Tomas used 65% of a dollar to purchase a highlighter. Write the percent as a fraction, as a dollar amount, and a decimal.

Set this up as a proportion, with inches on the top and feet on the bottom for our scale. We will find the actual length first, then we'll find the width.

$\frac{in}{ft}:\frac{1}{5}=\frac{2.5}{x}$

Cross multiply to get that the actual length is 5(2.5) = 12.5 feet. Now for the width:

$\frac{in}{ft}:\frac{1}{5}=\frac{3}{x}$

Cross multiply to get that the actual width is 5(3) = 15 feet.

If you want the area of the room, multiply the length times the width to get

A = 15(12.5)

A = 187.5 feet squared

7 0

3 years ago

The equation y = 155x + 110, 419 approximates the total cost in dollars, of raising a child in the United States from birth to 1

faust18 [17]

Answer: Third option.

Step-by-step explanation:

According to the information given in the exercise, you can find an approximation of the the total cost in dollars of raising a child in the United States ( from birth to 17 years) given a household's annual income, with the following equation:

$y = 1.55x + 110, 419$

Where "x" represents the household's annual income in dollars.

Therefore, if the annual income is $62,500; you can identify that:

$x=62 ,500$

Then, in order to calculat the approximated cost to raise a child in a household with that annual income given in the exercise, you need to substitute that value of "x" into the equation and then you must evaluate in order to find the value of "y".

Through this procedure you get the following result:

$y = 1.55(62 ,500) + 110, 419\\\\y=96,875+ 110, 419\\\\y=207,294$

6 0

3 years ago

Suppose that a company needs 1, 200,000 items during a year and that preparation for each production run costs $500. Suppose als

MAVERICK [17]

Answer:

The number of items in each production run so that the total costs of production and storage are minimized is 8165 items/run

Step-by-step explanation:

We will use the following variables:

Q = Quantity being ordered

Q* = the optimal order Quantity: the result being sought

D = annual Demand for the item, over the year

P = unit Production cost

S = cost of setting up a production run, regardless of the number of units in the production run (fixed cost per production run)

H = annual cost to Hold one unit

It is important to note which variables are annualized, which are per-order and which are per-unit.

Using the variables, here are the components of the first equation

Total Cost, TC = PC + SC + HC

PC = P x D : Production Cost = unit Production cost times the annual Demand

SC = (D x S)/Q : Setting up Cost = annual Demand times cost per production setup, divided by the order Quantity (number of units)

HC = (H x Q)/2: Holding Cost = annual unit Holding cost times order Quantity (number of units), divided by 2 (because throughout the year, on average the warehouse is half full).

So TC = PC + SC + HC = (P x D) + ((D x S)/Q) + ((H x Q)/2) = PD + (DS/Q) + HQ/2

To obtain the optimal order quantity, Q* that minimizes TC, at the minimum TC, dTC/dQ = 0

dTC/dQ = (H/2) – (D x S)/(Q²) = 0

(H/2) – (D x S)/(Q²) = 0

Solving for Q, which is Q* at this point.

(Q*)² = 2DS/H

Q* = √(2DS/H)

D = annual demand for the item = 200000

S = cost of setting up a production run, regardless of the number of units in the production run (fixed cost per production run) = $500

H = annual cost to Hold one unit = $3

Q* = √(2×200000×500/3) = 8164.97 = 8165 items.

3 0

4 years ago