Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).

The area of a trapezoid is equal to 1/2 times the 2 bases added together (bases of a trapezoid are parallel, and in this case it looks like it's 2m and 2.5m) times the height of the trapezoid (perpendicular to the opposite side, and forms a right angle).

So the equation would be 1/2 (2 + 2.5) times 6, which is 13.5 meters squared.

Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation:

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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Answer:

Phn10x12

Step-by-step explanation:

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]​

Answer:

27.78%

Step-by-step explanation:

To calculate the percentage of the total spending that is on rent, we need to divide the amount spent on rent by the total amount spent, and then multiply by 100 to get the percentage.

Total spending = food + rent + other + fun

Total spending = $400 + $500 + $600 + $300

Total spending = $1800

So, the percentage of the total spending that is on rent is:

($500 / $1800) x 100% = 27.78%

Therefore, approximately 27.78% of the total spending is on rent.

Step-by-step explanation:

We can use Euler's formula to approach this problem:

For a connected planar graph with V vertices, E edges, and F faces (including the outer face), Euler's formula states that:

V - E + F = 2

We know that our graph has 7 vertices and 16 edges. Assume, for the sake of contradiction, that this graph is planar. Then it must have a certain number of faces.

We know that each face of a planar graph must have at least 3 edges, and each edge is adjacent to two faces. Thus, the total number of edges in all the faces is at least 3F. On the other hand, each edge in the graph is adjacent to two vertices, so the total number of edges is 2V. Therefore:

3F ≤ 2V (1)

Using the fact that the graph is simple, each face of the graph is bounded by at least three edges. Therefore, the total number of edges in the graph is at least 3F/2. On the other hand, we know that the graph has 16 edges. Thus:

3F/2 ≤ 16 (2)

Combining inequalities (1) and (2) gives:

3F/2 ≤ 2V

3F/2 ≤ 14 (since V = 7)

F ≤ 9/2

This means that the number of faces in the graph is less than or equal to 9/2, which is impossible since the number of faces must be a non-negative integer. Therefore, our assumption that the graph is planar must be false, and we have proven that any simple connected graph with 7 vertices and 16 edges is not planar.

The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).

In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.

For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.

In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.

The formula for calculating the volume of air passing through a filter is:

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

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Answer:

The surface area is 65.94 ft

For regular nonagon the no, of One int = 40° and the One ext = 140°.

A regular nonagon is a two-dimensional polygon that has nine equal sides and nine equal angles. It is also called an enneagon. The word "regular" means that all the sides and angles of the nonagon are congruent, or equal.

The sum of the interior angles of a regular nonagon is given by the formula:

Sum of interior angles = (n - 2) x 180 degrees, where n is the number of sides

For a regular nonagon, n = 9, so the sum of the interior angles is:

Sum of interior angles = (9 - 2) x 180 degrees = 1260 degrees

Each angle of a regular nonagon can be calculated by dividing the sum of the interior angles by the number of angles. For a regular nonagon, each angle is:

Angle = Sum of interior angles / Number of angles = 1260 degrees / 9 = 140 degrees.

In a regular nonagon each of the 9 exterior angles will be 40° , 360/9 and their sum being 360°.

In the same way,

Each of the 9 interior angles will be 140°, ( 180 -40) , and their sum 1260°

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To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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Answer:

circumference of a circle is

[tex]2\pi\:r[/tex]

And the area of the circle is

[tex]\pi \: r {}^{2} [/tex]

Answer: x=14

Step-by-step explanation:

cb=10.

ac=14

The value of X will be 14.

This is a simple mathematics problem that can be solved by using ratios.

Given, AC : BC : AB = 7 : 5 : 8

AC = X ; BC = 10 ; AB = X + 2

AC/ BC = X/ 10 = 7/5  (Ratios can also be represented as fractions)

X/10 = 7/5

On Transposing,

5X = 70

X = 70/5

X = 14

Alternatively,

BC/AB = 5/8 = 10/ (X + 2)

5/8 = 10/ (X + 2)

On Transposing,

80 = 5X + 10

5X = 70

X = 14

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The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.

Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary by angles

m∠4=180°-m∠3 ----> equation B

substitute the equation- B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary to angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of any of tAnswer:

Step-by-step explanation:

he interior angles that of a triangle must be equal to 180 degrees

therefore

This option is true for sure

case E) we have

m∠2+m∠3+m∠5=180°.

