Ethan makes punch by mixing orange juice with sparkling water. He uses the same ratio of orange juice
to sparkling water each time he makes punch. The table
shows some of the amounts of orange juice and
sparkling water he uses for different amounts of punch.
Orange Juice (fl oz) 7 21 28 ?
Sparkling Water (fl oz) 4 12 16 28

If Ethan uses 28 fl oz of sparkling water, how much orange juice will he use and what will be the total amount of punch?

Use the number pad to enter your answers in the boxes.

Ethan will use _
fl oz of orange juice, and he will have a total of ___
fl oz of punch.

Ethan will use 49

fl oz of orange juice, and he will have a total of 77

fl oz of punch.

Step-by-step explanation:

He uses a ratio of 7 to 4 of orange juice to sparkling water.

7/4 = ?/28

4 * ? = 7 * 28

Divide both sides by 4.

? = 7 * 7

? = 49

He will use 49 fl oz of orange juice.

The total amount made is: 49 fl oz + 28 fl oz = 77 fl oz

Ethan will use 49

fl oz of orange juice, and he will have a total of 77

fl oz of punch.

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:

where is the diagram? shown below where? ?

step-by-step explanation: