Task : carnival games

the community carnival has a ball toss game with three rectangular boards as targets. all three rectangles have the same dimensions. the holes in the middle of the boards have different shapes and dimensions, as shown in the image below. (note: the images are not drawn to scale.)

what is the probability of hitting each target if it is assumed that a player’s throw will always hit the board? hint: the probability of hitting each target is the area of the target hole divided by the total area of the target. take the value of π to be 3.14.

type your response here:

to win the grand prize, a player must toss the ball into the hole in one try for each of the three targets. find the probability of winning the grand prize. (hint: the probability of a set of events occurring is equal to the product of the probabilities of each individual event occurring.)

type your response here:

rewrite the expression you found in part b into the form .

type your response here:

if the value of x is 2, find the probability of a player winning the grand prize.

type your response here:

a player who hits only the first two targets gets a runner-up prize. write an expression that represents this scenario. (hint: to find the probability of hitting the first two targets, divide the expression you derived in part b by the expression representing the probability of hitting the third target.)

type your response here:

rewrite the expression you obtained in part e in the form.

type your response here:

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

no

step-by-step explanation: