Here are 12 marbles in a bag, and the marbles are either yellow or green. two marbles will be randomly picked from the bag, without replacing the first one picked. the probability that both marbles will be yellow is 5 33 . how many green marbles are in the bag? a) 4 b) 5 c) 6 d) 7

D)7

Step-by-step explanation:

Let y = number of yellow marbles in the bag

For the first marble

P(yellow) = number of yellow marbles over total

                =y/12

For the second draw, there are y-1 yellow marbles in the bag, and only 11 marbles left since we keep the first marble

P(2nd marble yellow) = (y-1)/11

The probability that the first and second marble are yellow when we keep the first marble is

y/12 * (y-1)/11 = 5/33

y * (y-1)       5

=

121               33

We can use cross products to solve

33 y(y-1) = 660

Divide each side by 33

y(y-1) = 660/33

y(y-1) = 20

Distribute

y^2 -y =20

Subtract 20

y^2 -y -20 =0

Factor

(y-5)(y+4) =0

Using the zero product property

y = 5 or y = -4

Since we cant have negative marbles

We have 5 yellow marbles

Since there are 12 marbles

12-5 =7

There are 7 green marbles

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

x=6 and x=3

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