Payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. The table shows his data.


A 2-row table with 9 columns. The first row is labeled number of hours with entries 1, 2, 3, 4, 5, 6, 7, 8. The second row is labeled number of errors with entries 36, 34, 30, 31, 23, 16, 11, 5.


Which is the approximate slope of the line of best fit for the data?

Answer:

This system of equations has one real solution, (2, 8).

Step-by-step explanation:

Given:

y = x² + 4

y = 4x

1. Substitute the given value of y into y = x² + 4:

⇒ 4x = x² + 4

2. Solve for x (by factoring):

⇒ 4x = x² + 4

⇒ 0 = x² - 4x + 4

⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]

⇒ 0 = (x - 2)² [take the square root of both sides]

⇒ [tex]\sqrt{0} = \sqrt{(x - 2)^2}[/tex]

⇒ 0 = x - 2 [add 2 to both sides]

⇒ 0 + 2 = x - 2 + 2

⇒ 2 = x

3. Find the value of y by substituting the given value of x into y = 4x:

⇒ y = 4(2)

⇒ y = 8

4. Check your work:

⇒ y = x² + 4          and          ⇒ y = 4x

⇒ 8 = 2² + 4         and          ⇒ 8 = 4(2)

⇒ 8 = 4 + 4          and           ⇒ 8 = 8 ✔

⇒ 8 = 8 ✔

Solution: (x, y) ⇒ (2, 8)

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Cindy gets (12-c) amount while others get 12 cookies.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

From the question, we are informed that Grandma baked 96 cookies

And there are 8 grandchildren available

To calculate the number of cookies each of them gets we have,

= 96 /8

= 12 cookies

This means each gets 12 cookies

But Cindy received fewer cookies with less C amount.

Therefore Cindy gets (12-c) amount while others get 12 cookies.

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Answer:3,5,7,9

Step-by-step explanation:I’m pretty sure all the inputs are the domains

A correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

A correlation can be defined as the relationship that exists between two variables when one of them is related to the other in some way.

It is also a measure that expresses the extent to which two variables are closely or linearly related which entails that they change together at a constant time.

Hence, correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

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The English phrase can be written as the fraction:

   [tex]\frac{m}{n + p}[/tex]

Remember that the quotient between two numbers gives a fraction.

Now, we have the sentence:

"the quotient of m and the sum of n and p."

Then we know that the numerator is m, and the denominator is (n + p) (the sum of n and p).

So the expression will just be the fraction:

[tex]\frac{m}{n + p}[/tex]

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The congruence theorem that can be used to prove that both triangles are congruent is: C. SSS.

The SSS congruence theorem is a triangle theorem which states that two triangle are congruent if they have three pairs of corresponding sides that are congruent.

The triangles in the image given have the following three corresponding sides that are congruent:

Therefore, the congruence theorem to prove they are congruent is: C. SSS.

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Answer: y = -8

Step-by-step explanation:

Lines that have a slope of Zero means that the line is horizontal and y is always the same. So your equation is y = -8

Answer:

y = - 8

Step-by-step explanation:

A line with a slope of 0 is a horizontal line parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (0, - 8 ) with y- coordinate - 8 , then

y = - 8 ← equation of line

Answer:

Decreasing

Step-by-step explanation:

Because the equation of that graph is Y=-X, and the - in the X represents that the graph is decreasing.

It’s extremely hard to tell, but it looks like it’s 3 over 2, which is 3/2.

3/2 is 1.5, or just 3/2. Since the line is going down, the slope would be negative, so -3/2.

Hope this helps!

Answer:

Step-by-step explanation:

-3/2 i think

THis might be wrong tho

Answer:

[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=y^2x+2 \cos(x)[/tex]

To find the derivative of the given equation, use implicit differentiation.

Add d/dx in front of each term:

[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x+\dfrac{d}{dx}\:2 \cos(x)[/tex]

Differentiate terms in x only (and constant terms) with respect to x:

[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]

Use the chain rule to differentiate terms in y only:

(in practice this means to differentiate with respect to y then place dy/dx on the end)

[tex]\dfrac{dy}{dx}\: =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]

Use the product rule on the term in x and y:

[tex]\textsf{let }u=y^2 \implies \dfrac{du}{dx}=2y \dfrac{dy}{dx}[/tex]

[tex]\textsf{let }v=x \implies \dfrac{dv}{dx}=1[/tex]

[tex]\implies u\dfrac{dv}{dx}+v\dfrac{du}{dx}=y^2+2xy \dfrac{dy}{dx}[/tex]

Therefore:

[tex]\dfrac{dy}{dx} =y^2+2xy \dfrac{dy}{dx}-2 \sin(x)[/tex]

Rearrange to make dy/dx the subject:

[tex]\dfrac{dy}{dx}-2xy \dfrac{dy}{dx} =y^2-2 \sin(x)[/tex]

[tex]\dfrac{dy}{dx}(1-2xy)=y^2-2 \sin(x)[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]

Answer:

3.5 gallons of punch

Step-by-step explanation:

There are 4 quarts in 1 gallon.

Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.

Elijah made 3.5 gallons of punch.

well, we know the discount is 4975 - 3781 = 1194.

if we take 4975 to be the 100%, what is 1194 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]

Answer:

0.76

Step-by-step explanation:

4975 × 0.76 = 3781

the discount percent given is .76%

The recursive formula will be equal to f(n + 1) = –2 f(n).

The complete question is given below:-

Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?

3, –6, 12, –24, 48, …

f (n + 1) = –3 f(n )

f (n + 1) = 3 f(n )

f (n + 1) = –2 f(n )

f (n + 1) = 2 f(n)

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The recursive formula for this sequence is calculated as we will put the different values of n to find the values of the function in the series.

n  =  1

f(n) = 3

n = 2

f(2) = -2 (3) = -6

n = 3

f(3) = -2 (-6) = 12 and so on

Therefore the recursive formula will be equal to f(n + 1) = –2 f(n).

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Answer:

see attached

Step-by-step explanation:

Morning:

12, 19, 19, 21, 23, 25, 27, 31, 36, 39

Min value: 12

Lower quartile (Q1): 19

Median (Q2): 24

Upper Quartile (Q3): 31

Max value: 39

Afternoon:

8, 8, 11, 15, 16, 27, 34, 39, 43, 51

Min value: 8

Lower quartile (Q1): 11

Median (Q2): 21.5

Upper Quartile (Q3): 39

Max value: 51

Answer:

7.  AM IQR: 12   PM: IQR: 28  8. see below in explanation

Step-by-step explanation:

7. 31-19=12

    39-11= 28

You subtract Q1 from Q3 to get the IQR.

8. I believe the morning group of dogs would be easier to walk as one group because the group has a closer range of weights (12-39) compared to the afternoon group of (8-51). Walking a large group of dogs with similar weights would be easier than walking a group of very small and very large dogs at the same time because their pace of walking would be so different.

Answer:

You can refer to the given attachment

Answer:

2 solutions   x = 3 y = -2.

Step-by-step explanation:

x + 2y = –1

2x + 3y = 0

Multiply first equation by -2:

-2x - 4y = 2      Adding this to second equation:

       - y = 2

y = -2.

Plug this into first equation:

x - 4 = -1

x = 3.

By using the given dimensions and volume of water, we will see that the height of the tank is 36.6cm

We know that 27,238 cm³ is the volume of water on the tank, and this is equal to 2/3 of the volume of the tank.

So we can write:

27,238 cm³ = (2/3)*V

Then the volume of the tank is:

V = (3/2)*27,238 cm³ = 40,992 cm³

The base of the tank measures 40cm by 28cm, then:

B = 40cm*28cm = 1,120 cm²

Then the height H is such that:

H*1,120 cm² = 40,992 cm³

Solving for H:

H = (40,992 cm³)/(1,120 cm²) = 36.6cm

The height of the tank is 36.6 centimeters.

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Answer:

1,290.6 in3                                                                                                                                                  

nut.

The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.

We need the answer in cubic centimeters. So let's convert 350 cubic inches to cubic centimeters. We will do it unit conversion way (the long way).

We will write cubic inches as three inches side-by-side

350 in^3

This way, we can multiply this by the ratio of centimeters to inches [2.54 cm = 1 inch], so that the units cancel and we have cubic centimeters (what we desire).

350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in

So, we can cancel the three inches top and bottom thus we have the answer in centimeters cubed. And the value is

350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in.

350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in=5735.47.

So 350 cubic inches is approximately 5735.5 cubic centimeters (rounded to 1 decimal place).

This is larger than a 5500 cubic centimeters engine.

5735.5-5500=235.5cubic centimeters.

The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.

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Its 48

33+15

Step-by-step explanation:11+11+11+15= Perimeter

33+15 = Perimeter

48 = Perimeter

THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS is 7/22.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Let's denote students

D = in the drama club ,

S = in a sports team

So, P(D) = 85/330

P(S) = 200/330

P(D and S) = 60/300

P(D or S) = P(D) + P(S) - P(D and S)  

P(D or S) = 85/330 + 200/330 - 60/330

P(D or S) = 15/22

P(neither D nor S) = 1- 15/22

P(neither D nor S) = 7/22

Thus, THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS is 7/22.

