A group of people pays$720 for admission tickets to an amusement part. The price of an adult ticket is $15 and a child ticket is $8. There are 25 more adults than children. How many children are in the group?

15

Step-by-step explanation:

Set the number of children to n.

The number of adults is, thus, n + 25.

The total price of admission is $720, made up of adult tickets and child tickets.

The children paid $8 per child, or

8 * n

The adults paid $15 per adult, or

15 * (n + 25)

These sum of these is equal to the total cost of $720.

8*n + 15*(n + 25) = 720

8n + 15(n + 25) = 720

Multiplying 15 with both n and 25.

8n + 15n + 25*15 = 720

8n + 15n + 375 = 720

Subtracting 375 from both sides.

8n + 15n + 375 - 375 = 720 - 375

8n + 15n = 345

Adding together 8n and 15n.

23n = 345

Dividing both sides by 23.

n = 345/23 = 15

n = 15

As n is the number of children, there are 15 children in the group.

15

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

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: