Select the correct answer from each drop-down menu. Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n. The function that models the number of cupcakes Lisa makes in h hours is n(h) = . The cost function in terms of hours, h, is given by . Lisa's cost for making cupcakes for 2 hours is .

Step-by-step explanation:

from the question, we are told that Lisa bakes 3dozens cupcakes every hour, to know the amount she makes in h hours, we will use the equality postulate as shown;.

3 dozens = 1hour

n(h) = h hour

Cross multiply

n(h) × 1 = 3×h

n(h) = 3h

Hence the function that models the number of cupcakes Lisa makes in h hours is n(h) = 3h

To get the cost function in terms of hours, we will find the composite function C(n(h))

C(n(h)) = C(3h)

Given C(n) = 60 + 0.45n

C(3h) is derived by substituting n as 3h in the function as shown;

C(3h) = 60+0.45(3h)

C(3h) = 60+1.35h

Hence the cost function in terms of hours, h, is given by 60+1.35h

To get the cost for making cupcakes for 2 hours, we will substitute h = 2 into the expression C(h) = 60+1.35h

C(2) = 60+1.35(2)

C(2) = 60+2.70

C(2) = 62.70

Hence the cost for making cupcakes for 2 hours is $62.70

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

if you are saying purchasing 3 social media ads and one newspaper ad counts as one purchase then there are:

6 purchases

if you are asking how many of each then:

18 social media ads

6 newspaper ads