What is wrong with the expression P(A) + P(A Ì) - 0.5?

The answer  is that the probability of randomly selecting the 5 oldest people in a group of 12 is very low.

Since we are selecting a specific group of 5 people (the oldest), we need to consider the total number of possible groups of 5 people that can be selected from the group of 12. This can be calculated using the combination formula, which is nCr = n! / (r! * (n-r)!), where n is the total number of people in the group (12), and r is the number of people we want to select (5).

Therefore, the total number of possible groups of 5 people that can be selected from the group of 12 is 12C5 = 792.

Now, we need to determine how many of these groups consist of the 5 oldest people in the group. Since we are selecting a specific group of people, the order in which they are selected does not matter. Therefore, we can calculate the number of groups consisting of the 5 oldest people by using the combination formula again, this time with n = 5 (the number of oldest people) and r = 5 (the number of people we want to select).

So, the number of groups consisting of the 5 oldest people is 5C5 = 1.

Therefore, the probability of randomly selecting the 5 oldest people in the group of 12 is 1/792.

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The resulting graph and shift it 2 units up by adding 2 to the whole expression. This graph up 1 unit to get y = -x2 + 1, which is the same as h(x) = (-x)2 + 1.

Part A:

The statement that is true about f and g is option B. The graph of g(x) can be drawn by translating the graph of f(x) 1 unit left and 2 units up.

We can see that the graph of g(x) is the graph of f(x) shifted 1 unit to the left and 2 units up. This is because the equation of g(x) is obtained by first taking the graph of f(x) and shifting it 1 unit to the left by subtracting 1 from x. Then, we take the resulting graph and shift it 2 units up by adding 2 to the whole expression.

Part B:

The equation that defines h(x) is option C, h(x) = (-x)2 + 1.

The graph of f(x) is y = x2, and the graph of h(x) is obtained by reflecting this graph over the x-axis and then translating it up 1 unit. The reflection over the x-axis changes the sign of y, so we get y = -x2. Then, we translate this graph up 1 unit to get y = -x2 + 1, which is the same as h(x) = (-x)2 + 1.

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To show that a nonzero integer d divides an integer n, we must show that there exists an integer k such that n = dk. In other words, n is a multiple of d.

This can be expressed using the notation d | n, which means that d divides n. If d does not divide n, we write d ∤ n, which means that d does not divide n.

To prove that d | n, we must find an integer k such that n = dk. One approach is to use the division algorithm, which states that for any two integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < |b|. If we apply this to n and d, we get n = dq + r, where 0 ≤ r < |d|.

If r = 0, then n = dq, which means that d divides n. If r ≠ 0, then d does not divide n. Therefore, to show that d divides n, we must show that r = 0, or equivalently, that n is a multiple of d.

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Answer:   C

Step-by-step explanation:

If they want to cover the park, that is area.  the shape is a trapezoid

Formula:

[tex]A=\frac{1}{2} (b_{1} +b_{2} )h[/tex]       where b1=10

                                           b2=20

                                           h=12.5           plug in

[tex]A=\frac{1}{2} (10 +20} )12.5[/tex]

A=1/2(30)12.5

A=15(12.5)

A=187.5

C

If you drive at a constant speed of 65.5 miles per hour for 8.5 hours, you can travel a distance of approximately 556.75 miles.

If you are driving at a speed of 65.5 miles per hour, you can cover a certain distance in a specific amount of time. To determine the distance you can travel in 8.5 hours, you can use the formula:

Distance = Speed x Time

In this case, Distance = 65.5 x 8.5 = 556.75 miles.

Therefore, if you drive at a constant speed of 65.5 miles per hour for 8.5 hours, you can travel a distance of approximately 556.75 miles.

It's important to note that this calculation assumes that you are driving at a constant speed without any stops or interruptions, which may affect your overall travel time and distance.

Additionally, it's important to always practice safe driving habits and obey traffic laws while on the road to ensure the safety of yourself and others around you.

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a.) The total number of students that where surveyed= 15 students

b.) The greatest number of minutes waited by a student = 3 minutes.

c.) The number of students that waited 9 minutes = 2 students.

d.) The number of students that waited for at least 5 minutes = 10 students.

e.) The median number of minutes waited = 4 minutes.

The line plot is defined as the type of representation of data whereby data area represented as points or check marks above a number line and the frequency of each value is shown.

For a.) The total number of students that where surveyed can be determined by counting the number of dots which would be = 15 students.

For b.) The greatest number of minutes waited by a student = 3 minutes.

For c.) The number of students that waited 9 minutes = 2 students.

For d.) The number of students that waited for at least 5 minutes = 10 students.

For e.) The median number of minutes waited =

The total number of minutes waited are listed below;

0, 1, 2, 3, 5, 7, 9 11

3+5/2 = 8/2 = 4 minutes

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Answer:

Let the other two sides of the isosceles triangle be x cm each. Since the triangle is isosceles, we know that the two equal sides have the same length.

Therefore, the perimeter of the triangle is:

6 cm + x cm + x cm = 22 cm

Simplifying this equation, we get:

2x + 6 = 22

Subtracting 6 from both sides, we get:

2x = 16

Dividing both sides by 2, we get:

x = 8

So the possible lengths of the other two sides are 8 cm each.

We can also check that this answer makes sense by verifying that the sum of the lengths of any two sides of the triangle is greater than the length of the remaining side. In this case, we have:

6 cm + 8 cm > 8 cm

6 cm + 8 cm > 6 cm

8 cm + 8 cm > 6 cm

All of these inequalities hold true, so we know that the triangle with sides of length 6 cm, 8 cm, and 8 cm is a valid isosceles triangle with a perimeter of 22 cm.

The Circumference of the circle is 31 .4159 centimeters and the Area is 78.5398 square centimeters

Circumference = 2πr

Area = πr^2

By implementing a radius value of 5 cm, the circumference is approximated as follows when simplifying the given formula:

Circumference= 2πr

Circumference= (2 x3.14159x5)

Circumference= 31 .4159 centimeters

In the case of calculating its area, similar steps should be followed:

Area = πr^2

Area = 3.14159 x (5)^2

Area = 3.14159 x 25

Area = 78.5398 square centimeters

The area is 78.5398 square centimeters.

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The values of

1. tan B = 3/5

2. cos B = 5/√34

3. sinA = 5/√34

4. tan A = 5/3

5. angle B = 31°

6. angle A = 59°

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

cos( tetha) = adj/hyp

tan ( tetha) = opp/adj

therefore;

tan B = 3/5

cos B = 5/√34

sinA = 5/√34

tan A = 5/3

Since tan A = 5/3

tanA = 1.67

A = tan^-1(1.67)

A = 59°

tanB = 3/5

B = tan^-1( 0.6)

B = 31°

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The width of the border is 1 meter.

Let's assume that the width of the border is x meters. Then, the overall dimensions of the garden including the border would be (4 + 2x) meters by (6 + 2x) meters.

The area of the garden is:

Garden area = length x width = 6 x 4 = 24² meters

The area of the garden including the border is:

Total area = (6 + 2x) x (4 + 2x) = 24 + 20x + 4x²meters

We want the area of the border to be equal to the area of the garden, which means that:

Area of border = Total area - Garden area = 20x + 4x² meters

Since we want the area of the border to be equal to the area of the garden, we can set these two expressions equal to each other and solve for x:

20x + 4x² = 24

Dividing both sides by 4:

x² + 5x - 6 = 0

Factoring the quadratic:

(x + 6)(x - 1) = 0

The negative solution does not make sense for this problem, so we take the positive solution:

x = 1

Therefore, the width of the border is 1 meter.

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The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

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The function in Excel that is used to compute the statistics required to create a histogram is the FREQUENCY function.

The FREQUENCY function is used to calculate how often values occur within a specified range or bin.

The output of the function is an array of values that represents the frequency distribution of the data, which can then be plotted to create a histogram.

To use the FREQUENCY function, we first need to define the bins or intervals that we want to use for our histogram.

These bins should cover the range of the data and should be of equal width.

Once we have defined our bins, we can use the FREQUENCY function to calculate the frequency of values that fall within each bin.

The syntax of the FREQUENCY function is as follows:

=FREQUENCY(data_array, bins_array)

The data_array argument is the array or range of data that we want to analyze, and the bins_array argument is the array or range of bins that we have defined.

The function returns an array of values that represents the frequency of values that fall within each bin.

Once we have the frequency distribution of our data, we can create a histogram by plotting the frequency values against the bin intervals.

Excel has built-in tools for creating histograms, which can be found under the "Data Analysis" menu.

By defining our bins and using the FREQUENCY function, we can quickly and easily analyze the distribution of our data and visualize it in a histogram.

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It's important to analyze the distribution of house prices in Smallville before selecting the best measure of central tendency.

If the data has no extreme outliers and is evenly distributed, the mean could be a good choice.

However, if there are outliers or a skewed distribution, the median would be more appropriate.

The mode could be useful if there's a highly common price in the dataset.

To determine which measure of central tendency is a better measurement of what a typical house in Smallville would cost, let's briefly discuss the three main measures: mean, median, and mode.
Mean:

The average of all the house prices.

To calculate the mean, add up all the prices and then divide by the total number of houses.
Median:

The middle value when all the house prices are arranged in ascending order.

If there's an even number of houses, the median is the average of the two middle values.
Mode:

The most frequently occurring house price.
Now, to decide which measure is the best representation of a typical house cost, we need to consider factors like outliers and the distribution of data.

If the house prices are evenly distributed and have no extreme outliers, the mean can be a good representation of a typical cost.

However, if there are extreme outliers or a skewed distribution, the median is usually a better choice, as it is less affected by outliers.
The mode, although less commonly used for this purpose, can be useful if there's a significantly common price that most houses in Smallville fall under.

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The number of people in Heckleburg after t months is P = (240)t + 3500.

The population after "m" months would be given by the expression P + Am.
Now, we want to find out the number of months it will take for the population to increase by 1,000 people.

Let's call this target population "T".

P = pt + P₀,

where P₀ is the initial population and p is the average increase in population per month.

Since the city increases the population by an average of p people per month, we can write:

p = average increase in population per month

Therefore, the expression becomes:

P = pt + P₀ = p(t) + P₀

Substituting the given values into the expression, we get:

P = (240)t + 3500
So, we need to solve the equation P + Am = T, where T = P + 1000.
Substituting T in the equation, we get P + Am = P + 1000.
Simplifying the equation, we get Am = 1000.
Now, to find the number of months "m", we can rearrange the equation as m = 1000/A.
Therefore, the expression that correctly gives the number of months it will take for the population to increase by 1,000 people is m = 1000/A.
For example, if the average increase in population per month is 50 people, it will take 20 months for the population to increase by 1,000 people (m = 1000/50 = 20).

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The number of people in Heckleburg after t months is P = (240)t + 3500.

The population after "m" months would be given by the expression P + Am.

Now, we want to find out the number of months it will take for the population to increase by 1,000 people.

Let's call this target population "T".

P = pt + P₀,

where P₀ is the initial population and p is the average increase in population per month.

Since the city increases the population by an average of p people per month, we can write:

p = average increase in population per month

Therefore, the expression becomes:

P = pt + P₀ = p(t) + P₀

Substituting the given values into the expression, we get:

P = (240)t + 3500

So, we need to solve the equation P + Am = T, where T = P + 1000.

Substituting T in the equation, we get P + Am = P + 1000.

Simplifying the equation, we get Am = 1000.

Now, to find the number of months "m", we can rearrange the equation as m = 1000/A.

Therefore, the expression that correctly gives the number of months it will take for the population to increase by 1,000 people is m = 1000/A.

For example, if the average increase in population per month is 50 people, it will take 20 months for the population to increase by 1,000 people (m = 1000/50 = 20).

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Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

X = 12.645 round to 12.7

Step-by-step explanation:

∆LMN ~ ∆OPQ

so the coresponding side ratio are proportional

LM/OP = LN/OQ

LM/OP = LN/OQ49/OP = 31/8 ... the u solve x

X = 12.645 round to 12.7

The solution is:

Last Year Length = 4 meters

This Year Length = 12 meters

This Year Width = 10 meters

Here, we have,

We know, area of the rectangle is given by the formula:

Area = Length * Width

Given width = 5

Area = 20

We solve for Length:

Area = Length * Width

20 = Length * 5

Length = 20/5 = 4

Last Year Length = 4 meters

Now, this year, the length would be 3 times as long, so new length would be:

This Year Length = 4 * 3 = 12 meters

This year, the width would be two times previous year, so width would be:

This Year Width = 5 * 2 = 10 meters

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complete question:

Last year, Mr. Petersen's rectangular garden had a width of 5 meters and an area of 20 square meters.

This year, he wants to make the garden three times as long and two times as wide.

a. Solve for the length of last year's garden using the area formula. Then, draw and label the

measurements of this year's garden.

Last Year

This Year

5 m

20

square

meters

S is bounded since we have found real numbers a and b such that for all s in S, a ≤ s ≤ b. Therefore, we have proven that S is bounded if and only if there exists a closed bounded interval I such that S ⊆ I.

First, let's define what it means for a set to be bounded. A set S is bounded if there exist real numbers M and m such that for all s in S, m ≤ s ≤ M.

Now, let's prove the statement "S is bounded if and only if there exists a closed bounded interval I such that S ⊆ I."

Forward direction: Assume that S is bounded. Then, by definition, there exist real numbers M and m such that for all s in S, m ≤ s ≤ M. Let I = [m, M]. I is a closed bounded interval since it contains its endpoints and is closed. Furthermore, since for all s in S, m ≤ s ≤ M, it follows that S is a subset of I. Therefore, S is bounded and there exists a closed bounded interval I such that S ⊆ I.

Backward direction: Assume that there exists a closed bounded interval I such that S ⊆ I. Let a and b be the endpoints of I. Then, for all s in S, a ≤ s ≤ b. Therefore, S is bounded since we have found real numbers a and b such that for all s in S, a ≤ s ≤ b.

Therefore, we have proven that S is bounded if and only if there exists a closed bounded interval I such that S ⊆ I.

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The measure of the angle R is 39. 1 degrees

We need to know the different trigonometric ratios, they are;

From the information given, we have that;

Hypotenuse = t = 30.1

Opposite for angle R is r = 19

Using the sine identity, we have;

sin R = 19/30. 1

Divide the values, we get;

sin R = 0. 6312

To determine the value, find the sine inverse of the value, we have;

R = 39. 14 degrees

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The complete question:

If t = 30.1 and r = 19 , find R.  such that;

t is the hypotenuse side

r is the opposite side

Round your answer to the nearest tenth

If Lucy invites 97 guests to her retirement party, it costs her $388 by using unit rates.

Given that, Lucy's retirement party will cost $228 if she invites 57 guests.

Now, we have to find the party cost if she invites 97 guests.

To find that, we need to find the cost per guest, which is the unit rate.

To find the unit rate, we need to divide 228 by 57.

228 / 57 = 4.

So, the unit rate is $4.

Now, we need to find the cost for 97 guests.

To find that, we need to multiply 97 by 4.

97×4 = 388.

Therefore, the party cost, if she invites 97 guests will be $388.

