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dimulka [17.4K]
2 years ago
11

Joseph buys a bag of 60 pieces of taffy. In the bag, there are 12 cinnamon pieces, 18 raspberry pieces, 18 key lime pieces, and

the rest are candy apple pieces. If he randomly draws one piece of taffy, what is the probability that it is a piece of raspberry taffy?
Mathematics
1 answer:
Sergeu [11.5K]2 years ago
3 0
Probability can be expressed as a ratio of desired cases to the whole number cases possible.

So, there a total of 60 pieces of taffy and we want to know what are the chances of drawing a raspberry taffy. We know there are 18 pieces of taffy that are raspberry flavor.

We can express this as a ratio. 18:60.

Simplify.

18:60 = 3:10

Convert the ratio into a decimal. To do this, divide the top by the bottom.

3:10 = 0.3

Now make it into a percent. Just move the decimal point two places to the right and make into a % sign.

0.3 = 30%

So, there will be a 30% of drawing a raspberry flavored taffy piece.
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Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)
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One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
(x-h)^2+(y-k)^2=r^2
the center is (h,k) and the radius is r

and the distance formula is
distance between (x_1,y_1) and (x_2,y_2) is
D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}


r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle


so
(x+2)^2+(y-3)^2=18
(x-(-2))^2+(y-3)^2=(\sqrt{18})^2
(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2

the radius is 3\sqrt{2}
center is (-2,3)

find distance between (8,4) and (-2,3)

D=\sqrt{(8-(-2))^2+(4-3)^2}
D=\sqrt{(8+2)^2+(1)^2}
D=\sqrt{10^2+1}
D=\sqrt{100+1}
D=\sqrt{101}




r=3\sqrt{2}≈4.2
D=\sqrt{101}≈10.04

do r<D

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