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3 years ago

What is the median for 6.74

Mathematics

2 answers:

Maksim231197 [3]3 years ago

7 0

Answer:

sorry i needed the points for school

Step-by-step explanation:

skad [1K]3 years ago

5 0

Answer:

Median normally is the middle figure in a set of numbers. not totally sure.

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A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

A cone with radius 5 units is shown below. Its volume is 105 cubic units. Find the height of the cone.

Ainat [17]

Answer:

height of the cone = 4.01273885 units

Step-by-step explanation:

Volume of a cone(V) is given by:

$V = \frac{1}{3} \pi r^2h$ ....[1]

where,

r is the radius and h is the height of the cone.

As per the statement:

A cone with radius 5 units and ts volume is 105 cubic units

⇒r = 5 units and V = 105 cubic units

Substitute these given values and use $\pi = 3.14$ in [1] we have;

$105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h$

Multiply both sides by 3 we have;

⇒ $315 = 78.5 \cdot h$

Divide both sides by 78.5 we have;

$4.01273885 = h$

h = 4.01273885 units

Therefore, the height of the cone is, 4.01273885 units

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4 years ago

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A group of tourists spends $156 to rent snorkels and fins. A total of 15 snorkels and 18 pairs of fins are rented. Renting a sno

Bas_tet [7]

You could use many methods to find the answer to this problem, but I am going to use the most efficient one I know.
18f+15(4f)=156
F is for fins. We should now solve the equation.
18f+60f=156
78f=156
156÷78=2
So fins cost 2 dollars. Now, we know snorkels cost four times the amount of fins. Four times 2 is eight. So the snorkels cost $8 to rent. Let's check our math.
15(8) + 18(2)
120+36=156
So it cost $8 to rent a snorkel.

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3 years ago

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Umnica [9.8K]

Answer:

Step-by-step explanation:

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3 years ago

Multiply. Write the answer in simplest form.<br> 2 1/3 x 3/10

rusak2 [61]

Answer: