Explain how you can use a part:part ratio to determine the part:whole ratio.

Answer:

  7.07 cm/min

Step-by-step explanation:

You want the rate of change of water level in a conical tank 16 m high with radius 4 m when the level is 12 m and the water is draining at 2 m³/min.

The level of water in the tank is 12/16 = 3/4 of the height of the tank, so the radius of its surface is (3/4)(4 m) = 3 m. The surface area is ...

  A = πr²

  A = π(3 m)² = 9π m² ≈ 28.3 m²

The rate of change of level is the rate of change of volume divided by the surface area:

  V'/A = (-2 m³/min)/(9π m²) = -2/(9π) m/min ≈ -0.07074 m/min

The water level is falling at about 7.07 cm/min.

Answer:

A) $75

B) y = 30x + 15

C) (24, 735) **graph below

D) Yes, there is a proportional relationship

Step-by-step explanation:

We can represent this relationship with an equation.

y = 30x + 15

where x would represent the months and y would be the total cost. The 15 would be the initial fee, which only occurs once.

A) Using the relationship [tex]y = 30x + 15[/tex], we can substitute 2 for x, since that would represent the months.

[tex]y = 30x + 15\\y = 30(2) + 15\\y = 75[/tex]

It would be 75 dollars.

B) The total cost for x months would just be the relationship

[tex]y = 30x + 15[/tex]

C) 2 years would represent 24 months. The screen shot below would represent the relationship. The y axis would be the total cost in dollars and the x axis would be the months. (24, 735)

D) Yes, there is a proportional relationship because as the time (months) progress or increases so does the price (dollars). The graph is linear too, which means it increases.

Answer: 274.05 dollars

Step-by-step explanation:

9.45 x 5 x 3 = 141.75

9.45 x 7 x 2 = 132.3

141.75 + 132.3 = 274.05

Brainliest by any chance?

The interior angles are 43°, 43° and 94°. and  exterior angle is 86°

Let the interior angles are ∠A, ∠B and ∠C.

From the question, we have

∠A = (5x-12)°

exterior angle = (8x-2)°

As the sides are equal

∠A =∠B = (5x-12)°

∠C = 180°-(8x-2)°

=182°-8x

Sum of interior angles of a triangle is equals to 180 degree.

∠A + ∠B + ∠C = 180°

(5x-12)°+(5x-12)°+182°-8x = 180°

2x+158° = 180°

x = 11°

Interior angles,

∠A =∠B = (5x-12)°

= (5*11-12)°

=43°

∠C =182°-8x

=182°-8*11

=94°

exterior angle = (8x-2)°

=8*11-2

=86°

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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AB = r AB

This is a dilation of similar triangles dilated by scale factor r.

Option B is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Dilation means the original triangle is resized by the given dilation scale factor.

We multiply the scale factor with the original value.

Here,

AB, DE, and DF are the sides of the triangle.

If a side of the triangle is dilated we must have the same side along with the dilation scale factor r.

Now,

A) AB = r DF

This is not correct.

B) AB = r AB

This is correct.

C) AB = r DE

This is not correct.

D) AB = r EF

This is not correct.

Thus,

AB = r AB

This is a dilation of similar triangles dilated by scale factor r.

Option B is the correct answer.

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Answer:

x^4 times q^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

this looks tough, but just remember that powers can be rewritten like this

[tex]\sqrt{x^{4} x^{2} q^{4} }[/tex]

then just break up the square root sign, which is another property of square roots

[tex]\sqrt{x^{4} }[/tex]*[tex]\sqrt{x^{2} }[/tex]*[tex]\sqrt{q^{4} }[/tex]

you could break the [tex]x^{4}[/tex] into two  [tex]x^{2}[/tex] but I think you can see that it will just be [tex]x^{2}[/tex] once it's pulled out of the square root

[tex]x^{2} *x*q^{2}[/tex]

[tex]x^{3}[/tex]*[tex]q^{2}[/tex]

Does this all make sense?

The equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.

The rational function has x-2 in the denominator.

The denominator cannot be zero.

The rational function will be:

[tex]y=\dfrac{\left(x^{2}-16\right)}{x-2}[/tex]

Thus, the equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.

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Answer:

its a

Step-by-step explanation:

JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis is J'(-1, 0), K'(-5, -3), L'(-7, 1).

In the given question we have to graph JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis.

The given vertices are J(1, 3), K(5, 0), and L(7, 4).

Firstly translation along (0,-3).

So translation is (x,y)→(x,y-3)

J'=(1, 3-3)=(1, 0)

K'=(5, 0-3)=(5, -3)

L'=(7, 4-3)=(7, 1)

We have to find the reflection in the y-axis so (x,y)→(-x,y).

Now the points are J'(-1, 0), K'(-5, -3), L'(-7, 1).

The graph of the glide reflection with a translation along <0,-3> and a reflection in the y-axis is given below.

