6. Approximately 75% of persons age 70 to 84 live in their own household and are income-qualified for home purchases. If three persons are randomly selected from this population, the probability that exactly two of the three lives in their own household and are income-qualified is: Question 5 options: a) 0.975 b) 0.8916 c) 0.4218 d) 0.5404 e) 0.141 Next Page

The required sample size to estimate the mean IQ score of statistics students with 99% confidence and a margin of error of 2 IQ points is 64.

The formula for the sample size is:

n = (z^2 * σ^2) / E^2

where:

* n is the sample size

* z is the z-score for the desired confidence level (in this case, 2.576)

* σ is the population standard deviation (9)

* E is the margin of error (2)

Plugging these values into the formula, we get:

n = (2.576^2 * 9^2) / 2^2 = 64

Therefore, a sample size of 64 is required to estimate the mean IQ score of statistics students with 99% confidence and a margin of error of 2 IQ points.

This is a reasonable sample size for a real-world calculation. IQ tests are typically administered to large groups of people, so it is not difficult to find a sample of 64 statistics students. This sample size will provide a good estimate of the mean IQ score of statistics students, and it is likely to be accurate enough for most purposes.

To learn more about sample size here brainly.com/question/30100088

#SPJ11

If the test is applied twice, the two test results are independent, and both are positive, then the posterior probability that the selected individual has the disease is 31.3%.

Bayes’ theorem can be used to find the posterior probability that the selected individual has the disease after two tests if the prior probability is given along with the test results.

Bayes' theorem is a statistical method that provides a way to update the probability of a hypothesis as additional evidence or information becomes available. It is used to find the posterior probability of a hypothesis given some prior probability and new evidence.

Here, let A denote the event that the selected individual has the disease, and B denote the event that both tests are positive.

Prior probability of having the disease:

P(A) = 0.06

Probability of both tests being positive, given that the person has the disease:

P(B | A) = Probability that both tests are positive given that the individual has the disease = (Probability of testing positive for the first test) * (Probability of testing positive for the second test) = (0.94) * (0.94) = 0.8836

Probability of both tests being positive, given that the person does not have the disease:

P(B | A') = Probability that both tests are positive given that the individual does not have the disease = (Probability of testing positive for the first test) * (Probability of testing positive for the second test) = (0.06) * (0.97) = 0.0582

Using Bayes' theorem:

Posterior probability of having the disease:

P(A | B) = Probability that the selected individual has the disease given that both tests are positive

P(B | A) * P(A)P(B | A) * P(A) + P(B | A') * P(A') = 0.8836 * 0.06/ (0.8836 * 0.06) + (0.0582 * 0.94) = 0.313 or 31.3%

Therefore, the posterior probability that the selected individual has the disease is 31.3%.

Learn more about Bayes' theorem here: https://brainly.com/question/29546122

#SPJ11

The probability of a person choosing a card from the second row is 50%.

The probability of an event occurring can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. In this case, there are four possible rows that the card could be chosen from, and each row has the same number of cards. Therefore, the probability of the card being chosen from any one row is 1/4, or 25%.

However, the question specifies that the person is choosing a card from the second row. Since there are two rows with 10 cards, the probability of the card being chosen from the second row is 2/4, or 50%.

It is important to note that this is just a theoretical probability. In reality, the probability of the card being chosen from any one row may be slightly different, depending on how the cards are arranged. For example, if the cards are arranged in a stack, the person may be more likely to choose a card from the top row. However, in the absence of any other information, the probability of the card being chosen from the second row is 50%.

To learn more about probability here brainly.com/question/31828911

#SPJ11

a) With 95% confidence the proportion of all smart phones that break before the warranty expires is between 0.0525 and 0.0635.

b) If many groups of 1666 randomly selected smart phones are selected, then a different confidence interval would be produced for each group. About 95 percent of these confidence intervals will contain the true population proportion of all smart phones that break before the warranty expires and about 5 percent will not contain the true population proportion.

A smart phone manufacturer is interested in constructing a 95% confidence interval for the proportion of smart phones that break before the warranty expires. 95 of the 1666 randomly selected smart phones broke before the warranty expired.To calculate the confidence interval for the proportion of smart phones that break before the warranty expires, we must first calculate the point estimate of the population proportion of smart phones that break before the warranty expires:95/1666 = 0.057 (rounded to three decimal places)Then, we have to find the margin of error that is, the maximum distance between the point estimate and the confidence interval limits.

We can do that with the help of the following formula:margin of error = critical value × standard errorThe critical value can be found in the z-table or t-table, depending on the sample size. Since we do not know the population standard deviation, we can use the t-distribution. The degrees of freedom are n − 1 = 1666 − 1 = 1665.Using the t-table with degrees of freedom 1665 and level of significance α = 0.05, the critical value is:t* = 1.96 (rounded to two decimal places)The standard error can be calculated using the following formula:standard error = √[(p-hat (1-p-hat))/n] = √[(0.057(1-0.057))/1666] ≈ 0.0083 (rounded to four decimal places)Finally, we can calculate the confidence interval using the following formula:confidence interval = point estimate ± margin of error confidence interval = 0.057 ± 1.96(0.0083) = (0.0525, 0.0635)The 95% confidence interval for the proportion of all smart phones that break before the warranty expires is between 0.0525 and 0.0635.

