you live halfway between you're school and the park. you're friend lives halfway you and the park. how far away does you're friend live from school if you live 1/4 mile from school

Using the concept of change of subject of formula, we can express the radius r₁ and r₂ as r₁ = r₂² / 18π

The formula of volume of a cylinder is given as;

V = πr²h

The equation for the volume of the cylindrical tank is V1 = 36πr₁ and the equation for the volume of the neighborhood pool is V2 = 1/2(4/3πr₂²).

Since V₁ = V₂, we can set the two equations equal to each other and solve for r₁:

36πr₁ = 1/2(4/3πr₂²)

To solve for r₁, we can first multiply both sides of the equation by 2/4/3, which gives:

18πr₁ = r₂²

Then we can divide both sides of the equation by 18π to get:

r₁ = r₂² / 18π

So we can say that r₁ is a function of r₂ because it can be expressed in terms of r₂.

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

8 Hours = $64  56 Hours = $432

Step-by-step explanation:

Judging by the information you gave me, every hour the person gets $8. So, just multiply the number of hours worked with 8 and you get the answers above.

Answer:

6 units

Step-by-step explanation:

There is only a translation being shown, meaning that the shape is only moving. It is not getting larger or smaller.

Answer:

your answer will be option C.6

because the length does not change on translation

Step-by-step explanation:

have a nice day

Here are the given information:

24 picture books

8 science books

Answer: There are 24/8 = 3 times more picture books than science books.

Answer:

11,100

Step-by-step explanation:

1% of 30,000 is 300 so if we times 300 by 37 we get 11,100

there is 11,100 sheep in 37%.

hope this helps :)

The width of the duck pond is,

⇒ 27 feet

We can see that the given diagram is a rectangle,

And we know that,

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Now, By given diagram we have;

We have to given that;

Use the scale drawing to determine how wide the duck pond is.

And there are 4.5 feet in 1 square,

Therefore,

1 square is equal to 4.5 feet

So, we get;

The width of the duck pond is,

⇒ 6 square

We know that,

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Then to find width of duck pond in feet,

Multiply 6 with 4.5

⇒ 6 × 4.5 feet

⇒ 27 feet

Thus, The width of the duck pond is,

⇒ 27 feet

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the measure of the angle will be 70°.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.

The sum of all angle of triangle = 180

The given triangle two angles are given 44° and 68°

The other angle is 180° - (44+68) = 180 - 110 = 70°

Hence the measure of the angle will be 70°.

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Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Answer:

306 miles

Step-by-step explanation:

6 x 51

Answer:

162.5 miles

Step-by-step explanation:

hope this helps :)

Answer:

x^2+x-6

Step-by-step explanation:

i did a thing

hope this is correct and helps

Answer:

\(y = x^2 + x - 6\)

Step-by-step explanation:

Hello!

We can utilize the factored form of a parabola to find a possible equation.

Factored Form: \(y = a(x - h)(x - k)\)

Since the roots of the parabola are given, we can plug in the roots for h and k, and plug in 1 for a and multiply to find the equation.

One possible equation is \(y = x^2 + x - 6\).

When a \(50\)-foot mast throws a \(10\) foot shadow, the angles of elevation of a sun is \(5\).

The elevation angle is the angle created when an item is viewed from above its height in relation to eye level or a horizontal line.

The angle from the ground upward to an item is referred to as the angle of elevation. The line of sight of an observer would rise above the horizontal. An angle from of the horizontal downwards to an item is referred to as the "angle of depression." The line of sight of an observer will be below the horizon.

Given that,

\(Perpendicular = 50 ft\)

\(Base = 10 ft\)

We must ascertain the sun's elevation angle. Trigonometry may be used to compute it as follows:

\(tan\)θ= \(\frac{P}{B}\)

\(tan\)θ= \(\frac{50}{10}\)

θ= \(5\)

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Answer:

No solutions

Step-by-step explanation:

the x's cancel out

Answer:

36 would be the answer

Step-by-step explanation:

The length of side b in triangle 2 is 36.

