Determine whether the following relation repreent y
a a function of x
5x3y=15

(bonus) prove the equation ∃x(a(x) ∧ ¬b(x)) ∀x(a(x) −→ c(x)) ∴ ∃x(c(x) ∧ ¬b(x))

Proof by Contradiction:Assume that ∃x(c(x) ∧ ¬b(x)) is false.

Therefore, we can conclude that ∀x(c(x) ∧ ¬b(x)) is true.

This implies that for all x, either c(x) is false or b(x) is true.

But, from our assumption, we know that ∃x(a(x) ∧ ¬b(x)) is true.

Therefore, there must exist an x such that a(x) is true and b(x) is false.

Since a(x) is true, we can conclude from ∀x(a(x) −→ c(x)) that c(x) must also be true.

But this is a contradiction since we previously assumed that the equation ∀x(c(x) ∧ ¬b(x)) is true, which implies that c(x) must be false.

Therefore, our initial assumption must be false, and we can conclude that ∃x(c(x) ∧ ¬

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Yes, Because the paces are 6 miles/hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Christy went jogging on a saturday. The table shows how far she had jogged after various times.

Now, Based on the given table;

⇒ 4.5 ÷ 0.75

⇒ 6

⇒ 7.5 ÷ 1.25

⇒ 6

Thus, She ran the same pace at 6 miles/hour.

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Answer:2

Step-by-step explanation: To solve the equation -2 1/3x = -1 3/4, we need to isolate the variable x on one side and simplify the equation.

First, we need to convert both sides to have the same denominator. We can choose the least common multiple of 3 and 4, which is 12.

-2 1/3x = -1 3/4

-2 1/3 * 4/4 * x = -1 3/4 * 3/3

-8/3 x = -5 1/3

Next, we isolate x by dividing both sides by -8/3:

(-8/3) x / (-8/3) = -5 1/3 / (-8/3)

x = (5 1/3) / (8/3)

x = (5 1/3) * (3/8)

Finally, we simplify the fraction to get the final solution:

x = (5 1/3) * (3/8)

x = (5 * 3 + 1 * 3) / 8

x = 16 / 8

x = 2

Therefore, the solution to the equation -2 1/3x = -1 3/4 is x = 2.

The area of the shape for the quilt block is approximately 189 square inches.

To find the area of the shape, we'll need to first find the area of the right triangle formed by the two sides that form a right angle, and then add that to the area of the parallelogram formed by the base and the side parallel to it.

The area of a right triangle can be found by multiplying the base by the height and dividing by 2, so the area of the right triangle with a base of 6 inches and height of 7.5 inches is:

(6 x 7.5) / 2 = 22.5 square inches

The area of a parallelogram is found by multiplying the base by the height, so the area of the parallelogram with a base of 16 inches and a height of 6.4 inches (6 and two fifths inches) is:

16 x 6.4 = 102.4 square inches

Adding the area of the triangle and parallelogram gives us the total area of the shape:

22.5 + 102.4 = 124.9 square inches

So, the area of the shape for the quilt block is approximately 189 square inches.

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Answer: C

Step-by-step explanation:

I got it correct on the test

At a local eatery, children who is 12 or under 12, eat free. The inequality for non-discounted people is x > 12.

The inequality to represent people who do not get a discount at the local restaurant is x > 12. This means that any person who is older than 12 years old will not receive a discount, as only those who are 12 years old or younger are eligible for the "Children 12 and under eat free" offer.

The inequality uses the greater than (>) symbol to indicate that the value on one side of the equation (x) must be greater than the value on the other side (12) in order for the inequality to be true. In this case, if a person's age (represented by x) is greater than 12, they do not receive the discount and have to pay full price for their meal.

This question should be provided as follows:

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Dani collecting rainwater in a 1 litre jug. So much water did Dani collect on Wedneday is 530 ml.

