What is the inverse of a relation?.

The sum symbol is represented as

Sum is determined by putting the values all together and results is called "total" or sum. The plus symbol (+) is used as sum symbol in case of small numbers of digits for addition. For example: sum of 5 and 6 is represented as 41 + 15 = 56 .

The symbol Σ (sigma) is used to denote a sum of multiple terms. This symbol is generally used by an index that varies to represent all terms that must be considered in the sum. For example, the sum of first whole numbers can be represented in the following 1 + 2 + 3 + 4 + .......+ n = [tex] \sum_{i = 1}^{n} {i}[/tex]

where, ∑ is the symbol that is denoted as "sigma".

Summation is used in case of sum of arithmetic sequence, geometric sequence and other sequences.

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Since a square is either positive or zero, negative numbers don't have real square roots.

No, we are unable to compute the negative number's square root. Positive is always the result of adding two numbers with the same sign.

Theorem: Square Roots of a Negative Number Simplifying an expression involving the square root of a negative number by simplifying the number as if it were a positive number and putting an i in front of it as a coefficient is one method. To put it another way, x=ix x = i x for every x where x is a positive number and where x is a negative number.

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Yes, Zero is a real answer because zero is a rational number, and any rational number is also a real number. In particular, the set of real numbers is the union of the set of irrational numbers with the set of rational numbers.

Zero is an even number, but it is not a prime as well as a composite number. Also, zero is neither a positive nor a negative number, but it completes the gap between them. Zero factorial is 1 (0! = 1).

Zero is rational, real, and an integer, but it is not a natural number. Any number divided by zero is undefined, as is zero divided by zero. Of course, zero did not always exist.

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A Perfect Number N is defined as any positive integer where the sum of its divisors minus the number itself equals the number.

A perfect number is a positive integer that is equal to the sum of its proper divisors, which are positive integers that divide the number without leaving a remainder. For example, 6 is a perfect number because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. The first four perfect numbers are 6, 28, 496, and 8128.

Perfect numbers have been studied by mathematicians for centuries, and continue to be an area of active research. They have connections to other areas of mathematics, such as number theory and algebraic number theory. Perfect numbers also have applications in computer science and cryptography.

It is also important to note that in number theory, a natural number is called abundant if it is less than the sum of its divisors and deficient if it is greater than the sum of its divisors. Perfect numbers are exactly equal to the sum of their divisors.

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Answer:

undefined

At x = 0 the function is undefined, because there is a zero denominator.

Step-by-step explanation:

There is no real number that, when multiplied by itself, produces a negative result. Therefore, the square root of a negative number is undefined in the context of real numbers.

A square root is defined as the value that, when multiplied by itself, equals a given number. The square of a real number is always positive, so the square root of a positive number is always positive or zero. However, there is no real number that, when multiplied by itself, produces a negative result. Therefore, the square root of a negative number is undefined in the context of real numbers.

Square root of a negative number is a complex number.

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Both coaches will charge $440 after 3 hours of coaching.

To find when the two coaches will charge the same amount, we need to set up the equation with help Compound Interest Formula:-

Where:-

Cost of Coach A = Cost of Coach B

200 + 80x = 230 + 70x

where x is the number of hours of coaching.

To solve for x, we can subtract 200 from both sides and 230 from both sides:

80x = 30 + 70x

10x = 30

x = 3

So, the two coaches will charge the same amount after 3 hours of coaching.

To find out how much it will cost, we can substitute 3 for x in the equation for either coach:

Cost of Coach A = 200 + 80x = 200 + 803 = $440

Cost of Coach B = 230 + 70x = 230 + 703 = $440

Therefore, both coaches will charge $440 after 3 hours of coaching.

It's important to note that this calculation assumes that the cost of the coaches is based solely on the hourly rate and initial fee, and does not take into account any other factors such as discounts, taxes, or additional services offered by the coaches.

