What is the average rate of change of the function on the interval from x = 0 to x = 5? f(x)=12(3)x.

[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{a}{nh} }[/tex]

Step-by-step explanation:

a=nr^2h

Divide both parts of the equation by nh:

[tex]\displaystyle\\\frac{a}{nh} =r^2\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\\sqrt{\frac{a}{nh} } =\sqrt{r^2} \\\\\sqrt{\frac{a}{nh} } =r\\\\Thus,\ r=\sqrt{\frac{a}{nh} }[/tex]

After solving for the internal angles of the given figure, we know that the value of ∠C is 44°.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex.

The name "angel" comes from the Latin word "angulus," which means "corner."

Acute, obtuse, right, straight, reflex and full rotation are examples of basic angles.

By joining two rays at their termini, a geometric shape known as an angle is produced.

An angle is often stated in degrees.

So, let the angle is x.

2x + 3 + 3x + 9 + 2x - 4 + x = 360

Now, calculate for x as follows:

8x + 12 - 4 = 360

8x + 8 = 360

8x = 360 - 8

8x = 352

x = 352/8

x = 44°

Therefore, after solving for the internal angles of the given figure, we know that the value of ∠C is 44°.

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Answer:

63

Step-by-step explanation:

trial and error aint that hard

First, let's calculate the total number of marks for each group:

Then, we can calculate the mean mark for the whole group by adding up the total number of marks for each group and dividing by the total number of students:

(144 marks + 192 marks) / (8 students + 12 students) = 336 marks / 20 students = 16.8 marks/student

Therefore, the mean mark for the whole group is 16.8.

The mathematical mean is a measure of central tendency that is calculated by adding up all the values in a data set and dividing by the number of values in the set. It is also commonly known as the "average."

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Answer:

34.5

Step-by-step explanation:

Steps to solve linear equations;

Given,

Linear equations;

The typical form for linear equations with two variables is Ax + By = C. For instance, the equation 2x + 3y = 5 is a standard form linear equation. Finding both intercepts of an equation in this style is quite easy (x and y).

Here,

To resolve linear equations, follow these steps:

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The probability that a bike is green given that it has road tyres is 2/3

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

The table of values

From the table of values, we have:

Number of bikes that are green and road tyres = 4

Number of bikes that are road tyres = 6

The probability is then calculated using the following formula

Probability = Number of bikes that are green and road tyres/Number of bikes that are road tyres

Substitute the known values in the above equation, so, we have the following representation

Probability = 4/6

Simplify

Probability = 2/3

Hence, the value of the probability is 2/3

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The maximum number of friends that he can invite without going over his limit is 9.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given,

Fixed fee = $50

Suppose the number of people is x.

Total fee = 50 + 5.50x

Total fee ≤ budget

50 + 5.50x ≤ 100

5.50x ≤ 50

x ≤ 9.09 thus, x = 9

Hence "The maximum number of friends that he can invite without going over his limit is 9".

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Answer:

The equation y = 34x - 2 is the slope-intercept form of the equation y = 34x + b, where b is the y-intercept, which is the point where the line crosses the y-axis. The value of b in this case is -2, so the equation can be written as y = 34x - 2. This form of the equation makes it easy to find the slope (which is 34 in this case) and the y-intercept (which is -2 in this case) of the line.

If X is a radom variable for amount you win, Then the excepted value of game or expected income i.e E(X) is 8/13.

Expected Income is the result of multiplying your income by the probability of earning it. This expected revenue can be subtracted by the expected cost to get the expected profit.

Mathematically, E(X) = X₁p₁ + X₂p₂ + ---+ Xₙpₙ

where Xᵢ are observation and pᵢ probability of Xᵢ.

We have given that,

Total number of cards in standard card deck = 52

i.e total possible outcomes = 52

One card is drawn from deck.

Total number of king cards in 52-card deck = 4

Favourable outcomes that drawn card is king = 4

Probability of getting a king card , p = 4/52 = 1/13

Probability of not getting a king ,q = 1 - p

= 1 - 1/13 = 12/13

let X be the amount you win . You win $20 if a king is drawn and lose $1 if king is not drawn . So, probability distribution is

Xᵢ pᵢ

$20 1/13

-$1 12/13

So, E(X) = ∑ Xᵢpᵢ = 20× 1/13 + (-1)× 12/13 = 20/13 - 1/13 = 8/13

Hence, required excepted value is 8/13.

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The first rider the displacement is, 17 km.

And the 2nd river the displacement is 20.22 km.

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.

Here we have two triangle with two arm know for both.

So we have to find the 3rd arm for both triangle.

Now we have for a right triangle

a^2 + b^2 = c^2

For other triangle we know the cosine law of triangle is,

a^2 + b^2 - 2ab cosθ = c^2

θ is the opposite angle of c

For the first rider the displacement is,

c = [tex]c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 15^2} = 17 km\\[/tex]

For the 2nd river the displacement is

[tex]c = \sqrt{a^2-b^2 -2abcosheta}[/tex],  θ = 120°

[tex]c = \sqrt{8^2 + 15^2 - 2ab cos(120)} \\c = \sqrt{289 - 240cos(120)} \\c = \sqrt{289 - (-120)} \\c = \sqrt{289 + 120}\\ c = \sqrt{409} \\c = 20.22km[/tex]

Hence, the first rider the displacement is, 17 km.

And  the 2nd river the displacement is 20.22 km.

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Answer:

It is not possible to determine whether the lines are parallel based on the information given. To determine whether two lines are parallel, we need to calculate the slope of each line and compare them. The slope is calculated as the change in the y-coordinate divided by the change in the x-coordinate, or (y2-y1)/(x2-x1). Since we only have the coordinates of the endpoints of the lines and not the equations of the lines, we cannot calculate the slope and therefore cannot determine whether the lines are parallel.

Answer: lines are parallel

Step-by-step explanation:

Lines are parallel if they have the same slope

                      [tex]\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }[/tex]

1) (2,6)  (4,10)

x₁=2    x₂=4    y₁=6    y₂=10

Hence,

[tex]\displaystyle\\m=\frac{10-6}{4-2} \\\\m=\frac{4}{2}\\\\m=2[/tex]

2) (-2,3)  (3,13)

x₁=-2   x₂=3   y₁=3   y₂=13

Hence,

[tex]\displaystyle\\m_1=\frac{13-3}{3-(-2)} \\\\m_1=\frac{10}{3+2} \\\\m_1=\frac{10}{5}\\\\m_1=2[/tex]

m=m₁=2

Hence, lines are parallel

Answer:

it’s no solution

Step-by-step explanation:

Answer:

0.15- Strong Association

-0.21 - Weak Association

0.71- Strong Association

0.55-Moderate Association

A cramers V value of O = No relationship, 0.2 or less = Weak relationship, from 0.21 to 0.3 = moderate, and above 0.3 = Strong relationship.

The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.

In the given question we have to explain, how we can find the range of a quadratic graph.

Because it is the most fundamental quadratic function, all quadratic functions collectively can be referred to as a family, with this particular function serving as the parent (i.e., not transformed in any way). This function can be used to start broadly generalising the domains and ranges of quadratic functions.

The range is partly determined by the pivotal point, or vertex. The parabola's opening direction is the other. The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.

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The explicit equations that describe the values in the table are y = 7(x - 57) - 49 and y = 7x - 448

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

As x increases by 1, y increases by 7

This means that the slope (m) is

m = 7

A linear equation is represented as

y = m(x - X) + Y

In this case, we have

(X, Y) = (57, -49)

m = 7

Substitute the known values in the above equation, so, we have the following representation

y = 7(x - 57) - 49

Expand

y = 7x - 448

Hence, the equation is y = 7x - 448

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The length of a side of the square is  8 unit.

Area of Square:

The area of ​​a square is defined as the number of square units required to fill the square. Area is generally defined as the area occupied within the bounds of a planar object. Measurements are in square units and the default unit is square meters (m²).

Area of a Square = Side × Side

Therefore, the area of square = Side²  square units

and, the perimeter of a square = 4 ×  side units

Given:-

Area of square is equal to twice its perimeter

To find:-

Side of square = ?

Now,

Let the side of square be a

Perimeter of square=4a

Area of Square = a²

Now,

According to the Question:

  Area of Square = 2 × Perimeter of Square

⇒ a² = 2 ×4a

⇒ a² = 8a

⇒ a = 8.

Therefore, the side of square is 8 unit.

