Jamal will cut a piece of wood that is 212
2
1
2
feet long into 14
1
4
-foot sections. How many sections will result?
Group of answer choices

The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.

The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.

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Answer:

1) A serious girl - Una chica seria/Una joven seria

2) The talented boy - El chico talentoso/El joven talentoso

3) An outgoing girl - Una chica extrovertida/Una joven extrovertida

4) The tasty ice cream - El helado delicioso/El helado sabroso

5) A funny book - Un libro divertido/Un libro entretenido

Step-by-step explanation:

Now, we present a possible set of solution, as there are solutions as many synonyms exist in Spanish. Then:

1) A serious girl - Una chica seria/Una joven seria

2) The talented boy - El chico talentoso/El joven talentoso

3) An outgoing girl - Una chica extrovertida/Una joven extrovertida

4) The tasty ice cream - El helado delicioso/El helado sabroso

5) A funny book - Un libro divertido/Un libro entretenido

The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.

1981: 11 kg

1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)

1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)

1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)

2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)

The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.

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Answer:

m<B=60°

Step-by-step explanation:

an exterior angles equals the sum of its two remote interior angles, so:

m<A+m<B=m<BCG:

3x+4x=10x-45

7x=10x-45

-3x=-45

x=15

to find the measure of <B:

since m<B=4x:

4(15)=60°

so, m<B=60°

Answer:

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

One should pay 2.1875 dollars.

Addition, subtraction, multiplication, and division are the most fundamental operations in arithmetic. However, arithmetic also includes more complex operations like manipulating percentages, square roots, exponentiation, logarithmic functions, and even trigonometric functions, which are analogous to logarithms. It is necessary to evaluate arithmetic expressions in accordance with the intended order of operations.

Given one yard of ribbon is 3.5 dollars

1y = 3.5

where y = yards

dollar for 5/8 yards is

1y x 5/8 = 3.5 x 5/8

5/8y = 2.1875

Hence one should pay 2.1875 dollars for 5/8 yards.

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Using the first index law, the solution provided indicates that this has a value of 1.

X to the power of A multiplied by X to a power of B results in X to the power of A + B, according to the first law of indices. Keep in mind that adding the indices when multiplying terms with them means that the base must remain constant throughout.

A topological invariant of a certain class of differential operations on a manifold is studied in index theory, as well as the invariant's local formula in terms of the manifold's geometry. inspirational cases. operator elliptic The index theorem by Atiyah-Singer.

(m³)⁶/m¹⁸ = m³ˣ⁸/m¹⁸

= m¹⁸/m¹⁸

= 1

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The 3 linear equations are

1. y = mx + b

2. ax + by = c

3. x/a + y/b = 1

1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.

2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.

3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.

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1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)

37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)

-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).

The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence. As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulae for arithmetic sequences.

The equation to determine the nth term in an arithmetic series

The formula for calculating the sum of an arithmetic sequence's first n terms

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."

Option 1, 4 and 6 are in Arithmatic Sequence as

In 1:

1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)

again in 4 :

37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)

and in 6

-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).

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Answer:6842

Step-by-step explanation:

13684/2

The value of x in the triangle WXY is 27°

An equation shows how two or more numbers and variables are related to each other.

∠VWY + ∠XWY = 180° (sum of angle in straight line)

6x + ∠XWY = 180°

∠XWY = 180 - 6x

∠XYW + ∠ZYW = 180° (sum of angle in straight line)

∠XYW + 4x = 180°

∠XYW = 180 - 4x

∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)

(180 - 6x) + (180 - 4x) + 90 = 180

450 - 10x = 180

10x = 270

x = 27°

The value of x is 27°

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Answer:

x = 71/5  (as an improper fraction)

x = 14 1/5 (as a proper fraction

x = 14.2 (as a decimal)

Step-by-step explanation:

It's a rectangle so the diagonals are equal

7x - 9 = 2x + 62

Subtract 2x from both sides

5x - 9 = 62

Add 9 to both sides

5x = 71

Divide both sides by 5

x = 71/5  (as an improper fraction)

x = 14 1/5 (as a proper fraction

x = 14.2 (as a decimal)

Answer:

x= 14.2

Step-by-step explanation:

BD and and AC are equal so

7x-9 = 2x+62

isolate the variable means x = 14.2

first time I had to take out pencil and paper so I hope it's right

Answer:

Step-by-step explanation:

These are the tests for similar triangles:

AA - if 2 pairs of corresponding angles are equal.  

SSS - if corresponding sides have the same ratio.

SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.

This diagram does not indicate any of these relationships exist.

Therefore the triangles are not similar.

Answer:

The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:

Step-by-step explanation:

The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:

f(–10) = (–10)^2 – 5(–10) + 12 = 100 – (–50) + 12 = 162

The statement "The graph of the function is a parabola" is true. Because the equation of the function is of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0, the graph of the function is a parabola.

The statement "The graph of the function opens down." is true. The coefficient of x^2 is a positive value, which means the parabola opens down.

So, the true statements are

The graph of the function is a parabola.

The graph of the function opens down.

The graph does not contain the point (20, –8)

The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.

As given in the question,

Let 'W' is the random variable represents the number of walleye.

'P(W)' represents its probability

The values are given as follow:

W      :        0                        1                       2

P(W)  :        0.09                0.42                  0.49

Mean of the walleye 'W' is given by :

= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)

= ( 0 ×  0.09 )  + ( 1 × 0.42 ) + ( 2 × 0.49 )

= 0 + 0.42 + 0.98

= 1.4

Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.

The above question is incomplete , the complete question is :

Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets

if she catches 2 fish.

W      :        0                        1                       2

P(W)  :        0.09                0.42                  0.49

Calculate the mean of W.

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Answer:

The area of this parallelogram is 140 square feet.

Step-by-step explanation:

A = bh

A = 14 * 10

A = 140

Hope this helps; have a wonderful day!

Answer:

x = -11

Step-by-step explanation:

3(1 - 3x) = 2(-4x + 7)

Distribute the 3.

(3 - 9x) = 2(-4x + 7)

Distribute the 2.

3 - 9x = -8x + 14

Add 8x to both sides.

3 - x = 14

Subtract 3 from both sides.

-x = 11

Multiply by -1.

x = -11.

Proof:

3(1 - 3x) = 2(-4x + 7)

3(1 - 3(-11)) = 2(-4(-11) + 7)

3(1 + 33) = 2(44 + 7)

3(34) = 2(51)

102 = 102

Answer:

the total surface area is 360 cm

Step-by-step explanation:

The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.

what is a quadratic equation?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.

where a, b, and c are constant terms and x is the unknown variable.

Here I am using the factoring method to solve a quadratic equation.

Given quadratic equation is

[tex]2x^2 - 5x -12 = 0.[/tex]

By comparing the General form of the quadratic equation we will get

a = 2, b = -5 and c = -12.

2x^2 - (8-3)x - 12 = 0.

2x^2 - 8x + 3x -12 = 0.

2x(x-4) + 3(x-4) = 0

(x - 4) (2x + 3) = 0.

x - 4 = 0 or 2x + 3  = 0

x = 4 or x = -3/2

Given Question is incomplete complete question here:

What are the solutions of the quadratic equation 2x^2-5x-12 =  0?

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Answer:

$95.39

Step-by-step explanation:

First, find sales tax

75.41×(11.5/100)=8.67

Then, tip

75.41×(15/100)=11.31

Therefore,

75.41+8.67+11.31

is the total cost

Answer:

95.39

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

0=18

Step-by-step explanation:

not simplified.

Answer:

There is no answer.

Step-by-step explanation:

-2(11 - 12x) = -4(1-6x)

First you need to simplify the equation, using distributive property.

Distribute -2 to the numbers within the parentheses.

-2*11 = -22

-2*-12x =24x

= 24x - 22

Then distribute -4 among 1 and -6.

-4*1 =-4

-4*-6x = +24x

= 24x - 4

And because

24x - 22 does NOT equal 24x - 4

There is no answer because they are not equivalent, making the equation itself false/untrue.

Answer: In this exercise we have to calculate the values ​​of the people who voted to expand the parking lot, so we have to:

Yes: parents will be 150 and not parents 40

No; parents will be 40 and not parents 30

As it is about sets, we have to use the data that were:

   total: 250 adults

   180 of whom were parents a park should be expanded.

   40 of the adults who were not parents thought the park should be expanded.

then calculate that:

Step-by-step explanation:

The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

The two-way table shown in the table is attached below.

What is two way table?

Two-way table is a way of representing of data to better understand it.

Given information-

The total number of adults took the survey is 250.

Total number of parents took the survey is 180.

150 of the adults with children and 40 of those without thought the park should be expanded.

Suppose the number of adults who are not the parents and took the survey is .

As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,

Suppose the parents who does not thing that the park should be expanded is .

There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,

Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.

Hence the two way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

the two way

YES                    NO

                          30  

                          30

(parents 150

not parents_40

Answer:

The solution should be log7^3(49)-1/3log7(49)=1/3*2

B-2/3

There are 10 integers that satisfy 0 < a < 100.

What are integers?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

Here, we have

Given: When working modulo m, the notation a⁻¹ is used to denote the residue b for which ab = 1 (mod m), if any exists.

We have to find integers that satisfy 0 < a < 100.

a(a − 1)⁻¹ ≡  4a⁻¹ (mod 20)

a ≡ 4a⁻¹(a − 1)(mod 20)

a² ≡ 4(a-1)(mod 20)

a² - 4a + 4 ≡ 0(mod 20)

(a - 2)² ≡ 0(mod 20)

a = 2 + 10n | for n = (0, 1, 2, 3.....9)

Hence, there are 10 integers that satisfy 0 < a < 100.

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60 students out of 210 in a school went both roller skating and water park.

What is algebraic equation ?

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Have given ,

Total students = 210

Let x = The number of students who went only to the roller skating

and y = The number of students who went to the water park and roller skating

x + 4x + y = 210  ⇒ 5x + y = 210 ......(i)

x + y + 2y = 210 ⇒ x + 3y = 210 ⇒ x = 210 - 3y

Put the value of x in equation no. (i),

5(210 - 3y) + y = 210 ⇒ 1050 - 14y = 210 ⇒ 14y = 1050 - 210

14y = 840 ⇒ y = 60

Hence , 60 students out of 210 in a school went both roller skating and water park.

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Answer:

the answer is $5.50

Step-by-step explanation:

32 total

10+11=21

32-21=11

so 11 left for college and saving account

now divide it with 2 so both gets same amount

11/2=5.50

The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.

We will calculate the interquartile range and us the rule 1.5 .

The formula to calculate  interquartile range is to subtract the value of first quartile by the value of second quartile.

IQR = Q3 - Q1

Therefore, interquartile range becomes,

IQR = 17 - 13

IQR = 4

Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first

4 * 1.5 = 6

and then,

17 + 6 = 23

on applying the rue we will get ,

13 - 6 = 7 .

This value means that there is no outlier in the displayed data set.

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x/2 = -1

=> x = -1 × 2

=> x = -2