Current Attempt in Progress In a poll, men and women were asked, "When someone yelled or snapped at you at work, how did you want to respond?" Twenty percent of the women in the survey said that they felt like crying (Time, April 4, 2011). Suppose that this result is true for the current population of women employees. A random sample of 23 women employees is selected. Use the binomial probabilities table or technology to find the probability that the number of women employees in this sample of 23 who will hold the above opinion in response to the said question is a. at least 5 Round your answer to four decimal places. P(at least 5) = i b. 7 to 9 Round your answer to four decimal places. P(at least 5) = i

The null hypothesis is that the proportion of people who would still vote for the government of Preon is still 67%, while the alternative hypothesis is that the proportion has changed from 67%.

The null hypothesis (H0) is that the proportion of people who would still vote for the government of Preon is still 67%, as it was at the last election.

The alternative hypothesis (H1) is that the proportion of people who would still vote for the government of Preon has changed from 67%, either increased or decreased.

In symbols, this can be written as:

H0: p = 0.67

H1: p ≠ 0.67

Where p is the proportion of people who would vote for the government of Preon in the upcoming election.

Note that the alternative hypothesis is two-tailed, indicating that the proportion could have either increased or decreased from 67%.

This is because the government suspects that their approval rating may have changed in either direction.

For similar question on hypothesis.

https://brainly.com/question/25263462

#SPJ11

Answer:

8.5 ounces.

Step-by-step explanation:

The volume of the conical cup is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Since the diameter of the cup is 3 inches, the radius is 1.5 inches. Thus, the volume of the conical cup is:

V = (1/3)π(1.5²)(3) = 7.07 cubic inches

The volume of the cylindrical cup is given by the formula V = πr²h. Since the radius is 1.5 inches and the height is 3 inches, the volume of the cylindrical cup is:

V = π(1.5²)(3) = 21.2 cubic inches

To find the weight of the water in each cup, we need to multiply the volume of each cup by the weight of 1 cubic inch of water:

Weight of water in conical cup = 7.07 × 0.6 = 4.24 ounces

Weight of water in cylindrical cup = 21.2 × 0.6 = 12.72 ounces

Therefore, the water in the cylindrical cup weighs 12.72 - 4.24 = 8.48 more ounces than the water in the conical cup. Rounded to the nearest tenth, this is 8.5 ounces.

The function graphed below is is described as.

D. not continuous, 2 holes

When we speak of "holes" in the realm of continuous functions, it implies a spot wherein said function is not defined yet can become continuous once it has been allotted an appropriate value.

Examining the graph shows the presence of two holes hence making option D the best choice

The holes ate located at points

Learn more about continuous functions at

https://brainly.com/question/20059354

#SPJ1

Answer:population: 39 million; parameter: 56%; sample: 98,422; statistic: 78%

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

4x + 13 = 9

4x + 13 - 13 = 9 -13

4x = -4

-4/4 = -1

X = -1

Answer:

-1.

Step-by-step explanation:

4x + 13 = 9

4x =  9 -13

4x = -4

x = -4/4

X = -1

The index form is simplified to give 3m/2n

It is important to note that the index forms are models that are used for the representation of variables or numbers that too small or large in more convenient forms.

Some of the rules of index forms are;

From the information given, we have that;

3m³/ n -²• 2m -² n³

Add the like exponents of the denominator

3m³/2m² n³⁻²

add the values

3m³/2m⁻²n¹

Now, subtract the exponents

3/2 n⁻¹ m¹

Then, we have;

3m/2n

Learn about index forms at: https://brainly.com/question/15361818

#SPJ1

9 5/2 in radical form is equal to 4√2 + √7.

We are able to rewrite 9 5/2 in radical form through first changing it to an improper fraction.

9 5/2 = (9 x 2 + 5) / 2 = 23/2

Now, we can express 23/2 as a mixed radical by using locating the largest perfect square that may be a aspect of 23. the largest perfect square which is much less than 23 is 16 (that's 4^2).

So, we are able to write:

23/2 = 16/2 + 7/2 = 8 + 7/2

Now, we will express 8 + 7/2 in radical form as:

8 + 7/2 = 4 x 2 + 7/2 = 4√2 + √7

Consequently, 9 5/2 in radical form is equal to 4√2 + √7.

Learn more about radical form:-

https://brainly.com/question/30347671

#SPJ4

The total sample size, because each pair of data provides one less degree of freedom than the number of individuals in the pair.

