a fromal state of theory usualyl a mathematical state of presumed relationship between two or more variables is called a

The kilogram is defined as follows: "The kilogram is defined by taking the fixed numerical value of h to be 6.626070151034 when stated in the unit Js, which is equivalent to kgm2s1, where the meter and the second are defined in terms of speed".

The K value of a cyclotron, also known as the bending limit, is determined by the charge-to-mass ratio and the achievable energy, where is the particle's kinetic energy and is the atomic mass number.

The absolute values of 3 and -3 are equal since they are both three steps away from zero. Temperature sensitivity See Hooke's law for the spring's force constant.

Vapor-liquid equilibrium is the ratio of the equilibrium vapor concentration to the equilibrium liquid concentration.

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The equation y = -2/3x + 1/2 is in slope-intercept form.

What is the slope intercept?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

A relationship that when graphed produces a straight line. Equation. A mathematical sentence that sets 2 expressions equal to each other.

It has the variable y on one side of the equation and the slope (-2/3) and y-intercept (1/2) are easily identifiable.

This is the equation of line AB.

Hence, the equation y = -2/3x + 1/2 is in slope-intercept form.

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The fee for Lewis college when Maria's mother graduated from there is 2874.79 or $2875.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

The yearly tuition at Lewis College is set at $13,655.25,

The percentage increase = 575%

Calculate the tuition fees of her mother as shown below,

The percentage increase = Maria fees - her mother fees / her mother fees  × 100

575 = 13655.25 - x / x × 100

575 / 100 = 13655.25 - x / x

5.75 = 13655.25 - x / x

5.75x = 13655.25 - x

4.75x = 13655.25

x = 13655.25 / 4.75

x = 2874.79

Thus, fee was $2874.79

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On February 22nd, Peter Chan will have 420 spring rolls in his stock already.

Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Given,

No. of spring rolls Elvin' cool truck delivers everyday = 200

No. of spring rolls used by Peter Chan food store everyday = 180

No. of spring rolls left in stock everyday = 200 - 180 = 20

Days to have 420 spring rolls in stock = 420/20 = 21 days

So, on 22nd day Peter Chan will have 420 spring rolls in stock.

On 3rd February he has 40 spring rolls which should be on 3rd day.

⇒ On 22nd February, he will have 420 spring rolls in

stock.

Hence, Peter Chan will have 420 spring rolls first in stock

on February 22nd.

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There is a rotational transformation, therefore Δ ABC ~ Δ A'B'C'

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

Given that, a figure triangle ABC is being rotated,

Answers :-

1) Δ ABC ~ Δ A'B'C'

2) Coordinates are ;

A = (2, 0), A' = (-2,0)

B = (7, 0), B' = (-7, 0)

C = (6, -4), C' = (-6, 4)

3) m ∠ ACB = m ∠ A'C'B'

AB = 16 in then A'B' = 16 in

m ∠ BAC = 55°, then  m ∠ B'A'C' = 55°

Hence, the answer are Δ ABC ~ Δ A'B'C'

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The equation for the line that passes through point (-5, 2) that is parallel  and perpendicular to y = 2/3x + 1

For the equation of the line parallel to the line the  y = 2/3x + 1 slope must be equal, hence m = 2/3

equation passing through point (-5, 2)

(y - y₁) = m  (x - x₁)

y - (-5) = 2/3(x - 2)

y + 5 = 2/3 x - 4/3

y = 2/3 x - 19/3

For the line perpendicular to the line y = 2/3x + 1 the slope is negative reciprocal of the slope in the line.

m = 2/3

perpendicular m' = -3/2

equation passing through point (-5, 2)

(y - y₁) = m'  (x - x₁)

y - (-5) = -3/2(x - 2)

y + 5 = -3/2 x + 3

y = -3/2 x + 3 - 5

y = -3/2 x - 2

the perpendicular line is y = -3/2 x - 2

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A) The  probability that the number who say cashews are their favorite nut is​  exactly​ three is; 18.49%

b) The probability that the number who say cashews are their favorite nut is​  at least four is; 67.99%

c) The probability that the number who say cashews are their favorite nut is​  at most two is; 13.52%

The binomial probability is defined as the probability of exactly x successes on n repeated trials, and X can only have two outcomes. It is given by the formula;

P(X = x) = [tex]^{n} C_{r}[/tex] * pˣ * (1 - p)⁽ⁿ⁻ˣ⁾

Where:

x = total number of “successes” (pass or fail, heads or tails etc.)