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Answer:

Re-arrange the terms and combine the like terms.

2

3

y

−

1

3

y

−

3

−

4

=

1

3

y

−

7

Step-by-step explanation:

Using graphing calculator, the solution to the inequality is attached

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

Using a graphing calculator;

Kindly find the attached graph as solution to the inequality

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Answer:

x = ± 9

Step-by-step explanation:

x² = 81 ( take square root of both sides )

x = ± [tex]\sqrt{81}[/tex] = ± 9

[tex]{ \red{ \boxed{ \pink{ \sf{x = 9}}}}}[/tex]

Step-by-step explanation:

Here, the question is,

[tex]{ \green{ \sf{ {x}^{2} = 81}}}[/tex]

Apply square root on both the sides then,

[tex]{ \green{ \sf{ \cancel { \sqrt{x} }^{ \cancel2}}}} \: = { \green{ \sf{ \sqrt{81}}}} [/tex]

Now,

[tex]{ \green{ \sf{x = \sqrt{81}}}} [/tex]

We got √81 as answer but what is the perfect square number of 81? That is 9. Same number when multiplied twice to get the resultant number makes a perfect square number. i.e. 9×9 = 81. So, the answer is

[tex]{ \green{ \boxed{ \red{ \tt{x = 9}}}}}[/tex]

Answer: The answer will be 74.07 percent.

According to the question, let the number be x

Then, x*54/100 = 40

x = 40 × 100 / 54

x = 74.07 (approx)

The value of an integer or any letter associated with a variable is known as its coefficient. In the expression 2x + 3y, for instance, the variable x has a coefficient of 2 and the variable y has a coefficient of 3.

There are 842 buttons in 36 shirts and 42 jackets if the number of buttons in each is equal to x.

Additionally, the collection of six shirts and seven jackets has 137 buttons.

It can be expressed using the following equations:

36 x + 42 y = 842 ------(1);

6 x + 7 y = 137 ------(2);

6 x + 36 x + 42 y = 822 ------(3).

Although the constant term on one side of equation is different, the x and y coefficients are the same in both of these equations. This indicates that neither equation has a solution.

I.e →a1/a2=b1/b2≠c1/c2

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Answer: 4 reds

Step-by-step explanation:

Answer:

508.94

Step-by-step explanation:

V = 1/3pi(r^2)(h)

plug in the values of r and h

V = 1/3(pi)(9^2)(6)

simplify

V = 508. 9380099

Round to nearest hundredth

V = 508.94

The initial bird population density is 3713.

Given info;

A certain county received a new species of bird 25 years ago. According to biologists, the population doubles every ten years and is currently 21,000 people.

To get the initial size of the bird population;

We use the formula,

[tex]P(t)=Po* 2^\frac{t}{10}[/tex]

Where Po is the initial population and t is the time in years.

[tex]21000= P(25)=Po*2^\frac{25}{10}[/tex]

[tex]21000= Po*2^\frac{5}{2}[/tex]

[tex]21000= 4\sqrt{2}*Po[/tex]

[tex]Po = 21000/4\sqrt{2}[/tex]

[tex]Po = 3712.31\\Po = 3713[/tex]

Hence, the initial size of the bird population is 3713.

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Answer:

Answer D

Step-by-step explanation:

Multiply them all out. D is 4.04

Answer: D is correct I took the test without having to see the answer just wanted to help u out:)

Step-by-step explanation:

The probability of selecting at least one experienced IPV is 0.598 and at least one did not experience IPV is 0.866.

In the given question we have to find the probability of selecting at least one experienced IPV and at least one did not experience IPV

From the given table

Probability of experiencing IPV

P(Experienced IPV) = 366 / 1000 = 0.366

Probability of not experiencing IPV

Q(Not-experienced IPV) = 634 / 1000 = 0.634

Now when n samples are chosen from the population, the binomial probabilty distribution follows (P + Q)^n.

Here, n = 2,

So, (p +q)^2 = p^2 + 2pq + q^2

p^2 = Both experienced IPV

2pq = One has experienced IPV and other hasn’t

q^2 = None have experienced IPV.

A. Finding the probability of at least one experienced IPV.

P(At least one has experienced IPV) = P^2 + 2PQ

                                                         = (0.366)^2 + 2(0.366)(0.634)

                                                         =0.1339+0.4641

                                                         = 0.598

B. Finding the probability of at least one did not experienced IPV.

Q(At least one did not experienced IPV) = Q^2 + 2PQ

                                                                   = (0.634)^2 + 2(0.366)(0.634)

                                                                   =0.4019+0.4641

                                                                   = 0.866

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Probability that the second card is an ace, given that the first card is an ace is 1/ 221

Without replacement means drawing the card first but not putting back to the deck and then drawing again.