The formula used to calculate the degrees of freedom for a test for dependent groups is:

df = n - 1

where n is the number of pairs of data in the sample.

In a dependent groups (or paired samples) test, the same group of individuals is measured twice, or two groups of individuals are matched in pairs. The difference between the two measurements or the two pairs of measurements is the data used in the test.

The degrees of freedom is a measure of the amount of information available to estimate a population parameter, such as the mean difference between the paired observations in the case of a dependent groups test. In general, a higher degrees of freedom value means more information and thus more precision in the estimate.

In the case of a dependent groups test, the degrees of freedom is determined by the number of pairs of data in the sample, rather than the total sample size, because each pair of data provides one less degree of freedom than the number of individuals in the pair.

To learn more about individuals visit:

https://brainly.com/question/19537863

#SPJ11

Answer:

50.6°

Step-by-step explanation:

complementary angles sum to 90° , that is

complementary angle + 39.4° = 90° ( subtract 39.4° from both sides )

complementary angle = 90° - 39.4° = 50.6°

The value of x is 19.44

Similar triangles are triangles that have the same shape, but their sizes may vary.

For two triangles to be similar, the corresponding angles must be congruent and also, the ratio of the corresponding sides of similar triangles are equal,

therefore,

27/9x-13 = 15/90

27 × 90 = 15(9x-13)

2430 = 135x - 195

collecting like terms

2430+195 = 135x

2625 = 135x

divide both sides by 135

x = 2625/135

x = 19.44

therefore the value of x is 19.44

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

Since there is no way to list all the infinite sequences of 0s and 1s, we have proved that S is uncountable.

To show that S is uncountable, we need to show that there is no one-to-one correspondence between the set of infinite sequences of 0s and 1s and the set of natural numbers (which are used to count elements in a set).
We can use the diagonal argument, which is similar to the one used to show that the real numbers are uncountable.
Assume that S is countable, meaning that there is a way to list all the infinite sequences of 0s and 1s as a sequence: s1, s2, s3, ...
We can construct a new sequence t by choosing the opposite of each digit on the diagonal of the previous sequences: if the diagonal digit of s1 is 0, then the first digit of t is 1, and vice versa. Similarly, if the diagonal digit of s2 is 1, then the second digit of t is 0, and vice versa. And so on for all the diagonal digits.
The sequence t is guaranteed to be different from all the sequences in the original list, because it differs from each sequence at least at one position (the diagonal position). Therefore, t cannot be in the original list, which means that the original list did not include all the infinite sequences of 0s and 1s.
Since we have shown that there is no way to list all the infinite sequences of 0s and 1s, we have proved that S is uncountable.

Learn more about infinite sequence here, https://brainly.com/question/16542679

#SPJ11

The probability that Chris will choose a pair of white socks is 0.75 or 75%.

Chris has a total of 2 + 4 + 18 = 24 pairs of socks in his drawer. Out of these, 18 pairs are white.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is concerned with measuring the likelihood or chance of an event occurring.

In probability theory, an event is any outcome or set of outcomes of a random experiment. The probability of an event is a number between 0 and 1 that represents the likelihood of that event occurring. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain.

If Chris reaches in his drawer without looking and selects a pair of socks at random, the probability of choosing a pair of white socks is:

(number of pairs of white socks) / (total number of pairs of socks)

= 18 / 24

= 3/4

= 0.75

Therefore, the probability that Chris will choose a pair of white socks is 0.75 or 75%.

To know more about probability here

https://brainly.com/question/13604758

#SPJ4

The matrix A with eigenvalues λ1 = 4, λ2 = 1, and corresponding eigenvectors v1 = (2, 1)t, v2 = (1,0)t is:

A = [v1 v2] = [2 1; 1 0]

Yes, it is possible to write a matrix A such that its eigenvalues and corresponding eigenvectors are λ1 = 4, λ2 = 1, and v1 = (2, 1)t, v2 = (1,0)t.

Let A be the matrix with columns given by the eigenvectors of A:

A = [v1 v2] = [2 1; 1 0]

Then, we can calculate the eigenvalues of A by finding the roots of its characteristic polynomial:

|A - λI| = |2-λ 1; 1 0-λ| = (2-λ)(-λ) - 1 = λ^2 - 2λ - 1

Solving for λ, we get:

λ1 = 4, λ2 = 1

which are the desired eigenvalues.

Next, we can find the corresponding eigenvectors by solving the equations (A - λI)x = 0 for each eigenvalue:

For λ1 = 4:

(A - λ1I)x = ([2 1; 1 0] - [4 0; 0 4])x = [-2 1; 1 -4]x = 0

Solving the system of equations, we get x1 = -1 and x2 = -1/2, so the eigenvector corresponding to λ1 is:

v1 = [-1; -1/2]

For λ2 = 1:

(A - λ2I)x = ([2 1; 1 0] - [1 0; 0 1])x = [1 1; 1 -1]x = 0

Solving the system of equations, we get x1 = 1 and x2 = -1, so the eigenvector corresponding to λ2 is:

v2 = [1; -1]

Therefore, the matrix A with eigenvalues λ1 = 4, λ2 = 1, and corresponding eigenvectors v1 = (2, 1)t, v2 = (1,0)t is:

A = [v1 v2] = [2 1; 1 0]

To learn more about  eigenvectors  visit: https://brainly.com/question/31013028

#SPJ11

According to the figure, the arc lengths are

The missing sides in the figure are sought knowing that central angles are equal to length of arcs. Hence we have that

arc CE = 180 degrees - arc CA

arc CE = 180 degrees - 50 degrees

arc CE = 130 degrees

arc DE = arc CA (vertical angles)

arc DE = 50 degrees

arc FAE = 360 degrees - 90 degrees

arc FAE = 270 degrees

Learn more about central angles at

https://brainly.com/question/10945528

#SPJ1

The translations of the functions are as follows

Reflection

Shift Right

Shift Up

Vertical Stretch: the coefficient of  the factor x when it is greater than one results to vertical stretch

Shift Left: this is translation of 3 units left

Vertical Shrink: the coefficient of  the factor x when it is less than one results to vertical shrink

Shift Left: this is translation of 2 units left

Vertical Stretch: the coefficient of  the factor x when it is greater than one results to vertical stretch. in this case 3/2 = 1.5 which is greater than one.

Shift Left: this is translation of 5 units left

Learn more about translation at

https://brainly.com/question/1574635

#SPJ1

The length of the two diagonals of a rhombus if one is twice as long as the other are 10 and 20.

Given that the length of two diagonals of the rhombus are 10 and 20.

Let d1 and d2 be the lengths of the diagonals of the rhombus. Since the area of the rhombus is 100, we have:

d1 * d2 / 2 = 100

We are also given that one diagonal is twice as long as the other, so:

d1 = 2d2

Substituting d1 = 2d2 into the first equation, we get:

2d2 * d2 / 2 = 100

d2^2 = 100

d2 = 10 or -10 (we ignore the negative solution)

Since d1 = 2d2, we have d1 = 20.

Therefore, the length of the two diagonals of the rhombus are 10 and 20.

Know more about rhombus here:

https://brainly.com/question/88523

#SPJ11

If by the baking of 81 muffins, the baker has completed 37.5% of the order. The customer placed an order for 216 muffins.

Percent refers to the ratio of numbers where the denominator is 100. The percentage of a given number is calculated as the percentage divided by 100 and multiply the given number.

Percentage of baked muffins = 37.5%

Number of the baked muffin = 81

Let the number of muffins ordered be x

37.5% of x = 81

37.5/100 * x = 81

0.375x = 81

x = 81/0.375

x = 216

Thus, 216 muffins were ordered by the customer.

Learn more about Percentage:

https://brainly.com/question/24339661

#SPJ4

Demand refers to the quantity of a product or service that buyers are willing and able to purchase at a certain price level. A demand curve is a graphical representation of the relationship between the quantity of a good or service that buyers are willing to purchase at different price levels.

In the market for VCRs, the demand and supply equations are Qd = 1,000 - 6P and Qs = 4P respectively. The government decides to impose a tax of $30 per unit sold on VCRs. This will lead to a shift in the supply curve upwards by $30, resulting in a new equilibrium point.

1. To find the new equilibrium quantity with the tax, we set Qd = Qs + tax. Thus, 1,000 - 6P = 4P + 30. Solving for P, we get P = $105. The equilibrium quantity is therefore Q = 1,000 - 6($105) = 370.

2. The price paid by buyers is the same as the equilibrium price, which is $105.

3. The price paid by sellers is the equilibrium price minus the tax, which is $75.

4. The diagram below illustrates the impact of the tax on the market for VCRs. The original equilibrium point is E0, with a price of $70 and a quantity of 400. With the tax, the new equilibrium point is E1, with a higher price of $105 and a lower quantity of 370. The tax creates a vertical distance between the two equilibrium points, which represents the tax revenue collected by the government.

[Insert Diagram Here]

5. The deadweight loss due to the tax is the reduction in total surplus (consumer surplus + producer surplus) that results from the tax. Using the original equilibrium as a benchmark, the total surplus is (1/2)($70)(400) = $14,000. With the tax, the total surplus is (1/2)($75)(340) = $6,375. Thus, the deadweight loss is $7,625.

6. To calculate the consumer surplus due to the tax, we need to compare the original consumer surplus with the new consumer surplus. Using the original equilibrium as a benchmark, the consumer surplus is (1/2)($70)(400 - 70) = $5,950. With the tax, the consumer surplus is (1/2)($105)(370 - 105) = $12,145. Thus, the consumer surplus due to the tax is $6,195.

More on demand curve : https://brainly.com/question/1139186

#SPJ11

If the arrow lands on yellow you win $75, blue gives $25, green gives $10, and red gives $1. The expected value of the game is $27.75, written as a decimal rounded to two places.

To find the expected value of the game, we need to multiply the value of each piece by the probability of landing on that piece, and then add up all the products.

First, let's determine the probability of landing on each colored piece of the wheel. Since each piece is equally likely, we can find the probability by dividing 1 by the number of pieces.
There are 4 colors on the wheel (yellow, blue, green, and red), so the probability of landing on any color is 1/4 or 0.25.
Now, let's calculate the expected value of the game:

Expected Value = (Probability of Yellow) × (Value of Yellow) + (Probability of Blue) × (Value of Blue) + (Probability of Green) × (Value of Green) + (Probability of Red) × (Value of Red)

The probability of landing on yellow is 1/4, so the value of yellow is $75.

The probability of landing on blue is also 1/4, so the value of blue is $25.

The probability of landing on the green is 1/4, so the value of green is $10.

The probability of landing on red is also 1/4, so the value of red is $1.

Now we can calculate the expected value:

Expected value = (1/4) x $75 + (1/4) x $25 + (1/4) x $10 + (1/4) x $1
Expected value = $18.75 + $6.25 + $2.50 + $0.25
Expected value = $27.75

So the expected value of the game is $27.75. Written as a decimal rounded to two places, the answer is $27.75.

Learn more about expected value:

brainly.com/question/29093746

#SPJ11

Answer:1/2

Step-by-step explanation:

If they both ate 2/8 of the pie, that means they ate 4/8 of the pie in total, which means that they ate 1/2 when simplified. If they ate one half of the pie, it also means there is 1/2 of the pie left.

The smaller number is 13

Let x and y represent the unknown number

x + y= 47........equation 1

x - y= 21.........equation 2

From equation 1

x + y= 47

x= 47-y

Substitute 47-y for x in equation 2

(47-y)-y= 21

47-y-y= 21

47-2y= 21

-2y= 21-47

-2y= -26

y= 26/2

y= 13

Substitute 13 for y in equation 1

x + y= 47

x + 13= 47

x= 47-13

x= 34

Hence the smaller number is 13

Read more on number here

https://brainly.com/question/15410025

#SPJ1

The number of people expected to go to the Youth Wing, would be 255 people.

Find the total amount of people who will be visiting on Saturday:

= 382 ( Youth Wing ) + 461 ( Social Issues ) + 355 ( Fiction and Literature )

= 1, 198

Then the proportion of those who went to Youth Wing :

= 382 / 1, 198

= 0. 319

The estimated people going for Youth Wing on Sunday :

= 0. 319 x 800

= 255 people

In conclusion, an estimated 255 people would be going to Youth Wing.

Find out more on people at https://brainly.com/question/23477098

#SPJ1

The required, equation to determine the number of people is T + (T + 5,500) + 2T + (2T + 300) = 36,700 and there were 10,300 people at the fair on Saturday.

