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Illusion [34]
3 years ago
10

3. Two identical balloons are filled, one with helium and one with nitrogen at the same temperature. If the nitrogen balloon lea

ks at the rate of 75 mL per hour, what will be the rate of leakage from the helium balloon
Mathematics
1 answer:
postnew [5]3 years ago
6 0

Answer:

140.32mL per hour

Step-by-step explanation:

Rate of leakage of nitrogen ballon = 75 mL/h

Rate of leakage of helium ballon = x

Molar mass of nitrogen= Mn = 14

Molar mass of helium = Mh = 4

Effusion formula

Rate of effusion of helium/ Rate of effusion of nitrogen= √(Molar mass of nitrogen/Molar mass of helium)

Rate of effusion of helium = 75mL/h * √(14/4)

= 140.32mL/h

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F(x)=-11x-2 and g(x) =7x-4 find (f°g)(x)​
tatyana61 [14]

Answer:

- 77x + 42

Step-by-step explanation:

note that (f ○ g)(x) = f(g(x)

Substitute x = g(x) into f(x)

f(g(x))

= f(7x - 4)

= - 11(7x - 4) - 2

= - 77x + 44 - 2

= - 77x + 42

7 0
3 years ago
First Class Airlines has 40 pilots for every 15 aircrafts. If they employ 250 pilots, how many aircrafts does First Class Airlin
love history [14]

Answer:

250÷ 40 = 6.25

6.25 x 15 = 94

4 0
3 years ago
250 is equal to the ratio ____ to 100​
Ksivusya [100]

Answer:

25

Step-by-step explanation:

if you look at it, 250 is 1/4 of 1000 and 100 is 1/10 of 1000 so divide 250 by 10 and you get your answer.

8 0
3 years ago
2 tan 30°<br>II<br>1 + tan- 300​
shusha [124]

Question:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Answer:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

Step-by-step explanation:

Given

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Required

Simplify

In trigonometry:

tan(30^{\circ}) = \frac{1}{\sqrt{3}}

So, the expression becomes:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}

Simplify the denominator

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}

Express the fraction as:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= \frac{2}{\sqrt 3} / \frac{4}{3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2}{\sqrt 3} * \frac{3}{4}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{1}{\sqrt 3} * \frac{3}{2}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3}

Rationalize

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3\sqrt{3}}{2* 3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\sqrt{3}}{2}

In trigonometry:

sin(60^{\circ}) =  \frac{\sqrt{3}}{2}

Hence:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

3 0
3 years ago
Christine worked from 8:15 AM to 11:50 AM, went to lunch, then worked from 12:45 PM to 5:15 PM on Monday through Friday of this
velikii [3]

The equation illustrated shows that the gross pay will be $97.

<h3>How to compute the value?</h3>

It should be noted that she earns an hourly rate of $17.15 and receives time and a half for overtime. The number of hours will be 3 hours 35 minutes at first. This will be:

= (17.15 × 3.58)

= 61.5

The amount for overtime will be:

= (1/2 × 17.15) × 4.5

= 35.59

The Total amount will be:

= 61.5 + 35.59

= $97

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

6 0
2 years ago
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