACTLY one red ball

it could be that the red ball is drawn first, and then white is OR
it could be that the white all is drawn first, and then red is... hence

(8/12 x 4/11) + (4/12 x 8/11)

so 8/33 + 8/33 = 16/33

 

[KyoPhan]

 

[AlbinoPolarBear]

1)

3)A soup can has a base diameter of 6 cm and a height of 8 cm. If the label on the can covers the sides, what is the area of the label in cm2, neglecting overlap

If you take a cylinder and lay it out in 2D, you'll get 2 circles and a rectangle.
The circumference of the circle is the length of the rectangle.

So diameter is 6cm
length = circumference = d*pi = 6*3.14 = 18.42 ~ 18.5 cm
height = 8 cm

area of rectangle = length * height
= 18.5cm * 8 cm
~ 148 cm^2

 

[KyoPhan]

Edit#3: Looks right now. I drew the hexagon really poorly.

 

[Demps]

nm I think I got it wrong. Also took wrong angle. I'll look at this some more.

Wouldn't it be just 6?

if you draw the inscribed a hexagon in a circle

the radius equaling 6 can be extened into two adjacent points. and that triangle is equilateral triangle with 60 degrees each angle. so the remaining side on that equilateral triangle... same thing as radius, so 6?

confirm me on it Kyophan
Thanks

 

[Demps]

Different approach, same answer. nice

 

[KyoPhan]

Wouldn't it be just 6?

if you draw the inscribed a hexagon in a circle

the radius equaling 6 can be extened into two adjacent points. and that triangle is equilateral triangle with 60 degrees each angle. so the remaining side on that equilateral triangle... same thing as radius, so 6?

confirm me on it Kyophan
Thanks

Wow, that's genius.

 

[toothhornet88]

or you can use a 30-60-90 triangle with 6 being the hypotenuse you can get the answer this way