Consider the axiomatic system and theorem below:



• Axiom 1: If there is a pair of points, then they are on a line together.

• Axiom 2: If there is a line, then there must be at least two points on it.

• Axiom 3: There exist at least two distinct points.

• Axiom 4: If there is a line, then not all the points can be on it.


Theorem 1: Each point is on at least two distinct lines.



A. List all undefined terms involved in the given axiomatic system, including all elements and relations.


B. Explain how the axioms require that the system has three distinct points.


Note: The use of models may be helpful in developing this explanation.


C. Prove theorem 1 for three points, using only the provided axioms.


Note: You do not need to use all four axioms.

Answer:

$800

Step-by-step explanation:

5% × 6000 = $350

14640 - 6000 = $8640

7.5% × 6000 = $450

8640 - 6000 = $2640

350 + 450 = $800

The insect measurement that was the most frequent is given as follows:

1 and 1/4 inches.

A dot plot is a simple graphical display that uses dots to represent data values. It is also sometimes called a dot chart or a scatterplot. In a dot plot, each data point is represented by a dot along a number line or axis, where the position of the dot corresponds to the value of the data point.

Hence, a dot plot shows the number of times that each observation appeared in the data-set.

The observation with the most dots is the observation 2/8 of the way between 1 and 2, hence the most frequent observation is given by the following mixed number:

1 and 2/8 = 1 and 1/4 inches.

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The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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Answer:  8 times 8 is 64

Answer:

8x8=64

Step-by-step explanation:

8x3=24        24x2= 48+12=64

I don't know if this makes sense but its how i do it

Answer:yes

Step-by-step explanation:

Im not that good but if there is a birth rate of 1000 people per day then if you estimate that awnser you have a possibility of 60%

Answer:

j <= 13

Step-by-step explanation:

10j <= 130

j <= 130/10

j <= 13

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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9514 1404 393

Answer:

Step-by-step explanation:

When the growth (or decay) amount is a fraction or percentage of the current amount, an exponential model is indicated. Here, it will be of the form ...

  value = (initial value) × (1 + (growth rate))^t

where t is the time period corresponding to the growth rate.

We are given that the initial value is $342,000 and the growth rate is 6% in a year. So, the model can be ...

  value = 342,000×1.06^t . . . . . where t is years after 2017

__

In 2025, we are 8 years after 2017, so the value is predicted to be ...

  value = $342,000×1.06^8 ≈ $545,096 . . . in 2025

__

In 2032, we are 15 years after 2017, so the value is predicted to be ...

  value = $342,000×1.06^15 ≈ $819,623 . . . in 2032

Exactly, Thank you again for these quotes!

-p.s you are loved <3

EDIT: THANKS FOR THE POINTS >:3

Work Shown:

(5.15)/(6.30) = (7.21)/(x)

5.15*x = 6.30*7.21 ....... cross multiply

5.15x = 45.423

x = (45.423)/(5.15) ...... dividing both sides by 5.15

x = 8.82

The discounted price of the ticket is $198.

The total cost of the ticket with the discount and service fee is $214.33.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

The cost of a ticket on an airline is $220.

And Jameson receives a discount of 10%.

To find the discounted price:

The discounted price = 220 - 220 x 10 / 100

The discounted price = $198.

And the service charge is 8.25%.

So, the amount of service charge,

= 198 x 8.25/100

= 16.33

The total cost of a ticket = $198 + $16.33 = $214.33

Therefore, the cost is $214.33.

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Answer:

1/9 rise 1 run 9

Step-by-step explanation:

if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run

The firm's accounting profit earnings as required to be determined in the task content is; $0.

As evident in the task content, the firm produces 275,000 units a year and sells them all for $8 each.

Therefore, the total revenue generated from sales is; 275,000 × $8 = $2,200,000.

Hence, since the total cost is the sum of $1,800,000 and $400,000 which is; $400,000 + $1,800,000 = $2,200,000.

Ultimately, the total accounting profit earned is; Revenue generated - Expenses = $2,200,000 - $2,200,000 = $0.

Therefore, the total accounting profit earned is; $0.

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Answer:

r = 3.42

Step-by-step explanation:

the equation for volume is V = pi r^2 h

550 = 3.14 r^2 15

36 2/3 = 3.14 r ^2

11.6772824 = r^2

3.41720389 = r

r = 3.42

Answer:

3.42

Step-by-step explanation:

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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The given expression is

Let's use the distributive property

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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Answer:

They are similar using the angle-angle property.

Step-by-step explanation:

Since you know that 2 of the angles are congruent, you can use this to prove triangle similarity.

By AA similarity, triangle PQR similar to triangle STU.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

The two given triangles PQR and STU.

Here, ∠P=63° and ∠R=45°

In triangle STU, ∠S=63° and ∠U=45°

Now, ∠P=∠S=63° and ∠R=∠U=45°

Since angles of triangle are congruent

By AA similarity, ΔPQR similar to ΔSTU

Therefore, triangles are similar.

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A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

The expression x + y is used to determine the least value of x and y. This expression can be written mathematically as x + y = min(x, y).

To calculate this value, we need to determine which of the two values is the smallest and add it to the other. For example, if x = 5 and y = 10, the least value of x + y would be 5 + 10 = 15. Similarly, if x = 10 and y = 5, the least value of x + y would still be 15. On the other hand, the expression x y is used to determine the closest value to zero of x and y. This expression can be written mathematically as x y = abs(x) + abs(y). To calculate this value, we need to determine the absolute value of both of the values, add them together and find the closest value to zero. For example, if x = 5 and y = -10, the closest value to zero of x y would be 5 + 10 = 15. Similarly, if x = 10 and y = -5, the closest value to zero of x y would still be 15. Finally, the expression x + y is used to determine the greatest value of x and y. This expression can be written mathematically as x + y = max(x, y). To calculate this value, we need to determine which of the two values is the largest and add it to the other. For example, if x = 5 and y = 10, the greatest value of x + y would be 5 + 10 = 15. Similarly, if x = 10 and y = 5, the greatest value of x + y would still be 15.

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0.3 feet/ hour is the average rate of change for the depth of the river, measured as feet per hour, between hour 9 and hour 18

Average rate of change for depth of the river = \(\frac{21 feet - 18 feet}{18 hours- 9 hours}\)

= \(\frac{21- 18}{18-9} feet/ hour\)
= \(\frac{3}{9}\)

=\(\frac{1}{3}\)

= 0.3 feet/ hour

an normal is a single number taken as representative of a list of figures, generally the sum of the figures divided by how numerous figures are in the list( the computation mean). For illustration, the normal of the figures 2, 3, 4, 7, and 9( summing to 25) is 5. Depending on the environment, an average might be another statistic similar as the standard, or mode.

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Complete Question

The depth of a river changes after a heavy rainstorm. Its depth, in feet, is modeled as a function of time, in hours. Consider this graph of the function. Write the average rate of change for the depth of the river, measured as feet per hour, between hour 9 and hour 18. Round your answer to the nearest tenth.