The table displays the scores of students on a recent exam. Find the mean of the

Mathematics

1 answer:

Natali5045456 [20]1 year ago

7 0

Answer:

84.5

Step-by-step explanation:

multiply score by number of students, add them, divide by total students.

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3√12•√6 please show a step by step explanation

Oduvanchick [21]

Answer: $18\sqrt{2}\\\\$

This is the same as saying 18*sqrt(2) or you could say 18√2

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Explanation:

We'll be using this square root rule: $\sqrt{A}*\sqrt{B} = \sqrt{A*B}$

So we could have this as our steps:

$3\sqrt{12}*\sqrt{6}\\\\3\sqrt{12*6} \ \text{ ... Apply the rule mentioned}\\\\3\sqrt{72}\\\\3\sqrt{36*2}\\\\3\sqrt{36}*\sqrt{2} \ \text{ ... Apply the rule again, but in reverse}\\\\3*6*\sqrt{2}\\\\18\sqrt{2}\\\\$

Therefore, $3\sqrt{12}*\sqrt{6} = 18\sqrt{2}$

The basic idea is to first combine the roots using that rule. From there, we factor the radicand such that we pull out the largest perfect square factor. This will allow us to break the root apart and fully simplify it.

5 0

2 years ago

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

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