A container has 400 liters of water, and a second container has 800 liters of water. The first container begins filling up at a rate of 4 liters per minute at the same time the second starts draining at a rate of 6 liters per minute. How many minutes will pass until the containers have the same amount of water?​

The quadratic equation \(b^2 - 4b + 4 = 0\) can be solved using the quadratic formula. The two solutions are b = 2.

To solve the equation \(b^2 - 4b + 4 = 0\) using the quadratic formula, we first identify the coefficients a, b, and c. In this case, a = 1, b = -4, and c = 4. Substituting these values into the quadratic formula:

\(\[b = \frac{{-(-4) \pm \sqrt{((-4)^2 - 4(1)(4))}}}{{2(1)}}\]\)

Simplifying the equation gives:

\(\[b = \frac{{4 \pm \sqrt{{16 - 16}}}}{2}\]\)

Since the discriminant (the term under the square root) is zero, we have:

b = (4 ± √0) / 2

The square root of zero is zero, so we can simplify further:

b = (4 ± 0) / 2

This yields two identical solutions:

b = 4 / 2 = 2

Hence, the quadratic equation \(b^2 - 4b + 4 = 0\) has a single solution, which is b = 2.

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1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

Answer:

This process is called

Producing. underwriting.

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

Distributive property on 3(c-3) is 3c-12=20. D is the same. Divide instead.

Answer:

the 2nd and 4th one

Step-by-step explanation:

4( c - 3 ) = 8

you can either distribute the 4 which means multiply whats inside of the parenthesis by 4 , 4 * c = 4c and 4 * -3 = -12 to get 4c - 12 = 8

or you can divide both sides by 4 which will get you c - 3 = 2

4(c-3)/4 = c - 3

8/4 = 2

c - 3 = 2

Answer:

Hi help in what?

Step-by-step explanation:

Answer:

$8.28

Step-by-step explanation:

0.18*46=8.28

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 62. As a result, the median and the mean would be smaller. The mode would not be affected by the outlier.

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Answer:

2. y=9x

3. 180*9 = 1620

Step-by-step explanation:

2. y = mx+b, so find the slop efirst

lacampanella avatar

so take the first two points you got

lacampanella avatar

(2,18) and (5,45),

lacampanella avatar

(45-18)/(5-2) = 9

lacampanella avatar

then use (2,18)

lacampanella avatar

18= 9*2+b

lacampanella avatar

so b=0

3. y = 9x

x= 180. y = 9*180 = 1620

To find the general solution for the given ordinary differential equation (ODE):

xdy - [y + xy^(2)(1 + ln(x))]dx = 0

We can rearrange the terms and separate the variables:

xdy = [y + xy^(2)(1 + ln(x))]dx

Dividing both sides by x and rearranging the terms:

dy/y + y(ln(x) + 1)dx = dx

Now, let's integrate both sides:

∫(dy/y) + ∫[y(ln(x) + 1)]dx = ∫dx

Integrating the left-hand side with respect to y and the right-hand side with respect to x:

ln|y| + y(ln(x) + 1) = x + C

where C is the constant of integration.

We can simplify the equation further:

ln|y| + yln(x) + y = x + C

Combining the logarithmic terms:

ln|y| + yln(x) = x + C - y

To eliminate the logarithm, we can take the exponential of both sides:

e^(ln|y| + yln(x)) = e^(x + C - y)

Using the properties of exponents:

|y| * x^y = e^(x + C - y)

We can rewrite the absolute value expression as a piecewise function:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

So, the general solution to the given ODE is the combination of these two equations:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

These equations represent the family of solutions to the given ordinary differential equation (ODE).

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Answer:

the numbers are -5 and 3

Step-by-step explanation:

First of all, the question is asking you to find the values of x from the given inequalities.

-8x -19<21 and 3x - 4 < 5

group all liked terms, in other words, make x and its coefficient stand alone.

