Answer:
<u>The percent decrease of the microwave from the original price to the sale price is 24%</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Original price of a microwave = $ 75
Mark-up price of the microwave = $ 90
Sale price of the microwave = $ 57
2. What is the percent decrease from the original price to the sale price?
For answering this question we will use the Direct Rule of Three this way:
Price Percentage
75 100%
57 x
75x = 57 * 100
75x = 5,700
x = 5,700/75
x = 76
76 = 100 - 24
<u>The percent decrease of the microwave from the original price to the sale price is 24%</u>
Answer:
6n
Step-by-step explanation:
A product refers to the multiplication of two or more numbers.
6n is the equivalent of 6*n
Answer:
Step-by-step explanation:
Given
Billy's Marble = x
Required
Determine a,b and c
a. Charlie's Marble
"5 more" means 5 + or + 5
Since Billy's Marble is represented with x, then Charlie's Marbles will be
b. Danny's Marbles
Having "8 fewer" means we have to subtract 8 from Billy's marble;
Since Billy's Marble is represented with x, then Danny's Marbles will be
c. Eric Marbles
Having "three times as " means we have to multiply Bill's marble by 3;
Since Billy's Marble is represented with x, then Danny's Marbles will be
You must develop a cost function C(x) and then minimize its value.
How much dwill the glass cost? It's $1 per sq ft, and the total area of the glass is 4(xh), where x is the length of one side of the base and h is the height of the tank. The area of the metal bottom is x^2, which we must multiply by $1.50 per sq ft.
This cost function will look like this: C(x) = 4($1/ft^2)xh + ($1.50/ft^2)x^2
but we know that (x^2)h= 6 cu ft, or h = (6 cu ft) / (x^2). Subst. this last result into the C(x) equation, immediately above:
C(x) = 4($1/ft^2)x[6 ft^3 / x^2] + ($1.50/ft^2)x^2
Let's focus on the numerical values and ditch the units of measurement for now:
C(x) = 4x(4/x^2) + 1.50x^2, or
C(x) = 16/x + 1.5x^2
Differentiate this with respect to x:
C '(x) = -16 / x^2 + 3 x
Set this equal to 0 and solve for x: -16/x^2 = -3x, or 16 = 3x^3
Then x^3 = 16/3, and x = 5 1/3 ft. We already have the formula
(x^2)h= 6 cu ft, so if x = 5 1/3, or 16/3, then (16/3)^2 h = 6, or
h = 6 / [16/3]^2.
h = 6 (9/256) = 0.21 ft. While possible, this h = 0.21 ft seems quite unlikely.
Please work through this problem yourself, making sure you understand each step. If questions arise, or if you find an error in my approach, please let me know.
Once again:
1. Write a formula for the total cost of the material used: 4 sides of dimensions xh each, plus 1 bottom, of dimensions x^2. Include the unit prices: $1 per square foot for the sides and $1.50 per square foot for the bottom.
2. Differentiate C(x) with respect to x.
3. Set C '(x) = 0 and solve for the critical value(s).
4. Calculate h from your value for x.
5. Write the dimensions of the tank: bottom: x^2; height: h