Let's call the number of people who attended the fair on Thursday "T". Then we can use the information in the problem to set up an equation:

Friday's attendance = T + 5,500

Saturday's attendance = 2T

Sunday's attendance = 2T + 300

Total attendance = T + (T + 5,500) + 2T + (2T + 300) = 36,700

Simplifying the equation, we get:

6T + 5,800 = 36,700

6T = 30,900

T = 5,150

Therefore, the attendance on Thursday was 5,150 people. We can use this information to find the attendance on Saturday:

Saturday's attendance = 2T = 2(5,150) = 10,300

Thus, there were 10,300 people at the fair on Saturday.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

The mean of all six sample means is equal to the population mean (18,750), the sample mean is an unbiased estimator of the population mean.

First, let's calculate the mean for each of the given samples:

1. R, B: (15,000 + 18,000) / 2 = 16,500 (already given)

2. R, G: (15,000 + 22,000) / 2 = 18,500 (already given)

3. R, W: (15,000 + 20,000) / 2 = 17,500 (already given)

4. B, G: (18,000 + 22,000) / 2 = 20,000 (already given)

5. B, W: (18,000 + 20,000) / 2 = 19,000 (already given)

6. G, W: (22,000 + 20,000) / 2 = 21,000 (already given)

Now, let's calculate the mean of all six sample means:

(16,500 + 18,500 + 17,500 + 20,000 + 19,000 + 21,000) / 6 = 112,500 / 6 = 18,750

The mean of all six sample means is 18,750.

Next, let's calculate the population mean:

(15,000 + 18,000 + 22,000 + 20,000) / 4 = 75,000 / 4 = 18,750

The population mean is 18,750.

Since the mean of all six sample means is equal to the population mean (18,750), the sample mean is an unbiased estimator of the population mean.

To learn more on mean click:

brainly.com/question/8192279

#SPJ1

The PDF of T1 is:

f(T1) = d/dt [P(T1 ≤ t)] = d/dt [1 - P(T1 > t)] = d/dt [1 - P(N(t) = 0)] = d/dt [1 - e^(-Lt)] = L * e^(-Lt)

So the PDF of T1 is an exponential distribution with parameter L.

To find the PDF of T1, we need to find the probability that the first event occurs at time t given that it has not occurred before time t. That is, we need to find P(T1 = t | N(t) = 0).

Using Bayes' rule, we have:

P(T1 = t | N(t) = 0) = P(N(t) = 0 | T1 = t) * P(T1 = t) / P(N(t) = 0)

Since T1 is the arrival time of the first event, we know that there are no events in the interval [0, t), so we can write:

P(N(t) = 0 | T1 = t) = P(N(t - T1) = 0)

Since {N(t) : t ≥ 0} is a conditional Poisson process with rate L that is distributed as Exp(λ), we know that the number of events in any interval of length t has a Poisson distribution with mean L*t. Therefore, the probability that there are no events in an interval of length t is:

P(N(t) = 0) = e^(-L*t)

So we can write:

P(T1 = t | N(t) = 0) = P(N(t - T1) = 0) * P(T1 = t) / e^(-L*t)

The probability density function (PDF) of the exponential distribution with parameter λ is given by:

f(x) = λ * e^(-λ*x)

Therefore, the PDF of T1 is:

f(T1) = d/dt [P(T1 ≤ t)] = d/dt [1 - P(T1 > t)] = d/dt [1 - P(N(t) = 0)] = d/dt [1 - e^(-Lt)] = L * e^(-Lt)

So the PDF of T1 is an exponential distribution with parameter L.

To learn more about distribution visit:

https://brainly.com/question/28060657

#SPJ11

In this scenario, there are two workers in a team, and each worker can either work hard or shirk. The probability of the overall project succeeding is dependent on the efforts of each worker. If both workers shirk, the probability of success is p0. If one worker shirks and the other works hard, the probability of success is p1. Finally, if both workers work hard, the probability of success is p2, where p2>p1>p0.

The cost of effort is c, and the principal cannot observe the individual efforts of each worker, but only the success or failure of the whole project. The challenge is to design an optimal contract that encourages both workers to exert effort all the time.

The optimal contract would offer a payment scheme to both workers that would incentivize them to work hard. If the workers work hard and the project succeeds, they receive a reward. If the workers shirk, they receive no reward.

The workers' efforts in this scenario are substitutes for each other. This is because if one worker shirks, the probability of success decreases, and the other worker would have to work harder to compensate for the first worker's lack of effort. Therefore, both workers must work hard to maximize the probability of success.

In conclusion, an optimal contract must be designed that encourages both workers to work hard and rewards them for the successful completion of the project. Additionally, the efforts of both workers in this scenario are substitutes for each other.

more on probability: https://brainly.com/question/13604758

#SPJ11

Answer: 17/25 miles per hour

Step-by-step explanation:

In order to find your answer, you will need to divide 3 and 2/5 by 5 hours

or (3.4/5) which equals 0.68.

As a fraction, 0.68 is 17/25 which is your answer :)

And if you want to check your work, simply multiply 0.68 x 5 and you get 3.4 (which is 3 and 2/5's)!

Good Luck!

The drive-thru that typically has more wait time, and why is C. Super Fast Food, because it has a larger median

According on the information supplied, Super Fast Food normally has a greater wait time. Although the Burger Quick box is larger, indicating a greater range of wait times, the median (15.5) is still lower than the Super Fast Food (12).

Furthermore, the Burger Quick line ends at 30, indicating that there are some extreme outliers with extremely long wait times, which could raise the mean wait time. As a result, the correct answer is Super Fast Food, which has a higher median.

Learn more about median on

https://brainly.com/question/26177250

#SPJ1

That we are 95% confident that the true population mean falls between 4.68 and 5.96. Based on this interval, it is likely that the true population mean is greater than 4.

a. The null hypothesis is that the average score on the Attributional Complexity scale is equal to or less than 4. The alternative hypothesis is that the average score is greater than 4. Symbolically:

H0: µ ≤ 4

Ha: µ > 4

b. We need to conduct a one-sample t-test, since we are comparing a sample mean to a known population mean (4). We will use a significance level of α = 0.05.

c. Using the information given, we can calculate the t-value as:

t = (x - µ) / (s / √n) = (5.32 - 4) / (0.54 / √10) = 5.04

where x is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size. The degrees of freedom (df) is n - 1 = 9.

At a significance level of α = 0.05 and with 9 degrees of freedom, the critical t-value is 1.833 (obtained from a t-table or calculator). Since our calculated t-value (5.04) is greater than the critical t-value (1.833), we can reject the null hypothesis.

Based on these sample data, we can say that there is evidence to suggest that the average score on the Attributional Complexity scale is greater than 4.

The p-value associated with the sample mean is less than 0.001. This means that there is less than a 0.1% chance of obtaining a sample mean of 5.32 (or higher) if the null hypothesis is true.

If the null hypothesis is true, we would expect the sample mean to be around 4. Therefore, the large difference between the sample mean (5.32) and the null hypothesis value (4) suggests that the null hypothesis is not true.

d. The 95% confidence interval can be calculated as:

CI =x ± t*(s / √n) = 5.32 ± 2.306*(0.54 / √10) = (4.68, 5.96)

This means that we are 95% confident that the true population mean falls between 4.68 and 5.96. Based on this interval, it is likely that the true population mean is greater than 4.

To learn more about  population visit:

https://brainly.com/question/24786731

#SPJ11

Every natural number n > 2 is a product of prime numbers.

To prove that every natural number n > 2 is a product of prime numbers, we will use the principle of complete induction (CVI).

First, let's establish the base case. For n = 3, we know that 3 is a prime number, and therefore it is a product of prime numbers. This satisfies the base case.

Now, let's assume that for some natural number k > 2, every natural number between 3 and k (inclusive) is a product of prime numbers. We want to prove that this implies that the next natural number, k+1, is also a product of prime numbers.

There are two possibilities for k+1: either it is a prime number itself, or it is composite (i.e. not prime). Let's consider each case separately.

Case 1: k+1 is a prime number.
If k+1 is a prime number, then it is obviously a product of prime numbers (since it is itself prime). Therefore, our assumption that every natural number between 3 and k is a product of prime numbers implies that k+1 is also a product of prime numbers.

Case 2: k+1 is composite.
If k+1 is composite, then it can be written as the product of two natural numbers a and b, where a and b are both greater than 1. Since a and b are both less than k+1, we know that they are both products of prime numbers (by our assumption). Therefore, k+1 can be written as the product of prime numbers (namely, the prime factors of a and b).

Since we have established the base case and shown that our assumption implies the next natural number is a product of prime numbers, we can conclude by CVI that every natural number n > 2 is a product of prime numbers.

To learn more about prime numbers

https://brainly.com/question/16733393

#SPJ11