P = probability of a success on an individual trial

n = number of trials

We are given;

p = 36% = 0.36

n = 12

A) The  probability that the number who say cashews are their favorite nut is​  exactly​ three is;

P(X = 3) = ¹²C₃ * (0.36)³ * (1 - 0.36)⁽¹²⁻³⁾

P(X = 3) = 0.1849 = 18.49%

b) The probability that the number who say cashews are their favorite nut is​  at least four is;

P(X ≥ 4) = 1 - P(X < 4)

Now, P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = 0) = ¹²C₀ * (0.36)⁰ * (1 - 0.36)⁽¹²⁻⁰⁾ =  0.0047

P(X = 1) = ¹²C₁ * (0.36)¹ * (1 - 0.36)⁽¹²⁻¹⁾ = 0.00319

P(X = 2) = ¹²C₂ * (0.36)² * (1 - 0.36)⁽¹²⁻²⁾ = 0.00986

P(X = 3) = ¹²C₃ * (0.36)³ * (1 - 0.36)⁽¹²⁻³⁾ = 0.1849

Thus;

P(X < 4)  = 0.0047 + 0.00319 + 0.00986 + 0.1849 = 0.3201

Thus;

P(X ≥ 4) = 1 - 0.3201

P(X ≥ 4) = 0.6799 = 67.99%

c) The probability that the number who say cashews are their favorite nut is​  at most two is;

P(X ≤ 2) =  P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = ¹²C₀ * (0.36)⁰ * (1 - 0.36)⁽¹²⁻⁰⁾ =  0.0047

P(X = 1) = ¹²C₁ * (0.36)¹ * (1 - 0.36)⁽¹²⁻¹⁾ = 0.00319

P(X = 2) = ¹²C₂ * (0.36)² * (1 - 0.36)⁽¹²⁻²⁾ = 0.00986

Thus;

P(X ≤ 2) = 0.0047 + 0.00319 + 0.00986

P(X ≤ 2) = 0.1352 = 13.52%

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Answer:

Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.

Step-by-step explanation:

The 12th term of the geometric sequence 5, 15, 45, ... can be found using the general formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where:

a1 is the first term of the sequence,

r is the common ratio, and

n is the position of the term that you're trying to find.

In this case,

a1 = 5

r = 15/5 = 3

n = 12

so:

a12 = 5 * 3^(12-1) = 5 * 3^11 = 5 * 177147 = 885735

Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.

Answer:

12th term = 885735

Step-by-step explanation:

Meaning: A geometric sequence is an ordered set of numbers that progresses by multiplying or dividing each term by the same number.

5 x 3 = 15

15 x 3 = 45

The number we multiply the terms by in this sequence is 3.

4th term = 45 x 3 = 135

5th term = 135 x 3 = 405

6th term = 405 x 3 = 1215

7th term = 1215 x 3 = 3645

8th term = 3645 x 3 = 10935

9th term = 10935 x 3 = 32805

10th term = 32805 x 3 = 98415

11th term = 98415 x 3 = 295245

12th term = 295245 x 3 = 885735

5, 15, 45, 135, 405, 1215, 3645, 10935, 32805, 98415, 295245, 885735

hope this helps :)

The pattern of association refers to the relationship that exists between two variables such as positive, negative, or no correlation.

In mathematics, a pattern of association refers to the relationship between two or more variables. This relationship can take several forms, such as a positive correlation, a negative correlation, or no correlation.

A positive correlation exists when the variables increase or decrease together. This means that as one variable increases, the other variable also increases and vice versa.

A negative correlation exists when the variables move in opposite directions. As one variable increases, the other variable decreases and vice versa.

A no correlation exists when there is no relationship between the variables. This means that the variables do not change together and there is no pattern in the data.

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The real part of the complex number - 5 + 3i is ''-5''.

The complex part of the complex number - 5 + 3i is ''3''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The complex number is,

⇒ - 5 + 3i

Now,

Since, The complex number is,

⇒ - 5 + 3i

Hence, The real part of the complex number = -5

The complex part of the complex number = 3

Thus, real part of the complex number - 5 + 3i is ''-5''.

The complex part of the complex number - 5 + 3i is ''3''.

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Answer:

-5 complex and 3 imaginary complex

Step-by-step explanation:

the proportions are the same the function is linear.

What is a function?

A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph since one is mapped to two different values. However, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.

The function machine receives the x-values as input. After finishing its operations, the function machine produces the y-values. Any function may be the one within.

Given table of data x and f(x)

the proportion -3/1, -3/1, -3/1...

As the proportions are the same the function is linear.

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Answer:

$161.38

Step-by-step explanation:

12*0.99=11.88$

50*2.99=149.50$

11.88+149.50=161.38

The sum of two square roots of 2 and 1/4 is the result having radical as (8√2 + 1)/4

The symbol √ is used to represent or show that a number is a radical. Radical expression is defined as any expression containing a radical (√) symbol

The square root 2 = √2

two square root of 2 = √2 + √2

two square root of 2 = 2√2

sum of two square roots of 2 and 1/4 = 2√2 + 1/4

adding in one fraction by taking LCM of the denominators, we have;

sum of two square roots of 2 and 1/4 = (4×2√2 + 1)/4

sum of two square roots of 2 and 1/4 = (8√2 + 1)/4

Therefore, the radical expression (8√2 + 1)/4 is the sum of two square roots of 2 and 1/4.

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The number of medium and large pieces of pizza Mr Brown ordered is 3 and 6 respectively.

Let

number of medium pieces = x

number of large pizzas = y

Number of slices in a medium pizza = 6

Number of slices in a large pizza = 8

Total pizzas ordered = 9

Total number of slices = 66

The simultaneous equation can be written as follows;

x + y = 9

6x + 8y = 66

From (1)

x = 9 - y

Substitute into (2)

6x + 8y = 66

6(9 - y) + 8y = 66

54 - 6y + 8y = 66

2y = 66 - 54

2y = 12

divide both sides by 2

y = 12/2

y = 6

Substitute y = 6 into (1)

x + y = 9

x + 6 = 9

x = 9 - 6

x = 3

In conclusion, Mr Brown ordered 3 pieces of medium and 6 pieces of large pizza.

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Answer:

x < [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

2(1 - 3x) - (x - 5) > 1 ← distribute parenthesis and simplify left side

2 - 6x - x + 5 > 1

- 7x + 7 > 1 ( subtract 7 from both sides )

- 7x > - 6

divide both sides by - 7, reversing the symbol as a result of dividing by a negative quantity.

x < [tex]\frac{6}{7}[/tex]

Answer:

x < (6/7)

Step-by-step explanation:

2(1-3x)-(x-5)>1

2 - 6x -x + 5 > 1

-7x + 7 > 1

-7x > -6

x < (6/7)     [The inequality is reversed when dividing or multiplying with a negative value]

The total width of the crystal as calculated from the given data is 0.001512 mm.

The spacing as given is 14.4 nm ,

on converting it into meters we get,

= 14.4 * 10^(-9) m

As we know,

1 mm = 1 * 10^(-3) m

Therefore,

14.4 nm * 105 = 1,512 nm

= 1.512 micrometers

= 0.001512 mm

or we can say that ,

1.512 * 10^(-3) mm

Therefore, the total width of crystal as calculated  is 0.001512 mm.

A crystal which is also known as a crystalline solid, is a solid material in which the constituents are atoms, molecules, or ions, they are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

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The pair between the histogram and the data is I-b, II-d, III-c, and IV-a.

Histogram is a graphical display of frequency tabulations illustrated by bar graphics, where each bar shows the proportion of frequencies in each category series that are adjacent with non-overlapping intervals. The histogram is frequently used to depict the main characteristics of the data distribution.

There are relations between the mean and median of the statistical data and the shape of a histogram.

Whilst, the standard deviation describes the range between the highest and the lowest bar of the histogram. The higher the standard deviation, the range is bigger, and vice versa.

