Solve each equation.

Answer: 8 plays.

Step-by-step explanation: I might be missing something here, but it says at least 1 times as many plays?? 8 * 1 = 8, so I guess 8 plays?

The conic water vessel of height 40 cm and radius 8 cm filled at 20 cm^3/s gives;

The volume of the vessel, v = π•r^2•h/3

[tex] \frac{h}{r} = \frac{40}{8} = 5[/tex]

h = 5•r

Therefore;

v = π•r^2•(h)/3 = π•(h/5)^2•h/3

v = π•h^3/75

By chain rule of differentiation, we have;

[tex] \frac{dv}{dh} = \frac{dv}{dt} \times \frac{dt}{dh} [/tex]

Which gives;

[tex]π• \frac{ {h}^{2} }{25} = 20 × \frac{dt}{dh} [/tex]

[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {h}^{2} }{25} } [/tex]

When the height is 12 cm from the vertex, we have;

[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {12}^{2} }{25} } = 1.1 [/tex]

When the vessel is one-quarter filled, we have;

v = π•h^3/75

π•(40)^3/(75×4) = π•h^3/75

10•(40)^2 = 16,000 = h^3

h = (16,000)^(1/3) = 25 (approx)

Which gives;

[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {25}^{2} }{25} } = 0.21 [/tex]

When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.

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Answer:

yes, it is

Step-by-step explanation:

10 = 4(2) + 2

10 = 8 +2

10 = 10

10  = 2 + 8

10 = 10

Answer:

The answer is yes

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

y = 4x + 2

y = x + 8

For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.

First, I will substitute the second equation, for y, in the first equation:

y = 4x + 2

y = x + 8

x + 8 = 4x + 2

Next, subtract 4x from both sides to isolate x:

x + 8 = 4x + 2

-4x      -4x

-3x + 8 = 2

Then, subtract 8 from both sides:

-3x + 8 = 2

     - 8    - 8

-3x = -6

Now, divide both sides by -3:

-3x = -6

/-3    /-3

x = 2

Now, we find the value of y by substituting 2 for x:

y = 4x + 2

y = 4(2) + 2

y = 8 + 2

y = 10

(x, y) ==> (2, 10)

Therefore, yes (2,10) is a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!

Answer: 22 ft

Step-by-step explanation:

The path that the dog can walk if he maximally extends his leash is the path of a semi-circle, which has a radius of 7ft.

The distance along a full circle is given by the circumference of the circle, which is related to the radius. To find the length of the path that the dog walks, we evaluate half the circumference.

[tex]\begin{aligned}&D=\frac{C}{2} \\&D=\frac{2 \pi r}{2} \\&D=\pi r \\&D=7 \pi \\&D \approx 22\end{aligned}[/tex]

Therefore, the dog can walk about 22 ft if he extends the leash as far as it can go.

Answer:

24 Letters and 4 Postcards

Step-by-step explanation:

We have to set up a system of equations, since we have two unknown variables. Lets say postcards is the variable "x" and letters is the variable "y".

Our first equation will be the money spent: 0.33x + 0.49y = 13.08, this comes from knowing that it costs 0.33 dollars to mail a postcard and 0.49 dollars to send a letter.

The second equation is the total sent: x + y =28.

Now we need to solve for a single variable, let's do y (or letters). If we subtract y from both sides we get: x = 28 - y.

We can plug that into our first equatino to get: 0.33(28 - y) + 0.49y = 13.08.

If we multiply things out we get: 9.24 - 0.33y + 0.49y = 13.08, and now we have like terms. 9.24 + 0.16y = 13.08.

Subtract 9.24 from both sides to get: 0.16y = 3.84

Divide both sides by 0.16 to get: y = 24.

Now we can plug this into x + y = 28 to see that x= 4.

You could make sure this is correct by solving for x instead of y and do the same process.

Hope this helps.

Answer:

C. 0.5..................

4 + 10 = 2 x 2 + 2 x 5 = 2 x (2 + 5)

[tex]4b(b+2)=16+4b^2\\4b^2+8b=16+4b^2\\8b = 16 + 4b^2-4b^2\\8b = 16\\b = 2[/tex]

Hope that helps!

44 students in  Mrs. Vitale's class read 11 books

Let the number of students that read 11 books in Mrs. Vitale's class be x

If One fourth of the students in Mrs. Vitale's class read 11 books, then

1/4 x = 11 books

x = 11 * 4

x = 44

Hence 44 students in  Mrs. Vitale's class read 11 books

Learn more on ratio and proportion here: https://brainly.com/question/2914376

Answer:

Step-by-step explanation:

The total number of students that are plotted on the line plot is 20.

We are given that Mrs. Vitale's class is the same size as Ms. Seiko's class so both classes have 20 students in each.

One fourth of the students in Mrs. Vitale's class read 11 books.