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The equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y =  -2 / 3x - 7, so option B is correct.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

A line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5)

Calculate the slope of the line,

m = 5 - (-7) / 6 - (-)

m = 12 / 8

m = 3 / 2

The slope of a line perpendicular to JK, M = - 1 / 3 / 2 = -2 / 3

Calculate the equation of the line as shown below,

y - (-3) = -2 / 3[x - (-6)]

y + 3 = -2 / 3x - 4

y =  -2 / 3x - 7

Therefore, the equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y =  -2 / 3x - 7.

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Expression for the earnings per person = $75/n

What is loss?

The amount of loss on any commodity expressed as a percentage is referred to as the loss percentage. Additionally known as percentage loss. Any time a commodity's selling price is less than its cost price, we consider this to be a loss. The magnitude of this loss may be determined by calculating the difference between the cost price and the selling price. The loss percentage measures the loss as a proportion of the actual cost price.

Given: company loss=$75

no. of owners =n

The loss must be split evenly between the two business owners.

Therefore, we must split the sum of money in order to determine how much each individual receives.

=$75/n

Expression for the earnings per person = $75/numer of owners

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If the speed of the vehicle is greater than or equal to 60 miles per hour, the angle will be greater than or equal to zero and the trooper should issue a ticket.

Distance is defined as the product of speed and time.

If the speed limit is 50 miles per hour and a speeding ticket is issued for speeds of 10 miles per hour or more over the limit, then the trooper should issue a ticket for any speed greater than 50 + 10 = 60 miles per hour.

In general, the speed of a vehicle is given by the formula v = d/t, where v is the speed, d is the distance traveled, and t is the time it takes to travel that distance.

The angle at which a speeding ticket should be issued is determined by the ratio of the speed of the vehicle to the speed limit. If the speed of the vehicle is greater than the speed limit, then the ratio of the speed of the vehicle to the speed limit will be greater than 1.

Therefore, the trooper should issue a ticket for any angle that is equal to or less than 1.

Alternatively, you could also say that the trooper should issue a ticket when the angle is greater than or equal to zero. Since any number divided by 1 is equal to the original number, this means that the angle will be equal to the speed of the vehicle in miles per hour.

Therefore, if the speed of the vehicle is greater than or equal to 60 miles per hour, the angle will be greater than or equal to zero and the trooper should issue a ticket.

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Answer:

2.5 feet = 30 inches.

Step-by-step explanation:

Let L = length not carpeted

L = 400/30

L = 13.3333333333

L = 13.33 inches

The least common multiple(LCM) of 3, 8, and 12 is 24.

What is the least common multiple(LCM)?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

We have,

3, 8 and 12

and least common multiple of 3, 8, and 12?

LCM of 3, 8, and 12 is the smallest number among all common multiples of 3, 8, and 12.

The smallest number that can be divisible by 3, 8, and 12 exactly is the LCM.

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, …..

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …..

Hence, the least common multiple(LCM) of 3, 8, and 12 is 24.

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Answer:

(-infinity, -2) ∪ (-3, infinity).

Step-by-step explanation:

To solve this compound inequality, we need to first solve each inequality separately. For the first inequality, 4(z+1) > -4, we can distribute the 4 to get 4z + 4 > -4. Then, we can subtract 4 from both sides to get 4z > -8. Finally, we can divide both sides by 4 to get z > -2.

For the second inequality, 2z - 4 < -10, we can add 4 to both sides to get 2z < -6. Then, we can divide both sides by 2 to get z < -3.

Now that we have solved both inequalities, we need to consider their intersection. Since the inequalities are joined by the "or" operator, the solution is the union of the solutions to each inequality. In interval notation, this is represented as the union of the intervals (-infinity, -2) and (-3, infinity).

Therefore, the solution to the compound inequality in interval notation is (-infinity, -2) ∪ (-3, infinity).

The value of x is 3√2/2.

A triangle with one angle being a right angle is called a right-angled triangle.

Given a right-angled triangle, with both acute angles equal to 45°

Since, acute angles = 45°

Therefore, both the legs of the triangle are equal.

Applying Pythagoras theorem,

x²+x² = 3²

2x² = 9

x² = 9/2

x = 3/√2

Rationalizing the denominator,

x = 3√2/√2x√2

x = 3√2/2

Hence, The value of x is 3√2/2.