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2(3b+6) =78

Expanding the left side of the equation:

6b + 12 = 78

Solving for b:

6b = 66

b = 11

Now we will check the left side and the right side of the equation:

2(3(11) + 6) = 2(33+6) = 2(39) = 78

On the other side of the equation:

-2(6c-3) = -72

Expanding the left side of the equation:

-12c + 6 = -72

Solving for c:

-12c = -78

c = 6.5

Now we will check the left side and the right side of the equation:

-2(6(6.5) - 3) = -2(39 -3) = -2(36) = -72

This equation is true, the left side of the equation equals to the right side of the equation.

The solution for the first equation is b = 11

The solution for the second equation is c = 6.5

From probability of occurence of events the large box holds 180 hats.

The probability of an event is the proportion of favorable outcomes to all other potential outcomes.The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The following formula can be used to determine how likely an event is to occur.

Here, probability can be used. When throwing coins, rolling dice, or drawing a card from a deck of cards, probability is employed to forecast the results.

The probability is classified into theoretical probability and experimental probability.

Probability(Event) = Positive Results/Total Results = x/n

Here, in the mall box, are 60 hats.

And a big box holds 18% more hats than the box provided by the mall.

So, 180/100 ×60 = 180

Therefore, from probability of occurence of events the large box holds 180 hats.

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We can use the tangent function to solve for the height of the lighthouse.

Let h be the height of the lighthouse from the top of the cliff.

tan(50.5 degrees) = (h + x) / 1100

tan(48.1 degrees) = h / 1100

We can divide the first equation by the second equation to get:

(h + x) / h = tan(50.5 degrees) / tan(48.1 degrees)

then we can simplify it by cross multiplying and canceling out h

h + x = (h * tan(50.5 degrees)) / tan(48.1 degrees)

then we can substract h from both sides

x = (h * tan(50.5 degrees)) / tan(48.1 degrees) - h

then we can substitute x = 1100

1100 = (h * tan(50.5 degrees)) / tan(48.1 degrees) - h

then we can add h to both sides

1100 + h = (h * tan(50.5 degrees)) / tan(48.1 degrees)

then we can multiply both sides by tan(48.1 degrees)

1100tan(48.1 degrees) + htan(48.1 degrees) = h * tan(50.5 degrees)

then we can divide both sides by tan(48.1 degrees)

h = (1100 * tan(48.1 degrees) + h * tan(48.1 degrees)) / tan(50.5 degrees)

after substituting the values we get:

h = (1100 * tan(48.1) + h * tan(48.1)) / tan(50.5)

we can round it to the nearest tenth

h = (1100 * tan(48.1) + h * tan(48.1)) / tan(50.5)

then we can use a calculator to get the exact number

h ≈ 191.5

Therefore, the height of the lighthouse from the top of the cliff is 191.5 meters.

The equation of the quadratic function y = x² + 6x + 3 in vertex form is y =  (x+ 3)² - 6

Quadratic function in math is defined as a polynomial function with one or more variables in which the highest exponent of the variable is two.

Here we have given the quadratic function y = x² + 6x + 3 and we need to find the vertex form of the given quadratic function.

As we all know that the vertex form of the equation is given by

=> f(x) = a(x - h)² + k

Here we have given the expression that can be written as,

=> y = x² + 6x + 3

Now, we have to convert it into vertex form, then we get,

=> x² + 6x + 3

Expand the expression as follows:

=> x² + 6x + 3 + 9 - 9

Now, we have rewritten the expression like the following,

=> y + 9 = (x + 3)² + 3

Here we have to subtract 9 on both sides, then we get

=> y =  (x+ 3)² + 3 - 9

Then the resulting equation is written as,

=> y =  (x+ 3)² - 6

Complete Question:

What is the equation of the quadratic function y = x² + 6x + 3 in vertex form?

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Answer:

Step-by-step explanation:

You want to know the consecutive integers that bound the values of 30^(1/5) and 45^(1/3).

The fifth root of 30 will lie between the two integers whose 5th powers lie on either side of 30:

  1^5 = 1 < 30

  2^5 = 32 > 30

So, the fifth root of 30 lies between 1 and 2:

  [tex]\boxed{1 < \sqrt[5]{30} < 2}[/tex]

The cube root of 45 will lie between the two integers whose cubes lie on either side of 45:

  3^3 = 27 < 45

  4^3 = 64 > 45

So, the cube root of 45 lies between 3 and 4:

  [tex]\boxed{3 < \sqrt[3]{45} < 4}[/tex]

__

Additional comment

A calculator confirms this:

  [tex]\sqrt[5]{30}\approx 1.974\\\sqrt[3]{45}\approx3.557[/tex]

The answer to (9a²b³) x (2a⁴b)/ 6b² is 3[tex]a^6[/tex]b².

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward manner.

To illustrate 3 x 3 x 3 x 3 in a straightforward manner, for instance, we could write it as 34, where 4 is the exponent and 3 is the base. It is claimed that the entire statement 34 has power.

Given:

(9a²b³) x (2a⁴b)/ 6b²

So, (9a²b³) x (2a⁴b)/ 6b²

= 3 x 3 x a x a x b x b x b x 2 x a x a x a x a x b / 2 x 3 x b x b

= 3 x a x a x a x a x a x a x b x b

= 3[tex]a^6[/tex]b²

Hence, the answer is 3[tex]a^6[/tex]b².

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Answer:

31.5

Step-by-step explanation:

Answer:

h= 13.6 ft

Step-by-step explanation:

Let,

a= 8 ft

b= 11 ft

The ladder against the top of the house is creating a right triangle

So, we can find the length of the ladder using

[tex]h^{2} = {a}^{2} + {b}^{2} \\ h^{2} = {8}^{2} + {11}^{2} \\ h^{2} = 64 + 121 \\ h = \sqrt{185} \\ = 13.6ft[/tex]

Therefore, the length of the ladder (h) = 13.6 ft ( rounded to the nearest tenth)

The factored form is when the equation is written as "a(x-r1)(x-r2) = 0", where r1 and r2 are the roots (or solutions) of the equation. The vertex form of a quadratic equation is "a(x-h)^2 + k" where (h,k) is the vertex of the parabola represented by the equation.

The standard form of a quadratic equation is "ax^2 + bx + c = 0", where a, b, and c are constants. The 'a' coefficient is called leading coefficient, it determines the direction of parabola (whether it opens upward or downward) and the degree of the equation. The factored form of the equation is obtained by solving the equation and factoring out the common factors of the roots. This form of the equation is useful for identifying the x-intercepts (or zeroes) of the parabola, which are the points where the graph of the equation crosses the x-axis.

The vertex form of a quadratic equation is "a(x-h)^2 + k" where (h,k) is the vertex of the parabola represented by the equation. The vertex is the lowest point on the parabola if the leading coefficient 'a' is positive and highest point if 'a' is negative. The 'h' value in the equation represents the x coordinate of the vertex and 'k' represents the y coordinate. This form of the equation is useful for identifying the vertex of the parabola and the axis of symmetry, which is the line that divides the parabola into two mirror images.

The vertex form can be obtained by completing the square on the quadratic equation in standard form. By adding and subtracting the square of half of the coefficient of x, we can convert the equation in the form of (x-h)^2 which is a square of binomial.

Hence, the factored form is when the equation is written as "a(x-r1)(x-r2) = 0", where r1 and r2 are the roots (or solutions) of the equation. The vertex form of a quadratic equation is "a(x-h)^2 + k" where (h,k) is the vertex of the parabola represented by the equation.

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The function for the area is:

A = 0.5H² + 2H

And if the height is 6ft, then the area is 30ft²

We know that the area of a triangle is the product between the base and the height over two.

Here the base is 4ft more than the height H, then:

A = B*H/2

A = (H + 4)*H/2

A = 0.5H² + 2H

If the height is 6ft, then the area is:

A = 0.5*(6ft)² + 2*6ft = 30ft²

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Answer: Question 1 - 1/2
Question 2 - 1/4

Step-by-step explanation:

Hello! The answer to the first question is 1/2 because the quarter can have either two possible outcomes.  The quarter could land on heads or tails, and the chance of landing on heads is 1/2 and the chance of landing on tails is 1/2.

