What is the smallest possible integer for which 18% of that integer is greater than 3.5 ?
A14
B 16
C 18
D 20
E 22

Moores law that number of transistors per IC Prediction = 4,096,000 and Prediction = 25.6 trillion.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. For example, the probability of flipping a fair coin and getting heads is 0.5, while the probability of rolling a six on a fair six-sided die is 1/6 or approximately 0.1667.

In mathematical terms, probability is calculated by dividing the number of ways an event can occur by the total number of possible outcomes. Probability theory is widely used in many fields, including statistics, finance, science, engineering, and economics, to help predict and analyze the likelihood of various outcomes and make informed decisions based on the probabilities involved.

According to the question:

Part a: Moore's Law predicts that the number of transistors per IC doubles every 18-24 months. Since 20 years is approximately 10 doublings (20/2), we can estimate the number of transistors in 1992 to be [tex]4,000 * 2^{10} = 4,096,000.[/tex]

Prediction = 4,096,000

Part b: Based on the chart, the number of transistors per IC in 2016 appears to be around 10 billion [tex](1 * 10^{10})[/tex]

Using Moore's Law, we can estimate the number of transistors per IC in 2040 to be [tex]1 * 10^{10} * 2^{24/18} = 25.6 * 10^{12} (or 25.6 trillion)[/tex].

Prediction = 25.6 trillion

Part c: The prediction in Part b may not be entirely believable, as there are physical limits to the number of transistors that can be placed on a single chip. Moore's Law has been slowing down in recent years, with transistor density growth rates dropping below historic trends. Additionally, new technologies beyond traditional silicon-based chips may become necessary to continue improving transistor density at the same pace as in the past. Therefore, while the prediction is technically possible, it may not be achievable without significant breakthroughs in semiconductor technology.


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Answer: c

Step-by-step explanation: i dont have one

1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .

An expression, as used in computer programming, is a grouping of values, variables, operators, and/or function calls that the computer evaluates to produce a final value. For instance, the equation 2 + 3 combines the numbers 2 and 3 using the + operator to produce the number 5. Similar to this, the equation x * (y + z) produces a value based on the current values of the variables x, y, and z by combining the variables x, y, and z with the * and + operators.

given

In terms of numbers, the phrase "one-half the difference of 6 and 8 hundredths and 2" is expressed as follows:

1/2 x (6.08 - 2) (6.08 - 2)

1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .

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When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is used to determine how likely or unlikely an occurrence is to occur. An event's likelihood is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of occurrence. The symbol P stands for the probability of an occurrence A. (A). It is determined by dividing the number of positive results of event A by all the potential outcomes.

given

(a) The result of rolling 3 or 6 times is 6 + 9 = 15.

Experimental chance = (Total number of rolls) / (Number of times 3 or 6 were rolled) = 15/40 = 0.375

(b) The theoretical likelihood of rolling either a 3 or a 6 on a fair number cube is equal to the total of those odds, which is 1/6 + 1/6 = 1/3 = 0.333. (rounded to three decimal places).

(c) When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

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(a) Experimental probability (5 or 8) = 0.193

(b) Theoretical probability (5 or 8) = 0.200

(c) As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.

(a) From these results, the experimental probability of getting a 5 or 8 will be:

Experimental probability (5 or 8) = P(5) + P(8)

Experimental probability (5 or 8) = (15/150) + (14/150)

Experimental probability (5 or 8) = 29/150

Experimental probability (5 or 8) = 0.193

(b) The theoretical probability of getting a 5 or 8 will be:

0,1, 2, 3, 4, 5, 6, 7, 8, 9

Theoretical probability (5 or 8) = P(5) + P(8)

Theoretical probability (5 or 8) = (1/10) + (1/10)

Theoretical probability (5 or 8) = 2/10

Theoretical probability (5 or 8) = 0.200

(c) As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

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Answer:

The solution x = 5 represents each friend's share of the food bill and tip.

RATE 5 stars and mark brainliest

In linear equation, 24 is the original number of the man​ .

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                    Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Original job = x men * 40 days = 40x man days  to complete

 now add 8 men     =    x+8  men

                                          man days now is   (x+8) (30)  to complete job

so     40x = (x+8)(30)

       40x = 30x + 240

         10 x = 240

             x = 24 men originally.

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the terminal point of the angle determined by sin(0) < 0 and cos(0) > 0 is in the fourth quadrant.

why it is and what is trigonometry?

If sin(0) < 0 and cos(0) > 0, then we know that the angle 0 is in the fourth quadrant of the unit circle.

