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3 years ago

13

In an inventory-sale, a department store offers 60% off on the original price of their selected clothes. What fraction is taken

off the price?

1 answer:

Colt1911 [192]3 years ago

8 0

I believe three fifths would be taken off.

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2/5 of a class are girls. 3/4 of the boys are called Paul. What fraction of the whole class is not called Paul?

Novay_Z [31]

Answer:

1/4

Step-by-step explanation:

3/4 + 1/4 = 4/4

7 0

3 years ago

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8 < -3x + 10<br><br>greater than sign meaning greater than or equal to!

goldfiish [28.3K]

Answer:

2/3 >=x

Step-by-step explanation:

8 =< -3x + 10

subtract 10 from each side

8-10 <= -3x+10-10

-2 <=-3x

divide by -3 (remember to flip the inequality)

-2/-3 >= -3x/-3

2/3 >=x

4 0

3 years ago

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A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

a. It is important to label all your variables and expressions clearly because: it will help you get your equations set up c. it

sveticcg [70]

Answer:

I'm pretty sure it's A. It will help you get your equations set up correctly

Step-by-step explanation:

For anyone needing this answer in the future lol

3 0

3 years ago

How to round to the nearest hundred

Andrews [41]

If it is less then 5 you do the next hundred down 5 and above the next one up

8 0

3 years ago

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