-8x < 21 + 19 and 3x < 5 + 4

-19 became +19 because it crossed the sign <, also -4 became +4 because it crossed the sign <.

so we get

-8x < 40 and 3x < 9

we divide each "x" by its coefficient

\( \frac{ - 8x}{ - 8} < \frac{40}{ - 8} \: and \: \frac{3x}{3} < \frac{9}{3} \)

then we get

x < -5 and x < 3

but x is positive so it's greater than -5 so we get

x > -5 and x < 3

Answer:

cone,258

Step-by-step explanation:

i got it right

The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

The formula for this type of test statistic is given by -

\($t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$\)

Here, the variables can be defined as below -

\($s_1^2, s_2^2=$\) variance of two samples

\($n_1, n_2=$\) respective sizes of the two samples

t = t - distribution test statistic

\($x_1, x_2=$\) Mean of the two samples

As a result, the variables of the test statistic can be determined to be \($s _1, s _2$\), which represents the variance of two samples, \($n _1, n _2$\), which represents the size of the two samples, t, which represents the t-distribution test statistic, and \($x _1, x _2$\), which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

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Answer: The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.

Step-by-step explanation:

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

Step-by-step explanation:

20ft($18.40/80ft)=$4.60

Answer:

$4.6

Step-by-step explanation:

Use 18.40 and 80. if $18.40 is 80 feet, divide 18.40 by 4 to get 4.60. Now you know that you got 4.60, see if you can add 4.6 four times to get to 18.4. (You can.) So, 20 feet is $4.60 or $4.6.

Answer:

23

Step-by-step explanation:

8 5/8 = 69/8

Each DVD is 3/8 inches

Ignore the denominators

We have 69 and 3

69 is 23 times bigger than 3, so 23 DVD's can fit

We can prove that the square is a special type of rectangle, which is one with all sides equal. Let us consider rectangles with perimeter 10, and determine which of them has the maximum area. Since the perimeter is 10, each of the dimensions, length, and width is less than 5.

Let us call the length of the rectangle l and its width w, so the perimeter P of the rectangle is given by: `P = 2(l + w) = 10`Solving this equation for l, we obtain `l = 5 - w`. The area A of the rectangle is given by `A = lw = w(5 - w)`. We can write the area as a function of w: `A(w) = 5w - w^2`.This function represents a parabola, and its vertex is located at `w = -5 / 2(-1) = 5 / 2`. Therefore, the maximum area of the rectangle with a perimeter of 10 is obtained when `w = 5 / 2`. In this case, the length of the rectangle is `l = 5 - w = 5 - 5 / 2 = 5 / 2`.

Thus, the rectangle with a perimeter of 10 and maximum area is a square with sides of length `5 / 2`. It is important to note that this result is true for any shape with four sides that has a fixed perimeter; the shape with the maximum area is always a square. Hence, we can conclude that the square has the largest area of all rectangles with a perimeter of 10.

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Answer:

22 people

Step-by-step explanation:

Sean has 2 3/4 candy bars. That is 11/4 candy bars.

He wants to give out 1/8 candy bars.

The number of people that will get candy is:

\(\frac{11}{4} / \frac{1}{8}\\ \\= \frac{\frac{11}{4} }{\frac{1}{8}} \\\\\frac{11}{4} * \frac{8}{1} \\\\22\)

22 people can get candy.

Answer:

22 people will get candy

Step-by-step explanation:

it's correct because I got it from khan academy

The ratio of the number of jackets to the number of sweaters is 1:4.

According to the question,

The ratio of the number of shirts to the number of trousers = 4:5

∴ Let the number of shirts be 4x and that of trousers be 5x.

The ratio of the number of jackets to the number of shirts = 3:8

∴ Let the number of jackets be 3y and that of the shirts be 8y.

The ratio of the number of sweaters to the number of trousers = 6:5

∴ Let the number of sweaters be 6z, and that of trousers be 5z.

Now,

Number of shirts = 4x = 8y

                           ⇒ x = 2y.               (1)

Number of trousers = 5x = 5z

                            ⇒ x = z                 (2)

From eq.(1) and eq.(2), we get,

x = 2y = z

⇒ z = 2y                                              (3)

But, from above, we have, the number of sweaters = 6z

                                                                                     = 6 × 2y    {from eq.(3)}

                                                                                     = 12y

∴ The ratio of the number of jackets to the number of sweaters = 3y ÷ 12y

                                                                                                    = 1:4

Hence, the ratio of the number of jackets to the number of sweaters is 1:4.