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Answer:

Step-by-step explanation:

Area of the sector :

[tex]Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}[/tex]

Finding the area given r = 30 ft. and θ = 60° :

⇒ Area = π × (30)² × 60/360

⇒ Area = π × 900/6

⇒ Area = 150π ft²

===========================================================

Length of the arc :

[tex]Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}[/tex]

Finding the arc length given r = 30 ft. and θ = 60° :

⇒ Arc Length = 2 × π × 30 × 60/360

⇒ Arc Length = 60/6 × π

⇒ Arc Length = 10π ft.

Answer:

1. 150π ft²

2. 10π ft²

Step-by-step explanation:

Hello there!

Here is how we solve the given problem:

L = ∆°/360° ×2πr

From our problem,

∆ = 60°, r = 30ft

Lets substitute the values

1. A = (∆°/360°) × πr²

= 60°/360° × π × 30²

= 150π ft²

2. L = ∆°/360° × 2πr

= (60/360) × 2 × 30 × π

= 10π ft²

NOTE:

Use the formulas given below to be on a save side;

I hope this helps.

Have a nice studies. :)

The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,

8/ Sin(30°) = 11/ Sin(θ)

Sin(θ) = [11 × Sin(30°)]/8

Sin(θ) = 0.6875

θ = Sin⁻¹ (0.6875)

θ = 43.4325° ≈ 43°

Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

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Answer:

3 I think.

Step-by-step explanation:

5 would be broken up to 2 groups of 2 and 1 group of 1.

In 20 different ways 5 dessert courses can be arranged taken 2 at a time.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, There are 5 dessert courses in a restaurant and they will be presented two at a time in an order.

Here we have to use permutation as order matters.

Now, the permutation of 5 different things taken 2 at a time is,

= [tex]^5P_2[/tex].

= 5!/(5 - 2)!.

= 5!/3!.

= 5 × 4.

= 20 different ways.

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The ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

The side length AB is given as:

AB = 8x

The area of the white square is calculated as

White = (AB)²

This gives

White = (8x)²

Evaluate

White = 64x²

The side length AB represents the diameter of the black circle.

So, the radius is:

r =AB/2

This gives

r = 8x/2 = 4x

The area is then calculated as:

Circle = πr²

This gives

Circle = π(4x)²

Evaluate

Circle = 16πx²

Next, calculate AW and AZ using:

AZ = AW = AB/2

Evaluate

AZ = AW = 8x/2 = 4x

Calculate WZ using the following Pythagoras theorem

WZ² = AW² + AZ²

This gives

WZ² = (4x)² + (4x)²

Evaluate

WZ² = 2(4x)²

Take the square root of both sides

WZ = 4x√2

The area of the gray square is:

Gray = WZ²

This gives

Gray = 2(4x)²

Evaluate

Gray = 32x²

At this point, the areas are:

The ratio is then represented as:

Ratio = Circle : White : Gray

This gives

Ratio = 16πx² : 64x² : 32x²

Divide through by 16x²

Ratio = π : 4 : 2

Hence, the ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

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The expression that represents the width of the patio is (x+3) feet

From the question, we are to determine the width of the patio

The area of the patio = Length of the patio × Width of the patio

From the given information,

Length of the patio = (x+11) feet

Area of the patio = x^2+14x+33 = x²+14x+33

Putting the parameters into the formula,

x²+14x+33 = (x+11)  × Width of the patio

∴ Width of the patio = (x²+14x+33) / (x+11)

First, we will factor x²+14x+33

x²+14x+33

x²+11x+3x+33

x(x+11) +3(x+11)

(x+3)(x+11)

Thus,

Width of the patio = [(x+3)(x+11)] / (x+11)

∴ Width of the patio = (x+3) feet

Hence, the expression that represents the width of the patio is (x+3) feet

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The length of the given golden rectangle is; 1.618 units

We are told that, for the golden rectangle;

Length = x units,

Width = (x - 1) units,

Area = 1 unit².

The area of this rectangle will have the formula;

A = x(x - 1)

Thus;

x(x - 1) = 1

Expanding gives;

x² - x - 1 = 0

Using online quadratic equation calculator, we have;

x = 1.618 or -0.618.

Length has to be positive and so we choose x = 1.618

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Answer:

it's 9

Step-by-step explanation:

type it in a calculater