Two triangles are similar if they have the same corresponding angles and their corresponding sides are in equal ratios.

Given that, there are two triangles, triangle 2 is a scale drawing of triangle 1.

Therefore, Δ 1~Δ 2,

According to the definition of similar triangles,

6/27 = 10/45 = 8/b

Therefore,

8/b = 6/27

8/b = 2/9

b = 36

Hence, the length of side b in triangle 2 is 36.

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Given :

To find :

Solution :-

The first set is ,

Solving the Quadratic equation ,

Hence ,

The second set is ,

Solving the Quadratic equation ,

Hence ,

Now ,

Since AΠ B is a null set , hence ,

Step-by-step explanation:

First get x on its own:

Subtract 3 from each side

y - 3 = 2x

Divide through by 2

y/2 - 3/2 = x

or x = y/2 - 3/2

Now simply switch labels: x↔y

y = x/2 - 3/2

Answer:

\(y=\frac{x}{2}+\frac{3}{2}\)

Step-by-step explanation:

To find inverse of an equation, replace the variables x with y and y with x:

x = 2y - 3

Now we get it in slope-intercept form:

x = 2y - 3

Add 3 to both sides.

x + 3 = 2y

Divide both sides by 2.

\(\frac{x}{2}+\frac{3}{2}=y\)

Swap left and right sides.

\(y=\frac{x}{2}+\frac{3}{2}\)

And this is the inverse of the equation y = 2x - 3.

I hope you find my answer helpful.

Answer: x=7

Step-by-step explanation:

To solve for x, you want to use algebraic properties.

20+8(x-11)=-12                  [distribute]

20+8x-88=-12                   [combine like terms]

8x-68=-12                          [add both sides by 68]

8x=56                                [divide both sides by 8]

x=7

Now we know that x=7.

Explanation:

Each vertical asymptote is due to a division by zero error.

For instance, the vertical asymptote x = 3 is from the factor (x-3) in the denominator. If we plugged x = 3 into (x-3), then it turns into 0 and we cannot have 0 in the denominator.

Similarly, the factor (x+3) leads to x = -3

So overall, we have (x-3)(x+3) in the denominator.

In every 10 minutes an average of 3 customers will arrive to the pizza station

Given,

The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.

We have to find the average number of customers arrives in each 10 minutes.

Here,

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

P (X = x) = (e^-μ × μ^x) / x!

Where,

The number of successes is x.

The Euler number is e = 2.71828.

μ is the average over the specified range.

Now,

Rate of 18 customers per hour;

μ = 18 n

n is the number of hours.

Number of customers arrive in each 10 minutes

10 minutes = 10/60 = 1/6

Then,

μ = 18 x 1/6 = 3

That is,

In every 10 minutes an average of 3 customers will arrive to the pizza station.

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Answer:

In fall 2019, female students made up 57 percent of total undergraduate enrollment (9.4 million students), and male students made up 43 percent (7.1 million students). Enrollment patterns for female and male students exhibited similar trends between 2009 and 2019.

Step-by-step explanation:

The well-known equation e(i*pi) + 1 = 0 represents Euler's identity, where e is the Euler number, or roughly 2.71828, I is the imaginary number, or roughly i2 = -1, and pi is the ratio of a circle's circumference to its diameter, or nearly 3.14.

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9514 1404 393

Answer:

  (c)  lies in the shaded regions of both the top and bottom inequalities.

Step-by-step explanation:

A point that is a solution to the system must be a solution to all of the inequalities in the system. It must lie in the shaded regions of both.

Answer:

False

Step-by-step explanation:

A composite figure would be any irregular shapes and can be made up of multiple shapes

Answer:

The best predicted value of weight for an adult male who is 185 cm tall is 111.5 kg.

Step-by-step explanation:

For this question, most of the heavy lifting has been done with the information provided in the question.

