Two different box-filling machines are used to fill cerealboxes on the assembly line. The critical measurement influenced bythese machines is the weight of the product in the machines. Engineers are quite certain that the variance of the weight ofproduct is σ^2=1 ounce. Experiments are conducted using bothmachines with sample sizes of 36 each. The sample averages formachine A and B are xA=4. 5 ounces and xB =4. 7 ounces. Engineers seemed surprisedthat the two sample averages for the filling machines were sodifferent.


a. Use the central limit theorem to determine


P(XB- XA >= 0. 2)


under the condition that μA=μB


b. Do the aforementioned experiments seem to, in any way,strongly support a conjecture that the two population means for thetwo machines are different?

The quadratic formula for solving quadratic equations of the form ax^2 + bx + c = 0 is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To put the quadratic equation y = 2x^2 - 4x + 2 into this formula, we need to identify the values of a, b, and c.

In this case, we have a = 2, b = -4, and c = 2. Substituting these values into the quadratic formula, we get:

x = (-(-4) ± sqrt((-4)^2 - 4(2)(2))) / (2 * 2)

x = (4 ± sqrt(16 - 16)) / 4

x = (4 ± 0) / 4

Simplifying this expression, we get:

x = 1 or x = 1/2

Therefore, the solutions to the quadratic equation y = 2x^2 - 4x + 2 are x = 1 and x = 1/2.

To explain this solution in more detail, we first need to understand the quadratic formula and how it can be used to solve quadratic equations. The quadratic formula is a formula that provides the solutions to any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

In this case, we were given a specific quadratic equation, y = 2x^2 - 4x + 2, and we needed to find its solutions. To do this, we identified the values of a, b, and c and substituted them into the quadratic formula. We then simplified the expression to obtain the solutions, which were x = 1 and x = 1/2.

It is important to be able to use the quadratic formula to solve quadratic equations because many real-world problems can be modeled using quadratic equations. By being able to solve these equations, we can find important information such as the roots, or solutions, of the equation, which can help us make predictions and solve problems.

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The value of x, which is  the sample mean and represents the average weight gain after quitting smoking, is 20. Therefore, the correct option is B.

Given that the random sample of 100 smokers reveals an average weight gain of 20 pounds after quitting smoking and a standard deviation of 6 pounds, the value of x is determined as follows.

1. Random sample of 100 smokers (n = 100)

2. Average weight gain after quitting smoking is 20 pounds (mean, x' = 20)

3. Standard deviation is 6 pounds (σ = 6)

Option A (6) is incorrect because it does not relate to the given information.

Option C (100) is also incorrect because it refers to the sample size, which is not relevant to finding the value of x.

Option D (6/√100 = 0.6) is incorrect because it calculates the standard error of the mean, which is not what the question is asking for.

Therefore, the correct answer is option B: 20, which is the sample mean and represents the average weight gain after quitting smoking.

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la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

La probabilidad de que anote un tiro libre es del 73%, lo que significa que la probabilidad de que falle es del 27%.

La probabilidad de que anote sus próximos 9 tiros libres es:

0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 = 0.0733

Por lo tanto, la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.

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The value of x is 26.5, found using the property of intersecting chords in a circle and the Pythagorean theorem.

To find the value of x, we can use the property that states that if two chords intersect in a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

In this case, we can draw radii from O to points P and S, and label their lengths as 19. Then, we can label the segments of chords FG and RS as follows:

                     Let a = FG and b = GP

                      Let c = RS and d = SP

Since OP is a radius of the circle, we know that a + b = 19. Similarly, since OS is a radius of the circle, we know that c + d = 19.

Using the property mentioned above, we can write:

                      a * b = c * d

Substituting the given values, we get:

                   25 * (19 - b) = 28 * (19 - d)

Expanding and simplifying, we get:

                      475 - 25b = 532 - 28d

Substituting a + b = 19 and c + d = 19, we get:

                 b = 19 - a and d = 19 - c

Substituting these values, we get:

                 25a - 25(19 - a) = 28c - 28(19 - c)

Simplifying, we get:

                    53a - 475 = 28c - 532

Rearranging, we get:

                       53a - 28c = -57

We also know that a + c = 25 + 28 = 53.

We can solve these two equations simultaneously to find the values of a and c:

                        a = 13.8

                        c = 39.2

Therefore, the length of the segment RS is 39.2, and the length of the segment RP19S is 58.2.

Using the Pythagorean theorem, we can find the length of the segment OP:

                  (OP)²= (RP19S)² - (19)²

                  (OP)² = (58.2)² - (19)²

                  (OP)² = 3136.24

                        OP = 56

Finally, we can find x using the fact that the chords FG and RS are parallel:

                           x = (1/2) * (FG + RS)

                           x = (1/2) * (25 + 28)

                           x = 26.5 (rounded to the nearest tenth)

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The correct equation is,

⇒ (5 - 6i) (2 + 4i)

Let us assume that;

⇒ (a + bi) (c + di)

⇒ ac + adi + bci + bdi²

⇒ (ac − bd) + (ad + bc)i

Matching coefficients:

30 < ac − bd < 80

ad + bc = 0

Hence, We need to pick four integers between -9 and 9 such that these two equations are satisfied.  One possible combination is:

a = 8, b = -4, c = 6, d = 3

The number would be:

ac − bd = (8)(6) − (-4)(3) = 60

Puzzle 2

Using the result from Puzzle 1:

ac − bd = 34

ad + bc = 8

Like before, it makes sense to assume b is negative.  With some trial and error, one possible answer is:

a = 5, b = -6, c = 2, d = 4

Thus, The correct equation is,

⇒ (5 - 6i) (2 + 4i)

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Answer: Regarding "Car Mr V Model 2017," I'm not sure what you're asking. Can you please provide more context or a clear question?

Step-by-step explanation:

To determine if Eugene's thinking is correct, we need to calculate his new monthly salary with the 3.5% raise.

3.5% of $2,700 is (3.5/100) x $2,700 = $94.50

Eugene's new monthly salary is $2,700 + $94.50 = $2,794.50

So, Eugene's thinking is not correct. His new monthly salary with the 3.5% raise is $2,794.50, which is still less than $2,800.

Today's lesson was not provided in your question. Please provide a topic or question for me to provide a summary of today's lesson.

Regarding "Car Mr V Model 2017," I'm not sure what you're asking. Can you please provide more context or a clear question?

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The value of x using the assumptions of angle are 17 and 22.5

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

Angles: 75° and (4x + 7)°

Angles: (2x+10)° and (2x - 10)°

Assume 75° and (4x + 7)° are congruent angles, we have

4x + 7 = 75

So, we have

4x = 68

Divide by 4

x = 17

Assume (2x+10)° and (2x - 10)° are complementary angles, we have

2x + 10 + 2x - 10 = 90

So, we have

4x = 90

Divide by 4

x = 22.5

Hence, the values of x are 17 and 22.5

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The number of favorable outcomes for spinning the same color twice will depend on the number of colors on the spinner.

If there are only two colors on the spinner, such as red and blue, then there will be only one favorable outcome, which is spinning either red or blue twice.

If there are more than two colors on the spinner, the number of favorable outcomes will depend on the number of times each color appears on the spinner.

For example, if there are four colors on the spinner, and each color appears equally, then there will be four favorable outcomes: spinning red twice, spinning blue twice, spinning green twice, or spinning yellow twice.

In general, if there are n colors on the spinner and each color appears with equal probability, then the number of favorable outcomes for spinning the same color twice will be n.

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The region enclosed by y = e and y = ez has an intersection point at (1, e), and the area of the region is infinite.

To sketch the region enclosed by y = e, y = ez, and 2 = 1, and find the area of the region, follow these steps:

1. Analyze the given equations:
  - y = e (a horizontal line with a constant value e ≈ 2.718)
  - y = ez (an exponential curve)
  - 2 = 1 (this equation is false and does not provide any relevant information for sketching the region)

2. Since the equation 2 = 1 is irrelevant, we'll focus on the two remaining equations.

3. Find the intersection points between y = e and y = ez:
  Set y = e equal to y = ez and solve for x:
  e = ex
  Divide both sides by e:
  1 = x

4. Sketch the region:
  - Plot the horizontal line y = e
  - Plot the exponential curve y = ez
  - Mark the intersection point (1, e)

5. Determine the area of the region:
  The region enclosed by the two given equations is unbounded, meaning that it extends infinitely in both the positive and negative x-directions. As a result, the area of the region is infinite.

In summary, the region enclosed by y = e and y = ez has an intersection point at (1, e), and the area of the region is infinite.

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The two supplied points (1, 4) and (1, −7), have identical x-values. These would create a vertical line if graphed, then joined.

The points where the lines representing the intersections where the two linear equations intersect are referred to as the solution of a linear equation.

Given that:

Line has points:  (1, 4) and (1, −7).

The two supplied points have identical x-values. These would create a vertical line if graphed, then joined.

The diagram is attached:

Hence, a vertical line would be formed by the points.

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Complete question:

Which of the following is true of (1, 4) and (1, −7).?

options:

Answer:

2

Step-by-step explanation:

The median of a data set is the middle value when the data is arranged in order of size.

The given table of data is:

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\frac{3}{4}&3&1&8\\\cline{1-4}\vphantom{\dfrac12}5&\frac{1}{4}&\frac{3}{5}&\frac{7}{2}\\\cline{1-4}\end{array}[/tex]

Arrange the data in order of size:

[tex]\dfrac{1}{4},\;\dfrac{3}{5},\;\dfrac{3}{4},\;1,\;3,\;\dfrac{7}{2},\;5,\;8[/tex]

As there are 8 data values, the median is the average of the two middle values.

The two middle values are 1 and 3.

The average of 1 and 3 is 2:  

[tex]\dfrac{1+3}{2}=\dfrac{4}{2}=2[/tex]

Therefore, the median of the given data is 2.

For the function f(x, y) = 1 - xy + y²= -y = -1, fy(-2,1) = 2y - x = 3.

When y is stationary, the rate of change of f with respect to x is determined by the partial derivative fx. Meanwhile, fy measures the rate of change of f in relation to y while holding x constant.

At the point (-2,1), the fx partial derivative symbolizes the incline of the level curve tangent line that follows the x-direction in relation to f. Its counterpart fy denotes the incline of the level curve tangent line that follows the y-direction regarding f at (-2,1).

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Complete answer - Let f(x, y) = 1 - xy + y² Compute fx(-2, 1) and fy(-2,1), and interpret these partial derivatives geometrically."

The function may still be continuous.

The lack of differentiability only implies that the function is not smooth at that point.

Here are three scenarios in which the derivative of a function may not exist, along with a sketch of each situation:

Corner: A function may not be differentiable at a corner, where the graph abruptly changes direction.

At a corner, the left and right-hand limits of the derivative do not match. Here is a sketch of the situation:

                   /

                  /

                 /

                /

               /

---------------/----------------

Cusp: A function may not be differentiable at a cusp, where the graph has a sharp point.

At a cusp, the left and right-hand limits of the derivative approach different values. Here is a sketch of the situation:

           /

          /

         /

        /

       /

------/--------

      \

       \

        \

         \

          \

Vertical tangent: A function may not be differentiable at a vertical tangent, where the graph has a vertical line tangent to the curve.

At a vertical tangent, the derivative is either infinite or undefined. Here is a sketch of the situation:

     |

     |

------|-------

     |

     |

Note that in all three of these situations, the function may still be continuous.

The lack of differentiability only implies that the function is not smooth at that point.

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Answer: b = 30°

Step-by-step explanation:

       The little square represents a 90-degree angle.

90° - 60° = b

30° =  b

b = 30°

Answer:

Recall 5%=.05 as a decimal. Then multiply 140(.05)=7 to get how many centimeters he grew. Add 140+7=147 to get his current height.

The polynomial expression becomes -20vz⁶ + 36v⁴z⁵ + 24v⁶ z⁶

In order to divide, first collect the like terms and then perform the operation. So, we have:

(-20vz⁶ + 32v⁴z⁵ +24v⁶ z⁶) + (4v⁴ z⁵) = -20vz⁶ + (32v⁴z⁵ +4v⁴ z⁵) + 24v⁶ z⁶

Simplifying the expression in parentheses, we get:

32v⁴z⁵ +4v⁴ z⁵ = 36v⁴z⁵

So, the expression becomes:

-20vz⁶ + 36v⁴z⁵ + 24v⁶ z⁶

This expression cannot be simplified any further.

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The final answer to this limit question is 1/4.

a function from a set X to a set Y assigns to each element of X exactly one element of Y.[1] The set X is called the domain of the function[2] and the set Y is called the codomain of the function.

Given that lim f(x) = 3 and lim g(x) = 12, we want to find the limit:
lim (f(x) / g(x)) as x approaches -5.
Using the limit rules, specifically the quotient rule, we have:
lim (f(x) / g(x)) = lim f(x) / lim g(x)

Now, substituting the given limits:
lim (f(x) / g(x)) = 3 / 12

Simplifying the fraction:

lim (f(x) / g(x)) = 1/4

So, the answer is 1/4.

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Answer:

Step-by-step explanation:

The length of UX (the length of a tangent segment to a circle) is approximately 4.9 inches.

To find the length of UX, we can use the formula for the length of a tangent segment to a circle:

Length of tangent segment = √(radius² - distance from center²)

In this case, we don't know the radius or the distance from the center, but we can use the fact that RU is perpendicular to UT to find them:

RU = RS + ST = 8 + 4 = 12 in.
UT = radius = RU/2 = 12/2 = 6 in.

Now we can plug these values into the formula:

Length of tangent segment = √(6² - 4²) ≈ 4.9 in.

Therefore, the length of UX is approximately 4.9 inches.

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For March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.

To determine the equivalent units of production for conversion costs in March 2020 for Dorchester Company, we need to follow these steps:
Calculate the equivalent units for the beginning work in process inventory:
Beginning WIP units = 6,000
Completion percentage for conversion costs = 50%
Equivalent units for beginning WIP = 6,000 * 50% = 3,000
Calculate the equivalent units for the units started and completed during March:
Units started and completed = 24,500
Completion percentage for conversion costs = 100%
Equivalent units for started and completed units = 24,500 * 100% = 24,500
Calculate the equivalent units for the ending work in process inventory:                                                                         Ending WIP units = 6,500
Completion percentage for conversion costs = 50%
Equivalent units for ending WIP = 6,500 * 50% = 3,250
Sum up the equivalent units from steps 1, 2, and 3:
Total equivalent units for conversion costs = 3,000 (beginning WIP) + 24,500 (started and completed units) + 3,250 (ending WIP) = 30,750
So, for March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.

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The slope of the line represent Parking cost $30 per day. The correct answer is C.

The slope of a line represents the rate of change between two variables. In this case, the line represents the relationship between Hector's parking fees and the number of days he parked his SUV.

The unit of the slope of the ine represents

Cost/ number of days = 30 $/day

The fact that the slope is negative (-$30) means that for each additional day Hector parked his SUV, his parking fees decreased by $30. This indicates that the parking fee is a function of the number of days parked, and it costs $30 per day. The correct option is C.

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--The given question is incomplete, the complete question is given

" Hector parked his SUV in long-term parking while he traveled to China. What does the slope of the line represent?

A Hector's parking fees decreased by $30 each week.

B Parking cost a flat fee of $30.

C Parking cost $30 per day.

D Hector got a $30 discount to park his SUV. ​ "--

Answer:

when the diameter of a spherical balloon shrinks to one-half of its original size, the surface area of the balloon will decrease to one-fourth of its original size, while the volume will decrease to one-eighth of its original size.

Step-by-step explanation:

When the diameter of a spherical balloon shrinks to one-half of its original size, it means the new diameter is half of the original diameter.

Let's assume the original diameter of the balloon was "d," then the new diameter will be "d/2."

Surface Area:

The surface area of a sphere is given by the formula 4πr², where "r" is the radius of the sphere. Since the diameter of the sphere is halved, the radius will also be halved. Therefore, the new surface area (SA') of the balloon will be:

SA' = 4π (d/4)² = πd²/4

Thus, the new surface area of the balloon will be one-fourth (1/4) of the original surface area.

Volume:

The volume of a sphere is given by the formula (4/3)πr³. Again, since the diameter of the sphere is halved, the radius will also be halved. Therefore, the new volume (V') of the balloon will be:

V' = (4/3)π (d/4)³ = πd³/24

Thus, the new volume of the balloon will be one-eighth (1/8) of the original volume.

The critical values are x = -4 and x = 2.

Given the function f(x) = (2-x)(x+4)^2, we need to find the critical values.

Critical values are the points where the derivative of the function is either zero or undefined.

Step 1: Find the derivative of f(x). f'(x) = d/dx((2-x)(x+4)^2)

Step 2: Apply the product rule, which states d(uv) = u*dv + v*du,

where u = (2-x) and v = (x+4)^2. f'(x) = (2-x)*d/dx((x+4)^2) + (x+4)^2*d/dx(2-x)

Step 3: Compute the individual derivatives. f'(x) = (2-x)*(2(x+4)) + (x+4)^2*(-1)

Step 4: Simplify the expression. f'(x) = -2(x+4)^2 + 4(x+4)(2-x)

Step 5: Set f'(x) equal to 0 and solve for x. 0 = -2(x+4)^2 + 4(x+4)(2-x)

Step 6: Factor out a common term. 0 = 2(x+4)[-1(x+4) + 2(2-x)]

Step 7: Solve for x. 0 = 2(x+4)(-x+2) x = -4, 2 The critical values are x = -4 and x = 2.

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Answer:

measure of angle GHJ = 1/2 the measure of arc GJ = (1/2)(86°) = 43°

measure of angle JIG = 1/2 the measure of arc GJ = (1/2)(86°) = 43°

The function can be expressed in terms of natural logarithms as f(x) = (1/2) ln (4x+5) - (1/2) ln (7x-4).

The function is, f(x) = ln √(4x+5)/√(7x-4)

First, note that we can simplify the expression inside the natural logarithm by applying the rules of radicals:

√(4x+5)/√(7x-4) = (4x+5)^(1/2) / (7x-4)^(1/2)

Now, we can apply the rule for the logarithm of a quotient, which states that:

ln (a/b) = ln a - ln b

Using this rule, we can rewrite the given function as:

f(x) = ln [(4x+5)^(1/2) / (7x-4)^(1/2)]

= ln (4x+5)^(1/2) - ln (7x-4)^(1/2)

Next, we can apply the rule for the logarithm of a power, which states that:

ln a^n = n ln a

Using this rule, we can simplify the logarithms in the expression above:

f(x) = (1/2) ln (4x+5) - (1/2) ln (7x-4).

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The makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

For one lipstick, the surface area is:

SA = 2π(0.4)² + 2π(0.4)(2.2)

SA = 1.024π + 1.408π

SA = 2.432π square inches

To wrap 3 lipsticks, the total surface area would be:

SA = 3(2.432π)

SA = 7.296π square inches

Therefore, the makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.

So the correct option is: 19.59π square inches.

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It appears that the relationship between the number of registered pleasure boats and manatee deaths fluctuates over the years. While there is no clear trend, it is important to consider the possible effects of increased boat registration on manatee populations.

The table you provided shows the number of registered pleasure boats (in tens of thousands) and the number of manatee deaths caused by boats in Florida from 1991 to 2014.

When the number of registered pleasure boats increases, there could be a higher likelihood of boat-related manatee deaths. As more boats are present in the water, manatees may face increased risks from boat strikes, which can lead to injuries or fatalities. Additionally, more boats may lead to habitat destruction, indirectly affecting manatee populations.

It is crucial for boat owners to follow safe boating practices to protect manatees and their habitats. Some measures to reduce manatee deaths include obeying speed limits in designated manatee zones, wearing polarized sunglasses to increase visibility, and being cautious in shallow areas where manatees might be feeding or resting.

In conclusion, the relationship between the number of registered pleasure boats and manatee deaths in Florida is complex and fluctuating. However, it is essential for boat owners to be aware of the potential risks and take necessary precautions to protect these gentle marine mammals.

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Answer: x(squared) + (y + 2)(squared) = 36

Step-by-step explanation:

The center of the circle is at (0 , -2), so we will eliminate the x value by just writing x(squared), and then we will write the y value as (y + 2)(squared) because the standard form for a circle is

(x - h)(squared) + (y + 2)(squared) = r(squared)

And if we count from the center to the top point of the circle, the number would be 6, so we would square 6 which would be 36.

Answer:  2.46

Step-by-step explanation:

Since you are compounding interest annually, your formula is:

[tex]A=P(1+r)^{t}[/tex]  

P=principal, what you start with =97000

r= rate of increase, changed to decimal

t=years increased = 16

A= what you end up= 143000  

Plug it all in:

[tex]A=P(1+r)^{t}[/tex]

[tex]143000=97000(1+r)^{16}[/tex]        >divide both sides by 97000

1.474 = [tex](1+r)^{16}[/tex]                    > take the 16th root of both sides or ^(1/16)

1.0246 = 1+r                          >subtract 1 from both sides

r=.0246                                >change to percent by moving decimal over 2

Rate = 2.46%

The  true triangle  statement regarding the diagram are:

1.  m∠5 + m∠6 = 180°  ________Linear Pair

2. ∠ 2+ ∠ 3 = ∠ 6________Exterior angle Property of Triangle

3. m∠2 + m∠3 + m∠5 = 180°________Triangle Sum Property

From the question,  Δ ABC with Exterior angles as ∠ 1 , ∠ 4 ,and ∠ 6

Note that the  Exterior angle Property of Triangle state that An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Hence: For Exterior ∠ 1 :

∠ 1 = ∠ 5 + ∠ 3 ________Exterior angle Property of Triangle

Also,

For Exterior ∠ 4:

∠ 4 = ∠ 5 + ∠ 2 ________Exterior angle Property of Triangle

Also,

In regards to Exterior ∠ 6:

∠ 6 = ∠ 2 + ∠ 3 ________ Exterior angle Property of Triangle

Using Triangle Sum Property, it state that In a triangle sum of the measures of angles is equal to 180° Hence:  m∠2 + m∠3 + m∠5 = 180° ________Triangle Sum Property

The Linear Pair will be: The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Therefore,  m∠5 + m∠6 = 180°  ________Linear Pair

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See full question below

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.

m∠5 + m∠3 = m∠4

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 =180°

m∠2 + m∠3 =

m∠6 m∠2 + m∠3 + m∠5 = 180°