Question 6
1 pts
Where does all the water go? According to the Environmental Protection Agency (EPA), in a typical wetland environment, 39% of the water is outflow,27% is seepage: 14% evaporates and 20% remains as water volume in the ecosystem (Referencer United
States Environmental Protection Agency Case Studies Report 832-R-93-005) Chloride compounds as residuals from residential areas are a problem for wetlands. Suppose that in a particular wetland environment the following concentrations in of chloride
compounds were found outflow. 45. seepage. 57, remaining due to evaporation 52, in the water volume 77. Compute the weighted average

Answer:

A.

Step-by-step explanation:

Recall that circumference is given by:

\(C=2\pi r\)

We know that the circumference is 8π inches. Thus, we can substitute 8π for C:

\(8\pi =2\pi r\)

To solve for r, the radius, we can divide both sides by 2π. Hence:

\(\displaystyle r = \frac{8\pi}{2\pi}=4\)

Therefore, the radius is four inches.

Our answer is A.

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

Learn more about local maximum and minimum here:

https://brainly.com/question/28983838s

#SPJ1

The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

Learn more about tangent function, click;

https://brainly.com/question/28994024

#SPJ1

A triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). The translation direction is 2 units to the left. The number of units of the image of triangle JKL is 2 units to the left only.

Given that a triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). We have to determine the translation direction and the number of units of the image of triangle JKL. Let's first find the translation direction to determine the image of triangle JKL.

Seeing the position of J and J', we can determine that the translation was made in the left direction because J has moved from the point (-1,-5) to (-3,-5). Thus, the translation direction is 2 units to the left. Now, let's calculate the number of units of the image of triangle JKL.

Let's draw a rough sketch of the triangle JKL and locate its vertices J(-1,-5), K(-2,-2), and L(2,-4).To find the number of units of the image of triangle JKL, we need to find the horizontal and vertical distances between the vertices of the original triangle and its image.

We can use the horizontal distance between J and J′ as a reference to calculate the remaining distances. J has moved 2 units to the left, so the horizontal distance between J and J′ is 2. Now, let's calculate the vertical distance between J and J′. The coordinates of J and J′ are (-1,-5) and (-3,-5), respectively.

The difference between the y-coordinates of J and J′ is 0, which means that J and J′ are on the same horizontal line. Therefore, the vertical distance between J and J′ is 0. Hence, the image of the triangle JKL has moved 2 units to the left and 0 units vertically. Thus, the number of units of the image of triangle JKL is 2 units to the left only.

For more questions on the triangle

https://brainly.com/question/17335144

#SPJ8

Answer:

D, liner function

Step-by-step explanation:

number of employees goes up every year. If graphed it would be a line.

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

For more such questions on vertex

https://brainly.com/question/25651698

#SPJ8

The quadratic equation that passes through points (1, - 9) and (0, - 8) is y = x² - 2 · x - 8.

Graphically speaking, quadratic equations are parabolas. The quadratic equation in vertex form is described by this formula:

y - k = C · (x - h)²

Where:

If we know that (x, y) = (0, - 8) and (h, k) = (1, - 9), then the vertex constant is:

- 8 + 9 = C · (0 - 1)²

1 = C · (- 1)²

1 = C

C = 1

Then, the quadratic equation in vertex form is:

y + 9 = (x - 1)²

Whose standard form is:

y + 9 = x² - 2 · x + 1

y = x² - 2 · x - 8

The quadratic equation that passes through points (1, - 9) and (0, - 8) is y = x² - 2 · x - 8.

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

Learn more about mean absolute deviation at: https://brainly.com/question/447169

#SPJ1

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

For more such questions on figures, click on:

https://brainly.com/question/24491627

#SPJ8

Answer: 9 shirts I think

Step-by-step explanation: 54/6=9

Step-by-step explanation:

either you made a typo, or this equation is true for all values of x.

the condition x² > 1 does not change that really.

it only eliminates any values for x between -1 and +1.

so,

-infinity < x < -1 or 1 < x < +infinity

x in (-infinity, -1) or x in (1, +infinity)

Step-by-step explanation:

Jalya's video games = x

She bought four more = +4

Now what she has = 10

1. x+4=10

2. The variable x represents the unknown value of the video games Jayla had.

3. x+4=10(Group like terms)

x=10-4

x=6

Answer:

4, 15, 6, 18.

Step-by-step explanation:

Try the others by yourself and if you have any questions ask me in the comments

Answer:

  51 inches

Step-by-step explanation:

The centroid G divides each median into the ratio 2:1, so GF is 1/3 of CF. That is, ...