These are the specified parameters:

Monday = 220 ml

Tuesday = 1/4 litre

Wednesday = 0.1 litre

Fill the jug = 1 liter

A lot of water that has not been collected

= Fill the jug - (monday + tuesday + wednesday)

= 1 litre - (220 ml + 1/4 litre + 0.1 litre)

= (1 × 1000) ml - (220 ml + (1/4 × 1000) ml + (0.1 × 1000) ml)

= 1000 ml - (220 ml + 250 ml + 100 ml)

= 1000 ml - 570 ml

= 430 ml

Much water did Dani collect on Wedneday

= 0.1 litre + 430 ml

= 100 ml + 430 ml

= 530 ml

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Answer:

Below

Step-by-step explanation:

Rate1 = 1 pool / 85 min = 1/85

rate2 = 1 / 40

now find how long it will take with the combined rates

pool / (rates) = time

1 / ( 1/85 + 1/40)   = 27.2 min

The shape is a triangular prism and the volume of the shape is 45 ft^3.

A triangular prism is a 3-dimensional shape with two parallel triangular bases and three rectangular sides connecting the bases. It has six faces and nine edges in total.

The volume of the triangular prism is;

V = 1/2(b * h * l)

b = base

h = height

l = length

V = 0.5 (6 * 3 * 5)

= 45 ft^3

Thus, we can see that the kind of shape that have been modelled in the image has six faces and corresponds to the triangular prism with a volume of 45 ft^3.

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Answer: 44.6 yards

Step-by-step explanation: The formula for the circumference of a circle is C = 2 * π * r, where r is the radius. We can rearrange the formula to solve for r:

r = C / (2 * π) = 279.46 / (2 * π) = 44.6 yards

So, the radius of the field is approximately 44.6 yards.

p.s. sorry it might be 44.6 yards or / 44.5 yards :)

The circumference of the circle is 54. 64 mm. Option B

It is important to note that the formula for calculating the circumference of a circle is expressed as;

C = 2πr

Given that the parameters are;

From the information given, we have that;

Circumference = 2 × 3.14 × 8.7

Now, multiply the values, we get;

Circumference = 54. 636

Approximate to two decimal place, we get;

Circumference = 54. 64 mm

Hence, the value is 54. 64 mm

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The probability of winning chess tournament is 0.375.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Let A₁ be the event of playing an opponent of type i.

A₁ = playing the half of the opponent pool where the probability of winning

P (winning∣A₁) = 0.3

A₂ = playing the half of the opponent pool type 2, where the probability of winning P(winning∣A₂) = 0.4

A₃ = playing the half of the opponent pool type 3, where the probability of winning P(winning∣A₃) =0.5

By total probability theorem, we get,

P(winning)=P(A₁) P(winning∣A₁) +P(A₂) P(winning∣A₂) +P(A₃) P(winning∣A₃)

P(winning)=50%×0.3+25%×0.4+25%×0.5

P(winning)=0.375.

The probability of winning chess tournament is 0.375.

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The probability of winning the game depends on the type of opponent. If the opponent is of type 1, the probability of winning is 0.3; type 2, 0.4; and type 3, 0.5.

The probability of winning the game depends on the type of opponent. There are three types of opponents: type 1, type 2, and type 3. Against type 1 opponents, the probability of winning is 0.3. Against type 2 opponents, the probability of winning is 0.4. Against type 3 opponents, the probability of winning is 0.5. As the opponent is chosen randomly, the probability of winning is the average of all three probabilities. This means that the probability of winning the game is 0.4. To calculate this, we first add the probabilities of winning against each type of opponent: 0.3 + 0.4 + 0.5 = 1.2. We then divide this result by the number of opponent types (3): 1.2/3 = 0.4. This means that the probability of winning the game is 0.4.

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The measure of angles for questions 19) and 20) are x = 32° and x = 115° respectively using the triangle sum and exterior angle theorem.

question 19 has 2 isosceles triangles and the measure of x can be derived by equating one of the base angles of the smaller triangle to the sum of its 2 opposite angles as follows;

let y be one of the base angles of the smaller triangle so that;

2y = 180 - 56 {sum of interior angles of a triangle}

2y = 124

y = 62

hence;

62 = x + x {exterior angle of a triangle equals the sum of its two opposite angles}

2x = 62

x = 31°

For question 20, we first find the two opposite angles of x as follows;

180 -(62 + 50) = 68

180 - (53 + 80) = 47

x = 68 + 47

x = 115°

Therefore, the measure of angles for questions 19) and 20) are x = 32° and x = 115° respectively using the triangle sum and exterior angle theorem.

