What is M in triangle properties

Answer:          To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).

In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.

Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:

I = $325 ∙ 0.08 ∙ 15 = $390

Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.

To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.

The total amount of money that Charlie will have after the 15 years is:

Total amount = Initial investment + Interest earned

Total amount = $325 + $390

Total amount = $715

Therefore, Charlie will have $715 after 15 years.

Step-by-step explanation:

The similes in the story are:

A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.

Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.

Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.

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Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:

x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923

Using the formula for the sum of a geometric series, we have:

x(1 - (1.1)^7)/(1 - 1.1) = 56.923

x(1 - 1.1^7)/(-0.1) = 56.923

x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles

Therefore, the hiker traveled approximately 4 miles on the first day.

Sn = x(1 - r^n)/(1 - r)

where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.

S14 = x(1 - 1.1^14)/(1 - 1.1)

S14 ≈ 167.63

Therefore, the hiker will travel approximately 167.63 miles in 14 days.

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For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.

A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.

Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.

For the given equation of the parabola, the value of a and b = 5 and 4.

Thus, we have horizontal length of 5 and vertical width of 4 units

The graph that depicts this hyperbola is: Option B.

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The complete question is:

Answer:

Step-by-step explanation:

A=1/2(b1+b2)h

=1/2 (11yd+11yd)(7yd)

=1/2(22yd)(7yd)

=(11yd)(7yd)

=77yd

The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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The next entry on the long division would be 0.054, and 0.0054

Long division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:

Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.

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the solution to the equation  is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation

what is distributive property ?

The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,

In the given question,

To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.

Here are the steps:

Distribute the 3 on the left-hand side of the equation:

3(x+6) = 3x + 18

Combine the two x terms on the right-hand side of the equation:

3x + 18 = 2x + 8

Subtract 2x from both sides of the equation:

3x - 2x + 18 = 2x - 2x + 8

Simplifying this expression gives:

x + 18 = 8

Finally, subtract 18 from both sides of the equation:

x + 18 - 18 = 8 - 18

Simplifying this expression gives:

x = -10

Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

Answer:

1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:

h(t) = -16t^2 + 72t + 4

To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:

t = -b/2a = -72/(2(-16)) = 2.25 seconds

To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):

h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet

The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.

2. Using the same kinematic equation as before, we have:

h(t) = -16t^2 + 80t + 3

To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:

t = -b/2a = -80/(2(-16)) = 2.5 seconds

To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):

h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet

The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.

Step-by-step explanation:

The measurements for area of Jacobs yard are;

Part A = 6m x 3m = 18m

Part B = 4.5m x 3m = 13 m

Part C = 1/2 x 3m x 3m = 4.5 m²

Total area = 18m² + 13.5m² + 4.5m² = 36m²

To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.

Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.

For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.

Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?

Part A = .............. x ........... = ...........m

Part B = + .............. x ............. = ............ m

Part C = 1/2 x ................. x ............ = ............... m²

Total area = ................... + ..................... + .................. = ..............m

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Answer: Amaterasu

Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.

The ratio of US to British coins is 25 to 4.

The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.

First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.

Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.

Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.

25 : 10 :: 10 : 2

Multiplying both sides by 2, we get:

50 : 20 :: 10 : 2

Simplifying, we get:

The ratio of US to British coins is 25 to 4.

2. To calculate Amanda's monthly pay, we can use the formula:

m = 10h + 50

where m is the total money Amanda receives in a month, and h is the number of hours she works.

The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

3. To calculate the cost of the holiday package for d days, we can use the formula:

C = 190 + 50d

where C is the cost of the holiday package, and d is the number of days.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

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After 6 fluid ounces , Naya uses 4 glasses as a result.

A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce .  A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce

In Naya's pitcher, there are three glasses of salted lassi.

She fills each glass with six fluid ounces of lassi.

By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.

8 fluid ounces make constitute a cup.

Consequently, 3 cups equal 24 fluid ounces (3 x 8).

24 divided by 6 results in:

4 glasses are equal to 24/6.

Naya uses four glasses as a result.

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The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.

The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.

Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.

According to the given information:

A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).

To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.

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In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.

If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.

The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.

The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.

A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.

If x = 0

Then,

1/2(0) + y = c

y = c

The proportionality constant, c, can be seen in the equation

1 over 2 x + y = c.

This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.

The slope of the line connecting the two variables is another name for the constant of proportionality.

Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that

are being compared are represented by these variables.

In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.

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The Complete questions as follows-

Explain what the constant of proportionality means in the equation 1 over 2 x + y = c

Answer: a.     c(n) = 15 + 0.75(n - 10)

b.   15 + 0.75(n - 10) = 2.50(n - 10)=

Simplifying and solving for n, we get:

n = 50

c.  n > 50

Step-by-step explanation:

a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:

c(n) = 15 + 0.75(n - 10)

The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

The cost c of the bank account in terms of the number of checks written n can be expressed as:

c(n) = 2.50(n - 10)

The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:

15 + 0.75(n - 10) = 2.50(n - 10)

Simplifying and solving for n, we get:

n = 50

So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.

c. The solution to the inequality is:

n > 50

This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.

The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.

Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.

We are to find the coordinates of the vertices of the image.

We know that

if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :

(a, b)   ⇒    (-a, -b).

So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes

A(-3, 0)   ⇒  (3, 0)

B(-2, 3)   ⇒   (2, -3)

C(-1, 1)    ⇒   (1, -1).

Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).

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Answer:

1  17/30.

Step-by-step explanation:

you can find this out by seeing how many 30s go into 47 which is 1.

Then subtract to find how much is leftover still over 30.

47 - 30 = 17

So 1 and 17/30

The cost of pizza with no toppings is $6. So correct option is C.

A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.

There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.

Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.

Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.

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The complete question is:

There are 13,800 different recital programs possible.

What is permutation?

In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.

The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:

25 x 24 x 23 = 13,800

There are 13,800 different recital programs possible.

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Answer:

29i

Step-by-step explanation:

While multiplying complex numbers we should remember that i^2=−1.

As p=2 and q=5i,

(2−5i)(p+q)i

= (2−5i)(2+5i)i

= (2×2+2×5i−5i×2−5i×5i)×i

= (4+10i−10i−25×i2)×i

= (4+10i−10i−25×(−1))×i

= (4+25)×i

=29i

Answer:

-4 + 8 = 4

-2 + 6 = 4

-1 + 5 = 4

So the three pairs are -4 and 8; -2 and 6; and -1 and 5.

The range is expressed in interval notation as (-1, ∞)

To find the linear function f(x), let us use the table given.

A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):

[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]

Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:

a = -6, g(a) = 16, b = -3 and, g(b) = 10

Therefore g(x)

[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]

now find the (f+g)(x).

[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]

(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1

The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:

[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]

Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.

As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.

The range is expressed in interval notation as (-1, ∞)

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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

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Answer: 5 * 5 = 20

20 divided by 1 = 20

If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.

a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE

a. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.

b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.

c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.

d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.

e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.

f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.

g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.

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