  CF = 3(GF) = 3(17 in)

  CF = 51 in

Answer:

a) \(\Delta A \approx 26.389\,cm^{2}\), b) \(r_{A} \approx 0.019\), c) \(\delta = 1.9\,\%\)

Step-by-step explanation:

a) The area of the circular disk is modelled after this expression:

\(A = \pi \cdot r^{2}\)

The total differential is given by the following formula:

\(\Delta A = 2\pi r \cdot \Delta r\)

The maximum absolute error in the calculated area of the disk is:

\(\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)\)

\(\Delta A \approx 26.389\,cm^{2}\)

b) The relative error is given by:

\(r_{A} = \frac{\Delta A}{A}\)

\(r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}\)

\(r_{A} \approx 0.019\)

c) The percentage error is:

\(\delta = r_{A}\times 100\,\%\)

\(\delta = 0.019 \times 100\,\%\)

\(\delta = 1.9\,\%\)

Answer:

\((f\circ g)(8)=-3\)

Step-by-step explanation:

Composite Function

Given f(x) and g(x) real functions, the composite function named \((f\circ g)(x)\) is defined as:

\((f\circ g)(x)=f(g(x))\)

For practical purposes, it can be found by substituting g into f.

The functions are defined as follows:

\(f(x)=x^2-4\)

\(g(x)=7-x\)

To find \((f\circ g)(8)\), we evaluate g in x=8 and then apply the composition formula.

\(g(8)=7-8=-1\)

\((f\circ g)(8)=f(g(8))\)

\((f\circ g)(8)=f(-1)\)

\((f\circ g)(8)=(-1)^2-4=1-4\)

\(\boxed{(f\circ g)(8)=-3}\)

\(\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=-70\)

\(\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=-70\)

\(\\ \tt\Rrightarrow y(2)(4)(7)=70\)

\(\\ \tt\Rrightarrow y(56)=70\)

\(\\ \tt\Rrightarrow y=\dfrac{70}{56}\)

\(\\ \tt\Rrightarrow y=\dfrac{5}{4}\)

#2

\(\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=120\)

\(\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=120\)

\(\\ \tt\Rrightarrow -y(2)(4)(7)=120\)

\(\\ \tt\Rrightarrow 56y=-120\)

\(\\ \tt\Rrightarrow y=\dfrac{-120}{56}\)

\(\\ \tt\Rrightarrow y=\dfrac{-15}{7}\)

Answer:

Step-by-step explanation:

We can see the divisors are 2 and 3 apart.

i.

Factorize -70 so that divisors are 2 and 3 apart:

The smallest one is 1 - y and -7:

ii

Factorize 120 so that divisors are 2 and 3 apart:

The smallest one is 1 - y and 3:

Answer:

answer is

24=12

solution

3(-2x+2x+8)=12

3(8)=12

24=12

2is a answer

Answer: I need more info

Step-by-step explanation: a buch of letters and such cant help me. Take a screen shot or a pic please

the answer will be 33.33% percent

Answer:

Slope EQUALS: \(-\frac{6}{7}\)

Step-by-step explanation:

y=-x+3

Answer:

  4

Step-by-step explanation:

You are given a table of function values in which x increases by 2, and you want to know the factor by which f(x) increases when x increases by 1.

Let k represent the factor by which f(x) increases when x increases by 1. This means ...

  f(2) = k·f(1)

  f(3) = k·f(2) = k·(k·f(1)) = k²·f(1)

  64 = k²·4

  k² = 64/4 = 16

  k = √16 = 4

The output value increases by a factor of 4 as the input value increases by 1.

__

Additional comment

The table values would also be obtained if the factor of increase were -4. That is, f(x) = -(-4)^x would give the same table. In that case, f(x) would not be a continuous function.

Answer:

2%

15%

25%

90%

Step-by-step explanation:

To turn decimals to percents, you just have to times them by 100 or you can just do the quick way and move the decimal 2 places to the right.

0.02*100 = 2%

0.9*100 = 90%

0.25*100 = 25%

0.15*100 = 15%

Then, you just put them in order:

2%

15%

25%

90%

Please mark me the brainliest!?!

The sides length and angle of the right triangle is as follows:

b = 19.3 units

c = 26.4 units

∠A = 43°

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the sides and angles of the right triangle as follows:

using trigonometric ratios,

tan 47 = opposite / adjacent

tan 47 = b / 18

cross multiply

b = 18 tan 47

b = 19.3 units

Let's find c

cos 47 = adjacent / hypotenuse

cos 47 = 18 / c

cross multiply

c = 18 / cos 47

c = 26.4 units

Let's find the angle A as follows:

∠A = 180 - 90 - 47

∠A = 43 degrees

learn more on right triangle here: https://brainly.com/question/28523734

#SPJ1

Answer:

about 80

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

Brainliest please~