HOW DO YOU FIND PERCENT INCREASE

If we have a finite group G and an element x in G, then there must exist a positive power of x which equals its inverse (i.e., x⁻¹ = \(x^{k}\) for some positive integer k).

A finite group is a mathematical object consisting of a set of elements and a binary operation that combines two elements to produce a third. The key feature of a finite group is that the set of elements is finite, meaning it contains only a finite number of elements.

More formally, a finite group is a set G, together with a binary operation * on G, such that:

For any two elements a and b in G, their product a*b is also in G.

The operation * is associative, meaning that for any three elements a, b, and c in G, the product (ab)c is equal to a(bc).

There exists an element e in G, called the identity element, such that for any element a in G, the products ea and ae are both equal to a.

For every element a in G, there exists an inverse element a⁻¹ in G such that the product aa^-1 and a^-1a are both equal to the identity element e.

This statement is saying that if we have a finite group G and an element x in G, then there must exist a positive power of x which equals its inverse (i.e., x⁻¹ = \(x^{k}\) for some positive integer k). This is because if we consider the powers of x, there are only a finite number of possibilities since G is finite. Therefore, at some point, there must be a repetition of a power of x (i.e., \(x^{m}\) = xⁿ for some integers m < n), which means that x^(n-m)\(x^{n-m}\) = 1 (the identity element). Then, we can rewrite x^(n-m-1)\(x^{n-m-1}\) as x⁻¹ and we see that x⁻¹ = \(x^{k}\) for some positive integer k. This statement is important in group theory because it shows that every element in a finite group has a well-defined inverse, which is a key property of groups.

To know more about positive visit:

https://brainly.com/question/28537148

#SPJ1

the variance will be 0.6217.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

A small data analysis class has six computer science majors among the fourteen total students.

Three people are chosen at random to form a group.

here this is hypergeometric distribution with parameter n=sample size =3 ; N =population size =14

and k=computer sience major =6

a) E(X) =nk/N =3*6/14 =18/14 =9/7 =1.2857

b)|varaince =σ²=(nk/N)*(1-k/N)*(N-n)/(N-1)) =(3*6/14)(1-6/14)*(14-3)/(14-1)= 0.6217

Hence, the variance will be 0.6217.

Learn more about frequency distribution, by the following link

https://brainly.com/question/16698786

#SPJ1

The equation of the parallel line is: y = 1/2x + 5.

The slope (m) of parallel lines are the same.

Given the equation, y = 1/2x - 7, the slope (m) is 1/2. Therefore, the slope of the line that passes through (-4, 3) would be m = 1/2.

To find the y-intercept (b), substitute m = 1/2 and (x, y) = (-4, 3) into y = mx + b.

3 = 1/2(-4) + b

3 = -2 + b

3 + 2 = b

5 = b

b = 5

Substitute m = 1/2 and b = 5 into y = mx + b:

y = 1/2x + 5

The equation is: y = 1/2x + 5.

Learn more about the equation of parallel lines on:

https://brainly.com/question/11345748

#SPJ1

Work Shown:

T = average Celsius temperature two Sundays ago

8% = 8/100 = 0.08

8% of T = 0.08T

L = average Celsius temperature last sunday

L = 8% higher than T

L = T + (8% of T)

L = T + 0.08T

L = 1.00T + 0.08T

L = (1.00 + 0.08)T

L = 1.08T

The 1.08 refers to the idea that L is 108% of T

Answer:

b and d

Step-by-step explanation:

khan

Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

For such more questions on Advantages of Mathematical Models

https://brainly.com/question/12653211

#SPJ8

\( m \angle B = 22 \degree\)

Explanation:

Given:

\(\sf m \angle A = 120 \\ \sf m\angle B =x \\\sf m \angle C = x+16\)

To find:

\(\sf m\angle B \: = ?\)

Solution:

We know that,

sum of all the interior angle of triangle equals 180 degrees.

\(\sf m \angle A + m\angle B + m \angle C = 180 \degree \\ \sf 120 + x + x + 16 = 180 \degree \\ \: \sf 2x+136= 180\degree \\ \: \sf 2x=180-136 \\ \:\sf 2x=44 \degree \\ \sf \: x= \frac{44}{2} \\ \:\sf x= 22 \degree\)

Measure of angle B is equal to x hence,

\( m \angle B = 22 \degree\)

Thanks for joining brainly community!

Answer:

The probability that exactly eight of them take more than 93.6 minutes is 5.6015 \(\times 10^{-6}\) .

Step-by-step explanation:

We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.

A random sample of twelve service calls is taken.

So, firstly we will find the probability that service calls take more than 93.6 minutes.

Let X = times for service calls.

So, X ~ Normal(\(\mu=75,\sigma^{2} =15^{2}\))

The z-score probability distribution for the normal distribution is given by;

                              Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean time = 75 minutes

           \(\sigma\) = standard deviation = 15 minutes

Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)

       P(X > 93.6 min) = P( \(\frac{X-\mu}{\sigma}\) > \(\frac{93.6-75}{15}\) ) = P(Z > 1.24) = 1 - P(Z \(\leq\) 1.24)

                                                                = 1 - 0.8925 = 0.1075

The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.

Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;

\(P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........\)

where, n = number of trials (samples) taken = 12 service calls

            r = number of success = exactly 8

            p = probability of success which in our question is probability that

                   it takes more than 93.6 minutes, i.e. p = 0.1075.

Let Y = Number of service calls which takes more than 93.6 minutes

So, Y ~ Binom(n = 12, p = 0.1075)

Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)

               P(Y = 8)  =  \(\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}\)

                             =  \(495 \times 0.1075^{8} \times 0.8925^{4}\)

                             =  5.6015 \(\times 10^{-6}\) .

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

More can be learned about the Empirical Rule at https://brainly.com/question/10093236

#SPJ1

Answer:

Step-by-step explanation:

I think I don't know. I wish I could help u sorry :(

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

Learn more about the present value at https://brainly.com/question/20813161.

#SPJ1

A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.

Given:

Length of the rectangular floor = 14 ft

Width of the rectangular floor = 6 ft

Edge length of square tile = 3/4 ft

First, let's calculate the number of tiles that can fit horizontally:

Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft

Since we want a whole number of tiles, we need to round down or take the floor value:

Number of tiles horizontally = floor(56/3) = 18 tiles

Next, let's calculate the number of tiles that can fit vertically:

Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft

Again, we round down or take the floor value:

Number of tiles vertically = floor(24/3) = 8 tiles

To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:

Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles

Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

for such more question on length

https://brainly.com/question/20339811

#SPJ8

Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

Learn more about the maximum height here:

https://brainly.com/question/15025354

#SPJ1

Answer:

Associative Property

Step-by-step explanation:

Associative Property= Uses parethesis and it doesnt matter the order you put it in it. You are going to get the same answer.

Answer:

The correct option is;

The amount of fertilizer applied to each plot of land

Step-by-step explanation:

The value which the family would like to predict = The amount of grain harvested per acre of land on their farm

The methodology to be used for the prediction = Linear regression equation

The general form of a linear regression equation is Y = a + b·X

Where;

X = The independent or explanatory variable

Y = The dependent variable

b = The gradient or slope which is the rate of change

a = The y-intercept, the initial value of the dependent variable at the start of observation when the explanatory variable is 0

Therefore, given that the family would like to predict the amount of grain produced per acre, we have;

The variable which is whose value depends on other variable is the variable to be predicted and it is the same as the dependent variable

Therefore, the dependent variable is to be predicted, which gives;

The amount of grain produced per acre which is the dependent variable is to be predicted

Hence, Y = The amount of grain produced per acre

The explanatory variable or the independent variable is the variable which determines the value and in which the dependent variable depends as such it can be used to explain the values of the amount of grain growing per acre, therefore, we have;

The explanatory variable can be the amount of fertilizer applied to each plot of land

Therefore;

X = The amount of fertilizer applied to each plot of land

Therefore, we have;

The amount of grain produced per acre = The initial growth of grain per acre + (Rate of change of grains produced per unit of fertilizer added) × (The amount of fertilizer applied to each plot of land).

The explanatory variable refers to the independent variable in an experiment which is used to tweak the value of the measured variable. An appropriate explanatory variable would be the amount of fertilizer applied to each plot of land

Therefore, the amount of fertilizer is a good factor to measure the yield or amount of grain harvested on each plot.

