Area of composite figures worksheet. How do you solve it. Step-By-Step​

ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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Answer:

I need that answer too

Step-by-step explanation:

The meaning of solving a formula for a variable is rewriting the formula in a way that the variable is "isolated" in one side of the formula, that is, one side of the equation has only the variable alone, without coefficients or other expressions.

For example, let's solve the formula below for the variable y:

We can see that in the formula above, the left side of the equation has only "y", this way it is solved for y.

La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer:

the answer is B

Step-by-step explanation:

i just did this.

Answer: A

Step-by-step explanation: Ethan has a 1:6 ratio while Mia has a 1:7 ratio

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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Answer:

a) -3x + y = 8

Step-by-step explanation:

Now we have to,

→ find which of these equations is linear.

Format of linear equation,

→ Ax + By = C

Then the linear equation is,

→ Ax + By = C

→ -3x + y = 8

Hence, answer is -3x + y = 8.

Answer:

A. -3x + y = 8

Step-by-step explanation:

Definition of a Linear Equation:

This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.

This is not a linear equation as the highest power of the term in x is 2.

This is not a linear equation as the highest power of the term in x is 3.

This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.

The cuboid in question has a surface area of 202 square units.

We must sum together the areas of all six faces to determine a cuboid's surface area.

The dimensions of the given cuboid are:

length (l) = 9 units

width (w) = 5 units

height (h) = 4 units

The area of each face is given by:

Top and bottom faces:\(lw = 9 * 5 = 45\) square units each

Front and back faces: \(lh = 9 *4 = 36\) square units each

Left and right faces: \(wh = 5 * 4 = 20\) square units each

Therefore, the total surface area of the cuboid is:

\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)

Hence, the surface area of the given cuboid is 202 square units.

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Answer:

Step-by-step explanation:

Let's represent the first even number as x, then the second consecutive even number is x + 2. Since their sum is 1322, we can set up the equation:

x + (x + 2) = 1322

Simplifying and solving for x:

2x + 2 = 1322

2x = 1322 - 2

2x = 1320

x = 660

So the first even number is 660, and the second consecutive even number is 660 + 2 = 662.

Therefore, the two consecutive even numbers whose sum is 1322 are 660 and 662.

Answer:

6x

Step-by-step explanation:

The relationship that represents a function with a greater rate of change than the function graphed is given as follows:

A. y = 4x - 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The slope represents the average rate of change of a linear function.

From the graph, when x increases by one, y decreases by two, hence the slope m is given as follows:

m = -2.

For function A, the function is defined as follows:

y = 4x + 3.

Hence the rate of change is given as follows:

m = 4, which is greater than -2.

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Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

9514 1404 393

Answer:

  about 0.299 kg/m³

Step-by-step explanation:

Density is the ratio of mass to volume.

  ρ = M/V

  ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³

Answer:

C

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

The number of quilt they need to make is 182.

We are given that;

Scores they made= 118

Measure=4inch

Now,

we need to convert the dimensions of the quilt from feet and inches to inches only. To do this, we multiply 5 by 12 to get 60 inches for the length, and we multiply 6 2/3 by 12 to get 80 inches for the width.

Multiply 60 by 80 to get 4800 square inches for the area.

Also we multiply 4 by 4 to get 16 square inches for the area of one square.

we divide 4800 by 16 to get 300 squares for the total number of squares.

To find how many more they need to make. we subtract 118 from 300 to get 182 squares for the remaining number of squares.

Therefore, by area the answer will be 182 more squares.

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Answer:

15x = 15x

or

0 = 0

Step-by-step explanation:

21(x + 1) - 6x = 15x + 21

21x + 21 -6x = 15x + 21

21x - 6x = 15x

15x = 15x

or

0 = 0

this equation is always true

The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.

It is the reverse of differentiation. The differentiation is the rate of change of the function with respect to variables.

The integration is given below.

\(\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{(1 +x)^{2022}} \ dx\)

Then the integration can be written as

\(\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{[(1 +x)^{1011}]^2} \ dx\)

Let (1 + x)¹⁰¹¹ = t. Then 1011x¹⁰¹⁰ dx = dt.

Then we have

\(\rightarrow \int_{1}^{\infty } \dfrac{dt}{1011 \ t^2}\)

Then integrate

\(\rightarrow \dfrac{1}{1011} \left [ \dfrac{-1}{t} \right ]_{1}^{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ \dfrac{1}{t} \right ]^{1}_{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ 1- 0 \right ]\\\\\\\rightarrow \dfrac{1}{1011}\)

The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.

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EXPLANATION

The coordinate for point A is x=9

Answer:

16/33

Step-by-step explanation:

half of 5 is 2.5

half of 11 is 5.5

half of 15 is 7.5

half of 33 is 16.5

so 16/33 is the only fraction less than half of the denominator

hope this helps chu <3

Answer:

16/33

Step-by-step explanation:

because 16 +16 is 32 not 33 and it is a 1 over what it's supposed to be so it's less than 1/2 because 1/2 it technically something divided by 2 because it's half of something.

Answer:

sure just bring the question and it will be answered

Answer:

p=-3

Step-by-step explanation:

Answer:

-4/2=2p

Step-by-step explanation:

5p - 8/2 = 7p +4/2

-5p           -5p

        -8/2 = 2p + 4/2

        -4/2            -4/2

Answer:

t and u are supplementary as opposite angles of a cyclic quadrilateral.

t = 180 - (81 + 53) = 46

u = 180 - t = 180 - 46 = 134

v and w are equal as opposite angles to equal sides.

v = w = 1/2(180 - u) = 1/2(180 - 134) = 23

Step-by-step explanation:

The given quadrilaterals, 1 and 2,  are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.

3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.

4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.

3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:

Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:

AB = √((7 - 0)² + (1 - 0)²) = √50

BC = √((5 - 7)² + (6 - 1)²) = √29

CD = √((-2 - 5)² + (5 - 6)²) =√50

DA = √((0 - (-2))² + (0 - 5)²) = √29

We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.

Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:

Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:

Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5

Slope of RS = (4 - 3) / (4 - (-1)) = 1/5

Slope of QR = (4 - 1) / (4 - 3) = 3

Slope of SP = (3 - 0) / (-1 - (-2)) = 3

The lengths of opposite sides can be calculated using the distance formula:

PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26

RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3

QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10

SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10

We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.

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Answer:

Step-by-step explanation:

23/40 = 0.575

Answer:

12

Step-by-step explanation:

Here we use SOHCAHTOA

Seeing as we have the hypotenuse and we are working to find out the opposite, we use SOH

Sin(x)= Opposite/Hypotenuse

Sin(45) = x/\(12\sqrt{2} \\\)

×12 root 2

sin(45) times 12 root 2=  12

x=12

Answer:

8.7

Step-by-step explanation:

If you like my answer mark me brainliest

Answer:

0

Step-by-step explanation:

By definition, if it is on the y-axis the x-coordinate is 0

Answer: 1.02

Step-by-step explanation:

Answer:

The answer would be 1.02

Step-by-step explanation:

The slash between the numbers mean you're doing division,

So you must divide 15.30 to 15

15.30 divided by 15 is 1.02.