a swimmer can do 4 laps in 2 minutes and 30 seconds how long does it take him to do one lap​

20 shares purchased at $30, means that the initial inversion is 20 times 30 = $600

they are sold for $710, so the difference is 710 - 600 = 110

the commision is 6, so the final gain is 110 -6 =104

profit divided by the inversion:

104/600 = 0.1733

the answer is 17.33 %

(a) Pr(S|burnt out) ≈ 0.965

(b) Pr(L|still lit) ≈ 0.643

(c) Pr(wrong decision) ≈ 0.019

Certainly! Here's the step-by-step calculation:

(a) To find Pr(B|A), we use Bayes' theorem: Pr(B|A) = (Pr(A|B) * Pr(B)) / Pr(A).

1. Pr(A|B) is the probability that the bulb burnt out given that it was S-type. From the information given, this probability is 0.1.

2. Pr(B) is the probability that the bulb was S-type. From the information given, this probability is 0.2.

3. Pr(A) is the probability that the bulb burnt out. This can be calculated using the exponential distribution. Since the average lifespan of the S-type bulb is 100 hours, we can convert this to a rate parameter λ = 1/100. The probability that the bulb burnt out over the weekend (48 hours) is equal to 1 - exp(-λ * 48). Evaluating this expression gives Pr(A) ≈ 0.465.

Substituting these values into the Bayes' theorem equation, we have:

Pr(B|A) = (0.1 * 0.2) / 0.465 ≈ 0.965.

Therefore, the probability that the bulb was S-type given that it burnt out over the weekend is approximately 0.965.

(b) To find Pr(D|C), we use Bayes' theorem: Pr(D|C) = (Pr(C|D) * Pr(D)) / Pr(C).

1. Pr(C|D) is the probability that the bulb is still lit given that it was L-type. From the information given, this probability is 0.5.

2. Pr(D) is the probability that the bulb was L-type. From the information given, this probability is 0.8.

3. Pr(C) is the probability that the bulb is still lit. This can be calculated using the exponential distribution. Since the average lifespan of the L-type bulb is 200 hours, we can convert this to a rate parameter λ = 1/200. The probability that the bulb is still lit at the end of the weekend (48 hours) is exp(-λ * 48). Evaluating this expression gives Pr(C) ≈ 0.643.

Substituting these values into the Bayes' theorem equation, we have:

Pr(D|C) = (0.5 * 0.8) / 0.643 ≈ 0.643.

Therefore, the probability that the bulb was L-type given that it is still lit at the end of the weekend is approximately 0.643.

(c) To calculate the probability of making a wrong decision, we need to consider the probabilities of false positive and false negative decisions.

1. The probability of a false positive decision is Pr(X<63|D), which is the probability that the observed lifespan of the L-type bulb is less than 63 hours, given that it is an L-type bulb. This can be calculated using the exponential distribution with the rate parameter λ = 1/200. Evaluating this expression gives Pr(X<63|D) ≈ 0.274.

2. The probability of a false negative decision is Pr(X>63|B), which is the probability that the observed lifespan of the S-type bulb is greater than 63 hours, given that it is an S-type bulb. This can be calculated using the exponential distribution with the rate parameter λ = 1/100. Evaluating this expression gives Pr(X>63|B) ≈ 0.045.

The probability of making a wrong decision is the sum of the probabilities of false positive and false negative decisions:

Pr(wrong decision) = Pr(X<63|D) + Pr(X>63|B) ≈ 0.274 + 0.045 ≈ 0.319.

Therefore, the probability of making a wrong decision based on the observed outcome is approximately 0.319.

To learn more about probability click here

brainly.com/question/32900629

#SPJ11

1) Calculating the P-value assumes that the sample is a random sample:

True. The P-value calculation is based on the assumption that the sample is randomly drawn from the population, ensuring unbiased results.

2) If you reject H0 with a test, you will be making a Type II error: False. If you reject the null hypothesis when it is true, you are making a Type I error, not a Type II error.

3) If you fail to reject H0 with a test, you will be making a Type I error: False. If you fail to reject the null hypothesis when it is false, you are making a Type II error, not a Type I error.

To know more about "NULL HYPOTHESIS" refer here:

https://brainly.com/question/16261813#

#SPJ11

The combination of entrees and desserts that the restaurant serve will be:

A. The restaurant could serve 40 entrees and 25 deserts.

E. The restaurant could serve 64 entrees and 40 deserts.

The word problem in mathematics refers to a question that is written as a sentence which requires an individual to use his or her mathematics knowledge.

In this case, the local restaurant serves 8 entrees for every 5 desserts.

In this case it should be noted that:

40 / 25 = 8 / 5

64 / 40 = 8 / 5

The correct options are A and E.

Learn more about word problem on

brainly.com/question/21405634

#SPJ1

Answer:-3,-2,0,1,5

Step-by-step explanation:

Answer:

114

Step-by-step explanation:

Both angle 8 and angle 1 have the same measure, so angle 1 would also be 114 degrees

Answer:

m∠=114°

Step-by-step explanation:

m∠8=m∠3= 114° (vert. opp ∠'s)

Therefore

m∠3=m∠1= 114° (corresponding angles, parallel lines)

1a) Complementary solution: y(t) = c₁ + c₂e^t + c₃e^(-t) + c₄cos(t) + c₅sin(t)

1b) Particular solutions:

(i) yp(t) = (1/2)e^t

(ii) yp(t) = (1/5)t^2 + (2/15)

(iii) yp(t) = [(3/20)t^2 + (1/4)t + C₁]cos(2t) - [(3/40)t^3 + (1/8)t^2 + C₂]sin(2t)

2) Linear differential equation: y''(x) + 4y'(x) + 5y(x) = 0

1a) To find the complementary solution of y(5) - y(3) = f(t), we need to find the homogeneous solution of the differential equation y(5) - y(3) = 0. We assume that y(t) = e^(rt) and substitute it into the differential equation to obtain the characteristic equation:

r^5 - r^3 = 0

r = 0, ±1

Since there are three distinct roots, the complementary solution is of the form:

y(t) = c₁ + c₂e^t + c₃e^(-t) + c₄cos(t) + c₅sin(t)

where c₁, c₂, c₃, c₄, and c₅ are constants.

1b) Using the method of undetermined coefficients, we can determine the particular solution of y(5) - y(3) = f(t) for each of the given functions f(t):

(i) f(t) = e^t

Assuming yp(t) = Ae^t, we obtain:

A(e^(5t) - e^(3t)) = e^t

A = 1/2

yp(t) = (1/2)e^t

(ii) f(t) = 2t^2

2A(t^5 - t^3) + 6B(t^3 - t) + 6C(t^2 - 1) = 2t^2

A = 1/5, B = 0, C = 2/15

yp(t) = (1/5)t^2 + (2/15)

(iii) f(t) = (3t+2)cos(2t)

A''(t)cos(2t) + B''(t)sin(2t) + 4A'(t)sin(2t) - 4B'(t)cos(2t) = (3t+2)cos(2t)

A(t) = (3/20)t^2 + (1/4)t + C₁

B(t) = -(3/40)t^3 + (1/8)t^2 + C₂

yp(t) = [(3/20)t^2 + (1/4)t + C₁]cos(2t) - [(3/40)t^3 + (1/8)t^2 + C₂]sin(2t)

2) The given general solution is:

y(x) = C₁e^x + C₂xe^x + C₃e^(-x)cos(2x) + C₄e^(-x)sin(2x)

y'(x) = C₁e^x + C₂(e^x + xe^x) - C₃e^(-x)sin(2x) + C₄e^(-x)cos(2x)

y''(x) = C₁e^x + C₂(2e^x + xe^x) + C₃e^(-x)cos(2x) - C₄e^(-x)sin(2x)

(C₁ + C₂ + C₃ + C₄)e^x + (2C₂ + C₂x - C₃sin(2x) + C₄cos(2x))e^x + (-C₁ + 2C₂ - C₃cos(2x) - C₄sin(2x))e^(-x) = 0

Since this equation must hold for all values of x, we obtain the following system of equations:

C₁ + C₂ + C₃ + C₄ = 0

2C₂ - C₁ - C₃cos(2x) - C₄sin(2x) = 0

C₂x - C

To know more about linear differential equation, visit:
brainly.com/question/30323408
#SPJ11

The range of the exponential function y = bx is all real numbers except 0.

The exponential function y = bx is defined as the equation where b is the base and x is the exponent. The range of this equation is all real numbers except 0. This is because when x is negative, the value of y will be a fraction (or a decimal) which is always a real number except for 0. When x is positive, the value of y will be a multiple of b which is also always a real number except for 0.

Therefore, the range of the exponential function y = bx is all real numbers except 0.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

To find the present value of the annuity, we can use the formula for the present value of an annuity:

PV = P * (1 - (1 + r)^(-n)) / r

Where:

PV = Present value

P = Annual payment

r = Interest rate per period (compounded annually in this case)

n = Number of periods

In this scenario, the annual payment is $2000, the interest rate is 9% (0.09), and the number of periods is 10 - 4 = 6 (since the annuity is deferred for 4 years).

Substituting these values into the formula:

PV = 2000 * (1 - (1 + 0.09)^(-6)) / 0.09

Calculating the expression inside the brackets first:

(1 + 0.09)^(-6) ≈ 0.6275

Plugging it back into the formula:

PV = 2000 * (1 - 0.6275) / 0.09

= 2000 * 0.3725 / 0.09

≈ $8294.44

Therefore, the present value of the annuity of $2000 per year at the end of each of 10 years after being deferred for 4 years, with an interest rate of 9% compounded annually, is approximately $8294.44.

To know more about interest visit-

brainly.com/question/29399147

#SPJ11

Answer:

2/7

Step-by-step explanation:

The total number of possibilities is 7 * 6 * 5

The number of possibilities for all girls is 5 * 4 * 3

so the probability is:

\(\frac{5*4*3}{7*6*5} \\\frac{4*3}{7*6} \\\frac{12}{42} = \frac{2}{7}\)

Answer:

$24 > $8

Step-by-step explanation:

Well if Mary has $32 and the food estimate costs $8 then the inequality would be written as $24 > $8.  So Mary would have 24 dollars to play games.

I am a 96.7 percent sure this is correct :D Hope i could help <3

Answer:

Step A is incorrect.

\( {x}^{2} = x - 6\)

\( {x}^{2} - x + 6 = 0\)

Jon should have subtracted x from both sides and then added 6 to both sides.

Answer:

f

Step-by-step explanation:

fgbdf

Answer:

x=3

Step-by-step explanation:

They are isosceles triangles and angle 2=56.  

56=53+x

x=3

The average rate of change of the function over the interval  4≤x≤6 is 36.

The rate of change of anything is how rapidly it changes over time (ROC).

To find the average rate of change:

The average rate of change of a function f(x) on an interval [a, b] can be found by,

The average rate of change = f(b) - f(a) / (b-a)

Over the interval [4, 6]:

The average rate of change = f(6) - f(4) / (6-4)

                                               = (81 - 9) / (2)

                                               = 72 / 2

                                               =  36

Therefore, the average rate of change is 36.

To learn more about the rate of change;

https://brainly.com/question/29518179

#SPJ1

For this problem, we are given the dimensions of a garden and the cost of planting seeds per square meter in this garden. We need to determine the total cost of planting the seeds.

The first step is to calculate the area of the garden, for which we need to multiply the length and width:

Now we need to multiply the area by the cost of the seeds per square meter. We have:

The total cost is 21.5x² + 40.85x -32.25

Answer:

b

Step-by-step explanation:

4x + 28 = 40

4x + 4*7 = 40

4(x+7) = 40

A distribution is a way of displaying data, consisting of three primary components: shape, center, and spread. The shape is the overall pattern of the distribution, while the center is the point where the distribution is balanced. The spread is the range of values of the data, often measured by the standard deviation or the interquartile range (IQR). The distribution can be visualized through graphs like histograms, box plots, or scatter plots.

A brief description of a distribution should include its shape, center, and spread. The spread is the term that should be included in the blank space.A distribution can be described as a way of displaying data. It gives us an idea about how the data are spread out.

The three primary components of any distribution are the shape, center, and spread. Shape refers to the overall pattern of the distribution. It tells us whether the data are symmetric or skewed. The symmetry means that the left half of the distribution is a mirror image of the right half, whereas a skewed distribution is not symmetrical. The tail of a distribution describes the spread of a skewed distribution. It refers to the parts of the distribution that extend out from the center of the graph.The center refers to the point where the distribution is balanced. In symmetric distributions, the center is the same as the mean and median. However, in a skewed distribution, the mean and median differ from each other.

The spread refers to the range of values of the data. It tells us how much the data are scattered or spread out. A small spread indicates that the data points are close to each other, while a large spread suggests that the data points are far from each other. It is often measured by the standard deviation or the interquartile range (IQR).The distribution of data can be visualized through different graphs like histograms, box plots, or scatter plots.

To know more about distribution Visit:

https://brainly.com/question/29664850

#SPJ11

Home prices are probably skewed to the right and not symmetric. So the correct option would be A.

This makes the median a better representation of the center than the mean which would be influenced by the extremely high-priced homes.

Reporting the mean would give the impression that the​ "typical" home price is higher than it is.

they substitute the median for the mean. The median is unaffected by severe outliers or asymmetric score distributions because it only takes one or two values. In contrast, skewed distributions might have different mean and mode values.

Know more about median

https://brainly.com/question/26151333

#SPJ4

Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.

One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.

Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.

To know more about radians and angles:

https://brainly.com/question/30989204

#SPJ4

In mathematics, a number is considered to be "even" if it is divisible by 2, and "odd" if it is not divisible by 2. The numbers from 1 to 100 can be divided into two groups: even numbers and odd numbers.

Even numbers are numbers that are divisible by 2, such as 2, 4, 6, 8, and so on. When you divide an even number by 2, the remainder will always be 0. Some examples of even numbers between 1 and 100 include: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, and 100.

Odd numbers are numbers that are not divisible by 2, such as 1, 3, 5, 7, and so on. When you divide an odd number by 2, the remainder will always be 1. Some examples of odd numbers between 1 and 100 include: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, and 99.

It is important to note that 0 is not a positive or negative number and it is not considered as odd or even.

Knowing the difference between even and odd numbers is an important concept in math, especially when working with patterns, sequences, and operations. Understanding even and odd numbers can help you better understand the properties of numbers and how they can be used in different contexts.

to know more about even numbers refer here

https://brainly.com/question/2289438#

#SPJ11

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

Learn more about approximately here:

https://brainly.com/question/31695967

#SPJ11

The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

To know more about constraints, visit:

https://brainly.com/question/17156848

#SPJ11

Answer:

(a)

• C(x)=88000+5500x

• R(x)=7500x

(b)55 times

Explanation:

Let the number of performances = x

• The cost of producing the musical = $88,000

• The cost per performance = $5900

(a)Thus, the total cost for x performances:

The revenue per performance is $7500, therefore, the equation for revenue is:

(b)To break even, the cost must be equal to revenue.

Next, solve for x.

The musical must be performed 55 times to break even.

Answer:

12 bags of sand

Step-by-step explanation:

The minimum number of sand to fill the sandbox = 30 cubic feet

The volume or quantity of sand per bag is = 2.5 cubic feet

The minimum number of bags needed to fill the sandbox = 30 / 2.5 = 12 bags  

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

Learn more about data life cycle here

brainly.com/question/28039445

#SPJ4

Answer:

39 acute isoceleleellsllelsls

Step-by-step explanation:

The angles of triangle always add to 180 degrees. So that angle on the bottom already takes up 102 so 180-102=78 and there are 2 angles left so both of those are 39 because 78/2=39  and 39 is an acute angle since its less than 90 degrees so ya

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

The value of \(f_X(0.5)\) is 0.75, given the uniform joint PDF of the random variables X and Y, \(f_{X,Y} (x,y)=3\), on the set {(x,y)|0≤x≤1, 0≤y≤1, y≤x²}.

We to find the value of \(f_X(0.5)\) given the uniform joint PDF of the random variables X and Y, \(f_{X,Y} (x,y)=3\), on the set {(x,y)|0≤x≤1, 0≤y≤1, y≤x²}.

To find \(f_X(0.5)\), we need to compute the marginal PDF of X by integrating the joint PDF over the range of Y.

First, determine the range of Y.
Since y ≤ x², and we're given x = 0.5, the range of Y is 0 ≤ y ≤ (0.5)² = 0.25.

Integrate the joint PDF over the range of Y.
\(\begin{aligned}f_X(x) & =\int_{y=0}^{y=0.25} f_{X, Y}(x, y) d y \\& =\int_{y=0}^{y=0.25} 3 d y \\& =[3 y]_{y=0}^{y=0.25} \\\end{aligned}\)

Substitute the given joint PDF.
fx(0.5) = 3(0.25) - 3(0) = 0.75.

So, the value of \(f_X(0.5)\) is 0.75.

Learn more about random variables:

https://brainly.com/question/17217746

#SPJ11

The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

Read more about proportion at:

https://brainly.com/question/16828793

#SPJ12