Hey everyone! I am on here to ask for help with a question on my little brother's math page. I'm a little stumped, as well as my mom, and we just want to be able to get him to the right answer. If anyone is willing to help out, it would be much appreciated! :) P.S: It is asking us to find the area of this trapezoid. ​

Answer:

s/3

Step-by-step explanation:

since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.

The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.

Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.

To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).

cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.

Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.

Substituting this value into the expression, we get:

sin⁻¹(0) = 0

Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.

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The density of nitrogen in the space will be 3.13 kg/m³

Density is the ratio of mass to volume of a substance. It is measured in kg/m³.

The volume of the shade part = volume of the cone- volume of the hemisphere

volume of the hemisphere = 2/3 πr³

= 2/3 × 3.14 × 40³

= 401920/3

= 133973.33m³

volume of the cone = 1/3 πr²h

= 1/3 × 3.14 × 40²× 500

= 2512000/3

= 837333.33 m³

volume of the shaded part = 837333.33-133973.33 = 703360m³

The density of the space = 2200000/703360

= 3.13kg/m³.

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The coordinate pairs to the correct location are:

B: (-4, 6)  

D: (-1, 0)

A coordinate pair, also known as an ordered pair, is a pair of numbers used to locate a point on a two-dimensional plane. The two numbers in the pair represent the horizontal and vertical distances from the origin (0, 0) on the plane, and are written in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

AC: Δx = -3 - (-6) = 3

       Δy = 10 - 4 = 6

AB:BC = 2:1

B: x = -6 + (2/3 × 3) = -4

   y = 10 - (2/3 × 6) = 6

so, B: (-4, 6)

AC:CD = 3:2

AC: Δx = 3, Δy = 6

So, CD:  Δx = 3 × 2/3 = 2

               Δy = 6 × 2/3 = 4

D: x = -3 + 2 = - 1

    y = 4 - 4 = 0

Thus, D: (-1, 0).

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Answer: there all divided by 2

so it's 2

According to the question the volume formula to find the height of the pyramid is 9 units.

Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.

The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h

108 = (1/3) × 36 × h

108 = 12 × h

h = 9 units

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Let's say you're trying to decide whether or not to invest in a certain stock. You've analyzed the company's financial reports and economic indicators, but you're still uncertain about the stock's future performance. Based on your intuition and experience with the stock market, you estimate that there is a 70% chance that the stock's value will rise in the next six months.

You decide to invest based on that probability, and six months later the stock has actually gone up in value. Your decision turned out to be a good one, but that doesn't necessarily mean your probability estimate was accurate. The stock could have gone down in value just as easily, despite your assessment of its likelihood of going up.

Therefore, even when we make decisions based on probability, there is always a level of uncertainty involved and the outcome may not always line up with our initial estimates. However, taking the time to consider the likelihood of different outcomes can help us make more informed decisions and better manage risk.

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The missing piece of information z-score is -1.

Explain information

Information refers to data or knowledge that has been transmitted or received. It can be expressed in different forms, including numerical data, text, images, or sound. The information serves as a basis for understanding, analysis, and decision-making. It can be processed and analyzed using mathematical methods and tools such as statistics, probability, and data analysis. The effective management and utilization of information are essential for progress and innovation in many fields, including science, technology, and business.

According to the given information

Using the formula z = (x - μ) / σ, we can plug in the given values and calculate:

z = (75 - 80) / 5

z = -1

Therefore, the z-score is -1.

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Answer:

Step-by-step explanation:

-9

The probability of the card is as stated at 7/52, which simplifies it to 1/8.

Probability is the study of the possibility that an event or phenomenon will occur. It can be expressed numerically as a number between 0 and 1, where 1 implies a certain outcome of an event and 0 denotes an inconceivable chance of occurrence.

There are four cards that are under a 3 (the 2, the Ace, the King, and the Queen) and four cards that are above an 8 (the 9, the 10, the Jack, and the Queen). However, the Queen is both above an 8 and under a 3, so we need to subtract one from the total count.

Therefore, the number of cards that are either under a 3 or above an 8 is 4 + 4 - 1 = 7.

Therefore, the probability that the card is as stated is 7/52, which simplifies it to 1/8.

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The calculated value of the volume of the solid is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx

To find the volume of the solid when the region R is rotated about the horizontal line y = -1, we can use the method of cylindrical shells.

The height of each cylindrical shell will be the difference between the function y = 2x and the horizontal line y = -1, which is (2x + 1).

The radius of each cylindrical shell will be the distance from the axis of rotation (y = -1) to the function y = x².

This distance is given by (x² + 1).

The thickness of each cylindrical shell will be dx.

Thus, the volume of the solid can be expressed as:

V = ∫[0,2] (x² + 1) - (2x + 1) dx

Hence, the expression is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx

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Answer:

21.6n-1.2

Step-by-step explanation:

=2.8n-24n-1.2-0.4n

=21.6n-1.2

The area of a sand dollar that is 3 inches wide is 7.0686 inch².

