Determine if triangle OPQ and triangle RST are or are not similar, and, if they are, state which triangle similarity shortcut (AA, SSS, SAS) you can use to prove it. Show your work below proving that the triangles met the shortcut's criteria (Note that figures are NOT necessarily drawn to scale.)​

Answer:

\(x = -6.5c\)

\(c = -\frac{x}{6.5}\)

Step-by-step explanation:

In both cases, you are simply isolating the variable you are trying to solve for:

\(\frac{-x}{c} = 6.5\)

Solve for x. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply c to both sides, and then divide -1 from both sides:

\(\frac{-x}{c} = 6.5\\\frac{-x}{c} * c = 6.5 * c\\-x = 6.5c\\\frac{-x}{-1} = \frac{6.5c}{-1}\\x = -6.5c\)

Solve for c. Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Multiply -1/x to both sides of the equation:

\(\frac{-x}{c} = 6.5\\\frac{-x}{c}(c)) = 6.5(c) \\-x = 6.5c\\\frac{-x}{6.5} = \frac{6.5c}{6.5}\\c = -\frac{x}{6.5}\)

Answer:

x = -6.5c

-x/6.5 = c

Step-by-step explanation:

-x/c=6.5

Multiply each side by -c

-x/c * -c=6.5*-c

x = -6.5c

-x/c=6.5

Multiply each side by c

-x/c *c=6.5*c

-x = 6.5c

Divide each side by 6.5

-x/6.5 = 6.5c/6.5

-x/6.5 = c

Answer:

\(\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)\)

Step-by-step explanation:

\(f\left(x\right)\:=\:2x^2\:+\:16x\:-\:9\)

- Given

\(\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)\)

By definition of zeros of  a function,  the zeros of the quadratic function f(x) = 2x² + 16x – 9 are \(x1=-4+\frac{\sqrt{82}}{2}\) and \(x2=-4-\frac{\sqrt{82}}{2}\) .

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

\(x1,x2=\frac{-b+-\sqrt{b^{2}-4ab } }{2a}\)

The quadratic function is f(x) = 2x² + 16x – 9

Being:

the zeros or roots are calculated as:

\(x1=\frac{-16+\sqrt{16^{2}-4x2x(-9) } }{2x2}\)

\(x1=\frac{-16+\sqrt{256 +72 } }{4}\)

\(x1=\frac{-16+\sqrt{328} }{4}\)

\(x1=\frac{-16+\sqrt{4x82} }{4}\)

\(x1=\frac{-16+2\sqrt{82} }{4}\)

\(x1=\frac{-16}{4}+\frac{2\sqrt{82}}{4}\)

\(x1=-4+\frac{\sqrt{82}}{2}\)

and

\(x2=\frac{-16-\sqrt{16^{2}-4x2x(-9) } }{2x2}\)

\(x2=\frac{-16-\sqrt{256 +72 } }{4}\)

\(x2=\frac{-16-\sqrt{328} }{4}\)

\(x2=\frac{-16-\sqrt{4x82} }{4}\)

\(x2=\frac{-16-2\sqrt{82} }{4}\)

\(x2=\frac{-16}{4}-\frac{2\sqrt{82}}{4}\)

\(x2=-4-\frac{\sqrt{82}}{2}\)

Finally, the zeros of the quadratic function f(x) = 2x² + 16x – 9 are \(x1=-4+\frac{\sqrt{82}}{2}\) and \(x2=-4-\frac{\sqrt{82}}{2}\) .

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Answer:

39x - 63

Step-by-step explanation:

5(3x - 3) + 4(6x - 12) ← distribute both parenthesis

= 15x - 15 + 24x - 48 ← collect like terms

= 39x - 63

The calculated distance is approximately 14.21 miles, which is less than the 15-mile radius of the cell tower. Therefore, you are within the region served by the tower.

To determine if you are within the region served by the cell tower, we can calculate the distance between your location and the tower using the Pythagorean theorem. According to the given information, you are 9 miles east and 11 miles north of the cell tower.

Using the Pythagorean theorem, the distance from your location to the cell tower can be calculated as follows:

Distance = √((east distance)^2 + (north distance)^2)

        = √((9 miles)^2 + (11 miles)^2)

        = √(81 + 121)

        = √202

        ≈ 14.21 miles

The calculated distance is approximately 14.21 miles, which is less than the 15-mile radius of the cell tower. Therefore, you are within the region served by the tower.

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\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)

\(\qquad❖ \: \sf \:g(f( - 5)) = 5\)

\(\textsf{\underline{\underline{Steps to solve the problem} }:}\)

\(\qquad❖ \: \sf \:f(x) = |2x + 9| \)

\(\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| \)

\(\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| \)

\(\qquad❖ \: \sf \:f( - 5) = | - 1| \)

\(\qquad❖ \: \sf \:f( - 5) = 1\)

next,

g(f(-5)) represents value of y at x = f(-5) = 1

hence,

\( \qquad \large \sf {Conclusion} : \)

Answer:

2e3t = 32 since you can divide by 3 on both sides.

Below are the answers to the question:

Answers to other questions are as follows;

10. 3.6*10^6 (Option D)

11. 4.53472*10^14 miles (Option B)

12. 9.217*10^7 (Option B)

13. 32 seconds (Option A)

14. Yes (Option A)

15. No (Option B)

16. 1,440 (Option A)

17. $3,696.00 (Option C)

18. $8,240.00 (Option C)

An exponential function is a mathematical function of the form:

f(x) = a^x

where a is a positive constant called the base, and x is the exponent. Exponential functions are commonly used in mathematics, science, and engineering to describe phenomena that grow or decay at a constant percentage rate.

Exponential functions are characterized by their rapid growth or decay. When the base a is greater than 1, the function grows exponentially, getting larger and larger as x increases. When the base a is between 0 and 1, the function decays exponentially, getting smaller and smaller as x increases.

Exponential functions are widely used to model a variety of real-world phenomena, including population growth, compound interest, radioactive decay, and the spread of infectious diseases. They are also used in statistical analysis, signal processing, and other fields of mathematics and science.

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Answer:

I mean, I think it varies by house and by location but a general range would be:

Min: 64 *F

Max: 74 *F

Answer:

74 yards wide and 116 yards long

Answer:

Step-by-step explanation:

Remark

Later on, in a not so distant future, you will learn that the maximum area of a rectangle can be obtained when you are dealing with a square.

So to get the maximum area, change the rectangle into a square. Leave the perimeter the same.

Formulas

Perimeter = 2L + 2W

Perimeter = 4*s for a square

Area = s^2

Givens

L = 115

P = 75

Solution

P = 2 * 115  + 2 * 75

P = 230 + 150

P = 380

Perimeter of a square

P = 4*s                Substitute

4s = 380            Divide by 4

s = 95

Check

Area of  original Rectangle = 115 * 75 = 8625

Area of the derived square = 95^2 = 9025

There are 2 parallel lines with the intersection. The angles of x=171° and y=9°.

Given that,

In the picture there is a diagram and we have to find the angle of x and y.

There are 2 parallel lines with the intersection.

If a transversal cuts two parallel lines, then the equivalent angles in the pair are equal.

The pair of corresponding angles are equal

x=19y

So,

We can say x and y are on the line

Then,

x+y=180°

19y+y=180°

20y=180°

y=180/20

y=9°

Now,

x=19y

x=19×9

x=171°

Therefore, the angles of x=171° and y=9°.

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You can rent time on computers at the local copy center for 35 minutes with $25.

To find out how much time you can rent for $25 at the local copy center, follow these steps:

1. Subtract the $10 setup charge from the total amount you have: $25 - $10 = $15.
2. Now you have $15 left for renting time on the computers. Since it costs $2 for every 5 minutes, you need to find out how many 5-minute increments can be covered by $15.
3. Divide the remaining amount by the cost per 5-minute increment: $15 / $2 = 7.5. Since you can't have half an increment, round down to 7.
4. Multiply the number of 5-minute increments by the time per increment: 7 * 5 = 35 minutes.

So, you can rent time on computers at the local copy center for 35 minutes with $25.

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A) The expression represent the area of the rectangle is \(x^2+30x-1000\) \(ft^2\)

B) For 50 ft, Area = 3000 \(\rm ft^2\), For 100 ft , area = \(\rm 12000\ ft^2\) and For 150 ft, area = 26000 \(\rm ft^2\)

C)  If area of the square is larger than new rectangle play ground then we need enough time to play.

The area of a rectangle οccupies is the space it takes up inside the limitatiοns οf its fοur sides. The dimensiοns οf a rectangle determine its area. In essence, the area οf a rectangle is equal tο the sum οf its length and breadth.