In the unit circle, the x-coordinate represents cos(θ) and the y-coordinate represents sin(θ). Since cos(0) > 0, we know that the terminal point of the angle is to the right of the origin. And since sin(0) < 0, we know that the terminal point is below the x-axis.

The fourth quadrant is the only quadrant where the x-coordinate is positive and the y-coordinate is negative, so that is the quadrant where the terminal point of the angle lies.

Therefore, the terminal point of the angle determined by sin(0) < 0 and cos(0) > 0 is in the fourth quadrant.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of the functions of angles and their applications to triangles, including the measurement of angles, the calculation of lengths and areas of triangles, and the analysis of periodic phenomena.

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Correct option is A - Ellipse with center at (-5,4) ; B - Ellipse with center at (4,-5) ; C - Hyperbola with center at (4,-5) ; D - Hyperbola with center at (-5,4).

What is conic section ?

Conic sections are curves that are formed by the intersection of a plane and a double cone. The conic sections include circles, ellipses, parabolas, and hyperbolas. Each of these curves has a unique set of characteristics that can be described by mathematical equations.

Explanation of the correct matching :

A - The equation represents an ellipse with center at (-5,4). The values 100 and 225 in the equation represent the squared lengths of the major and minor axes, respectively. The center of the ellipse is (h,k), which is (-5,4) in this case.

B - The equation represents an ellipse with center at (4,-5). The values 16 and 9 in the equation represent the squared lengths of the major and minor axes, respectively. The center of the ellipse is (h,k), which is (4,-5) in this case.

C - The equation represents a hyperbola with center at (4,-5). The values 64 and 81 in the equation represent the squared distances between the center and the vertices on the y-axis and x-axis, respectively. The center of the hyperbola is (h,k), which is (4,-5) in this case.

D - The equation represents a hyperbola with center at (-5,4). The values 16 and 9 in the equation represent the squared distances between the center and the vertices on the x-axis and y-axis, respectively. The center of the hyperbola is (h,k), which is (-5,4) in this case.

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Answer:

C A D B

Step-by-step explanation:

on edge

Answer:

Step-by-step explanation:

Combine like terms: [tex]8x^{2} -5x-8x+3x^3+3[/tex]  =  [tex]3x^3+8x^2-13x+3[/tex]

[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]

Set of sophomores taking discrete math = A ∩ B. Set of sophomores not taking discrete math = A - B or A ∩ B^c. Set of students who are sophomores or in discrete math = A ∪ B. Set of students who are not sophomores or not in discrete math = (A ∩ B)^c or A ∪ B^c.

The set of sophomores taking discrete math at your school is the intersection of the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A ∩ B.

The set of sophomores at your school who are not taking discrete math is the difference between the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A - B or A ∩ B^c, where B^c is the complement of B (i.e., the set of students who are not in discrete math).

The set of students at your school who either are sophomores or are taking discrete math is the union of the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A ∪ B.

The set of students at your school who either are not sophomores or are not taking discrete math is the complement of the intersection of the set of sophomores A and the set of students in discrete math B.

This can be expressed as (A ∩ B)^c or as A ∪ B^c, where B^c is the complement of B (i.e., the set of students who are not in discrete math). Note that this set includes all students who are either juniors, seniors, or not enrolled in discrete math.

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We can say with 90% confidence that the true proportion of voters who cast their ballot for the candidate lies between 0.564 and 0.636. We can calculate it in the following manner.

To calculate the 90% confidence interval for the proportion of voters who cast their ballot for the candidate, we need to use the following formula:

CI = p ± z√(p(1-p)/n)

where:

CI is the confidence interval

p is the sample proportion

z is the z-score corresponding to the desired confidence level (90% in this case)

n is the sample size

Assuming we have a sample of size n and a sample proportion of p who voted for the candidate, we need to find the value of z for the 90% confidence level. The z-score can be found using a z-table or a calculator, and for a 90% confidence level, the z-score is 1.645.

Substituting the values into the formula, we get:

CI = p ± 1.645√(p(1-p)/n)

For example, if the sample size is 1000 and the sample proportion is 0.6 (60% of voters voted for the candidate), then the 90% confidence interval would be:

CI = 0.6 ± 1.645√(0.6(1-0.6)/1000) = (0.564, 0.636)

Therefore, we can say with 90% confidence that the true proportion of voters who cast their ballot for the candidate lies between 0.564 and 0.636.

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Full question here:

Calculate the 90% confidence interval for the proportion of voters who cast their ballot for the candidate. Number of votes: 125

Voter Response Dummy Variable

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Answer:

D I believe

Step-by-step explanation:

Answer:

smallest no-- 9829, 9289.

greatest no. 9982,9929.

Answer:

Step-by-step explanation:

use the formula of gradient:

                                        slope=change in y/ change in x

                                             =    [tex]\frac{Y2-Y1}{X2-X1}[/tex]

                                             = [tex]\frac{-6-2}{-9--9}[/tex]

                                             =[tex]\frac{-8}{0}[/tex]

      the answer is definite because we cannot divide by 0.

the intensity pattern visible on a screen at 1.168 metres behind the slit.

That is the answer to the question "650 nm light shines on two slits that are separated by 0.20 mm. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).

How far away from you is the screen?"

It is possible to specify that the distance to the screen is d=1.168m.

The answer to the question is that 650 nm light illuminates two slits that are 0.20 mm apart. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).

How far is the screen from you?

The equation for the distance is typically presented mathematically as

d=1.168m

As a result,

d=1.168m is the distance to the screen.

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Answer:

375

Step-by-step explanation:

Based on the given conditions, formulate: 53 +2x = 803

Rearrange variables to the left side of the equation:

2x = 803 - 53

Calculate the sum or difference:

2x = 750

Divide both sides of the equation by the coefficient of variable:

x = 750/2

Cross out the common factor: x = 375

Answer:

a

Step-by-step explanation:

889-0494444)()54837

Since the p-value (0.0803) exceeds the significance threshold (0.05), the null hypothesis cannot be ruled out.

The mean in mathematics is a measurement of a collection of numerical data's central tendency. It is determined by adding up all of the values in the set and dividing the result by the total number of values. This value is frequently referred to as the average value. The mean (or mathematical mean) is calculated as follows: (Sum of Values) / Mean (number of values)

given

The null hypothesis states that the mean number of units generated during the day and night shifts is the same. The contrary hypothesis (Ha) states that more units are created on average on the night shift than on the day shift.

"day" + "night"

Bravo! Night precedes day.

b. The following method can be used to calculate the test statistic:

t = sqrt(1/n night + 1/n day) * sqrt(x night - x day)

where s p is the pooled standard deviation and x night and x day are the sample averages, n night and n day are the sample sizes, and s p is represented by:

Sqrt(((n night - 1)*s night2 + (n day - 1)*s day2) / (n night + n day - 2)) yields the value s p.

S p is equal to sqrt(((74 - 1)*35 + (68 - 1)*28) / (74 + 68 - 2)), which equals 31.88.

t = (358 - 352) / (31.88 * sqrt(1/74 + 1/68)) = 1.19

1.19 is the test result.

the p-value is 0.0803 as a result (rounded to 4 decimal places).

Since the p-value (0.0803) exceeds the significance threshold (0.05), the null hypothesis cannot be ruled out.

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The complete question is :- Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced by a sample of 68 day-shift workers was 352. The mean number of units produced by a sample of 74 night-shift workers was 358. Assume the population standard deviation of the number of units produced is 28 on the day shift and 35 on the night shift.

Using the 0.05 significance level, is the number of units produced on the night shift larger?

a. State the null and alternate hypotheses.

O : Day/Night: H:

Day Night

b. Compute the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

c. Compute the p-value. (Round your answer to 4 decimal places.) p-value

After completing your data analysis, the write-up should only include a discussion of the steps of the IMPACT model that really matter.

Data analysis is the methodical application of logical and/or statistical approaches to explain and demonstrate, summarise and assess, and assess data. Different analytical techniques "offer a mechanism of deriving inductive inferences from data and differentiating the signal (the phenomena of interest) from the noise (statistical fluctuations) inherent in the data," according to Shamoo and Resnik (2003).

The proper and accurate interpretation of study findings is a crucial part of preserving data integrity. Inadequate statistical analyses distort scientific results, confuse lay readers, and may have a detrimental impact on how the general public views research (Shepard, 2002). Integrity concerns apply equally to the study of non-statistical data.

Impact analysis examines required data to determine the advantages and disadvantages of any change. Even in a well evolved system, adjustments are inevitable as the world develops. Modifications might occur for a number of reasons, including modifications to company demands, changes in customer requirements, or the introduction of new technology.

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The mean of x is 1.25 and the variance of x is approximately 0.1458.

The continuous uniform distribution has a constant probability density function (PDF) between its minimum and maximum values. In this case, the minimum value is 1/2 and the maximum value is 2.

The mean of a continuous uniform distribution is the average of the minimum and maximum values:

mean = (minimum + maximum) / 2

    = (1/2 + 2) / 2

    = 1.25

The variance of a continuous uniform distribution is defined as:

[tex]variance = (maximum - minimum)^2 / 12[/tex]

        [tex]= (2 - 1/2)^2 / 12[/tex]

        = 7/48

        ≈ 0.1458

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The required value is 1.5(IQR) equals 6.

A dataset is a collection of facts that relates to a particular subject. The test results of each pupil in a particular class are an illustration of a dataset. Datasets can be expressed as a table, a collection of integers in a random sequence, or by enclosing them in curly brackets.

The IQR (interquartile range) is the difference between the third quartile (Q3) and the first quartile (Q1). So, we first need to calculate IQR:

IQR = Q3 - Q1 = 16 - 12 = 4

Now we can calculate 1.5 times the IQR:

1.5(IQR) = 1.5(4) = 6

Therefore, 1.5(IQR) equals 6.

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Complete question:

The five-number summary of a data set is given below.

Minimum: 3 Q1: 12 Median: 15 Q3: 16 Maximum: 20

Which of the following equals 1.5(IQR)?

Add the times together:

19/100 + 4/10

Find the common denominator, which is 100 so rewrite 4/10 as 40/100

Now add:

19/100 + 40/100 = 59/100

The first car beat the third car by 59/100 seconds.

Answers of angle degrees of p and q

q = 79

p = 101

Explanation

Each angle given has an adjacent angle creating a straight angle of 180 degrees.

First I found the missing adjacent angle degree - see attachment.

We know four of the five interior angle degrees are 85, 136, 138, 102.

Since we know the sum of angles in a pentagon = 540°, we can subtract the known angles from 540 to find “q”

540 - 85 - 136 - 138 - 102 = 79 angle q

To find “p” we know p and q create a straight angle of 180 degrees. We can subtract to find p.

180 - 79 = 101 angle p.

I attached a picture to help

By answering the presented question, we may conclude that so by SAS congruency property we have said that all these triangles are similar.

A triangle is a closed, a double geometric shape made up of three line segments known as sides that connect at three parameters known as vertices.

Triangles are differentiated by their angles and their sides. Triangles can be collinear (all sides equal), angles, or scalene dependent on their sides.

Triangles are classed as acute (all angles just under 90 degrees), right (one angle of approximately to 90 degrees), or ambiguous (all angles greater than 90 degrees).

The area of a triangle may be determined with the formula A = (1/2)bh, where A is the surface, b is really the right triangle base, and h is the triangle's height.

Here, from the figure, we have

Two sides of the triangle are equal.

And also each of the angles are also same.

Therefore, by SAS congruency property, we have say that all these triangles are similar.

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Answer:

The point on the graph that is closest to the point (8, 1.5) is:

[tex]\left(\sqrt[3]{4}, 2 \sqrt[3]{2}+1\right) \approx \left(1.587,3.520)[/tex]

Step-by-step explanation:

To find the point on the graph of y = x² + 1 that is closest to the point (8, 1.5), we need to find the point on the parabola that is at the shortest distance from (8, 1.5). We can use the distance formula to do this.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Any point (x, y) on the parabola y = x² + 1 can be defined as (x, x²+1).

Therefore:

Substitute these points into the distance formula to create an equation for the distance between any point on the parabola and (8, 1.5):

[tex]d = \sqrt{(x - 8)^2 + (x^2+1 - 1.5)^2}[/tex]

Simplifying this expression for d², we get:

[tex]d = \sqrt{(x - 8)^2 + (x^2-0.5)^2}[/tex]

[tex]d^2 = (x - 8)^2 + (x^2-0.5)^2[/tex]

[tex]d^2 = x^2-16x+64 + x^4-x^2+0.25[/tex]

[tex]d^2=x^4-16x+64.25[/tex]

To find the x-coordinate that will minimize this distance, take the derivative of the expression with respect to x, set it equal to zero and solve for x:

[tex]\implies 2d \dfrac{\text{d}d}{\text{d}{x}}=4x^3-16[/tex]

[tex]\implies \dfrac{\text{d}d}{\text{d}{x}}=\dfrac{4x^3-16}{2d}[/tex]

Set it equal to zero and solve for x:

[tex]\implies \dfrac{4x^3-16}{2d}=0[/tex]

[tex]\implies 4x^3-16=0[/tex]

[tex]\implies 4x^3=16[/tex]

[tex]\implies x^3=4[/tex]

[tex]\implies x=\sqrt[3]{4}[/tex]

Finally, to find the y-coordinate of the point on the graph that is closest to the point (8, 1.5), substitute the found value of x into the equation of the parabola:

[tex]\implies y=\left(\sqrt[3]{4}\right)^2+1[/tex]

[tex]\implies y=\sqrt[3]{4^2}+1[/tex]

[tex]\implies y=\sqrt[3]{16}+1[/tex]

[tex]\implies y=\sqrt[3]{2^3 \cdot 2}+1[/tex]

[tex]\implies y=\sqrt[3]{2^3} \sqrt[3]{2}+1[/tex]

[tex]\implies y=2 \sqrt[3]{2}+1[/tex]

Therefore, the point on the graph that is closest to the point (8, 1.5) is:

[tex]\left(\sqrt[3]{4}, 2 \sqrt[3]{2}+1\right) \approx \left(1.587,3.520)[/tex]

Additional information

To find the minimum distance between the point on the graph and (8, 1.5), substitute x = ∛4 into the distance equation:

[tex]\implies d = \sqrt{(\sqrt[3]{4} - 8)^2 + ((\sqrt[3]{4})^2-0.5)^2}[/tex]

[tex]\implies d = 6.72318283...[/tex]

Answer: C

Step-by-step explanation:

it can't be A because it has 3 groups of four negatives and two positives

it can't be B because when you distribute solution A, you get -12 + 6

it can't be D because there are 3 groups of four negatives and two positives, and if you look at it in a different way, the two positives cancel out the two negatives which leave you with 3 groups of -2

so the answer is c

This is not generally accurate. A polynomial function's degree can vary between one, three, or five more or less than the sum of its local peaks and minima.

Consider the formula f(x) = x3 - 3x as an illustration. Two local extrema exist for this function: a local maximum at x = -1 and a local minimum at x = 1. The polynomial's degree, however, is only 3, not one, three, or five more than the sum of the local peaks and minima.

Consider the formula g(x) = x5 - 5x3 + 4x as an alternative. Moreover there are two local extrema for this function: a local maximum at x = -1 and a local minimum at x = 1. The polynomial's degree, however, is 5, which is three more than the sum of its local peaks and minima.

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The sum of the eigenvalues of A is equal to the trace of A, and we have proved the desired result.

Let A be an n x n square matrix with eigenvalues λ1, λ2, ..., λn.

The trace of A is defined as the sum of the diagonal elements of A, i.e.,

tr(A) = a11 + a22 + ... + ann

where aij is the element of A in the ith row and jth column.

Now, consider the characteristic equation of A, which is given by

det(A - λI) = 0

where I is the n x n identity matrix.

Expanding the determinant, we get

(-1)^n λ^n + (-1)^(n-1) tr(A) λ^(n-1) + ... + det(A) = 0

By Vieta's formulas, the sum of the roots of this polynomial equation is equal to the negative of the coefficient of the (n-1)th power of λ divided by the coefficient of the nth power of λ.

Thus, the sum of the eigenvalues of A is given by

λ1 + λ2 + ... + λn = -(-1)^(n-1) tr(A)/(-1)^n

= tr(A)

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The cumulative distribution function (CDF) for given random variable fx(x)  is given by F(x) = 1 - e^[(-a²)(x²/2)]        x > 0,

                           F(x) = 0                                x ≤ 0.

The cumulative distribution function (CDF) F(x) for a Rayleigh random variable X is defined as,

F(x) = P(X ≤ x)

To find the CDF of X, we integrate the PDF of X over the interval [0, x],

F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx

Using the substitution u = (-a²x²/2),

Simplify the integral as follows,

F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx

= ∫₀^((-a²x²)/2) -e^u du (where u = (-a²x²/2) and x = √(2u/a²))

= [e^u]₀^((-a²x²)/2)

= 1 - e^[(-a²)(x²/2)]

Therefore, the CDF of X  for the Rayleigh random variable X has PDF fx (x)   is equal to,

F(x) = 1 - e^[(-a²)(x²/2)]        x > 0,

F(x) = 0                                x ≤ 0.

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The above question is incomplete, the complete question is:

For a constant parameter a > 0, a Rayleigh random variable X has PDF

fx (x)        =    a²xe^[(-a²)(x²/2)]      x > 0

                     0                              otherwise.

What is the CDF of X?