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The percent of the finishers were not from the youth division is 64.84%

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

Given ,

A recent Boston Mayor's Cup race boasted the largest number of finishers in the history of the event with 825 finishers, 290 of the finishers were from the youth division.

So,

Total  =  825  finishers

Who are not form young division = 825 - 290

= 535

So,

The percent of the finishers were not from the youth division

= 535 / 825  *  100

= 0.6484 * 100

= 64.84 %

Therefore, The percent of the finishers were not from the youth division is 64.84%

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The length of the line through the center that touches two points on the edge of the circle.

The spikes extending from one end to the other end through the center of a bicycle wheel are an illustration of diameter. We may compare this to the diameter of a circle, as the diameter is the line segment that runs from one end of the circle to the other, passing through the center.

The diameter of a circle goes from edge to edge and cuts through the center, whereas the radius travels from center to edge. The diameter of a circle divides the form in half.Every circle have infinite no. of diameter.

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The measure of angle B from the given hexagon ABCDEF is 108°.

In geometry, a hexagon or sexagon is a six-sided polygon or 6-gon creating the outline of a cube. The total of the internal angles of any simple hexagon is 720°.

In the given hexagon ABCDEF, ∠A=170°, ∠C=133°, ∠D=102°, ∠E=117° and ∠F=90°.

Here, ∠A+∠B+∠C+∠D+∠E+∠F=720°

170°+∠B+133°+102°+117°+90°=720°

612°+∠B=720°

∠B=720°-612°

∠B=108°

Therefore, the measure of angle B from the given hexagon ABCDEF is 108°.

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The volume of the given figure which is the sum of two rectangular prism would be = 1,490cm³

The formula the is used to calculate the volume of a rectangular prism = v= length×width×height

There are two rectangular prism:

For the smaller prism;

where;

length= 6cm

height= 2cm

width= 5cm

volume = 6×2×5= 60cm³

For the larger prism;

length= 22cm

height= 5cm

width= 13cm

volume = 22×5×13 = 1,430cm³

The total volume of the figure = 1430 +60 = 1,490cm³

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The root of the expression is 3/4

The index form of a number can be described as that number written in the nature of an exponential expression.

They are also forms that are written as a single numbers raised to another number.

Exponents explains the number of times to multiply the base of by itself to simply or evaluate the expression.

Note that the cube root of a number is the value which when multiplied by itself thrice gives the original value.

Given the expression;

[tex]\sqrt[3]{\frac{27}{y} }[/tex]

Find the cube root

3/4

Hence, the value is 3/4

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The event that "a or b but not both" P{(A∩B) ∪ (A ∩B)}

= P(A∩B) + P(A∩B) - P(A∩B∩A ∩B)

In this question, we will use the addition rule of the probability to calculate the required probability. The probability is a positive quantity from zero to one inclusively. The negative probability of an event does not exist

This is for independent events

P(A U B): This is A or B or both:

P(A n B): This is A and B.

P(A U B) = P(A) + P(B) - P(A n B)

P( A n B) = P(A) x P(B)

Hence:

A or B but not both:

P(A U B) = P(A) + P(B) - P(A n B) - P(A n B) = P(A) + P(B) - 2 x P(A n B)

can also be written in terms of the conditional probability P(A|B)

So we can write

P{(A∩B) ∪ (A ∩B)}

= P(A∩B) + P(A∩B) - P(A∩B∩A ∩B)

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The required measure of an angle is 73 degrees which supplement is 253.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

The supplement of an angle is equal to 180 degrees minus the angle.

So if we call the angle "x", we can set up an equation as follows:

2x + (180 - x) = 253

Simplifying the equation:

x = 253 - 180

Apply the subtraction operation, and we get

x = 73

So the angle is 73 degrees.

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The expression which is equivalent to x² - 2x -5 /x-3 from the following is  x+1 - 2/x-3.

When working with fractions, the numerator and denominator are crucial in mathematics. That fraction, as we all know, indicates a numerical value that identifies the components of a whole. If a number must be divided into five pieces, it is denoted by the symbol p/5. In this case, the fraction p/5 denotes the fifth of the integer p. The numerator will be on the left if the fraction's line component is inclined.

The denominator of a fraction is the fraction's divisor. The number or integer that appears in a fraction below the horizontal line is known as the denominator. whereas in a fraction, the numerator is above the line. A denominator cannot have a value of zero because that would yield an indefinite value.