Learn more :https://brainly.com/question/18405415

Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

Answer:

2

Step-by-step explanation:

Given:

There is a bicycle that is cost $175

There are two friends:

The first has $45 and save $5 each week

So, we have the following equation, let (x) is the number of weeks

Solve the equation to find (x):

So, the first can buy the bicycle after 26 weeks

The second friend has an amount (y) after (x) weeks according to the shown graph of the line:

As shown the line passes through the points (0, 15) and (3, 39)

The slope of the line represents the saving each week =

The y-intercept represents the initial saving = $15

So, after (x) week we have the following equation:

Now, solve to find (x)

So, the second can buy the bicycle after 20 weeks

So, the answer will be

Answer:

Undefined.

Step-by-step explanation:

Answer:

The answer is 170

PLEASE  MARK ME BRAINIIEST PLEASE AND THANK YOU

Step-by-step explanation:

The slope-intercept form of an equation for the line containing the point (0,-3) with slope -1 is y = -x - 3. This equation expresses the relationship between the x-coordinate and the y-coordinate of the line. It means that for any given x-value, the corresponding y-value can be calculated by multiplying the x-value by -1 and subtracting 3 from that result.

The slope-intercept form of an equation for the line containing the point (0,-3) with slope -1 is y = -x - 3. This equation can be used to describe the relationship between the x-coordinate and the y-coordinate of the line. The slope of the line is -1, which means that for every unit increase in the x-value, the y-value will decrease by one unit. The intercept of the line is -3, which means that the line crosses the y-axis at the point (0,-3). This equation can be used to calculate the y-value for any given x-value. To do this, simply multiply the x-value by -1 and subtract 3 from the result. For example, if the x-value is 4, the corresponding y-value would be calculated as -4 - 3 = -7. This equation can be used to graph the line, and can also be used to calculate the slope, intercept, and any other points on the line.

Learn more about  slope-intercept here

https://brainly.com/question/19824331

#SPJ4

Answer:

Option A. 5

Step-by-step explanation:

From the question given above, the following data were obtained:

First term (a) = –3

Common ratio (r) = 6

Sum of series (Sₙ) = –4665

Number of term (n) =?

The number of terms in the series can be obtained as follow:

Sₙ = a[rⁿ – 1] / r – 1

–4665 = –3[6ⁿ – 1] / 6 – 1

–4665 = –3[6ⁿ – 1] / 5

Cross multiply

–4665 × 5 = –3[6ⁿ – 1]

–23325 = –3[6ⁿ – 1]

Divide both side by –3

–23325 / –3 = 6ⁿ – 1

7775 = 6ⁿ – 1

Collect like terms

7775 + 1 = 6ⁿ

7776 = 6ⁿ

Express 7776 in index form with 6 as the base

6⁵ = 6ⁿ

n = 5

Thus, the number of terms in the geometric series is 5.

16cm this answer for the quetion

Answer:

2

Step-by-step explanation:

x*x*x=8

2*2*2=8

The function that has a remainder of 18 when divided by ( x-2 ) is
f ( x ) = 2x⁴ + 4x² - 10x - 10

What is a polynomial function?

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given data ,

The divisor = ( x - 2 )

The remainder = 18

The function will be f( x ) = 2x⁴ + 4x² - 10x - 10

Step 1 :

Divide f ( x ) by ( x-2 ) = \(\frac{2x^4+4x^2-10x-10}{x-2}\)

=

\(2x^3+\frac{4x^3+4x^2-10x-10}{x-2}\)

Step 2 :

Divide  \(\frac{4x^3+4x^2-10x-10}{x-2}\)

=

\(2x^3+4x^2+\frac{12x^2-10x-10}{x-2}\)

Step 3 :

Divide  \(\frac{12x^2-10x-10}{x-2}\)

=

\(2x^3+4x^2+12x+\frac{14x-10}{x-2}\)

Step 4 :

Divide  \(\frac{14x-10}{x-2}\)

=

\(2x^3+4x^2+12x+14+\frac{18}{x-2}\)

The remainder is 18 at the end of step 4

Hence , the function that has a remainder of 18 when divided by ( x-2 ) is
f ( x ) = 2x⁴ + 4x² - 10x - 10

To learn more about fractions click :

https://brainly.com/question/2929160

#SPJ2

Answer:

Step-by-step explanation:

angle 1 is a central angle because the vertex is at the center of the circle and the central angles have same measure as the arc it inscribes, so

arc AB =30 °

Answer:

60

Step-by-step explanation:

Answer:

need the line

Step-by-step explanation: