What is domain and range of a function?.

The coordinate of the point after a rotation of 90° counterclockwise will be (-3, -7).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The point is given below.

⇒ (-7, 3)

The coordinate of the point after a rotation of 90° counterclockwise will be given as,

(x', y') = (-y, x)

(x', y') = (-3, -7)

The coordinate of the point after a rotation of 90° counterclockwise will be (-3, -7).

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All the parts of the given problem have been solved using the concepts of the percentage below.

It is given that the principal amount that Ram has, as his income is 40,000.

i) Ram spends 30% of his income on food

that will be,

40,000×30/100

=40,000×0.3

=12,000

ii) Ram spends 20% of his income on his education

that will be,

40,000×20/100

=40,000×0.2

=8,000

iii) Ram spends 20% of his income to buy his clothes

that will be,

40,000×20/100

=40,000×0.2

=8,000

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Using fundamental counting principle, the total total number of outfits that can be worn is  6.

A way for keeping track of all the possible outcomes in a circumstance is the fundamental counting principle.

If there are n ways to carry out one activity and m ways to carry out another activity after that, then there are n m n times n methods to carry out both of these activities, according to this assertion.

The Fundamental Principle of Counting dictates how choices are made depending on options.

The Fundamental Principle of Counting makes it easier to apply the selection method, which considers all feasible alternatives and their combinations for calculating the probability.

Total number of pants = 2

Total number of shirts = 3

Total number of outfits that can be worn = 3 × 2

= 6

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Answer: 3/2

Step-by-step explanation:

To find the slope of the line, we are going to look at that change in rise (meaning the change of the y values) over the change in the run (meaning the change of the x values). The easiest way to do this is to pick two points on the line and use the slope equation: (y2-y1)/(x2-x1). I will pick two points at random, though multiple can work to find the slope.

point one: (1,-3) *it is easiest to make the first point to the left of point two*

point two: (3,0)

now, use the equation to solve.

(0 - -3)/(3-1) = (0+3)/(3-1) = 3/2

Hope this helps!

The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)

The inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.

The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.

The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.

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The 99th percentile for the mean height of a random sample of 20 adult women is approximately 68.7 inches, which is 3.7 inches above the mean of 65 inches.

The 99th percentile for the mean height of a random sample of 20 adult women can be calculated using the normal distribution. The normal distribution is a bell-shaped curve that describes the probability of a given event occurring. In this case, the mean and standard deviation of the height of adult women is used to calculate the probability of the mean height of a sample of 20 adult women being a certain value. For the 99th percentile, this means that the probability of the mean of the sample of 20 adult women being equal to or less than the value of 68.7 inches is 99%. This value is 3.7 inches above the mean of 65 inches, which is the expected mean height of adult women.

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Answer:

See picture attachment.

Hope this helps :)

The larger number is x = 71 and the smaller number y is 17

An equation is a mathematical statement showing the equality of two things.

The equations are

x = 14 +3y and x+y = 90

To solve the equations, we substitute x = 14 + 3y in the equation x +y = 90

⇒14+3y+y = 90

Collecting like terms to have

4y = 90-14

4y = 76

Making y the subject

y=76/4

y=19

By substitution we have

x=14+3(19)

x=14+57

Therefore the value of x = 71

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The sum is an Arithmetic operation that results in the addition of 2 values to get the final value. Let the first number be X and the second be Y. Adding X and Y, we get the resultant as, X + Y = Z.

Sum most commonly means the whole of two or greater numbers delivered collectively; see addition. A summation additionally known as a sum is the result of arithmetically adding numbers or portions. A summation constantly includes a whole range of terms. There can be as few as two terms, or as many as one hundred, a thousand, or one million. some summations include infinitely many terms.

In arithmetic, the summation is the addition of a chain of any form of numbers, called addends or summands; the result is their sum or general. the combination of two or extra numbers, magnitudes, portions, or details as decided via or as if via the mathematical technique of addition: The sum of 6 and 8 is 14. a selected combination or overall, specifically with regards to money: The fees came to a giant sum.

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Complete Question:

How do you find the sum of two numbers?

We are aware that x2(a+b)x+ab=0 is one such equation if a and b are the roots of a quadratic equation.

In other words, if a times the square of the phrase after b plus b times the same expression not squared plus c equals 0, then you have an equation with the quadratic form. The original equation will change to a quadratic equation if the value in the () is replaced with a variable like t.

Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

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Sine law  work's for acute angles ,obtuse angles and right triangles.

Sine Law states that "When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.It is given by :

[tex]\frac{a}{sin A}= \frac{b}{sin B}= \frac{c}{sin C}[/tex]

The Law of Sines is valid for obtuse triangles as well as acute and right triangles, because the value of the sine is positive in both the first and second quadrant—that is, for angles less than 180°. You can use this relationship to solve triangles given the length of a side and the measure of two angles, or given the lengths of two sides and one opposite angle.

Sine law  work's for acute angles ,obtuse angles and right triangles.

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The age of the sample of the carbon material is 19042 years.

We have to note that the half life of the sample has to do with the time that it takes for us to have only half of the original amount of the isotopes that are in the sample to be present.

Using the formula;

0.693/[tex]t{\frac{1}{2} }[/tex] = 2.303/t log (No/N)

[tex]t{\frac{1}{2} }[/tex] = Half life of the sample

t = time taken

No = Number of atoms initially present

N = Number of atoms at time t

Then;

0.693/5730 = 2.303/t log (No/0.1No)

0.693/5730 = 2.303/t  * 1

1.21 * 10^-4 = 2.303/t

t = 2.303/1.21 * 10^-4

t = 19042 years

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To work out the value of k, we can use the given information that fg(2) = 12. We know that fg(x) is the composition of two functions f and g, so we can write fg(x) = f(g(x))

In this case, fg(2) = f(g(2)) = f(k*2^2) = f(4k)

We know that fg(2) = 12. So we can substitute this value into the equation above:

12 = f(4k)

Since we are only interested in the value of k, we can set the equation equal to 12 and solve for k.

12 = 4k

k = 12/4

k = 3

Therefore, k = 3 is the value of k in the function g(x) = kx^2

An angle that turns through 1/360 of a circle is called a “one-degree angle” and can be used to measure angles.

A degree, generally represented by the symbol ° (the degree), is a unit of measurement for a plane angle, where one full revolution equals 360 degrees.

A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.

One-degree angles are used to measure angles because they turn around 1/360 of a circle; an angle is said to have an angle measure of n degrees if it turns through n one-degree angles.

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Answer:

x = 83

Step-by-step explanation:

This question tests on the concept of Angle Properties

Properties required: Sum of Angles in a triangle.

Given information from the question:

x + 44° + 53° = 180°

x = 180° - 44° - 53°

x = 180° - 97°

x = 83°

Therefore the value of x is 83.

The 4 types of multiplication properties are

Properties of multiplication : the four properties of multiplication are the following :

1) Commutative property of multiplication : The commutative property of multiplication says that when we multiply numbers, the answer remains the same even if the order of the numbers changes. Example : Consider two numbers 3 and 8. Then 3× 8 = 8× 3.

2) Associative property of multiplication :

The associative property of multiplication says that if we want to multiply any three numbers together, the answer will always be the same regardless of the order in which we multiply the numbers. Example: Consider any three numbers say 2, 3 and 7 we get, 2 ×( 3×7) = 2×21 = 42.

3) Distributive property of multiplication :

The distributive property of multiplication says that multiplication can be distributed over addition, just like subtraction. Example : Consider the calculation, 2×(3+1) = 2×3 + 2× 1 = 8.

4) Identity Property of multiplication :

The Multiplication Identity Property says that if we multiply any number by 1, the answer will always be the same number. For example, 1 × 3 = 3× 1 = 3

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Answer:

(0,3)

Step-by-step explanation:

y = mx + b

[tex]y=\frac{1}{2}x+b[/tex]

[tex]4=\frac{1}{2}(2)+b[/tex]

4 = 1 + b

b = 3

[tex]y=\frac{1}{2}x+3[/tex]

'b' represents the y-intercept in slope-intercept form. Another point is (0,3)

Sam' speed for the first 15 minute of her journey is 80km/hr.

Speed refers to the rate of change of an object’s position in any direction. It is measured as the ratio of distance to the time (period in which the distance was covered). It is a scalar quantity. The formula for speed is given by:

Speed = Distance/ Time

Based on the provided travel graph,

Distance d = 20 km

Time t = 15 min = 15/60 = 0.25 hr

Hence,

Speed = d/t = 20/0.25 = 80km/hr

The speed in the first 15 minutes of Sam’s journey is 80km/hr.

Note: The question is incomplete. The complete question is: Sam drives his car on a journey. The travel graph for the first 15 minutes of his journey. Work out Sam' speed for the first 15 minute of her journey. Give your answer in km/h.

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a) The probability of event occur is  [tex]\frac{1}{5}[/tex].

b) The probability of event not occur is  [tex]\frac{4}{5}[/tex].

What is probability?

The likelihood of an event happening is gauged by probability. It is difficult to provide a complete prediction for many events. We can only anticipate the likelihood of an event occurring by using it. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here The ratio of the odds of an event occurring are 1:4.