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An example of discrete data is the number of pencils in a pencil case. Option D

Discrete data can be defined as a numerical type of data including concrete or whole numbers with fixed and specific data values determined by counting.

Some features of discrete data are;

Examples of discrete data are;

Hence, the correct option is the number of pencils in a pencil case.

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Theory is the correct answer, theory  represents the lowest degree of certainty.

What is certainty?
The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it. Other popular definitions of certainty refer to the beliefs' incontrovertibility or describe certainty as a characteristic of those beliefs with the strongest foundation. Although certainty and knowledge are closely related, modern philosophers frequently treat knowledge as having less conditions than certainty.

The rest of the options given in the questions which are conclusion, fact, hypothesis are evidence based and they provides comparatively higher degree of certainty than theory.

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Answer:

96 m²

Step-by-step explanation:

area = base × height

area = 8 m × 12 m

area = 96 m²

Using the basic percentage change rule, the answer is 6.5%.

In essence, percentages are fractions with a 100 as the denominator. In order to indicate that a number is a percentage, the percent symbol (%) is placed next to the number.

The required formula is:

[tex]Percentage = \frac {change}{inital} * 100[/tex]

initial=72000

final=76680

change=76680-72000

=4680

% change = 4680 / 72000 * 100

=6.5%

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According to ERG theory, frustration over not being able to satisfy a higher-order need may cause regression to a lower level.

ERG theory is a psychological theory put forth by Clayton Alderfer.

ERG concept, An individual will put more effort into the higher category once needs in the lower category are met. An individual will put more effort into the lower category if needs in the higher category are not met.

Maslow's hierarchy of needs was further developed by Alderfer by being categorised into his ERG theory (Existence, Relatedness and Growth). The necessity of meeting the essential material needs of people falls under the existence category. Concerned in the relatedness category is the desire to uphold significant interpersonal connections.

The desire for personal growth is addressed in the growth category. These include the self-actualization traits and the intrinsic component from Maslow's esteem category.

in a simple manner we define the three stages of ERG theory

1. Existence -  what we need from a physiological point of view .

examples- a house , healthcare, etc.

2- Relatedness -  our social needs.

examples -  friendship, social connectivity, national identity, etc.

3-growth -  Self-realization needs.

examples- feelings , success, failure ,etc.

Hence, ERG Theory suggests that failure to meet higher-order need may trigger regression to an already fulfilled lower-order need.

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All the properties of whole numbers are closed under addition and multiplication.

Whole numbers are a set of natural numbers including zero, but the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}

To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.

Let us consider each property one by one -

1. The closure property-

let's take two whole numbers say 5 and 3.

now, 5+3=8

and 5 × 3 =15

Thus, whole numbers are closed under addition and multiplication by closure property.

2. The commutative property-

let's take two whole numbers say 5 and 3.

now, 5+3=8 and 3+5=8,

hence, we get 3+5 = 5+3.

Also, 5 × 3 =15 and 3 × 5 =15

hence, we get 5 × 3 = 3 × 5

Thus, whole numbers are closed under addition and multiplication by commutative property.

3. The associative property-

let's take three whole numbers say 5, 3, and 1.

now (5+3)+1 = 9 and 5+(3+1)= 9

hence, we get (5+3)+1 = 5+(3+1).

Also, (5×3)×1 = 15 and 5×(3×1)= 15

hence, we get (5×3)×1 = 5×(3×1).

Thus, whole numbers are closed under addition and multiplication by associative property.

4. The distributive property-

let's take three whole numbers say 1, 6, and 5.

now, 1 × ( 6 + 5 ) =  1 + 6 – 1 × 5  = 1

        and 1 × ( 6 – 5 ) = 1 × 1 = 1

Hence, 1=1.

Also,  1 × (6×5)= (1 × 6) × (1 ×5) = 6 × 5 =30

and  1 × (6×5) = 1 × 30 =30

hence, we get 30=30.

Thus, whole numbers are closed under addition and multiplication by distributive property.

Hence, we can conclude that all the properties of whole numbers are closed under addition and multiplication.

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The complete question is-

What properties are whole numbers closed under addition and multiplication?

The y-intercept of the line on the graph is -60.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the y-intercept is the point where the graph intersects the y-axis.  The y-intercept is the value of y when x = 0.

Therefore, on the graph the value of y when x is equals to zero is -60.

Hence,

y-intercept = -60

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