Take a look at the given data and the given histograms:

Data       Mean      Median      SD

  I             56             56          1.6          

  II            65             65          9      

  III           56             56          10      

  IV          56             56          21      

Based on that, we can conclude that:

The pair between the histogram and the data is I-b, II-d, III-c, and IV-a.

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In order to make Natasha's survey data more reliable, she could increase the sample size, conduct the survey on different day or time, or extend the days of the survey.

Conducting a survey with a sample size of only 30 workers, the survey results may not be representative of the entire population of 215 workers. Increasing the sample size would help to ensure that the survey results are more representative of the population. Moreover, she could also increase the data reliability by conducting the survey on different day or time can also gives different results since the transportation way can vary day by day. Another way Natasha could make the survey data more reliable would be to extend the survey over the course of several days rather than just one day.

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In order to make Natasha's survey data more reliable, she could increase the sample size, conduct the survey on different day or time, or extend the days of the survey.

Conducting a survey with a sample size of only 30 workers, the survey results may not be representative of the entire population of 215 workers. Increasing the sample size would help to ensure that the survey results are more representative of the population. Moreover, she could also increase the data reliability by conducting the survey on different day or time can also gives different results since the transportation way can vary day by day. Another way Natasha could make the survey data more reliable would be to extend the survey over the course of several days rather than just one day.

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Monitoring Instruments are essential instruments for analyzing event data that is occurring in real-time to see whether anything is there.

The measuring device that generates the seismogram is called a seismograph or seismometer. The foundation of almost all seismometers is the concept of inertia, which states that when the ground shakes, a hanging object prefers to stay stationary. A creepmeter is a device used to track the gradual surface movement caused by an active geologic fault in the ground.

Its job is to capture the aseismic creep that occurs in between earthquakes. A creepmeter's measurement range is typically 10–30 mm only. In order to monitor ground tilt (rotation) near faults and volcanoes brought on by fault slip and volcanic uplift, tiltmeters are highly sensitive sensors.

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The solution set of this system of equations is a no solution or zero solution.

In Mathematics, the solution set of any system of equations simply refers to all of the set of values that correctly satisfy all the equations.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = x² + 2x + 2         ........equation 1.

y = x + 1                    ........equation 2.

Based on the graph (see attachment), we can reasonably infer and logically deduce that the given system of equations has no solution (zero solution) because it does not have a point of intersection for the lines on the graph representing each of the system of equations.

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A linear graph represents a proportional relationship include the following: C. A graph of a straight line that passes through the points 0 comma negative 4 and 1 comma negative 4.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

In this context, we can reasonably infer and logically deduce that a graph of a straight line that passes through the data points (0, -4) and (1, -4) represents a proportional relationship because it would go through the origin (0, 0).

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The option 1 is not an example of direct variation.Because this equation does not hold direct variation formula y=kx.

In mathematical relationship between two variables which can be expressed by an equation in which one variable is equal to a constant times the other. If the proportionality constant needs to be determined divide y by x to get the answer.

The general form of a direct variation formula is y=kx, where x and y are variables and k is a constant.The formula for direct variation is y = kx or k = y/x.. It is represented by the proportional symbol ∝.

NOW

Option b, c and d hold direct variation proportion and option a does not hold direct variation.

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The equation that will be used to represent the number of purple and pink flowers would be =

For the pink flowers = r = 180 - 4(0)

For the purple flowers = r = 180 - 4(45)

A garden is defined as an area that is being prepared for the purpose of cultivation of various flower, shrubs and grass.