Let us take side length οf the square = x

Adding 50 feet fοr οne side then , length οf rectangle = x+50 feet.

Nοw decreasing 20 feet fοr οther side then, width οf rectangle = x- 20 feet.

A) Now area of the rectangle is ,

A = length*width

=> A = (x+50)(x-20)

=> A = \(x^2-20x+50x-1000\)

=> A = \(x^2+30x-1000\)

Then , the expression represent the area of the rectangle is \(x^2+30x-1000\) \(ft^2\)

B) If side length x= 50 ft then

Area = \(50^2+30\times50-1000 = 2500+1500-1000 = 3000 ft^2\)

If side length x = 100 ft then

Area = \(100^2+30\times100-1000 = 10000+3000-1000 = 12000 ft^2\)

If side length = 150 ft then

Area = \(150^2+30\times150-1000= 22500+4500-1000= 26000 ft^2\).

C) If area of the square is larger than new rectangle play ground then we need enough time to play.

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The coordinates of the vertex are (0, 27).

A parabola is a symmetrical, U-shaped curve that can be formed by intersecting a cone with a plane that is parallel to one of its sides. In mathematics, a parabola is a type of quadratic function that can be written in the standard form y = ax² + bx + c, where x and y are variables, a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term. The coefficient a determines the shape of the parabola: if a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.

To find the vertex of the parabola, we need to use the formula:

x = -b / 2a

where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c), which describes the parabola.

In this case, the equation of the parabola can be written as:

h = -0.045t² + 27

where h is the height of the cable (in meters) above the deck of the bridge, and t is the distance (in meters) from the first tower.

By comparing this equation with the standard form, we can see that a = -0.045 and b = 0. To find the vertex, we can substitute these values into the formula:

x = -b / 2a = 0 / (-2 * 0.045) = 0

So the x-coordinate of the vertex is 0. To find the y-coordinate, we can substitute this value back into the equation:

h = -0.045(0)² + 27 = 27

So the coordinates of the vertex are (0, 27).

The correct interpretation of the vertex is that it represents the highest point on the parabola, which in this case is the highest point of the cable above the deck of the bridge. The vertex is also the axis of symmetry of the parabola, which means that the distance from the first tower to the vertex is the same as the distance from the vertex to the second tower.

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Step-by-step explanation:

the ratio of 1/18 simply means that 1 inch in the drawing represents 18 inches in reality.

so, the real flag is therefore

2×18 = 36 inches long and 1×18 = 18 inches wide (or high).

the area of the actual flag is therefore

36 × 18 = 648 in²

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

According to the given statement the solution for r₂ in the given equation is (-Rr²) / (R - r²).

To solve the formula R(r² + r₂) = r² r₂ for r₂, we need to isolate the variable r₂.
1. Distribute R to the terms inside the parentheses:
  R * r² + R * r₂ = r² * r₂
2. Simplify the equation:
  Rr² + Rr₂ = r²r₂
3. Move all the terms containing r₂ to one side of the equation by subtracting Rr₂ from both sides:
  Rr₂ - r²r₂ = -Rr²
4. Factor out r₂ from the left side of the equation:
  r₂(R - r²) = -Rr²
5. Finally, solve for r₂ by dividing both sides of the equation by (R - r²):
  r₂ = (-Rr²) / (R - r²)
The solution for r₂ in the given equation is (-Rr²) / (R - r²).

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We solved the given formula R(r² + r₂) = r² r₂ for r₂ and obtained the equation r₂ = -Rr² / (R - r²). This formula allows us to calculate the value of r₂ based on the values of R and r².

To solve the formula R(r² + r₂) = r² r₂ for r₂, we can follow these steps:

1. Distribute R to both terms inside the parentheses:
  R * r² + R * r₂ = r² r₂

2. Simplify the equation by multiplying:
  Rr² + Rr₂ = r² r₂

3. Move all the terms involving r₂ to one side of the equation:
  Rr₂ - r² r₂ = -Rr²

4. Factor out r₂ from the left side of the equation:
  r₂ (R - r²) = -Rr²

5. Divide both sides of the equation by (R - r²):
  r₂ = -Rr² / (R - r²)

So the formula for r₂ in terms of R and r² is:
  r₂ = -Rr² / (R - r²)

In conclusion, we solved the given formula R(r² + r₂) = r² r₂ for r₂ and obtained the equation r₂ = -Rr² / (R - r²). This formula allows us to calculate the value of r₂ based on the values of R and r².

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Answer:

2 = 22

3 = 19

5 = 13

6 = 10

Step-by-step explanation:

To help with future questions, take whatever is for the x and plug it into the equation

Answer:

22,19,13,10

Step-by-step explanation:

First, Replace the x in the equation with parenthesis (), then inside of the () put the x value in the table so it would look like: y=28-3(2). Then solve by multiplying 2 by 3 so you have y=28-6. Then just subtract 6 from 28 to get 22. Rinse and repeat for the rest of the values. Your first value will be 22, second 19, third 13, and lastly 10. Hope this helps!

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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4.59 g will be the amount of substance that will be present after 5 year.

Given: 16g of radioactive substance

            8g left after 8 year

Concept: In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to drop to half its original value. In a first-order reaction, the half-life of the reactant is ln(2)/λ, where λ (also referred to as k) is the reaction rate constant.

The half-life is given as 5 years, so the amount remaining after 9 years will be found by using the steps done below:

Remaining amount of radioactive substance = initial × (1/2)^(t/(half-life))

Remaining substance = (16 g)×(1/2)^(9/5) ≈ 4.59 g

After 9 years i.e., after 8 years have passed

About 4.59 g of the substance remains.

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Answer:

Given the diameter is 8, the answer is approximately 50.27.

Step-by-step explanation:

\(A = \frac{1}{4} \times \pi \times d^2\\A = 0.25 \times (22/7) \times 8^2\\A = 50.27\)

Step-by-step explanation:

A= πr² d=8 r=d/2 = 8/2 = 4

A= π4²

A = 50.265

The equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.

We are given;

y = 3x³ - 7x² + 5

y = 7x^4 + 2x

We will solve the given equation by substitution method:

Using the substitution method, let us substitute y = 7x^4 + 2x in the equation y = 3x³ - 7x² + 5, we get,

3x³ - 7x² + 5 = 7x^4 + 2x

So, 3x³ - 7x² + 5 = 7x^4 + 2x will be solved by using the given system of equations.

Thus, the equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.

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A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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The reason why the number of failures and successes in two population proportions must be up to 10 is because it is important to have many of samples from both populations.

This refers to the probability displayed that a parameter will exist between a pair of values around the mean.

It measures the extent to which one can be certain or uncertain about ones sampling method. Confidence Intervals are usually constructed using levels of 95% or 99%.

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Answer: So we can assume that the two samples are independent.

Answer:

Graph b.

Step-by-step explanation:

B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.

Solution:

We know that:

\(Original \ price = \$11\)

\(Sale \ price = \$9.25\)

\(\frac{9.25}{11} + \frac{1.75}{11} =100\%\)

Simplify the equation to find the percent off:

\(\frac{9.25}{11} + \frac{1.75}{11} =100\%\)

\(84\% + \bold{16\%} = 100\% \space\ \space\ \space\ \ \ \ \ [Rounded]\)

This means that the original price has decreased about 16%.

Answer:

The answer is C. 1/81

Step-by-step explanation:

The expression that can be used to determine how long it will take for the tank to fill completely is C. 1 over 4 . 12.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

In this case, the oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline.

The rate will be:

= 1/4 ÷ 1/12

= 1/4 × 12

= 3

The correct option is C

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Answer:

Inequality: 25x + 30 < 155

Step-by-step explanation:

25x is the cost per lesson. 30 is the recital fee. 155 is the total cost. We used the < sign because she has to pay LESS than $155.

Solve...

25x + 30 < 155

Subtract 30 on both sides...

25x < 125

Divide 25 on both sides...

x < 5

THATS NOT YOUR ANSWER YET Always make sure to plug in the answer you got BEFORE inputting it.

Plug in 5 for x...

25 ( 5 ) + 30 < 155

125 + 30 < 155

155 < 155

You know that she wants to spend LESS than $155, when she takes 5 lessons, as shown above, she spends exactly $155, your answer would be 4 because she spends less than $155 when taking 4 classes, but exactly $155 when taking five.

Really hope this helps! :)

Answer:

537 in²

Step-by-step explanation:

11.4 x 15 = 171

2(7 x 9) = 126

7 x 15 = 105

9 x 15 = 135

171 + 126 + 105 + 135 = 537

Answer:

474 sq. inches

Step-by-step explanation:

15 x (7+9+11.4) = 411

2x 1/2 x 7 x 9 = 63

= 474

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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