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In a case whereby Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing,  the closest to the area of the largest circular pond he can make with the fencing is 1471.61ft^2

We were told that he will bw making a pond which is circular in nature, then We can assume that the radius is R, then 2 πR = 136

R= 136/2 π

R= 68/π

The the are of the pond= πR^2

=  π * (68/π)^2

=1471.61ft^2

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Answer: a) The exponential function that describes the amount in the account after time t, in years, is given by:

A(t) = Pe^(rt)

where P is the initial amount invested, r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

A(t) = 19665e^(0.068t)

b) To find the balance after 1 year, we substitute t = 1 in the above formula:

A(1) = 19665e^(0.068*1) = $20,983.88

To find the balance after 2 years, we substitute t = 2:

A(2) = 19665e^(0.068*2) = $22,429.45

To find the balance after 5 years, we substitute t = 5:

A(5) = 19665e^(0.068*5) = $29,137.27

To find the balance after 10 years, we substitute t = 10:

A(10) = 19665e^(0.068*10) = $43,127.22

c) The doubling time can be found using the formula:

t = ln(2)/r

where ln is the natural logarithm function. Substituting the given values, we get:

t = ln(2)/0.068 ≈ 10.20 years

Therefore, the doubling time is approximately 10.20 years.

Step-by-step explanation:

One such tool that enables us to visualise the given math issue using various-sized rectangles or bars is the bar model.

A bar model in mathematics is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes. To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilised.

To help kids "see" mathematical structure, the bar model is utilised in teaching for mastery. It is not a method for solving issues, but rather a strategy to uncover the mathematical underpinnings of a problem and obtain knowledge and clarity to aid in its resolution.

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Image attached below,

The translation vector for the rectangle is described by T(x, y) = (- 3, - 6).

In this problem we must derive the translation vector between a rectangle and its image set on Cartesian plane (let assume that the origin is on the lower left corner of the square). The translation formula is:

B(x, y) = A(x, y) + T(x, y)

Where:

If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:

T(x, y) = B(x, y) - A(x, y)

T(x, y) = (3, 3) - (6, 9)

T(x, y) = (- 3, - 6)

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The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.

Subjects are the different sets of information which is studied.

9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.

The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.

Thus, the correct option is C, 9th graders in her school.

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An equation in slope-intercept form that models the situation is y = 1.50x + 4.

The table has been completed below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation in slope-intercept form that models the situation is given by;

y = mx + c

y = 1.50x + 4

When x = 2, the total cost (y) is given by;

y = 1.50(2) + 4

y = $7.

When x = 4, the total cost (y) is given by;

y = 1.50(4) + 4

y = $10.

When x = 6, the total cost (y) is given by;

y = 1.50(6) + 4

y = $13.

When x = 8, the total cost (y) is given by;

y = 1.50(8) + 4

y = $16.

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Answer: Let the two numbers be x and y. We know that:

x*y = 2420 ---(1)

LCM(x, y) = 110 ---(2)

We can write the LCM as:

LCM(x, y) = (x*y)/HCF(x, y)

Substituting the given values, we get:

110 = (x*y)/HCF(x, y)

Multiplying both sides by HCF(x, y), we get:

HCF(x, y) * 110 = x*y

Substituting equation (1), we get:

HCF(x, y) * 110 = 2420

Dividing both sides by 110, we get:

HCF(x, y) = 2420/110

HCF(x, y) = 22

Therefore, the HCF of the two numbers is 22.

Step-by-step explanation:

The cost per share of the technology stock is $14.

What is a variable?

In mathematics, a variable is a symbol or letter that represents a value or a quantity that can change or vary in a given context or problem. Variables are used to express mathematical relationships and to formulate equations and functions.

Let's use variables to represent the cost per share of the technology stock and the mutual fund. We can call the cost per share of the technology stock "T" and the cost per share of the mutual fund "M".

From the problem, we know:

Nora bought 100 shares of the technology stock and 200 shares of the mutual fund for a total of $3600:

100T + 200M = 3600

Erin bought 300 shares of the technology stock and 50 shares of the mutual fund for a total of $5300:

300T + 50M = 5300

We now have a system of two equations with two variables. We can solve for T and M by using elimination or substitution. Here, we will use the substitution method:

From the first equation, we can isolate T by subtracting 200M from both sides:

100T = 3600 - 200M

Divide both sides by 100 to get:

T = 36 - 2M

Now substitute this expression for T into the second equation:

300(36 - 2M) + 50M = 5300

Expand and simplify:

10M = 1100

Divide both sides by 10 to get:

M = 110

So the cost per share of the mutual fund is $110.

To find the cost per share of the technology stock, we can substitute M = 110 into either of the original equations. Let's use the first equation:

100T + 200(110) = 3600

Simplify:

100T = 1400

Divide both sides by 100 to get:

T = 14

So the cost per share of the technology stock is $14.