Then probability of that the event will occur is ,

=>P(event will occur = [tex]\frac{1}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Now the probability of that event not will occur is ,

=> P(event will not occur) = 1 -[tex]\frac{1}{5}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Hence the answers are a) [tex]\frac{1}{5}[/tex] and b) [tex]\frac{4}{5}[/tex].

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Hope it helps.

If you have any query, feel free to ask.

$ 240,437.74 - the balance of her fund on her 17th birthday.

His daughter turned 10 years old. Her reward was 5000.

subsequently, she began getting monthly interest compounded at a rate of 15%

She would thus have 5000 (the deposit from her birthday) + 15% = 5750 in her account at the end of the first month.

The amount would have been 5750 + 15% = 6612.50 at the conclusion of the second month.

She would have 6612.50 + 15% + 5000 (quarterly deposit) at the conclusion of the third month, which equals 12,604.38.

When she becomes 17 years old, if you keep doing these calculations, she will have a fun

$1,832,087,983.19

Only 145,000, including the 5,000 deposit made on her father's 17th birthday, would have been made by her father.

I would be grateful if someone could let me know where I can earn 15% compounded monthly.

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Answer:64

Step-by-step explanation:

A limit is generally written as

[tex]lim _{x- > c} f(x) = L[/tex]

It is read as “the limit of f of x, as x approaches c equals L”

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly defined.

Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as:

[tex]lim _{x- > c} f(x) = L[/tex]

It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.

Let us take an example to fully understand how to write limits.

[tex]lim_{x- > 2} 2x + 2[/tex]

= 2(2) + 2 = 6

This is how to write and represent limits.

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The answer is to the problem is 5x-5

The length the diameter of the circle will be 10 units. And the graph of the circle is given below.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let d be the diameter of the circle. The circumference of the circle will be

C = πd units

Vince wrote the following equation, where C is the circumference in inches, to represent the value of π for a circle that he drew. Then the diameter of the circle is calculated as,

π = C / 10

C = π x 10

πd = 10π

d = 10

The length the diameter of the circle will be 10 units. And the graph of the circle is given below.

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Answer:

Let the two numbers be x and y

Given ,

[tex]x + y = 95 \: \: ...(1)[/tex]

Also ,

[tex]y = x + 15 \: \: ...(2)[/tex]

Substiting equation 2 in equation 1 ,

[tex]x + x + 15 = 95 \\ \dashrightarrow \: 2x + 15 = 95 \\ \dashrightarrow \: 2x = 95 - 15 \\ \dashrightarrow \: 2x = 80 \\ \: \: \: \: dividing \: both \: sides \: by \: 2 \: \\ \dashrightarrow \: \cancel\frac{2x}{2} = \cancel\frac{80}{2} \\ \\ \dashrightarrow \: \: \boxed{ x = 40}[/tex]

Now , y = x + 15

therefore ,

[tex] y = 40 + 15 \\ \dashrightarrow \boxed{ y = 55 } [/tex]

Hence ,

the two numbers are 40 and 55 .

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For the given data, independent variable = time in hours, dependent variable = distance traveled in miles.

An independent variable is one that is tweaked or changed to explore its effects when performing an experimental study. It is called "independent" because it is unaffected by any other study variables.

These are also referred to as independent variables:

Various justifications (they explain an event or outcome)

elements that predict (they can be used to predict the value of a dependent variable)

Those on the right side are variables (they appear on the right-hand side of a regression equation).

These expressions are particularly useful in statistics when calculating how effectively a change in one independent variable can forecast or explain changes in the dependent variable.

Given, the data is -

(0, 0), (2, 100), (3, 140), (4, 140), (5, 200), (8, 360)

time in hours = {0,2,3,4,5,8}

distance traveled in miles = {0, 100, 140, 140, 200, 360}

independent variable = time in hours

dependent variable = distance traveled in miles

Yes, the given relation is a function.

x variable represents the input of the relation

y variable represents the output of the relation

Domain = {0,2,3,4,5,8}

Range =  {0, 100, 140, 140, 200, 360}

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Answer:

(a + 8)(a - 5)

Step-by-step explanation:

a² + 3a - 40 =

= (a      )(        )

Find two numbers that multiply to -40 and add to 3.

They are 8 and -5.

= (a + 8)(a - 5)

solution :

a²+3a-40

find the roots (2 numbers in which you can add and multiply to give 3a and 40)

(a-5) (a+8)

substitute the roots with 3a and multiply 40 by a²

a²-5a+8a-40a²

a(a-5) +8(a-40a²)

(a-5) (a+8)