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Answer:

The ratio of the number of jackets to the number of sweaters is 1/4.

Step-by-step explanation:

Let's assign variables to the quantities mentioned in the problem:

Let S be the number of shirts.

Let T be the number of trousers.

Let J be the number of jackets.

Let W be the number of sweaters.

We are given the following ratios:

The ratio of shirts to trousers: S/T = 4/5

The ratio of jackets to shirts: J/S = 3/8

The ratio of sweaters to trousers: W/T = 6/5

We need to relate these variables using the given information to find the ratio of jackets to sweaters (J/W).

First, let's simplify the given ratios:

S/T = 4/5 can be rewritten as S = (4/5)T

J/S = 3/8 can be rewritten as J = (3/8)S

W/T = 6/5 can be rewritten as W = (6/5)T

Now, substitute these expressions into the ratio we are trying to find:

J/W = (J/S)/(W/T)

= [(3/8)S]/[(6/5)T]

= [(3/8)(4/5)T]/[(6/5)T]

= (3/8)(4/5)/(6/5)

= (3/8)(4/6)

= (3/8)(2/3)

= 6/24

= 1/4

Therefore, the ratio of the number of jackets to the number of sweaters is 1/4.

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Answer:

C

Step-by-step explanation:

-5x-49>113

    +49  +49

———————-

-5x>162

—-   ——

-5     -5

x<32.4

Answer:

200 miles

Step-by-step explanation:

1 3/4 can be turned into a decimal as 1.75

Now let’s create fractions to prepare for cross multiplication

1.75/50=7/x

1.75x=7(50)

1.75x=350

/1.75.  /1.75

x=200

200 miles

hopes this helps please mark brainliest

Answer:

Answer would be 1/81 or 0.01 as a decimal rounded to the nearest hundredth

Answer:

-5 is the slope

Step-by-step explanation:

if there's a number in front of x, it's most likely the slope.

Answer:

x

−

6

Step-by-step explanation:

"Six less than.." means "Subtract 6 from".

Do not confuse this with "Six less..." which means "Subtract from 6".

Confusing, I know.

We know that "Double a number" means

2

x

, where

x

is your mystery number.

Therefore, we have:

2

x

−

6

, which translates to "6 less than 2x" or "6 less than twice a number"

Answer:

2 Packages of Napkins, 3 Packages of Cups

Step-by-step explanation:

12 * 2 = 24

8 * 3 = 24

Answer:

3 packages of cups and 2 packages of napkins

Answer:

x = 1, y = 5

Step-by-step explanation:

- 2x + y = 3

Add 2x on both sides

y = 3 + 2x

5x + 2y = 15

5x + 2(3 + 2x) = 15

5x + 2(3) + 2(2x) = 15

5x + 6 + 4x = 15

5x + 4x = 15 - 6

9x = 9

x = 9/9

x = 1

y = 3 + 2x

  = 3 + 2(1)

  = 3 + 2

y = 5

Answer:

y = 3x - 6

Step-by-step explanation:

The line here is parallel

Equation of line

Answer:

Step-by-step explanation:

A

Never terminates. The answer is 6.1111111 ....

B

3^3 and 27 cancel. 3^3 is 27

5^2 and 5^3 partially cancel, you are left with 5 in the denominator.

2 is raised to the 1

1/(2 * 5 ) = 1/10 = 0.1 which terminates right where it is.

A non terminating repeating expansion

B terminating decimal expansion

In circle P, the segments can be matched to their names as follows:

Chord: AB, Diameter: AC, Secant: AD, Tangent: AE.

Chord: A chord is a line segment that connects two points on the circumference of a circle. In circle P, the chord is represented by the line segment AB, which connects points A and B on the circle.

Diameter: The diameter of a circle is a chord that passes through the center of the circle. In circle P, the diameter is represented by the line segment AC, which passes through the center point of the circle.

Secant: A secant is a line that intersects a circle at two distinct points. In circle P, the secant is represented by the line segment AD, which intersects the circle at points A and D.

Tangent: A tangent is a line that intersects a circle at exactly one point, known as the point of tangency. In circle P, the tangent is represented by the line segment AE, which intersects the circle at point A.

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