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3 years ago

I need help on number 8 and 10. thanks!

Mathematics

2 answers:

ch4aika [34]3 years ago

7 0

No 10 is false for sure

Genrish500 [490]3 years ago

5 0

10 is never. I don’t know the rest, I’m sorry

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Which of the following rational numbers is equal to 3/5?

Vedmedyk [2.9K]

3/5 = 60%
20 ÷ 5 = 4
3 x 4 = 12

Answer is A) 12/20

4 0

3 years ago

Read 2 more answers

Someone please help out

exis [7]

Answer:

$39+0.15m \leqslant 50$

Step-by-step explanation:

From the question, Diana wants her total bill to be less than $50.

Diana pays a fixed monthly bill of

$39 for her mobile phone and an additional

$0.15 per minute for phone internet service.

The bill Diana pays for m minutes of using the internet is $0.15m in a month.

The total monthly bill becomes,

$39+0.15m$

The maximum bill she wants to pay is $50.

$\implies39+0.15m \leqslant 50$

This inequality can be solved to determine the number of available minutes.

4 0

3 years ago

Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

The number of children at the liberty was 3 times the number of adults. The total number of people at the liberty was 48. How ma

Black_prince [1.1K]

Answer: 32

Step-by-step explanation:

48 people at the liberty and there are 3 times the number of adults 48 divided by 3 would be 16 kids and 48 - 16 would be 32

5 0

3 years ago

What is -4√12+√75 in the simplest radical form?

nekit [7.7K]

Answer: -3 $\sqrt{3}$

Step-by-step explanation:

-4 $\sqrt{12}$ + $\sqrt{75}$

$\sqrt{12}$ can be written as $\sqrt{4}$ x $\sqrt{3}$

which is the same as 2 $\sqrt{3}$

Also , $\sqrt{75}$ can be written as $\sqrt{25}$ x $\sqrt{3}$ , which is the same as 5 $\sqrt{3}$

Substituting into the main question , we have

-4 (2 $\sqrt{3}$ ) + 5 $\sqrt{3}$

= -8 $\sqrt{3}$ + 5 $\sqrt{3}$

= -3 $\sqrt{3}$

3 0

3 years ago