1/4 *20/1 =5 students

When the triangle XYZ is dilated by a scale factor of 4/3, the resulting triangle would have a bigger side lengths

The algebraic rule  is [tex](x,y) \to (\frac 43x,\frac 43y)[/tex]

From the question, we understand that:

The scale factor (k) of the dilation is:

k = 4/3

The dilation rule across the origin is represented as:

[tex](x,y) \to k(x,y)[/tex]

Substitute 4/3 for k

[tex](x,y) \to \frac 43(x,y)[/tex]

Expand

[tex](x,y) \to (\frac 43x,\frac 43y)[/tex]

Hence, the algebraic rule that represents how to find the coordinates of triangle X’Y’Z’ is [tex](x,y) \to (\frac 43x,\frac 43y)[/tex]

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96cm

Step-by-step explanation:

From the question,

Area of rectangle(A) =Area of square(A)

or,32*18=Area of square

or, 576= l^2

or√576=l

or, 24cm

Now, we know,

Perimeter of the square=4l

=4*24cm

=96cm

Answer:

b i took this exam 90% sure its B

Step-by-step explanation:

B

B

B

second 1

Answer:

$103.75

Step-by-step explanation:

Hours worked on Monday: 8.30 hours (4.15 h in the morning and 4.15 h in the afternoon)

8.30 hours x $12.50 per hour: $103.75

Answer:

what's up w u people and not giving context

Step-by-step explanation:

1. add ur complete problem

2. show a picture or add the question(s)

3. ur done at that point

Answer:

Dont have an answer but maybe this will help

Step-by-step explanation:

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.

Answer:

you need 32 eggs

Step-by-step explanation:

48 divided by 12=4

8x4=32

Answer:

2 eggs

Step-by-step explanation:

take the 48 and divide by 12 to get the answer, then take the 8 eggs and divide it by the answer you get to the first part, and you will get the amount of eggs.

Answer:

Hello there! The answer is 3 seconds.

Step-by-step explanation:

[tex] {m}^{3} = {cm}^{3} = \div {10}^{6} [/tex]

0.2m^3 = 0.0000002 cm^3

1. Volume of 1 tennis ball = volume of sphere = 33.51 in.³

2. Volume of the cylinder = 150.8 in.³

3. Amount of space not occupied by the tennis ball = Volume of cylinder - 3(volume 1 tennis ball) = 50.27 in.³

Diameter of the tennis ball = 4 in. (given)

1. Volume of 1 tennis ball = volume of sphere = 4/3πr³

r = 1/2(4 in.) = 2 in.

Volume of 1 tennis ball = 4/3π(2)³ = 33.51 in.³

2. Volume of the cylinder = πr²h

Radius of the cylinder (r) = 1/2(4 in.) = 2 in

Height of the cylinder (h) = 3(4 in.) = 12 in

Volume of the cylinder = πr²h = π(2²)(12) = 150.8 in.³

3. Amount of space not occupied by the tennis ball = Volume of cylinder - 3(volume 1 tennis ball)

= 150.8 - 3(33.51) = 50.27 in.³

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n = last test

(87 + 78 + 61 + n) : 4 = 78,5

87 + 78 + 61 + n   = 78,5 x 4

n = 314 - 226

n = 88

If the value of the function f(x) is 7, then the value of x is –16, and 24. Then the correct option is B.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The given function is f(x) = 0.5 |x – 4| – 3

If the value of the function f(x) is 7, then the value of x will be

0.5 |x – 4| – 3 = 7

      0.5 |x – 4| = 10

            |x – 4| = 20

             x – 4 = ±20

For positive signs, we have

x – 4 = 20

      x = 24

For negative signs, we have

x – 4 = –20

     x = –16

More about the function link is given below.

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Answer:

○ [tex]\displaystyle \textcolor{black}{C.}\:\sqrt{193}\:km.[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem to define the hypotenuse:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 7^2 + 12^2 = x^2 \hookrightarrow 49 + 144 = x^2 \hookrightarrow \sqrt{193} = \sqrt{x^2} \\ \\ \boxed{\sqrt{193} = x}[/tex]

I am joyous to assist you at any time.

[tex] \huge \underline\text{ Hello There}[/tex]

[tex] \text{We know, Pythagoras Theorem}[/tex]

[tex]\implies \text{ (Hypotenuse)²= (Base)² + (Altitude)²}[/tex]

[tex] \text{Here, \red{Hypotenuse}= x, \red{Base}= 7, \red{Altitude}= 12}[/tex]

[tex] \underline \text{To Find, } \text{Value of'x'}[/tex]

[tex] \huge \underline\text \red {Solution}[/tex]

[tex] \implies {x}^{2} = (7) {}^{2} + {(12)}^{2} \\ \implies(x) {}^{2} = 49 + 144 \\ \implies( {x})^{2} = 193 \\ \implies x = \sqrt{193} [/tex]

[tex] \therefore \text{Hypotenuse}= \sqrt{ 193} \text{ km}[/tex]

[tex] \text{Correct Opt. C}= \sqrt{ 193} \text{ km}[/tex]

Answer:

find the product of (4m-n) and (3m-2n)

Answer:

She has about 2 choices

Step-by-step explanation:

7 ÷ 3 ≈ 2.3

≈ 2

[tex]3xy(5x+3-7y)=15x^2y+9xy-21xy^2[/tex]