A tank contains 9,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
(a) How much salt is in the tank after t minutes?
(b) How much salt is in the tank after 20 minutes?

Answer:

200

Step-by-step explanation:

6.6/3.3 = 2

10^-2 - (-4) = 10^2

The answer is 2 * 10^2 or 200.

After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

"It is a polynomial equation with degree two."

"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "

For given example,

We have been given a quadratic equation.

[tex]3x^{2} -12x-15=0[/tex]

First we divide above quadratic equation by 3,

[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex]                             ................(i)

Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]

[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]

Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),

[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]

Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

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Step-by-step explanation:

[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3} [/tex]

[tex] = \frac{1}{2} + 180 + 2 \times \frac{2}{1} [/tex]

[tex] = \frac{1}{2} + 180 + 4[/tex]

[tex] = \frac{1 + 360 + 8}{2} [/tex]

[tex] = \frac{369}{2} [/tex]

[tex] = 184 \frac{1}{2} \: or \: 184.5(ans)[/tex]

Answer:

h²=p²+b²

(7√2)²=x²+x²

(49×2)=2x²

2x²=49ײ

x²=49×2/2

x²=49

x=√49=7

x=7

OAmalOHopeO

Answer:

Step-by-step explanation:

1 are = 100 m²

Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are

16 are × 100 m²/are = 1600 m²

each side is √1600 = 40 m

The length of side of plot is 40 meters.

The total space occupied by a flat (2-D) surface or shape of an object is known as area.

Draw a square on a piece of paper with a pencil. It has two dimensions. The term "area" refers to the area that the shape occupies on the paper.

Now picture your square as being comprised of smaller unit squares. The number of unit squares required to cover a 2-D shape's total surface area is used to calculate its area.

Given the area of 10 square plot is 160 are,

here 1 are = 100 m²

area of 10 square plot = 160 x 100 = 16,000 m²

area of 1 square plot = 16000/10 = 1600 m²

area of square is "a²"

where a is side of square

area = a² = 1600 m²

a = √1600

a = 40 m

Hence the length of side of each plot is 40 meters.

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Answer:

failure to correctly define the problem

Step-by-step explanation:

He changes the menu without identify that the real problem was the service.

Answer:

<5

Step-by-step explanation:

exterior angles + the corresponding interior angle of the triangle = 180º or a straight angle

the only exterior angle shown in the diagram is <5, which corresponds to the interior <2

hope this helps!

Answer:

<5

Step-by-step explanation:

everything else is matched up perfectly so it has to be <5

Answer:

The addition should be divided by 4 and not 3 since there are 4 meals.

Step-by-step explanation:

Answer:

30.10

Step-by-step explanation:

First find the amount of tax

28 * 7.5%

28 * .075

2.10

Add this to the price of the pants

28+2.10 =30.10

Explanation:

There are 20 choices for president, and 20-1 = 19 choices for vice president. You count down by 1 each time you fill a seat. So that means you'll have 19-1 = 18 choices for the third seat, and 18-1 = 17 choices for the fourth seat.

Answer:

0.705 = 70.5% probability that a finished calculator will be satisfactory.

Step-by-step explanation:

Probability of independent events:

If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this question:

Event A: Keystroke assembly are satisfactory.

Event B: Logic circuits are satisfactory.

75% of the keystroke assemblies and 94% of the logic circuits are satisfactory.

This means that [tex]P(A) = 0.75, P(B) = 0.94[/tex]

Find the probability that a finished calculator will be satisfactory.

Both satisfactory, and since they are independent:

[tex]P(A \cap B) = P(A)P(B) = 0.75*0.94 = 0.705[/tex]

0.705 = 70.5% probability that a finished calculator will be satisfactory.

Answer:

12.04

Step-by-step explanation:

Find the number in the hundredth place  4  and look one place to the right for the rounding digit  1 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

Answer:

4x-3 is the expression to your question

Answer:

3[tex]\leq[/tex]4x

Step-by-step explanation:

the answer is: combation

Answer:

Easy, all you ha

Step-by-step explanation:

Answer:

f^-1 (x) = x+1

Step-by-step explanation:

f(x) = x-1

y = x-1

Exchange x and y

x = y-1

Solve for y

Add 1 to each side

x+1 = y-1+1

x+1 = y

The inverse is x+1

f^-1 (x) = x+1

Answer:

machine fed copies = 25, hand fed copies = 55

Step-by-step explanation:

let machine fed = x, hand fed = y

0.08x+0.2y = 13 (1)

x+y = 80

x= 80-y (2)

sub (2) into (1)

0.08(80-y)+0.2y=13

6.4-0.08y+0.2y=13

0.12y=6.6

y = 55

sub y=55 into eqn 2

x = 80-55 = 25

Answer:

1/(x^3 + 6x^2 + 12x + 8)

Step-by-step explanation:

The first thing we do is rationalize this expression. (2+x)^-3 is written as

1/(2+x)^3

Then from there we can foil out the denominator. It is easiest to foil (2+x)(2+x) first and then multiply that product by (2+x).

