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2 years ago

What is the value of a in the equation , when ? 3 15 21 39

Mathematics

1 answer:

kupik [55]2 years ago

8 0

Answer:

the mean =19.5

Step-by-step explanation:

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The youth group is going on a trip to the state fair. The trip costs $63. Included in that price is $13 for a concert ticket and

forsale [732]

Ok,

The total is 63$:

= 63

It shows us one of the numbers for the equation, 13

+ 13 = 63

Two passes together plus the thirteen equals the total of 63$

the price of the pass is unknown, so we can use a variable to figure it out:

2x + 13 = 63

Now we solve

First subtract 13 from both sides:

2x + 13 - 13 = 63 - 13

Then divide both sides by 2:

2x ÷ 2 = 50 ÷ 2

Now we get our answer:

x = 25

3 0

3 years ago

Read 2 more answers

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

2 years ago

PLEASE HELP ASAP<br> ITS GEOMETRY

omeli [17]

Angle 1 and angle 3 are vertically opposite angles. And both angles are congruent with each other.

<h3>What is an angle?</h3>

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Line L and line M intersect each other.

Angle 1 and angle 2 are supplementary angles.

∠1 + ∠2 = 180° ...1

Angle 2 and angle 3 are supplementary angles.

∠2 + ∠3 = 180° ...2

From equations 1 and 2, then we have

∠1 + ∠2 = ∠2 + ∠3

∠1 = ∠3

The vertically opposite angles are angle 1 and angle 3. Furthermore, the two angles line up perfectly.

More about the angled link is given below.

brainly.com/question/15767203

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5 0

11 months ago

viktelen [127]

Answer:

altemate interior angles

7 0

2 years ago

The number of students in the period 7 study hall at jins school is 4 times the number of students in Jin’s home room how many s

Vlada [557]

I think it's 64. Not positive, but pretty sure it is.

4 0

2 years ago

Read 2 more answers