Will’s Widget Works can produce 2½ tons of widgets in an 8 hour work day.

a. How many widgets can Will’s Widget Works produce between 9 am and noon?

b. McGee Manufacturing, Inc. needs to order 17 tons of widgets. How many work days
will it take Will’s Widget works to fill this order?

a. 15/16 tons or 0.9375 tons

b. 6 4/5 work days  or 6.8 work days

Step-by-step explanation:

a.

there are 3 hours between 9am and noon

rewrite 2 1/2 as 5/2 or 2.5

make a proportion:

cross multiply: 5/2 * 3 = 8x →15/2 = 8x

divide   15/2 by 8 = 15/2 * 1/8 = 15/16

b. make another proportion

cross multiply:(5/2) y = 8*17 → (5/2) y = 136

divide   136 by 5/2 = 136 * 2/5 =54 2/5 hours

1 work day = 8 hours

so 54 2/5 hours / 8 hours = 6 4/5 work days  or 6.8 work days

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

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: