a search and rescue pilot is flying over a section of forest. The angle of depression to two clearings is 32 degrees and 56 degrees respectively. According to her co-pilot, the two clearings are 5.7km apart. find the distance from airplane to clearing A, rounded to nearest hundredth of a kilometre

The midline y of the given function f(x)=3(cos(x-(\pi )/(3))+1) is 3.

A sinusoidal function's midline is the horizontal axis around which the signal goes up and down above and below. The midline is y = 0 for y = sin x. (the x-axis). The maximum and minimum values of the graph are situated on either side of the midline, which runs parallel to the x-axis.

Comparing the given function f(x) = 3(cos(x-(\pi )/(3))+1) with the standard form of cosine function:

y = acos(bx + c) + d

a = 3 and d = 1

The maximum value = 3 + 2 = 5

The minimum value = 3 - 2 = 1

The midline is given as:

midline = 1/2(maximum value - minimum value)

midline = 1/2(5 + 1)

midline = 3

Hence, the midline y of the given function is 3.

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The proportional equation to graph is y= 5/3x + 10.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

From the graph we take two points as (6, 15) and (0,0).

So, the slope of line

= (0- 15)/ (0-6)

= -15 /(-6)

= 15/6

= 5/3

and, Equation of line is

y= mx+ b

15 = 5/3(6) + b

15 = 10 + b

b= 5

Thus, the proportional equation to graph is y= 5/3x + 10.

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For the given percenatge of total cost, the total value of Gabe's health care coverage for the year is $9,984.

What is percentage?

Percentage is a way of expressing a fraction or a part of a whole as a portion out of 100. It is represented by the symbol "%".

We can start by using the information given to determine the total cost of the health care coverage. Let's call this cost "C". Since Gabe contributes 15% of this cost and pays $28.80 per week, we can write:

0.15C = 28.80

To solve for C, we can divide both sides by 0.15:

C = 28.80 / 0.15

= 192

So the total cost of the health care coverage is $192 per week. To find the total value of Gabe's health care coverage for the year, we need to multiply this weekly cost by the number of weeks in a year.

Assuming there are 52 weeks in a year, we have:

Total value of Gabe's health care coverage = 192 x 52

= 9984

Therefore, the total value of Gabe's health care coverage for the year is $9,984.

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The properties to the equation are

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

y = 2x^2 - 4x + 8

The above expression is a quadratic equation

Next, we plot the graph

From the graph, we have the following summary

Vertex: (1, 6)

Axis of symmetry: x = 1

Zero(s) = None (complex roots)

See attachment for the graph of the equation

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Answer:

Step-by-step explanation:

To find the third year value of the deposit, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money after t years, P is the principal (the initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

For the first year, we have:

P = $500

r = 0.05

n = 1 (compounded annually)

t = 1

So, the amount after the first year is:

A1 = $500(1 + 0.05/1)^(1*1) = $525

For the second year, we have:

P = $525 (the amount after the first year)

r = 0.06

n = 1

t = 1

So, the amount after the second year is:

A2 = $525(1 + 0.06/1)^(1*1) = $556.50

For the third year, we have:

P = $556.50 (the amount after the second year)

r = 0.07

n = 1

t = 1

So, the amount after the third year is:

A3 = $556.50(1 + 0.07/1)^(1*1) = $594.64

Therefore, the third year value of the deposit is $594.64.

The sinusoidal function is y = sin(2/3x) - 5

The general form of a sinusoidal function is given by:

y = A sin(Bx + C) + D

where:

We know that the period is 3π and the amplitude is 1.

So, we have

A = 1

B = (2π)/(3π) = 2/3

So, we have

y = sin(2/3x + C) + D

The point (-3π/2, -5) implies that, the function is shifted down by 5 units

So, we have

y = sin(2/3x) - 5

Hence, the function is y = sin(2/3x) - 5

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Answer:

≅20.9%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the old value (349) and the new value (276), divide that by the old value, and then multiply by 100 to express it as a percentage.

The formula for percent decrease is:

percent decrease = ((old value - new value) / old value) x 100%

Substituting the given values, we get:

percent decrease = ((349 - 276) / 349) x 100%

percent decrease = (73 / 349) x 100%

percent decrease = 20.92%

Rounding to the nearest tenth of a percent, we get:

percent decrease ≈ 20.9%

Therefore, the percent decrease in the number of petty crimes this year is [approximately 20.9%.]

The type of transformation that happened is a composition of a reflection across the y-axis followed by a translation upwards by 3 units.

The point (a, b) is the top of a rectangle, which means that the bottom of the rectangle must be at the point (a, c) for some c < b. Let's assume that the rectangle is centered at the origin, so its height is 2b and its width is 2c.

After the transformation, the point (a, b) maps to the point (-a, b+3). We can see that the x-coordinate of the point has been negated, and the y-coordinate has been increased by 3. This suggests that the transformation is a reflection across the y-axis followed by a translation upwards by 3 units.

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Answer:

Step-by-step explanation:

The digit 3 in the number 4693 has a place value of 3 tens or 30. Therefore, the value of the number 3 in the number 4693 is 30.

The measures of the angles are given as A' = 103, B' =100, c' = 80, D' = 77

∠x

125 + ∠x = 180 (angle on a straight line)

∠x = 55 degrees

∠y

∠x + ∠y + 48 = 180 angles in a triangle

55 + ∠y + 48 = 180

∠y = 77 degrees

∠D

∠d = ∠Y vertically opposite

∠a + ∠D = 180

∠A = 180 - 77

= 103 degrees

∠B  + 80 = 180

∠b = 100 degrees

∠c + ∠ b = 180

∠c = 180 - 100

= 80 degrees

hence A' = 103, B' =100, c' = 80, D' = 77

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Answer:

First choice

Step-by-step explanation:

Answer:

Th answer is the FIRST CHOICE(A).

Have a GOOD DAY!

After Justin leaves his house he reaches a maximum distance of 20 blocks away from his house after 7 minutes of being out of his home.

To graph Justin's displacement we must use a Catersian plane. In this case we put the time on the X axis (time) and the distance on the Y axis (blocks). Once we set these parameters, we must put the information on the graph.

In the places where a time takes only the progressing of time without any displacement. Additionally, when you travel it is important to take into account the speed (blocks/minute) that Justin has to obtain a correct graph.

According to the above, after 7 minutes Justin is 20 blocks away from his house and this distance travels in 4 minutes to return home.

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Answer:

A

Step-by-step explanation:

hope this helps

Equation of the line passing through (1, 5) is y = 3x + 2

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A line with no curve is called straight line.

Given,

A line is parallel to the line y = 3x - 2

To find slope of the given line, comparing with slope-intercept equation of line

y = mx + c

Slope m = 3

Line passes through point (1 , 5)

Slope of parallel lines are equal

m' = m = 3

Equation of the line

y - y' = m'(x - x')

y - 5 = 3(x - 1)

y - 5 = 3x - 3

y = 3x + 2

Hence, y = 3x + 2 is equation of the line passing through point (1,5).

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y=3x+2 is the equation of the line which is parallel to the line y=3x-2 and passes through the point 1,5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given equation is y=3x-2

3 is the slope of given line.

The line parallel to this line will have same slope, slope is 3.

Now, the equation of line passing through 1, 5

5=3(1)+b

b=2

So slope intercept form y=3x+2

Hence,  y=3x+2 is the equation of the line which is parallel to the line y=3x-2 and passes through the point 1,5

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The ratio of people waiting in line for the slingshot is 2:21

A ratio is a relationship between two quantities that expresses how many times one quantity is contained in the other. It can be expressed in different ways, such as with the use of a colon (:), a fraction (/), or the word "to.

From the question, the total number of people is 15 + 4 + 12 + 11 = 42

The number of people waiting for slingshot is = 4

The ratio of slingshot waiting in line = 4/42

The ratio = 2:21

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esta es la respuesta 8 B)

porque si lo restas y sumas da a 8

Answer:

Step-by-step explanation:

In a circle with a radius of 0.1, an arc length of 0.4 is intercepted by an angle. To find the angle in radians, we use the formula:

angle in radians = arc length / radius

Substituting the given values, we have:

angle in radians = 0.4 / 0.1 = 4

So the angle in radians is 4 radians, to the nearest tenth.

Answer:

Step-by-step explanation:

a) To find the probability that Mateo will die in his 60th year, we use the value of the probability distribution given in the problem statement: P(x=60) = 0.01051.

To calculate the expected cost to Big Rock Insurance if Mateo dies in his 60th year, we multiply the death benefit of $50,000 by the probability of death:

Expected cost = P(x=60) * $50,000 = 0.01051 * $50,000 = $525.50.

So the expected cost to Big Rock Insurance if Mateo dies in his 60th year is $525.50.

b) To find the probabilities that Mateo will die in years 61, 62, 63, and 64, we use the values of the probability distribution given in the problem statement: P(x=61) = 0.01477, P(x=62) = 0.01744, P(x=63) = 0.02035, and P(x=64) = 0.02227.

To calculate the expected cost to Big Rock Insurance if Mateo dies in each of these years, we multiply the death benefit of $50,000 by the corresponding probability of death:

Expected cost if Mateo dies in his 61st year = P(x=61) * $50,000 = 0.01477 * $50,000 = $738.50.

Expected cost if Mateo dies in his 62nd year = P(x=62) * $50,000 = 0.01744 * $50,000 = $872.00.

Expected cost if Mateo dies in his 63rd year = P(x=63) * $50,000 = 0.02035 * $50,000 = $1017.50.

Expected cost if Mateo dies in his 64th year = P(x=64) * $50,000 = 0.02227 * $50,000 = $1113.50.

So the expected costs to Big Rock Insurance if Mateo dies in his 61st, 62nd, 63rd, and 64th years are $738.50, $872.00, $1017.50, and $1113.50, respectively.

c) To calculate the total expected cost to Big Rock Insurance over the years 60 through 64, we add up the expected costs for each year:

Total expected cost = Expected cost in year 60 + Expected cost in year 61 + Expected cost in year 62 + Expected cost in year 63 + Expected cost in year 64

Total expected cost = $525.50 + $738.50 + $872.00 + $1017.50 + $1113.50

Total expected cost = $4267.00

So the total expected cost to Big Rock Insurance over the years 60 through 64 is $4267.00.

d) If Big Rock Insurance wants to make a profit of $700 above the expected total cost payout for Mateo's death, it would need to charge a premium equal to the expected cost plus the desired profit:

Premium = Total expected cost + Desired profit

Premium = $4267.00 + $700.00

Premium = $4967.00

So Big Rock Insurance should charge a premium of $4967.00 for the policy if it wants to make a profit of $700 above the expected total cost payout for Mateo's death.

Answer:

[tex]5x^{7} -x+2[/tex]

Step-by-step explanation:

[tex]6x^{7} -x+8[/tex] minus [tex]x^{7} +2[/tex] equals to [tex]5x^{7} -x+2[/tex].

We can solve this by subtracting [tex]x^{7}[/tex] from [tex]6x^7[/tex]. This will make it [tex]5x^7[/tex].

x cannot be subtracted, so it becomes [tex]5x^7 -x[/tex].
8-6 is 2, so it becomes [tex]5x^7-x+2[/tex]

The coordinates of the point R: (0, 3.4)

What is the slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line

Slope PQ 5–0/ 2–6 = 5 /-4

equation of PQ y =-5/4 x +c ;

this passing through 2,5

5 =-5/4*2 +c ; C = 5 -5/2 =5/2

y =-5x/4+5/2 =-5x+10/4 ; 4y =-5x +10 ;

equation of PQ =5x +4y-10 =0 ;

slope of PR : m1 *m2 =-1 ;m2 = -1/ [-5/4 ] = 4/5

equation of PR y = mx +c this passes through [2,5]

5 = 4/5*2 +C so C = 5- 8/5 =17/5

y =4 x /5 +17/5 so coordinates of R = [0, 3.4]

Hence, the coordinates of the point R: (0, 3.4)

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a) Let x denote the quality rating and y denote the meal price.

b. From the above table, the marginal density function of x is 1.94

c. From the probability table, the marginal density function of y is 2.09

The probability distribution table for quality and meal price is obtained by dividing each and every frequency by the total frequency of 300 is attached in the image.

The probability distribution is obtained in the attached image below.

The expected value of x is,

1 x 0.28  + 2 x 0.50 + 3 x 0.22

= 1.94

To find the marginal density function of y

1 x 0.26  + 2 x 0.39 + 3 x 0.35

= 2.09

Given that var(x+y)=1.6691

var(x)=0.4964 and var(y)=0.6019

var(x+y) =1.6691

var(x) + var(y) +2* cov(x,y)=1.6691

0.4964+0.6019+ 2 *cov(x,y) =1.6691

1.0983+ 2 * cov(x,y) =1.6691

2 * cov(x,y) =1.6691-1.0983

2* cov(x,y)=0.5708

cov(x,y) =(0.5708)/2

cov(x,y)= 0.2854

Thus, the covariance of x and y is, 0.2854.

Here, the covariance of x and y is positive.

Thus, the relationship between quality and meal price is positive.

If the quality of the meal increases then the meal price also increases.

Yes, the expected result is positive because if the quality of the meal is good then meal price increases.

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Therefore, a function equivalent to y = x² - 8x + 10 is: y = (x - 4)² + 4.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range), with the property that each input is associated with exactly one output. Functions are often denoted using function notation, such as f(x) or g(y), where the letter in parentheses represents the input and the expression to the right of the parentheses represents the output. Functions are used in many areas of mathematics, science, and engineering to model real-world phenomena and to solve problems. They are essential tools for analyzing data, making predictions, and creating mathematical models of physical and natural systems.

Here,

The function y = x² - 8x + 10 is a quadratic function, which has a U-shaped graph. To find a function that is equivalent to this function, we can start by completing the square, which involves adding and subtracting a constant term to create a perfect square trinomial. We can then write the function in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Completing the square, we get:

y = x² - 8x + 10

= (x² - 8x + 16) - 6 + 10 // Add and subtract (8/2)² = 16 to create a perfect square

= (x - 4)² + 4

Now we can see that the vertex of the parabola is at (4, 4). We also see that the coefficient of the squared term is 1, which means the parabola opens upward.

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that in the second year, we use the beginning book value of $639,900

a. Sum-of-the-years’-digits method:

To compute the depreciation using the sum-of-the-years’-digits method, we first need to determine the total number of years of the asset's useful life. We do this by subtracting the salvage value from the cost and dividing by the estimated yearly depreciation.

Cost of asset = $711,000

Salvage value = $60,000

Useful life = 20 years

Yearly depreciation = (Cost - Salvage value) / Useful life

Yearly depreciation = ($711,000 - $60,000) / 20 = $32,550

To calculate the sum-of-the-years’-digits (SYD) for this asset, we add up the digits of the useful life in descending order. For a 20-year useful life, the SYD would be:

SYD = 20 + 19 + 18 + ... + 1 = 210

Using the SYD and the number of remaining years, we can calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = (20/210) x ($711,000 - $60,000) = $64,286

Year 2021:

Depreciation expense = (19/210) x ($711,000 - $60,000) = $60,952

b. Double-declining-balance method:

To compute the depreciation using the double-declining-balance (DDB) method, we first need to determine the asset's straight-line depreciation rate, which is calculated as follows:

Straight-line depreciation rate = 1 / Useful life

Straight-line depreciation rate = 1 / 20 = 0.05

The DDB depreciation rate is twice the straight-line rate, or 0.10. We can then calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset

Depreciation expense = $711,000 x 0.10 = $71,100

Year 2021:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset - Accumulated depreciation from previous years

Accumulated depreciation (2020) = $71,100

Beginning book value (2021) = $711,000 - $71,100 = $639,900

Depreciation expense = $639,900 x 0.10 = $63,990

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Maura will have 5, 206 points at either hotel by booking 301 nights.

To find the number of points, we shall assume that nights are denoted as n. The number of points for Hotel Elegance will be shown as :

= Signing up points + ( Number of points per night x Number of nights)

= 89 + 17 n

The number of points for Hotel Paradiso is:

= 691 + 15 n

The number of nights that Maura needs to stay for the points to be the same is :
89 + 17 n = 691 + 15 n

17 n - 15 n = 691 - 89

2 n = 602

n = 602 / 2

n = 301 nights

The number of points would be :

= 691 + 15 n

= 691 + 15 x 301

= 5, 206 points

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The surface area will be multiplied by 1/8.

A cone is a three-dimensional geometric shape that has a circular base and a curved surface that tapers to a point called the apex or vertex.

The height of a cone is the perpendicular distance from the vertex to the base. The radius of the base is the distance from the center of the circle to its edge.

The slant height is the distance from the vertex to any point on the edge of the base, The formula for the surface area of the cone is given by  

Here we have  

A right cone has a radius of 2 ft and a slant height of 5 ft.  

As we know, the total Surface Area of the cone  = πr(r + l) square units

Surface Area of cone  = π(2)(2 + 5) ft² = 44 ft²

Given that both the radius and slant height are multiplied by 1/4.

Radius, r = (1/4)(2) = 1/2 ft

Slant height, h = (1/4)5 = 5/4 ft

Surface Area of cone will be  = π(1/2)(1/2 + 5/4) ft²  

= π(1/2)(7/4) ft²  

= 11/4 ft²  

Let the surface area is multiplied by 'x'

=> 44x = 11/4

=> 4x = 11/4

=>  x = 1/8

Therefore,

The surface area will be multiplied by 1/8

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The volume of the sand pit is V = 694.6 feet²

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangle be represented as V

Now , the length of the sand pit = 30.2 feet

The width of the sand pit = 9.2 feet

The depth of the sand pit = 30 inches = 2.5 feet

Now , the volume of the rectangular pit = L x W x H

On simplifying the equation , we get

The volume of the rectangular pit V = 30.2 x 9.2 x 2.5

The volume of the rectangular pit V = 694.6 feet²

Hence , the volume of the rectangular sand pit is 694.6 feet²

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The angles which are co-terminal with the given angle and less than 1080 but greater than -720 are 450°, 810°, -270° and -630°. The solution has been obtained using concept of co-terminal angles.

What is co-terminal angle?

Co-terminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). The angles where the difference could be 360 degrees or multiples of 360 degrees are known as co-terminal angles.

The calculation of the two positive angles and the two negative angles, which are co-terminal, is as follows:

(a) For 90°, the two positive angles are

90° + 360° = 450°

450° + 360° = 810°

(b) The two negative angles are

90° - 360° = -270°

-270° - 360° = -630°

Hence, the angles which are co-terminal with the given angle and less than 1080 but greater than -720 are 450°, 810°, -270° and -630°.

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Reflection across x=3 is a transformation that involves reflecting a figure across a vertical line of symmetry at x=3.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.


This transformation produces a mirror image of the original figure. Reflection across x=3 can be represented in the form of a matrix equation,

A= [[-1, 0],
   [ 0, 1]]

This matrix equation demonstrates that the x coordinates of a point will be multiplied by -1, while the y coordinates will remain unchanged. This transformation is also known as a reflection over the y-axis.

Reflection across x=3 can be used to change the orientation of a figure in a 2-dimensional coordinate plane. For example, if a triangle is located at the position (2,4) and the coordinates need to be changed so the triangle is reflected across x=3, the coordinates would be transformed to (-2,4).

Reflection across x=3 can also be used to solve various types of mathematical problems. For example, if a problem asks for the coordinates of a point that is the reflection of a point across x=3, the coordinates of the reflected point can be calculated by multiplying the original x coordinate by -1 and leaving the y coordinate unchanged.

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The solution to the matrix is x1 = (-555 - 356x3)/90, x2 = (138 + 89x3)/10 and x3 = free variable

To find the solution to this matrix, we need to perform row operations to put it into row echelon form or reduced row echelon form. We can do this by adding multiples of one row to another row, multiplying a row by a nonzero scalar, and swapping two rows.

Here are the row operations we can use to put this matrix into row echelon form:

1. Add 5 times the first row to the third row to eliminate the 5 in the (3,1) entry:

0 0 -9 6

0 -1 -4 4

25 35 11 38

2. Multiply the second row by -1 to make the pivot in the second row, second column equal to 1:

0 0 -9 6

0 1 4 -4

25 35 11 38

3. Add 9 times the second row to the first row to eliminate the -9 in the (1,3) entry:

0 9 0 -30

0 1 4 -4

25 35 11 38

4. Add -25 times the second row to the third row to eliminate the 25 in the (3,1) entry:

0 9 0 -30

0 1 4 -4

0 10 -89 138

5. This matrix is now in row echelon form. We can solve for the variables by back-substitution. Starting with the last row:

0 10 -89 138 | x3

We have:

10x2 - 89x3 = 138

Solving for x2, we get:

x2 = (138 + 89x3)/10

Substituting this expression for x2 in the second row, we have:

Copy code

0 1 4 -4 | (138 + 89x3)/10

Solving for x1, we get:

9x1 + 4(138 + 89x3)/10 = -30

Simplifying and solving for x1, we get:

x1 = (-555 - 356x3)/90

So the solution to the matrix is:

x1 = (-555 - 356x3)/90

x2 = (138 + 89x3)/10

x3 = free variable

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The probabilities are given as follows:

1) Blue eyes: 0.132.

2) Female with green eyes: 0.09.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of people is given as follows:

20 + 25 + 30 + 15 + 10 + 12 + 15 + 20 + 10 + 10 = 167.

10 + 12 = 22 people out of 167 have blue eyes, hence the probability is given as follows:

p = 22/167 = 0.132.

15 people out of 167 are female with green eyes, hence the probability is given as follows:

p = 15/167 = 0.09.

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Answer:

Note that the line passes through the points (1,0) and (2,6).