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If a sample contains 300 mg, 129.6 mg of Radium-226 will remain after 2000 years.

The period of time it takes for half of the radioactive atoms in a sample to decay is known as the half-life. This means that if you start with a given amount of a radioactive chemical, half of it will have decayed after one half-life, and so on. After two half-lives, just one quarter will be left.

A radioactive substance's half-life, which is one of its distinguishing characteristics, can be used to forecast how quickly it will degrade over time. Scientists can compute a radioactive substance's half-life and use it to infer the age of rocks and fossils by measuring how much of the radioactive substance is still there after a predetermined period of time.

The radioactive decay is given by the formula:

[tex]N(t) = N_0 * (1/2)^{(t/T)}[/tex]

Substituting the given values we have:

[tex]N(2000) = 300 * (1/2)^{(2000/1590)}[/tex]

N(2000) ≈ 129.6 mg

Therefore, approximately 129.6 mg of Radium-226 will remain after 2000 years.

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Thus, for the given similar triangles-

11. ΔCAG ≈ Δ CEF (Angle-Angle similarity)

12. ΔACB ≈ ΔCED (Angle-Angle similarity)

13. ∠ACB = ∠ECD = 92° (vertical angles)

17. BC = √32

Congruent triangles and similar triangles are two distinct but closely related concepts. Similar triangles are any two or more triangles having the identical proportions of their corresponding sides, an equal pair with corresponding angles, and their similar shape.

For the given values:

11. ΔCAG ≈ Δ CEF (Angle-Angle similarity)

∠ACG = ∠ECF (vertical angles)

∠GAC= ∠CEF (alternate interior angles)

12. ΔACB ≈ ΔCED (Angle-Angle similarity)

∠ACB = ∠ECD (vertical angles)

∠BAC = ∠CED (alternate interior angles)

13. m∠ECD = ?

In Δ ACB

53 + 45 + ∠ACB = 180

∠ACB = 180 - 98

∠ACB = 92

∠ACB = ∠ECD = 92° (vertical angles)

17. BC = ?

BC² = GB² + GC²

BC² = 4² + 4²

BC = √32

14. m∠ECF = m∠GCA  (vertical angles)

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Complete question:

For the following figure- Determine:

11. ΔCAG ≈

12. ΔACB ≈

13. m∠ECD = ?

17. BC = ?

Answer:125 meters

Step-by-step explanation:

volume of a cube is w^3

w=5

5*5*5

125 meters

As the counselor recommends that the client reconsider marrying her fiancé based on his belief discretion, this is an example of harmful use of bias.

The counselor's personal beliefs against interfaith marriages are influencing their professional advice, which can be harmful to the client's well-being and may even violate ethical guidelines for mental health professionals.

The counselor should provide unbiased and objective guidance to the client based on their specific needs and circumstances, rather than imposing their own beliefs or values onto the client's decision-making process.

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Answer:

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In the equation 2x^2 + 2x - 1 = 0, we have:

a = 2

b = 2

c = -1

Substituting these values into the formula, we get:

x = (-2 ± sqrt(2^2 - 4(2)(-1))) / (2)(2)

Simplifying this expression, we get:

x = (-2 ± sqrt(4 + 8)) / 4

x = (-2 ± sqrt(12)) / 4

x = (-2 ± 2sqrt(3)) / 4

x = (-1 ± sqrt(3)) / 2

Therefore, the solutions to the equation 2x^2 + 2x - 1 = 0 are:

x = (-1 + sqrt(3)) / 2

x = (-1 - sqrt(3)) / 2

The equation that shows how to find a percentage is:

part/whole = percent/100

This equation can be used to solve for any of the three variables, given the values of the other two.

The solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is p > 6 or p > -3.

A compound inequality is a mathematical statement that involves two or more inequalities joined by either the word "and" or "or". The solution set of a compound inequality is the set of all values that satisfy both (in the case of "and") or either (in the case of "or") of the individual inequalities.

Let's solve each inequality separately:

4p + 1 < −11

Subtracting 1 from both sides, we get:

4p < -12

Dividing both sides by 4 (and remembering to flip the inequality because we are dividing by a negative number), we get:

p > -3

So the solution to the first inequality is:

p > -3

Now let's look at the second inequality:

6p + 3 > 39

Subtracting 3 from both sides, we get:

6p > 36

Dividing both sides by 6, we get:

p > 6

So the solution to the second inequality is:

p > 6

Therefore, the solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is:

p > 6 or p > -3

This can be written more simply as:

p > -3

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Answer:

55°

Step-by-step explanation:

the total sum of a triangle is 180.

75+50= 125

180-125= 55

& since x is an acute angle we know x is less than 90.