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3 years ago

A school has 825 students and 55 teachers. How many students are there per teacher?

2 answers:

4 0

Answer: There are 15 students per teacher in the school. To find out the number of students per teacher, we must divide the number of students by the number of teachers.

DochEvi [55]3 years ago

3 0

15 students after dividing 825 with 55

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Dave paints 125 feet of the fence in 5 hours. Eric paints 175 feet in 7 hours whose rate is faster

eduard

Answer:

Erics rate is faster

Explanation: If you only get 125 feet in 5 hours, that good but, if you get 175 feet in hours, thats really good :) PLEASE MARK BRAINLIEST!!!

7 0

3 years ago

A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flo

djverab [1.8K]

Answer:

a) $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) $31690.7 g/L$

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is $\frac{dy}{dt}=R_{i}-R_{o}$ , where $R_{i}$ is the rate of salt entering and $R_{o}$ is the rate of salt going outside.

Then we have, $R_{i}=80\frac{L}{min}*50\frac{g}{L}=4000\frac{g}{min}$ , and

$R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}$

So we obtain. $\frac{dy}{dt}=4000-\frac{2y}{25}$ , then

$\frac{dy}{dt}+\frac{2y}{25}=4000$ , and using the integrating factor $e^{\int {\frac{2}{25}} \, dt=e^{\frac{2t}{25}$ , therefore $(\frac{dy }{dt}+\frac{2y}{25}}=4000)e^{\frac{2t}{25}$ , we get $\frac{d}{dt}(y*e^{\frac{2t}{25}})= 4000 e^{\frac{2t}{25}$ , after integrating both sides $y*e^{\frac{2t}{25}}= 50000 e^{\frac{2t}{25}}+C$ , therefore $y(t)= 50000 +Ce^{\frac{-2t}{25}}$ , to find $C$ we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions $y(0)=10$ , so $10= 50000+Ce^{\frac{-0*2}{25}}$

$10=50000+C\\C=10-50000=-49990$

Finally we can write an expression for the amount of salt in the tank at any time t, it is $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) The tank will overflow due Rin>Rout, at a rate of $80 L/min-40L/min=40L/min$ , due we have 500 L to overflow $\frac{500L}{40L/min} =\frac{25}{2} min=t$ , so we can evualuate the expression of a) $y(25/2)=50000-49990e^{\frac{-2}{25}\frac{25}{2}}=50000-49990e^{-1}=31690.7$ , is the salt concentration when the tank overflows

4 0

3 years ago

45% of what number is 17.1?<br> Please help <br> 20 points

vitfil [10]

45% × ? = 17.1

17.1 ÷ 45% =

17.1 ÷ (45 ÷ 100) =

(100 × 17.1) ÷ 45 =

1,710 ÷ 45 =

38;

so 45% of 38 = 17.1

7 0

3 years ago

Read 2 more answers

If the shaded cross sections of the solids have the same area, which of the following corresponds to the value of a: the side le

Nikolay [14]

Answer:

$4\sqrt{\pi}$

Step-by-step explanation:

The cross section of a sphere is a circle with area $\pi r^2$ , where radius is given as 4
The cross section of the cube is a square with area $a^2$ , where a is side length of square

The circle area = the square area. Thus we have:

$\pi r^2 = a^2 \\\pi(4)^2=a^2\\16\pi=a^2\\\sqrt{16\pi}=a\\ a=\sqrt{16} \sqrt{\pi} \\a=4\sqrt{\pi}$

6 0

2 years ago

Read 2 more answers

Given lines p and q are parallel, find the value of x that makes each diagram true.

Klio2033 [76]

Answer: for a the answer is 140° and for b x=25°

Step-by-step explanation:

for a, when you have 2 parallel lines cut by a transversal,the corresponding angles are congruent. and the angle140 is congruent to the corresponding angle as they are vertical angles are congruent.

for b, angle x is congruent to the angle that is supplementary to 155 therefore 180-155=25°

5 0

3 years ago