A regression analysis has been carried using the sample of 100 randomly selected adult males to find the correlation between the weight and height of the men.

x represents the height, which is then used to calculate y, the weight of the adult men.

The regression analysis yielded

x overbar x = 167.90 ​cm

y overbar y = 81.40 ​kg

r = 0.108​

P-value = 0.285 and

Y = -107 + 1.181X

For an adult man with height 185 cm, X = 185, and the predicted weight is calculated as

Y = -107 + 1.181(185) = 111.485 = 111.5 kg

But for the p-value,

The p-value for each independent variable tests the null hypothesis that the variable has no correlation with the dependent variable. In other words, there is insufficient evidence to conclude that there is effect at the population level.

If the p-value for a variable is less than your significance level, your sample data provide enough evidence to reject the null hypothesis for the entire population. Your data favor the hypothesis that there is a non-zero correlation.

On the other hand, a p-value that is greater than the significance level indicates that there is insufficient evidence in your sample to conclude that a non-zero correlation exists, especially at population level.

Here, the p-value = 0.285, significance level = 0.05, p-value > significance level, hence, the predicted weight might not hold true at the population level though.

Hope this Helps!!!

Midpoint has coordinates \((x_m,y_m)\) which equal to,

\(x_m=\frac{x_1+x_2}{2}\)

\(y_m=\frac{y_1+y_2}{2}\)

We know the coordinates of a midpoint as well as the coordinates of \(A(x_1,y_1)\) so we should be able to find coordinates of \(B(x_2,y_2)\).

First solve both equations for \(x_2\) and \(y_2\) respectively,

\(x_2=2x_m-x_1\)

\(y_2=2y_m-y_1\)

Now insert the data,

\(x_2=2\cdot1-(-3)=\boxed{5}\)

\(y_2=2\cdot2-6=\boxed{-2}\)

The coordinates of B are therefore \((5,-2)\).

Hope this helps :)

The midpoint of AB is (1, 2) the coordinates of A are (-3,6) coordinates of B coordinates of point B are (5, -2).

To find the coordinates of point B given that the midpoint of AB is (1, 2) and the coordinates of A are (-3, 6),  use the midpoint formula:

Midpoint formula: M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)

Given that M is the midpoint (1, 2) and A is (-3, 6), we have:

(1, 2) = ((-3 + x2) / 2, (6 + y2) / 2)

Solve for x2 and y2:

For x-coordinate:

1 = (-3 + x2) / 2

2 = -3 + x2

x2 = 2 + 3

x2 = 5

For y-coordinate:

2 = (6 + y2) / 2

4 = 6 + y2

y2 = 4 - 6

y2 = -2

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Answer:

1/27 in^3.

Step-by-step explanation:

1/3 * 1/3 * 1/3

The value of the expression when m = 3 is 13/15. So option(2) is correct.

The equation is defined in its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, x + 3 = 4 is an equation, in which x + 3 and 4 are two expressions separated by an 'equal' sign.

Given the expression as shown below:

2/5 m - 1/3

If m is equal to 3, then the expression will be;

2/5(3) - 1/3

6/5 - 1/3

Find the LCM

6/5 - 1/3 = 3(6)-5/15

6/5 - 1/3 = 18-5/15

6/5 - 1/3 = 13/15

Therefore the value of the expression if m = 3 is 13/15

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The amount of cups of lemonade sold by Abbie is 6 x 8 = a.

Hence, option A is correct.

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Number of lemonade cups sold by Lust = 8

Number of lemonade cups sold by Abbie =  6 times of lust

Let 'a' represents the number of cups sold by Abbie,

Therefore,

6 x 8 = a

Hence,

The correct expression is 6 x 8 = a which is option A.

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The complete question is:

Luct sold 8 cups of lemonade Abbie sold 6 times as many cups of lemonade. Which equation helps us find how many cups Abbie sold if the number of cups sold by Abbie is 'a'.

A. 6x8 = a

B. 8xa = 6

C. 6xa = 8