Total number of cards in a deck = 52

Number of an ace in whole deck = 4

let event of getting an ace in first draw be A

and event of getting an ace in second draw be B

P(A) = 4 / 52 = 1 /13

drawing without replacement

P(B) = 3 / 51 = 1 / 17

Probability that second card is an ace given that first card is an ace is

P(A).P(B) =

1/13 × 1/ 17 = 1 / 221

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The speed of the football in the air is 7.1 yards per second

From the question, the given parameters are:

Distance = 60 yards

Time to cover this distance = 8,5 seconds

The speed of the football in the air is calculated as

Speed = Distance/Time to cover this distance

Substitute the known values in the above equation

So, we have the following equation

Speed = 60/8.5

Evaluating the quotient in the above equation, we have

Speed = 7.1

Hence, the ball's speed in air is 7.1 yards per second

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The equation of the perpendicular line that passes through the point (- 3, - 1) is y = 2 · x + 5.

In this question we must determine the equation of a line that is perpendicular to another line and pass through a given point. Mathematically speaking, lines are represented by the following equation:

y = m · x + b

Where:

And the slopes of two lines perpendicular to each other satisfy the following relationship:

m · m' = - 1

Where:

First, determine the slope of the perpendicular line by means of the slope relationship:

m = - 1 / 2

m' = - 1 / m

m' = - 1 / (- 1 / 2)

m' = 2

Second, find the intercept of the perpendicular line by the equation of the line:

b = y - m · x

b = - 1 - 2 · (- 3)

b = - 1 + 6

b = 5

Third, write the equation of resulting line:

y = 2 · x + 5

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Answer:

Rs. 450

Step-by-step explanation:

Selling Price ----- 750

Reduced by 40% therefore 40/100 x 750

=300

750-300= 450

Answer:

$450

Step-by-step explanation:

40 percent *750 =

(40:100)*750 =

(40*750):100 =

30000:100 = 300

750-300=$450

The coordinates that represents the position of the library is (0, -8)

Each unit on the grid represents 1 mile

Tia is going from park to library

The coordinates of the park = (5, -5)

First she must go 3 miles to the south, Therefore there will be change in the y coordinates and the x coordinates will be same

New coordinate of the Tia's position = (5, -8)

Then she must go 5 miles west, there will be change in the x coordinates and the y coordinates will be same

New coordinates of the Tia's position = (0, -8)

Hence, the coordinates that represents the position of the library is (0, -8)

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Answer:

Basically Mate you gotta make a perpendicular line from the letter your told make a line from and then thats for the 2 pages basically they want you to do the same thing that is done but you do it for the letter.

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The volume of the cylinder is 18149.2 yards³.

It is important to note that the volume of a cylinder is calculated as:

Volume = πr²h

Radius = 17

Height = 20

Therefore, the volume will be:

Volume = πr²h

Volume = 3.14 × 17² × 20

Volume = 18149.2

The volume is 18149.2 yards³.

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Answer:

y=-1(-3)+2

Step-by-step explanation:

on my test

The width and length of the rectangle will be 4 units and 8 units, respectively.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The width of a square shape is 4 units less than the length. The region of the square shape is 32 square units. Then the equations are given below.

W = L - 4               ...1

L × W = 32           ...2

From equations 1 and 2, then we have

L × (L - 4) = 32

L² - 4L = 32

L² - 4L - 32 = 0

L² - 8L + 4L - 32 = 0

L(L - 8) + 4(L - 8) = 0

(L - 8)(L + 4) = 0

L = 8, -4

Then the width of the rectangle is given as,

W = 8 - 4

W = 4 units

The width and length of the rectangular shape will be 4 units and 8 units, separately.

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The equation that represents the situation is 2(x+17/4+x) = 249/2 where x is the width, the width of the postage stamp is 29 millimeters and its length is 33.25 millimeters.

According to the question,

We have the following information:

The length of a postage stamp is [tex]4\frac{1}{4}[/tex] millimeters longer than its width. The perimeter of the stamp is [tex]124\frac{1}{2}[/tex] millimeters.

Now, let's take the width of the stamp to be x millimeters.

Length of the stamp = x + 17/4

(We have the converted the fractions from the mixed fraction.)

Now, we have the following expression because the stamp is in the shape of a rectangle:

2(length+width) = 249/2

a) 2(x+17/4+x) = 249/2

b) 2(2x+17/4) = 249/2

Dividing by 2 on both sides of the equation:

2x+17/4 = 249/2*2

2x+17/4 = 249/4

Subtracting 17/4 from both sides of the equation:

2x = 249/4 - 17/4

2x = 232/4

Dividing by 2 on both sides:

x = 232/(4*2)

x = 116/4

x = 29 millimeters

c) Length of the stamp = 29+17/4

Length = (116+17)/4

Length = 133/4

Length = 33.25 millimeters

Hence, the equation that represents the situation is 2(x+17/4+x) = 249/2 where x is the width, the width of the postage stamp is 29 millimeters and its length is 33.25 millimeters.

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