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Saving account is an example of a demand account.

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The value of x in the given proportion is determined as 10.56.

The value of x in the given proportion is calculated by applying the following equation as shown below.

1650 = x ( 156.25 )

where;

The value of x in the given expression is calculated as follows;

x = ( 1650 ) / ( 156.25 )

x = 10.56

Thus, the value of x in the proportion is obtained by dividing both sides of the equation by 156.25 and thereby making the unknown ( x ) the subject of the formula.

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The product of the given expressions is 2x squared + 7x minus 4.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expressions are 2x - 1 and x + 4.

We have to multiply both the expressions.

(2x - 1) (x + 4) = (2x . x) + (-1 . x) + (2x . 4) + (-1 . 4)

                      = 2x² - x + 8x - 4

Adding the like terms together,

(2x - 1) (x + 4) = 2x² + 7x - 4

Hence the multiplication of the given expression gives the expression 2x² + 7x - 4.

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The Perimeter is 16.97 inch, and the Area is 18 square inch units.

Given, Length, l = 4 1/5 inch = 21/5 inch

Breadth, b = 4 2/7 inch = 30/7 inch

The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as the product of its length and width times two. As a linear measurement, the perimeter can be expressed in metres, centimetres, inches, feet, etc.

Perimeter of the rectangle = 2 (l + b) = 2 (21/5 + 30/7)

= (147 + 150)(2/35)

= 297 x 2/35 = 16.97 inch

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle called its area. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes. To determine the area that these objects occupy, use the rectangle's area formula.

Area of the rectangle = l x b

= 21/5 x 30/7 = 18 inch square units

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The Perimeter is 16.97 inches, and the Area is 18 square inch units.

Given, Length, l = 4 1/5 inch = 21/5 inch

Breadth, b = 4 2/7 inch = 30/7 inch

The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as the product of its length and width times two. As a linear measurement, the perimeter can be expressed in meters, centimeters, inches, feet, etc.

Perimeter of the rectangle = 2 (l + b) = 2 (21/5 + 30/7)

= (147 + 150)(2/35)

= 297 x 2/35 = 16.97 inch

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle is called its area. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes. To determine the area that these objects occupy, use the rectangle's area formula.

Area of the rectangle = l x b

= 21/5 x 30/7 = 18 inch square units

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Step-by-step explanation:

This is a question where everyone's answer will be different. Here's my example answer.

Two goals for me:

A used car (2011 Honda Pilot is $11500)

A diamond necklace (14k white gold from Jared is $11900)

The used car would be a need because it would be my only way to get to work and school

The diamond necklace would be a want because I don't need it to stay alive and we'll, just to look good

Answer: x=7

Step-by-step explanation:

50 many adult and 75 children tickets did they sell. This can be solved using the concept of equations.

Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

For instance, two equations with the identical variables, x and y, are x + y = 12 and 2x + 5y = 8. They are an equational system.

Let,

cost of adult tickets = x

cost of children tickets = y

tickets cost $7.00 each and children tickets cost $2.00 each. The student council made $500.00 from the ticket sales.

Now, 7x + 2y = 500 ................. (i)

They sold a total of 125 tickets:

x + y = 125 .......... (ii)

Solving these two equations we get:

7x + 2y = 500

2x + 2y = 250

5x = 250

or, x = 50

putting the value of x we get:

50 + y = 125

or, y = 75

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The best first step to begin to simplify the equation -2(x + 3) = -10​ is:

Dividing both sides of the equation by -2 to get x + 3 = 5

As per the given data, the equation is given by -2(x + 3) = -10

We have to determine the best first step in solving the equation:

-2(x + 3) = -10​

Firstly we start by distributing -2 in the bracket (x + 3)

-2x - 6 = -10

Or

-2(x + 3) = -10​

Also if we divide both sides of the equation by -2, we get

x + 3 = 5

Now, we can easily solve the equation.

Hence, the first best step to begin to simplify the equation -2(x + 3) = -10​ is:

Distributing -2 in the bracket (x+3)

We get -2x -6 = -10

Or Dividing both sides of the equation by -2

We get x + 3 = 5

Here in options given x + 3 = 5

Hence option (c) is correct.

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