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to solve for surface area find the area of all sides and add them together, start with the the triangles. Half of 10 is 5 so do 5x14 to get 70, since this is a triangle you would half it but because we only solved one side of the triangle we would keep 70 for the combined area of both. Now multiply 70 by 4 since there are 4 sides of the triangle and get 280. To find the bottom do 10x10 to get 100 and add that to 280. The total surface area should be 380in squared

Answer:

380

Step-by-step explanation:

s= B + 1/2 P (slant height)

B is area of base which is 10x10 which is 100

P is perimeter of base which is 10+10+10+10 = 40

100+1/2 (40)(14)

100+ 20(14)

100+280 = 380

The earthquake in the ocean was about 15.85 times more intense than the one in the city.

The Richter scale is a logarithmic scale used to measure the intensity of earthquakes. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves. Therefore, to find out how many times more intense the earthquake in the ocean was compared to the one in the city, we need to calculate the difference in their Richter scale readings:

8.1 - 6.9 = 1.2

Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a difference of 1.2 on the Richter scale means that the earthquake in the ocean was:

[tex]10^{(1.2)} = 15.85[/tex]

times more intense than the one in the city.

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We can see that Mr. Knott's work simplifies the given expression to (x^3 - 2x^2 + x) / (x + 1)(x - 1)(x^2 + 1).

To evaluate the difference of the expressions, let's simplify each fraction separately and then find their difference.

First expression:

Start with the fraction: startfraction x over x squared minus 1 endfraction

To simplify, we can factor the denominator using the difference of squares formula:

x squared minus 1 = (x + 1)(x - 1)

The fraction becomes: startfraction x over (x + 1)(x - 1) endfraction

Second expression:

Start with the fraction: startfraction 1 over x minus 1 endfraction

To simplify, we can find a common denominator by multiplying the numerator and denominator by (x + 1):

1 over x minus 1 = (1(x + 1))/(x(x + 1) - (x - 1)) = (x + 1)/(x^2 + x - (x - 1)) = (x + 1)/(x^2 + 1)

Now, let's find the difference between the two expressions:

(startfraction x over (x + 1)(x - 1) endfraction) - (startfraction (x + 1)/(x^2 + 1) endfraction)

To subtract fractions, we need to find a common denominator:

The common denominator is (x + 1)(x - 1)(x^2 + 1)

Now, we can rewrite the expressions with the common denominator:

(startfraction x(x^2 + 1) endfraction - startfraction (x + 1)(x - 1) endfraction) / (x + 1)(x - 1)(x^2 + 1)

Expanding and simplifying:

(x(x^2 + 1) - (x + 1)(x - 1)) / (x + 1)(x - 1)(x^2 + 1)

(x^3 + x - x^2 - 1 - (x^2 - 1)) / (x + 1)(x - 1)(x^2 + 1)

(x^3 + x - x^2 - 1 - x^2 + 1) / (x + 1)(x - 1)(x^2 + 1)

(x^3 - x^2 + x - x^2) / (x + 1)(x - 1)(x^2 + 1)

(x^3 - 2x^2 + x) / (x + 1)(x - 1)(x^2 + 1)

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B' represents the complement of set B, which includes all elements in U that are not in B. Therefore, B' = {0, 1, 2, 5, 6, 7}.

A - B' means all elements in set A that are not in set B'. In other words, we need to remove all the elements in set B' from set A.

A - B' = {3, 6}

Therefore, the elements in A - B' are 3 and 6.

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The amount that Imran put into his savings account each week is $57.2

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

Using the above as a guide, we have the following:

20% of Wage = Amount paid

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

20% of 286 = Amount paid

Rewrite as

Amount paid = 20% of 286

Evaluate

Amount paid = 57.2

Hence, the weekly amount is $57.2

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Step-by-step explanation:

in this graph we r going to see the relation of tge angles so

For angle 1

For angle 2

For angle 3

For angle 4

The same is true for the rest of angles.