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

Width of sand dollar's circular body  = d = 3 inches

Radius of the  sand dollar's circular body  = r

 r = d/2 = 3/2 = 1.5 inch

area of circle = πr²

So, the area of a sand dollar that is 3 inches wide:

  A = 3.14 * (1.5)² = 7.0686 inch²

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The linear regression model from a set of data is y =5.2956+4.0946*X.

A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.

The regression line is determined using the formula:

y = bo + b1 X

Now, using the table we have:

sum of (x) = ∑x = 103

sum of (y) = ∑y = 480

Calculating the squares we have:

sum of (x^2)= ∑x² = 1073

sum of (y^2)= ∑y² = 22868

Multiplying the variables we have:

sum of (x*y)= ∑x*y = 4939

mean(x)= ∑x/n = 9.3636

mean(y)= ∑y/n = 43.6364

Now, the intercept is given as:

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

Substituting the values we have:

intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2

intercept (bo) = (515040-508717) / (11803-10609)

intercept (bo) = 5.2956

The slope is given as:

slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²

Substituting the values we have:

slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2

slope (b1) = (54329-49440)/(11803-10609)

slope (b1) = 4.0946

regression equation is, y = bo + b1 X

Substituting the values we have:

y =5.2956+4.0946*X

Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.

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The complete question is:

The pre-image ABCD was translated into the picture A'B'C'D' by moving 7 units to the right. answer is option (a).

A translation transformation is one in which the pre-image's size and orientation are maintained while the position of the points on the pre-image changes.

The polygon ABCD's vertices are located at these coordinates (1, 5), (3, 1), (7, 1), (5, 5)

The polygon's vertices are located at these coordinates: (8, 5), (10, 1), (14, 1), (12, 5)

where the preimage's and image's vertices are;

A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5),

the x and y values disagree, which shows;

A' - A = (8 - 1, 5 - 5) = (7, 0)

B' - B = (10 - 3, 1 - 1) = (7, 0)

C' - C = (14 - 7, 1 - 1) = (7, 0)

D' - D = (12 - 5, 5 - 5) = (7, 0)

In view of this, the transformation employed to produce the image A'B'C'D' from the pre-image, ABCD, is a translation, 7 units to the right.

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Answer:

7 units to the right

Step-by-step explanation:

Answer:

K = √-6k

i did the math and got this answer and it was right

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

[tex] \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 [/tex]

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Answer:

a. To find the rate per minute, we need to convert the rate from feet per second to feet per minute:

5.6 ft/s * 60 s/min = 336 ft/min

Therefore, the camera goes through film at a rate of 336 feet per minute.

b. The camera uses 500 feet of film at a rate of 336 ft/min, so we can use the formula:

time = distance/rate

where the distance is 500 feet and the rate is 336 ft/min.

time = 500 ft / 336 ft/min

time ≈ 1.49 min

To convert minutes to seconds, we can multiply by 60:

1.49 min * 60 s/min ≈ 89.4 s

Therefore, the camera uses a 500-foot roll of 65-mm film in approximately 89 seconds.

The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.

The set 2Z is defined as follows:

2Z = {2n | n ∈ Z, a * b = a + b}

Associative element:

There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.

Let a, b, and c be arbitrary elements of 2Z:

a = 2n₁

b = 2n₂

c = 2n₃

Then we have:

a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)

(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)

Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.

Identity element:

There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.

Let e be an arbitrary element of 2Z:

e = 2n

Then we have:

ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z

ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z

Therefore, e = 2n is an identity element in 2Z.

Inverse element:

There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.

Let a be an arbitrary element of 2Z:

a = 2n

Then we need to find an element b in 2Z such that ab = ba = e = 2.

We have:

ab = ba = 2n*b = 2

Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.

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Answer:

1/4 of the pot is left.

Step-by-step explanation:

Let x be the total amount of pasta in the pot.

Then the amount of pasta her mother got= 1x/12

The amount of pasta her brother got=  1x/6

The total amount of pasta he serve= 1x/12 + 1x/6

First, convert them into like fractions, then

The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4

Hence, 1/4 of the pot is left over.

Step-by-step explanation:

Mom: 1/12

Brother: 1/6

1/6 × 2/2 = 2/12

2/12 + 1/12 = 3/12

12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left

The three interior angles of the triangle are answer (C): 38°, 52°, 90

Hypotenuse: This is the largest side of the triangle. It is also opposite the right angle of the triangle. Base: The side on which a right  triangle stands is called its base.  We can use trigonometric ratios to find the angles of this right triangle.

 Let's call the angle between the hypotenuse and the  side of the 4 legs "A" and the angle between the hypotenuse and the other leg "B". Then we have:

sin(A) = opposite/hypotenuse = 4/6.5 = 0.615

cos(A) = adjacent/hypotenic =√ (1 - sin²(A)) = 0.789

tan(A) = opposite/adjacent = 4/√(6.5² - 4²) = 0.646

We also have:

sin(B) = opposite/hypotenuse = 6.5/6.5 = 1

cos(B) = adjacent/hypotenuse = 4/6.5 = 0.615

tan(B) = opposite/adjacent = √(6.5² - 4²)/4 = 1.361

Since angle A is  opposite the 4-foot side, it is the smallest angle of the triangle. Therefore, the answer must be either A or C.

 To distinguish between the two, we can use the fact that the sum of the angles of a triangle is always 180 degrees. So if you add  A, B and the right angle (90 degrees) you should get 180 degrees.  

A + B + 90 = 180

A + B = 90

Using the values ​​we calculated for the tangent of A and B, we can solve for their sum:

tan(A) + tan(B) = 0.646 + 1.361 = 2.007

We can then use the inverse tangent function to find the angle whose tangent is 2.007:

[tex]tan^-1(2.007)[/tex] = 63.4 degrees

Since A B = 90, we can subtract 63.4 from 90 to find the value of angle A:

A = 90 - 63.4 = 26.6 degrees

Therefore, the answer is C: 38°, 52°, 90

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The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the base, h is the height, and π is approximately 3.14.

Plugging in the values given, we get:

SA = 2π(3²) + 2π(3)(7)

SA = 2π(9) + 2π(21)

SA = 18π + 42π

Adding these two terms, we get:

SA = 60π

So the surface area of the cylinder is 60π square meters. If you want a numerical approximation, you can use a calculator and round to an appropriate number of decimal places.

Answer: Without the options for the vector matrices resulting from rotation, I cannot provide a specific matching. However, I can provide the general formula for rotating a vector by an angle of θ degrees counterclockwise as follows:

To rotate a vector with coordinates (x, y) counterclockwise about the origin by an angle of θ degrees, we use the following formula to find the new coordinates (x', y'):

x' = xcos(θ) - ysin(θ)

y' = xsin(θ) + ycos(θ)

Therefore, to obtain the vector matrix resulting from rotating the vector (-6, -3) by a certain angle of rotation, we plug in the values of x = -6 and y = -3 into the above formulas, and use the corresponding angle of rotation in degrees for θ.

Step-by-step explanation:

Using matrix form, the solution to the system of linear equations are 55/12 and 5/4

a) To write the system of equations in matrix form, we can use the coefficient matrix A and the vector of constants B:

| 15  -7 |   | V₁ |   |  60 |

| -3   3 | * | V₂ | = | -10 |

b) To find V₁ and V₂, we can use matrix algebra to solve the equation AV = B for V:

AV = B

V = A^-1 B

First, we need to find the inverse of the coefficient matrix A:

| 15  -7 |   |  3  7 |

| -3   3 | → | -5 15 | * (1/60)

So, A^-1 = (1/60) * | 3 7 | |-5 15 |

Solving for both equations

v₁ = 55/12, v₂ = 5/4

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Answer:

The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both things together. This principle can be applied to find the total number of possible outcomes in a given situation.

For example, if you have 3 shirts, 4 pants, and 2 shoes to choose from, and you want to find the total number of possible outfits you can make, you would use the Fundamental Counting Principle as follows:

Number of possible outfits = (number of shirt choices) x (number of pants choices) x (number of shoe choices)

= 3 x 4 x 2

= 24

Therefore, there are 24 possible outfits that you can make from the given choices of shirts, pants, and shoes.

a) The system of equations can be written in the matrix form AV-B as: | -3 3 | | V2 | | -10 |

b) V1 = 369/22 volts and V2 = -51/22 volts.

A matrix is a rectangular array of numbers or symbols, arranged in rows and columns. Matrices are often used in mathematics, science, engineering, and other fields to represent and manipulate data, perform operations, and solve equations. The size of a matrix is determined by the number of rows and columns it contains, and is usually written in the form "m x n", where "m" is the number of rows and "n" is the number of columns. Matrices can be added, subtracted, multiplied, transposed, and inverted, and can be used to represent a wide range of mathematical objects, including systems of linear equations, transformations, and graphs.

a) The system of equations can be written in the matrix form AV-B as:

| 15 -7 | | V1 | | 60 |

| | x | | = | |

| -3 3 | | V2 | | -10 |

b) To solve for V1 and V2 using matrix algebra, we can use the inverse of matrix A as follows:

AV = B

V = A⁻¹B

First, let's find the inverse of matrix A:

A = | 15 -7 |

| -3 3 |

To find the inverse of A, we need to calculate the determinant of A:

det(A) = (15)(3) - (-7)(-3) = 66

Then, we can find the inverse of A as follows:

A⁻¹ = (1/det(A)) x | 3 7 |

| 3 15 |

Now, we can solve for V by multiplying A⁻¹ and B:

| V1 | | 3 7 | | 60 | | 369/22 |

| | = | | x | | = | |

| V2 | | 3 15 | |-10 | | -51/22 |

Therefore, V1 = 369/22 volts and V2 = -51/22 volts.

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