All of your solutions must be clearly justified with brief explanations. write your final answers in two ways: 1. as a formula involving only products, quotients, sums, differences, factorials, or powers 2. as one final concrete number (where you might need to make use of a calculator***)
suppose a 5-member council is being formed from among a group of 22 people, each of whom belongs to one of the following 4 houses: baratheon, stark, lannister, and targaryen. in this group of people, 3 are baratheons, 8 are starks, 9 are lannisters, and 2 are targaryens. a. [1pt] in how many ways can a 5-member council be created from among these 22 people? b. 1pt) in how many ways can a 5-member council be created from among these 22 people if the council must have exactly 1 baratheon? c. [2pts in how many ways can a 5-member council be created from among these 22 people if the council must have at most 3 lannisters?
d. 3pts in how many ways can a 5-member council be created from among these 22 people if the council must have exactly 1 baratheon and at most 3 lannisters?
e. [2pts in how many ways can a 5-member council be created from among these 22 people if the council must have exactly 1 baratheon or at most 3 lannisters?

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

77

step-by-step explanation:

a. (14,375+570)(5.3) b. 158,417$

step-by-step explanation:

a. you are basically just setting up the equation. f= amount of debt hence 14,375. g= how much she is borrowing from her parents weekly hence 570 and t= the interest on her debt. creating the equation.

b.   14,375+570= 14,945

      14,945 x 5.3 = 79,208.5

      79,208.5 x 2(years) = 158,417(answer)

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.