We are creating a new card game with a new deck. unlike the normal deck that has 13 ranks (ace through king) and 4 suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following. each card will have: i) one rank from 1 to 15. ii) one of 9 different suits. hence, there are 135 cards in the deck with 15 ranks for each of the 9 different suits, and none of the cards will be face cards! so, a card rank 11 would just have an 11 on it. hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like king or queen, and no face cards! the game is played by dealing each player 5 cards from the deck. our goal is to determine which hands would beat other hands using probability. obviously the hands that are harder to get (i. e. are more rare) should beat hands that are easier to get. a) how many different ways are there to get any 5 card hand?

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.