.X and Y are independent exponential random variables with mean µX and µY respectively.

Find the MGF of Z = X − Y

We can simplify the formula for the coefficient of each power by using the binomial coefficient notation:
n(n-1)[a_n + 2a_{n-2} + 3a_n/n] = n(n-1)a_n[1 + 2(n-1)/(n(n-1)) + 3/n] = n(a_n/2)[6/n + (n-2)/n]

To rewrite the given expression as a single power series, we can first combine the three summations into one by adjusting the indices. This gives us:
[infinity]∑n=1 [n(n-1)a_nx^n + 2(n-1)(n-2)a_{n-2}x^n + 3na_nx^n]
Next, we can simplify the coefficients of each term by factoring out n(n-1) and rearranging:
[infinity]∑n=1 n(n-1)[a_nx^n + 2a_{n-2}x^n + 3a_nx^n/n]
Now, we can focus on the general term of this series. For a given n, the term involves three coefficients: a_n, a_{n-2}, and a_n/n. Using these, we can write the general term as:
n(n-1)[a_n + 2a_{n-2} + 3a_n/n]x^n
This expression involves only a single power of x, and the coefficient of each power is given by the above formula. Thus, we have successfully rewritten the given expression as a single power series whose general term involves x^n.
Note that this series only converges for values of x within the radius of convergence of each of the original series. Additionally, we can simplify the formula for the coefficient of each power by using the binomial coefficient notation:
n(n-1)[a_n + 2a_{n-2} + 3a_n/n] = n(n-1)a_n[1 + 2(n-1)/(n(n-1)) + 3/n] = n(a_n/2)[6/n + (n-2)/n]
To know more about Expression visit:

https://brainly.com/question/30091641

#SPJ11

The solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.

To solve the equation 3.3 + 4x = -6.9x + 6.6, we need to isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms:

3.3 + 4x = -6.9x + 6.6

Next, let's move the variable terms (4x and -6.9x) to one side and the constant terms (3.3 and 6.6) to the other side:

4x + 6.9x = 6.6 - 3.3

Combine the x terms on the left side:

10.9x = 3.3

Now, divide both sides of the equation by 10.9 to solve for x:

x = 3.3 / 10.9

Using a calculator, we can find the decimal approximation of x:

x ≈ 0.3028

Rounding to the nearest tenth, the solution to the equation is x ≈ 0.3.

In summary, the solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ1

The probability of the event, given the odds in favor of 21 to 9, is 0.7

To calculate the probability of an event given the odds in favor, we can use the formula:

Probability = Odds in Favor / (Odds in Favor + Odds against)

In this case, the odds in favor are given as 21 to 9. This means that for every 21 favorable outcomes, there are 9 unfavorable outcomes.

To calculate the probability, we divide the number of favorable outcomes (21) by the total number of outcomes (21 + 9 = 30):

Probability = 21 / 30 = 7/10

Learn more about Probability

brainly.com/question/32004014

#SPJ11

Answer:

1. D

4. C

Step-by-step explanation:

1. 4 basketballs / 10 footballs

divide both the numerator and denominator by 2, as both are multiples of 2, to get

2 basketballs/5 footballs

4. 112 = 35 % = 35/100

multiply all sides by 100 to get rid of the denominator

112 * 100 = 3500 % = 35 =

11200

divide by 35 to get to 100%

11200/35 = 100% = 1 = 320

What’s the description of the ridged motions

Answer:

Statement A. The value of money that you save increases over time is true.

Step-by-step explanation:

Inflation is a common phenomenon in most economies, which generally leads to the erosion of purchasing power over time. In other words, the same amount of money will typically buy less in the future due to the rising prices of goods and services. Therefore, if you save money and do not invest or earn any interest, the value of your savings will decrease in terms of what it can purchase over time.

To combat the effects of inflation and maintain the value of money, it is important to consider investing or earning interest on your savings. By doing so, you can potentially grow the value of your money over time and offset the impact of inflation.

Assessing a community's need for a smoking cessation program and evaluating whether the state nicotine help hotline is meeting those needs is a form of context evaluation.

Context evaluation focuses on understanding the environmental factors, needs, and circumstances surrounding a program or intervention.

It aims to assess the fit between a program and its intended context, as well as determine the relevance and appropriateness of the program in addressing specific needs.

In the given scenario, the evaluation process involves assessing the community's need for a smoking cessation program.

This includes understanding the prevalence of smoking in the community, identifying the specific challenges and barriers individuals face in quitting smoking, and determining the demand for support services.

This assessment helps to determine whether there is a need for a smoking cessation program in the community.

Additionally, the evaluation involves assessing whether the state nicotine help hotline is meeting those needs.

This evaluation examines the effectiveness and efficiency of the hotline in providing support and assistance to individuals seeking help with nicotine addiction.

It assesses factors such as the accessibility of the hotline, the quality of services provided, and the satisfaction of the users.

By conducting this evaluation, stakeholders can gather important information about the community's needs, the effectiveness of the hotline, and make informed decisions regarding the implementation or improvement of smoking cessation programs.

The evaluation findings can guide future planning and resource allocation to better address the community's needs and enhance the effectiveness of the state nicotine help hotline.

Learn more about nicotine here:

https://brainly.com/question/15241838

#SPJ11

Answer:

64

Step-by-step explanation:

-2√x = -12-4

√x = -16 ÷ -2

= 8

x = 8²

Using the conversion given to be able to convert 24 m / s into mph gives us 54 mph.

To convert 24 m/s to mph, utilize the conversion factor 1 m / s = 2.23694 mph.

First, convert 24 m / s to km / h by multiplying it by 3. 6 (since 1 km / h = 3.6 m/s):

= 24 m / s x 3.6 km / h  

= 86. 4 km / h

Use the given conversion 8 km / h = 5 mph to convert km/h to mph:

= 86. 4 km / h x ( 5 mph / 8 km / h )

= 54 mph

Find out more on conversion at https://brainly.com/question/145654

#SPJ1

(a) The chance that the sum of the draws will be more than 1,500

(b) The chance that there will be fewer than 90 occurrences of the number 3.

(a) To estimate the chance that the sum of the draws will be more than 1,500, we need to consider the possible combinations and their probabilities. Since there are four numbers in the box, each with an equal chance of being drawn, we can calculate the mean and standard deviation of the draws. With this information, we can use statistical methods such as the normal distribution to estimate the probability of the sum exceeding 1,500.

(b) To estimate the chance that there will be fewer than 90 occurrences of the number 3, we need to calculate the probability of drawing a 3 in each individual draw and then consider the distribution of the number of 3's over the 400 draws. Using statistical techniques such as the binomial distribution, we can estimate the probability of having fewer than 90 occurrences of 3 in the 400 draws.

Both estimations involve applying statistical methods to analyze the probabilities of specific events occurring in the random drawing process. The precise calculations and estimations would require detailed information about the probabilities of drawing each number and the distribution of these numbers in the box.

Learn more about binomial distribution here:

https://brainly.com/question/29163389

#SPj11

Answer:

Here’s your answer simplified! Good luck and don’t forget to leave a thanks

Yes, the identity [tex]cos^{2}[/tex](2x) + [tex]sin^{2}[/tex](2x) = 1 is true. This identity is a fundamental trigonometric identity known as the Pythagorean identity.

The Pythagorean identity states that for any angle x, the square of the cosine of x plus the square of the sine of x is always equal to 1. Mathematically, it can be written as [tex]cos^{2}[/tex](x) + [tex]sin^{2}[/tex](x) = 1.

In the given expression, [tex]cos^{2}[/tex](2x) + [tex]sin^{2}[/tex](2x), we have an angle of 2x. According to the Pythagorean identity, the sum of the squares of the cosine and sine of this angle will also equal 1. Therefore, [tex]cos^{2}[/tex](2x) + [tex]sin^{2}[/tex](2x) simplifies to 1.

This identity is fundamental in trigonometry and has numerous applications in solving trigonometric equations and identities. It demonstrates the relationship between the cosine and sine functions and their squares, highlighting their complementary nature.

learn more about Pythagorean identity  here:

https://brainly.com/question/24220091

#SPJ11

Therefore, the probability that x < 14 is approximately 0.1635.

To find the probability that x < 14, we need to calculate the cumulative distribution function (CDF) of the normal distribution with the given parameters.

Since x follows a normal distribution with mean μ and variance σ^2, we have x ~ N(μ, σ^2). In this case, μ = 15 and σ^2 = a^2/7 = 7.

Using the standardization formula for normal random variables, we can convert x to the standard normal distribution Z ~ N(0, 1):

Z = (x - μ) / σ

Substituting the given values, we get:

Z = (x - 15) / sqrt(7)

Now we need to calculate the probability that Z < (14 - 15) / sqrt(7) = -1 / sqrt(7).

Using a standard normal table or a statistical software, we can find the corresponding probability. In this case, p(Z < -1 / sqrt(7)) is approximately 0.1635 (rounded to four decimal places).

To know more about probability,

https://brainly.com/question/14310139

#SPJ11

The slope of the line is 2.4 / 3.

The slope of a line is the change in the dependent variables with respect to the change in the independent variables.

In other words, the slope of a line is the change in y with respect to the change in x.

Therefore,

slope of the line = y₂ - y₁ / x₂ - x₁

Hence, (4, 1.2)(10, 6)

x₁ = 4

x₂ = 10

y₁ = 1.2

y₂ = 6

Therefore,

slope of the line = 6 - 1.2 / 10 - 4

slope of the line = 4.8 / 6

slope of the line = 2.4 / 3

learn more on slope here: https://brainly.com/question/29149364

#SPJ1

as the test statistic becomes larger, the p-value gets smaller, indicating stronger evidence against the null hypothesis.

The p-value is a measure of the strength of evidence against the null hypothesis in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.

In general, a larger test statistic indicates stronger evidence against the null hypothesis, suggesting that the observed data deviates more from what would be expected under the null hypothesis. As a result, the p-value associated with a larger test statistic becomes smaller.

The p-value is calculated based on the test statistic and the null distribution, which represents the distribution of the test statistic under the assumption that the null hypothesis is true. A larger test statistic corresponds to a point further into the tails of the null distribution, where the probability density is lower. Hence, the p-value, which represents the tail probability beyond the observed test statistic, decreases as the test statistic becomes larger.

Learn more about p-value here:

https://brainly.com/question/30461126

#SPJ11

Answer: Area= 15.4375

Step-by-step explanation:

3.25*4.75=15.4375

3.25/0.5=6.5

4.75/0.5=9.5

*Draw box 6.5 boxes wide and 9.5 boxes long.*

Main Answer:

a)det (3A^−1B^2A^T) is equal to 1728

b)det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] is equal to -3.

Supporting Question and Answer:

How can we calculate the determinant of a matrix?

To calculate the determinant of a matrix, we can use various methods such as cofactor expansion, row reduction, or properties of determinants.

Body of the Solution:

(a) To calculate det (3A^−1B^2A^T), we can use the properties of determinants:

det (3A^−1B^2A^T) = 3^3 * det (A^−1) * det (B^2) * det (A^T)

Since det (A^−1) is the reciprocal of det (A) and det (A^T) is equal to det (A), we can simplify further:

det (3A^−1B^2A^T) = 3^3 * (1/det (A)) * det (B^2) * det (A)

We are given that det (A) = 1 and det (B) = -4, so we substitute these values:

det (3A^−1B^2A^T) = 3^3 * (1/1) * (-4)^2 * 1

det (3A^−1B^2A^T) = 3^3 * 4 * 16

det (3A^−1B^2A^T) = 1728

Therefore, det (3A^−1B^2A^T) is equal to 1728.

(b) To calculate det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c], we can expand the determinant using the properties of determinants:

det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = (a + 3d)(3h - 2b)(-c) + (b + 3e)(3g - 2a)(-c) + (c + 3f)(3g - 2a)(-b)

Expanding and simplifying further:

= -abc - 3bcd - 3acf + 2bcd + 6cdh + 6afh - 2bgh - 6agh - 6a^2c - 2bci - 6afi - 6efg

Combining like terms:

= -abc - 3aci - 2bci - 6a^2c + 6cdh - 6afg - 2bgh - 6agh - 6efg

= -abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg

We are given that det [a b c d e f g h i] = -3, so we can set the expanded expression equal to -3:

-abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg = -3

Therefore, we have determined the expression for det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] in terms of the given variables and the constant -3.

Final Answer:Thus, det (3A^−1B^2A^T) is equal to 1728 and det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = -3.

To learn more about the determinant of a matrix from the given link

https://brainly.com/question/14218479

#SPJ4

a) Determinant  (3A^−1B^2A^T) is equal to 1728

b)det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] is equal to -3.

To calculate the determinant of a matrix, we can use various methods such as cofactor expansion, row reduction, or properties of determinants.

(a) To calculate det (3A^−1B^2A^T), we can use the properties of determinants:

det (3A^−1B^2A^T) = 3^3 * det (A^−1) * det (B^2) * det (A^T)

Since det (A^−1) is the reciprocal of det (A) and det (A^T) is equal to det (A), we can simplify further:

det (3A^−1B^2A^T) = 3^3 * (1/det (A)) * det (B^2) * det (A)

We are given that det (A) = 1 and det (B) = -4, so we substitute these values:

det (3A^−1B^2A^T) = 3^3 * (1/1) * (-4)^2 * 1

det (3A^−1B^2A^T) = 3^3 * 4 * 16

det (3A^−1B^2A^T) = 1728

Therefore, det (3A^−1B^2A^T) is equal to 1728.

(b) To calculate det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c], we can expand the determinant using the properties of determinants:

det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = (a + 3d)(3h - 2b)(-c) + (b + 3e)(3g - 2a)(-c) + (c + 3f)(3g - 2a)(-b)

Expanding and simplifying further:

= -abc - 3bcd - 3acf + 2bcd + 6cdh + 6afh - 2bgh - 6agh - 6a^2c - 2bci - 6afi - 6efg

Combining like terms:

= -abc - 3aci - 2bci - 6a^2c + 6cdh - 6afg - 2bgh - 6agh - 6efg

= -abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg

We are given that det [a b c d e f g h i] = -3, so we can set the expanded expression equal to -3:

-abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg = -3

Therefore, we have determined the expression for det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] in terms of the given variables and the constant -3.

Thus, det (3A^−1B^2A^T) is equal to 1728 and det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = -3.

To learn more about the determinant of a matrix

brainly.com/question/14218479

#SPJ4

Note that the  the quotient of the expression is 7a³  + a²b - 3.

The expression can be written this way

(28a⁴ᵃᵇ + 4a²b² - 12ab) / (4ab)

To simplify the expression, we can cancel out common factors in the numerator and denominator.

In this case, we can divide every term by 4ab:

(28a⁴ᵃᵇ / 4ab) + ( 4a²b² / 4ab) - (12ab / 4ab)

Simplifying further, we have:

7a³ + a²b - 3

Thus, we can state that , the quotient of the expression is 7a³ + a²b - 3

Learn more about quotient:
https://brainly.com/question/16134410
#SPJ1

The  matching of the properties with their corresponding values:

MAX_VALUE: represents the highest value for numeric data types. The value is 1.8 x 10³⁰⁸. It's the highest possible number within the data type's range.

NEGATIVE_INFINITY is a special value representing negative infinity. It's a math concept for the lowest value.

POSITIVE_INFINITY: Represents positive infinity. Positive infinity in math represents a value greater than any other number, like negative infinity.

Learn more about Infinity from

https://brainly.com/question/7697090

#SPJ1

The function position of the particle is equal to s(t) = 10 · t² + 4 · t³ + 6. The position of the particle at t = 1 s is 20 feet.

In this problem we find the function velocity of a particle in time and the initial value for the position of the particle in time. This can be done by using indefinite integrals. First, write the function velocity:

v(t) = 20 · t + 12 · t²

Second, integrate the function:

s(t) = 20 ∫ t dt + 12 ∫ t² dt

s(t) = 10 · t² + 4 · t³ + C, where C is the integration constant.

Third, determine the integration constant:

C = s(t) - 10 · t² - 4 · t³

C = 6

Fourth, write the resulting function:

s(t) = 10 · t² + 4 · t³ + 6

Fifth, evaluate the function at t = 1 s:

s(1) = 10 · 1² + 4 · 1³ + 6

s(1) = 20

To learn more on indefinite integrals: https://brainly.com/question/31617899

#SPJ1

The 4 cm segment on the map corresponds to 0.96 kilometers on the ground.

Representative fraction of the map: 1:24,000

Length of the segment on the map: 4 cm

Let's denote the distance on the ground as 'x' in kilometers.

We can set up the proportion as follows

1 cm on the map represents 24,000 cm on the ground 4 cm on the map represents x km on the ground

Using cross-multiplication, we can solve for 'x'

1 cm / 24,000 cm = 4 cm / x km

x km = (4 cm × 24,000 cm) / 1 cm

Simplifying:

x km = 96,000 cm

Now, we can convert centimeters to kilometers:

x km = 96,000 cm / 100,000 cm/km

x km = 0.96 km

Therefore, the 4 cm segment on the map corresponds to approximately 0.96 kilometers on the ground.

To know more about segment click here :

https://brainly.com/question/1439616

#SPJ4

The series diverges according to the integral test.

To determine whether the series ∑(n=1 to infinity) (n-7) converges or diverges, we can use the integral test. The integral test states that if the series ∑(n=1 to infinity) a_n converges or diverges, where a_n is a positive, continuous, and decreasing function, then it is equivalent to the convergence or divergence of the integral ∫(1 to infinity) f(x) dx, where f(x) is the continuous and positive function that represents a_n.

In this case, we have the series ∑(n=1 to infinity) (n-7). To apply the integral test, we need to find the corresponding function f(x). We can see that (n-7) represents the value of the series at the nth term, so we can write it as a_n = n - 7.

Now, we need to find the function f(x) such that f(x) represents a_n = n - 7. Since a_n = n - 7, we can rewrite it as n = a_n + 7. We replace n with x in the equation to find f(x): x = a_n + 7. Solving for a_n, we get a_n = x - 7.

Now we have the function f(x) = x - 7. We can integrate this function to determine the convergence or divergence of the series:

∫(1 to infinity) (x - 7) dx.

Evaluating this integral, we get:

∫(1 to infinity)[tex](x - 7) dx = [x^2/2 - 7x][/tex]evaluated from 1 to infinity.

Taking the limit as x approaches infinity, we have:

lim[tex](x→∞) [x^2/2 - 7x] - [1^2/2 - 7(1)][/tex]

= lim(x→∞)[tex][x^2/2 - 7x - 1/2 + 7][/tex]

= lim(x→∞)[tex][x^2/2 - 7x - 6.5].[/tex]

As x approaches infinity, the dominant term is[tex]x^2/2. \\[/tex]Therefore, the limit becomes:

lim(x→∞)[tex]x^2/2.[/tex]

Since this limit is divergent (approaches positive infinity), the integral ∫(1 to infinity) (x - 7) dx diverges.

By the integral test, we can conclude that the series ∑(n=1 to infinity) (n-7) also diverges.

Learn more about   integral test

brainly.com/question/31033808

#SPJ11

To maintain a familywise significance level of 0.1 across all ten hypothesis tests use a significance level of 0.01.

To maintain a familywise significance level of 0.1 for ten hypothesis tests, you need to adjust the significance level for each individual test to account for multiple testing.

One commonly used method is the Bonferroni correction.

The Bonferroni correction involves dividing the desired overall significance level (0.1) by the number of tests (10) to obtain the adjusted significance level for each individual test.

Adjusted significance level = Overall significance level / Number of tests

Adjusted significance level = 0.1 / 10 = 0.01

Therefore, for each individual test, you should use a significance level of 0.01 to maintain a familywise significance level of 0.1 across all ten hypothesis tests.

Learn more about Bonferroni correction here:

https://brainly.com/question/32293811

#SPJ1

In the passage above, a parallel is drawn between Karen's friend, Brody, and a shining beacon of light. The Option B.

A parallel sentence occurs when words are formed in the same way or have the same structure.

In the passage, Brody is compared to a shining beacon of light. This suggests that Brody is portrayed as someone who brings brightness and positivity into Karen's life just like a beacon of light guides and illuminates the way.

So, the comparison implies that Brody has a significant and uplifting impact on Karen's experiences or emotions.

Read more about parallel sentence

brainly.com/question/537838

#SPJ1

Answer:

If the area is four, the radius would be two.

Step-by-step explanation:

Remember that the radius is always half of the area! I hope this help.

The system of the equations x/3 = 5y - 1 and 2 + 5y = x/3 are parallel lines and have no solution.

Inconsistent equations are a system of equations that do not have a common solution. In other words  there is no set of values for the variables that simultaneously satisfies all the equations in the system.

There are two types of inconsistent systems:

There is no solution because the line graphs are parallel and do not overlap or intersect

plotting the graph of the system of the equations shows that the equations are parallel lines

x/3 = 5y - 1

2 + 5y = x/3

hence no solution

Learn more about simultaneous equations  at

https://brainly.com/question/148035

#SPJ1

Answer:

x = 18

Step-by-step explanation:

The average is defined as the sum of a set of values divided by the total number of values.

Since the average is 10 and there are 6 values, we can find x by setting the sum of the 6 values divided by 6 equal to 10:

Step 1:  Plug in the values and simplify inside the parentheses:

(9 + 8 + 5 + 16 + 4 + x) / 6 = 10

(42 + x) / 6 = 10

Step 2:  Multiply both sides by 6:

((42 + x) / 6 = 10) * 6

42 + x = 60

Step 3:  Subtract 42 from both sides to find x:

(42 + x = 60) - 42

x = 18

Thus, x must be 18 in order to have an average of 10 given that the other values are 9, 8, 5, 16, and 4

The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.

To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.

The money multiplier is given by the formula: MM = 1 / reserve requirement.

Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.

The initial deposit is $400.

To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:

Maximum Money Supply = Initial Deposit * Money Multiplier

= $400 * 20

= $8,000.

Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.

Learn more about money

brainly.com/question/2696748

#SPJ11

The probability of a drill bit lasting at least 100 hours is approximately 0.98 or 98%.

The shape parameter (beta) of the Weibull distribution for the length of life of a drill bit in a mechanical operation is 2 and the scale parameter (lambda) is 50. The probability of a drill bit lasting at least 100 hours can be calculated using the Weibull cumulative distribution function (CDF), which is:

CDF(x) = 1 - e (-((x/lambda) beta))

Where x is the length of life of the drill bit.

So, to find the probability of a drill bit lasting at least 100 hours, we plug in x = 100:

CDF(100) = 1 - e(-((100/50)²))
CDF(100) = 1 - e⁻⁴
CDF(100) = 0.9817

0.9817= 98%

Note: The other values (1, 0, 0.5, 0.8) do not have a specific application in this question, so they cannot be used to answer the question.

You can learn more about probability at: brainly.com/question/31828911

#SPJ11