Joyce is buying a pair of jeans for $39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of the jeans.
Jason bought a vase with $50 gift certificate. The vase was marked 33% off, and the sales tax was 5.5%. If he paid $45.95 for the vase, use the composition of functions to determine the original price of the vase.
An auto mechanic charges $35 per hour for labor plus $45 for parts for a tune up on six-cylinder car. The cost of a tune up function determined by the formula C(t)=35t+45. The amount of time for the tune up is determined by a formula given in the manual, A(x)=0.5x, where x is a numerical code for the particle make of car.Write a formula for the cost of tune up in terms of the numerical code. If the numerical code for certain car is 3, determine the final cost of the tune up.
Joyce is buying a pair of jeans for $39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of the jeans.
The price of a necklace is $15.99. if the salesperson earns 9% commission on their sales, how much commission is earned on the sale of the necklace
To find the total cost of an item with 7% sales tax, we can use the following formula:
T(x) = x + (7% of x)
Here, x represents the original price of the item.
Now, let's find the composite function (T of S)(x) for the jeans:
S(x) = x - (20% of x) [to calculate the price after the 20% discount]
(T of S)(x) = T(S(x)) = T(x - (20% of x)) = (x - (20% of x)) + (7% of (x - (20% of x)))
Now, let's substitute the values for the jeans:
Original price (x) = $39.99
(T of S)(x) = ($39.99 - (20% of $39.99)) + (7% of ($39.99 - (20% of $39.99)))
(T of S)(x) = ($39.99 - $8) + (7% of ($39.99 - $8))
(T of S)(x) = $31.99 + (7% of $31.99)
Now, we can solve for the final cost of the jeans:
(T of S)(x) = $31.99 + (0.07 * $31.99)
(T of S)(x) = $31.99 + $2.2393
(T of S)(x) = $34.2293
Therefore, the final cost of the jeans is $34.23.
Now, let's move on to the question about Jason's vase:
Let x represent the original price of the vase.
The composition of functions for this scenario would be:
(T of S)(x) = x - (33% of x) + (5.5% of (x - (33% of x)))
Let's substitute the values for the vase:
(T of S)(x) = x - (33% of x) + (5.5% of (x - (33% of x)))
(T of S)(x) = x - (0.33x) + (0.055 * (x - (0.33x)))
(T of S)(x) = x - 0.33x + (0.055 * (x - 0.33x))
(T of S)(x) = x - 0.33x + (0.055x - 0.01815x)
(T of S)(x) = (1 - 0.33 + 0.055 - 0.01815)x
(T of S)(x) = 0.69685x
Now, let's solve for the original price of the vase:
0.69685x = $45.95
x ≈ $45.95 / 0.69685
x ≈ $65.90
Therefore, the original price of the vase was approximately $65.90.
Moving on to the final question about the cost of a tune-up:
The cost of a tune-up function is given by the formula:
C(t) = 35t + 45
Here, t represents the amount of time for the tune-up in hours.
The time for the tune-up is determined by the formula:
A(x) = 0.5x
Here, x represents the numerical code for the particular make of the car.
To find the cost of the tune-up in terms of the numerical code, we need to substitute the value of A(x) into the formula for C(t):
C(t) = 35t + 45
C(A(x)) = 35(A(x)) + 45
C(A(x)) = 35(0.5x) + 45
C(A(x)) = 17.5x + 45
Now, let's substitute the value for the numerical code:
Numerical code (x) = 3
C(A(x)) = 17.5(3) + 45
C(A(x)) = 52.5 + 45
C(A(x)) = $97.50
Therefore, the final cost of the tune-up for a car with a numerical code of 3 is $97.50.