The probability that Terri will draw a heart and then a red face card from a standard 52-card deck is . Using this probability, determine if the event of drawing a heart and the event of drawing a red face card was independent, dependent, both, or neither.

Step-by-step explanation:

Here, the total number of cards in a deck = 52

The total number of heart cards  =  13

The total number of red faces in the deck  = 6 ( 3 of heart and 3 of diamonds)

Now, out of the TOTAL 6 red face cards, 3 are of hearts.

So, (Red cards) ∩ (Heart cards)  = 3 cards ( J, Q and K)

Now let E : Event of picking card which is of heart.

So, the probability of picking a heart =

Now let F : Event of picking card which is of red face.

So, the probability of picking a red face card  =

Hence, the both events E and F are not independent as the intersection of outcomes of both the events is 3  and  not equal to .

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4