The total number of flowers in the garden = 180

The number of pink flower beds = 4

The number of purple flower beds = 4

The number of pink flowers in each bed = 45

Therefore, the number of total pink flowers = 4 × 45 = 180

Since the pink flowers is the total of 180 which is also the quantity of flowers in the garden, the quantity of flowers in the purple bed would be = 0

Thus, 180 = 4(45) + 4(0)

For the pink flowers = r = 180 - 4(0)

For the purple flowers = r = 180 - 4(45)

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So the slope of the line between these two points is 0.177, which can be rounded to 0.18

To calculate the slope of a line between two points, you need to use the following formula:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we are using weight as the explanatory variable, so x1 = 3.5 (the weight of the rat), y1 = 4.5 (the cost of feeding the rat), x2 = 30 (the weight of the beagle), and y2 = 9.2 (the cost of feeding the beagle). Plugging these values into the formula, we get:

slope = (9.2 - 4.5) / (30 - 3.5)

slope = 4.7 / 26.5

slope = 0.177

So the slope of the line between these two points is 0.177, which can be rounded to 0.18. The slope represents the average change in the dependent variable (feed cost) per unit change in the independent variable (weight). So, in this case it means that the feed cost increase of 0.18 dollar per pound.

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Using weight as the explanatory variable, the slope of the line between two points (3,5, 4.50) and (30, 9.20) is 0.17

In this question we have been given a Rat weighs 3. 5 pounds and costs $4. 50 per week to feed, while a Beagle weighs 30 pounds and costs $9. 20 per week to feed.

Using weight as the explanatory variable, we need to find the slope of the line between these two points.

Here weight is  the explanatory variable i.e., an independent Variable

This means, we place the values of weight on the x-axis and the feed cost on the y-axis.

So, the two data points from the weight and feed cost data set would be:

(3,5, 4.50) and (30, 9.20)

Let m be the slope of line between these two points

Using the formula of slope,

m = (9.20 - 4.50) / (30 - 3)

m = 0.1741

m = 0.17

Therefore, the required slope is 0.17

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Answer:

Step-by-step explanation:

n

nnn,'

Answer:

x = 23

Step-by-step explanation:

Since the lines m and n are parallel, then x+1 is complimentary to 7x-5, both of them forming a 180º angle:

x + 1 + 7x - 5 = 180

8x - 4 = 180

8x = 180 + 4

8x = 184

x = 184 / 8

x = 23

The standard equation of the line is -2.5x + y = 5.

Slope of a line is the measure of ratio of the change in the y coordinate values to change in the x coordinate values when two points are given. Slope of a line is denoted by 'm'.

From the given graph, we have two points that the line passes through.

The point where the line touches the X axis is (-2, 0) which is called the x-intercept.

And the point where the line touches the Y axis is (0, 5) which is called the y-intercept.

We have the slope-intercept form of a line as,

y = mx + c, where m is slope and c is y intercept.

We have y intercept, c = 5.

Slope = (5 - 0) / (0 - -2) = 5 / 2 = 2.5

Equation of line in slope intercept form is,

y = 2.5x + 5

y - 2.5x = 5

-2.5x + y = 5, which is the standard equation.

Hence the standard equation of the line shown in the graph is -2.5x + y = 5.

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The percentage rate of growth will be 50%. Then the correct option is C.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

At x = 0, the value of the variable 'y' is 15. Then we have

15 = ab⁰

a = 15

At x = 2, the value of the variable 'y' is 35. Then we have

35 = ab²

35 = 15b²

b² = 2.333

b ≅ 1.50

Then the equation is written as,

y = 15 (1.50)ˣ

y = 15 (1 + 0.50)ˣ

The percentage rate of growth will be 50%. Then the correct option is C.

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The complete question is given below.

Enrollment at a golf academy has grown exponentially since the academy opened. A graph depicting this growth is shown. Determine the percentage rate of growth.

A.) 1.5%

B.) 5%

C.) 50%

D.) 0.5%

Answer:

y = -5x + 60

Step-by-step explanation:

You have two ordered pairs (3, 45) and (5,35)

y = mx + b

We need to find the slope and the y-intercept

Slope:

change in y over the change in x

(3,45) (5, 35)

The y's are 35 and 45.  You find the change by subtracting.

35 - 45 = -10

The x's are 5 and 3.  You find the change by subtracting,

5-3 = 2

[tex]\frac{-10}{2}[/tex] = -5

The slope (m) is -5

y-intercept:

Use of the on the points.  I will use (3, 45)

x = 3

y = 45

slope = -5

y = mx + b  Substitute in what you know and solve for b

45 = -5(3) + b

45 = -15 +b  Add 15 to both sides

60 = b

The y-intercept (b) is 60.

y = -5x + 60