For the second question, the answer is 1/4 because the probability of a nickel landing on heads is 1/2 and the probability of a penny landing on heads is also 1/2.  To find the probability of both landing on heads.  You have to multiply both probabilities together.  1/2 x 1/2 = 1/4, which is your answer for the second question.

Hope this helps!

Together, fixed and variable costs make up the overall cost.When n is 4, the price is $33.00.

Together, fixed and variable costs make up the overall cost.The total cost, for instance, would be $35 if a company had a fixed cost per unit of $30 and a variable cost per unit of $5 that increased as output increased.The formula for average total cost is created by dividing the sum of all production costs by the sum of all payments in money.

The total-cost formula is a simple and user-friendly process that works by dividing the total production cost by the quantity of goods produced.

Y River

c = 33

Z River

Where n is the number of hours, c is equal to 5n + 13.

Graph

Include nothing before to n = 0

The cost will be the same when both sides of the equation are equal.

Where the two lines meet is the answer.

Both of them come together at a single place.

The point is this (4,33)

When n is 4, the price is $33.00.

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The  60.42 percentage of 8th graders believe they spend less than an hour per day on social media.

A percentage is a ratio expressed as a fraction of 100.

A random sample of students was asked in a survey if they estimated they spent more or less than an hour per day on social media.

To calculate the percentage of 8th graders who say they spend more than an hour a day on social media, divide the number of students who said "less" by the total number of 8th grade students surveyed, then multiply by 100.

29 students out of 48 students responded "less,".

To find the percentage,

(obtained value / total score ) x 100%

So here,

percentage = (29/48) x 100

accounting for 60.42% of the total.

As a result, 60.42% of 8th graders believe they spend less than an hour a day on social media.

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Answer:

4/3

Step-by-step explanation:

The slope of line e

[tex]\frac{5-8}{8-4}[/tex] = [tex]\frac{-3}{4}[/tex]

Perpendicular slopes are opposite reciprocals.

So the slope of line f = 4/3

Yes, there can be a triangle with three angles equal to 60.

The triangle is called the equilateral triangle where all three angles of a triangle is equal to 60 degree.

As we all knows that the sum of all the angles of a triangle is 180 and there are three angles that present in a triangle.

So, 60+60+60 = 180.

Now, Some properties of equilateral triangle:

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The ratio of the two legs of the triangle 30-90-60 will be 1 : √3.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The triangle is 30-90-60. The ratio of the two legs will be calculated as,

tan(30) = AB / BC

1 / √3 = AB / BC

Hence, the ratio of the two legs will be 1 : √3.

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The proof that ∠FCB≅∠DCE is shown below

Given that AECF is a rhombus, opposite angles of the rhombus are congruent.

This is represented as

∠EAF = ∠ECF

Also, given that EB ≅ FD, we can conclude that:

∠EBF = ∠DFC

This is by the definition of congruent segments having equal corresponding angles

Add the angles

∠CEB + ∠EBF = ∠CEB + ∠DFC = 180°

Recall that

Since ∠CEB = ∠AEF

So, we have:

∠AEF + ∠EBF = ∠AEF + ∠DFC = 180°

Hence, ∠FCB=∠DCE.

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The statement "In the statement ~(M ⊃ X)~) governs the simple statement M" is false

From the question, we have the following parameters that can be used in our computation:

In the statement ~(M ⊃ X)~) governs the simple statement M.

In logic and binary, the negation of an implication (M ⊃ X) is written as ~(M ⊃ X), which is read as "not (M implies X)".

This statement does not govern or control the simple statement M. The simple statement M can be true or false independently of the negation of the implication.

In other words, the truth value of ~(M ⊃ X)is dependent on the truth values of both M and X, not just M.

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Answer:

Tewanda reads 162 words per minute

Step-by-step explanation:

To find the unit rate of how fast Tewanda reads:

1458/9 = 162

Tewanda reads 162 words per minute