(2+x)(2+x) = 4 + 4x + x^2

(4+4x+x^2)(2+x) = 8+8x+2x^2+4x+4x^2+x^3.

Then we combine like terms and put them in order to get:

x^3 + 6x^2 + 12x + 8

And of course we can't forget that this was raised to the negative third power, so our answer is 1/(x^3 + 6x^2 + 12x + 8)

Answer:

Hello,

Step-by-step explanation:

[tex](a+x)^n=a^n+\left(\begin{array}{c}n\\ 1\end{array}\right)*a^{n-1}*x+\left(\begin{array}{c}n\\ 2\end{array}\right)*a^{n-2}*x^2+\left(\begin{array}{c}n\\ 3\end{array}\right)*a^{n-3}*x^3+\left(\begin{array}{c}n\\ 4\end{array}\right)*a^{n-4}*x^4+...+\left(\begin{array}{c}n\\ n\end{array}\right)*a^{n-n}*x^n[/tex]

[tex]with \\\\\left(\begin{array}{c}n\\ 1\end{array}\right)=n\\\\\left(\begin{array}{c}n\\ 2\end{array}\right)=\dfrac{n(n-1)}{2!} \\\\\left(\begin{array}{c}n\\3 \end{array}\right)=\dfrac{n(n-1)(n-2)}{3!} \\\\...\\[/tex]

[tex]\dfrac{1}{(2+x)^3} =\dfrac{1}{8} +3*\dfrac{x}{4}+3\dfrac{x^2}{2}+x^3\\\\[/tex]

Answer:

$500

Step-by-step explanation:

Intrest = P. A * Intrest Rate * Time

Time = 1 year, Intrest Rate = 9%, P. A. is what we need to find, Intrest is 45

45=x*9/100*1, x=500

Answer:

500

Step-by-step explanation:

I = PRT  where I is the interest, P is the amount invested, R is the rate and T is the time

We want 1 year at 9% to get 45 dollars in interest

45 = P ( .09) (1)

45 = .09P

Divide each side by .09

45/ .09 = P

500 =P

Answer:

0

Step-by-step explanation:

Answer:

Step-by-step explanation:

⅝ - 5/9 = 5/72

Answer:

123123 3213123 12312 dasdsd aw dasd sda asdasd

Step-by-step explanation:

Answer:

I say Its letter d

Step-by-step explanation:

I hope this help

Answer:

4y+x-3=0

Step-by-step explanation:

The equation is y=mx+b

1) Use the coordinates from the first point

(-1,1)

1= -m+b

2) Use the coordinates frm the second point

(-5,2) (y=mx+b, use x=-5, y=2)

2=-5m+b

You have the system of equations

1=-m+b (multiply by -1)  -1= m-b

2=-5m+b

Add the first equation (multiplied by -1) and the second one

-1+2= m-b-5m+b

1= -4m

m=-0.25

2=1.25+b

b=0.75

y=-0.25x+0.75

4y= -x+3

4y+x-3=0

Step-by-step explanation:

the graph will be compressed vertically

A quadratic a function has a form of,

[tex]f(x)=ax^2+bx+c,a\neq0[/tex]

The first function has a term [tex]x^3[/tex] which doesn't fit the profile of a quadratic function. The highest exponent on x inside a quadratic function can be 2, but here we have 3 so this is not a quadratic function, but rather a cubic function.

The second function fits the form of a quadratic function perfectly.

The third function is a bit tricky. While technically the third function could be considered quadratic if the leading term would be something like [tex]0x^2[/tex] and we did't even see it written out because multiplying with 0. But when we specified the form of a quadratic function, we strictly said that the number before [tex]x^2[/tex] aka [tex]a[/tex] cannot equal to zero. So the last function is not a quadratic function but rather a linear function.

Hope this helps :)

Step-by-step explanation:

f(x) = 4x² + x - 3

[tex]f(x) = 4x {}^{2} + 3 - 2[/tex]

r3t40 is correct

Answer:

299.88 mi. !!!!!

you just multiple all of them together to get the area!!!

Answer:

The 100 trees closest to a ranger station are assessed for damage.

Step-by-step explanation:

Convenience samples are samples taken from only around the focal point.

Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.

Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:

The 100 trees closest to a ranger station are assessed for damage.

This method is a convenience sample because it does not involve random selection of trees.

Instead, the trees are chosen based on their proximity to a specific location.

This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.

Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

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Answer:

3/56

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome.

Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.

The total number of marbles in the box

= 1 + 3 + 2 + 2

= 8 marbles

The probability that the first marble is white and the second marble is blue

= 3/8 * 1/7

= 3/56