If many groups of 1666 randomly selected smart phones are selected, then a different confidence interval would be produced for each group. About 95 percent of these confidence intervals will contain the true population proportion of all smart phones that break before the warranty expires and about 5 percent will not contain the true population proportion.

Learn more about the word warranty here,

https://brainly.com/question/27919230

#SPJ11

She bought b. 6 black ranchu goldfish, 9 calico gold fish.

Marsha bought 15 fish for a total cost of $29.25, where the black ranchu goldfish cost $2.10 each and calico goldfish cost $1.85 each.

Let b be the number of black ranchu goldfish and c be the number of calico goldfish. We can write the following two equations:

b + c = 15 ..........(i)

2.1b + 1.85c = 29.25 ..........(ii)

Multiplying equation (i) by 1.85 and subtracting from (ii) yields:

2.1b + 1.85c - (1.85b + 1.85c) = 29.25 - (1.85 x 15)

0.25b = 1.5

b = 6

Putting this value of b in equation (i) gives:

c = 15 - b = 9

Thus, Marsha bought 6 black ranchu goldfish and 9 calico goldfish.

To learn more about equations, refer below:

https://brainly.com/question/29657983

#SPJ11

The supplier's claim that no more than 1% of the cards are defective is valid.

Hypothesis Testing

Hypothesis testing is a statistical technique that helps in making a decision about the population parameter. Here, we need to conduct a hypothesis testing to the claim about a population proportion. The hypothesis testing is given below:

Null Hypothesis H0: p ≤ 0.01 (Supplier's claim)

Alternate Hypothesis Ha: p > 0.01 (Supplier's claim is not correct)

Where, p is the population proportion. Significance level (b) = 0.01, this means b = 0.01,

The test statistics formula is given by:

z = (p1 - p) / √(p(1 - p) / n)

Here, p1 is the sample proportion, p is the hypothesized population proportion, n is the sample size.

Substituting the given values, we get

z = (0.02 - 0.01) / √(0.01(0.99) / 600 )= 2.04 (approx.)

The critical value for the significance level of 0.01 with right-tailed z-test is given by:

zb= 2.33

Since the calculated value of z (2.04) is less than the critical value of zb (2.33), we fail to reject the null hypothesis. Hence, there is not enough evidence to claim that the supplier's claim is not correct.

Therefore, the supplier's claim that no more than 1% of the cards are defective is valid.

Hence, we can conclude that the null hypothesis is accepted.

To know more about the Hypothesis Testing, refer to:

https://brainly.com/question/17099835

#SPJ11

The two events are independent.

Given,

A person is chosen in random .

Now,

Independent events are those events that are not affected by each other.

If events X and Y are independent then the occurrence of one of these two events does not depend on the other in any way.

For two independent events X and Y the joint probability is:

P(X∩Y) = P(X) × P(Y)

Define X and Y as follows:

X = a person has eyes

Y = a person is associated/independent.

The event of a person being  associated/independent does not depend on the event of the person having eyes.

The two events are not at all related.

Thus, the two events are independent.

Know more about independent events,

https://brainly.com/question/32716243

#SPJ4

Answer: x^2 - 3x - 18 = 0

Step-by-step explanation:

Since the solutions are x = -3 and x = 6, another way this could be written is (x+3)(x-6) = 0 (*This is because either x+3 or x-6 must equal 0 to make this true. So when you set x+3 = 0 or x-6= 0, you get the solutions x = -3 and 6)

After this, you can FOIL* the equation above, (This is a method where the first, outside, inside and last terms of the binomials are multiplied together to get the solution.)

So we get: x*x + x*-6+ x*3 + 3*-6 = 0

We can then simplify to get x^2 - 3x - 18 = 0.

*I hope I explained this well enough, but for more information try googling Zero property with binomials for the first part and FOIL method for the second part. Hope this helps :)

Quadratic polynomial with a degree of 2.

The given polynomial is[tex]-2x^2 - x^2.[/tex] To classify this polynomial and determine its degree, we need to consider the highest power of x in the expression.

In this case, the highest power of x is 2. Since the power is 2, the polynomial is quadratic. Therefore, options a and c can be eliminated.

Now, let's focus on the degree of the polynomial. The degree of a polynomial is the highest exponent of the variable in the expression.

In the given polynomial, the highest exponent is 2. Hence, the degree of the polynomial is 2.

Based on the above analysis, we can conclude that the correct answer is:

b. Quadratic, 2.

Learn more about Polynomial.

brainly.com/question/11536910

#SPJ11

The probability that the one math major and one computer science major who refuse to serve together wind up on the committee together is 3/7.

The probability that the one math major and one computer science major who refuse to serve together wind up on the committee together, we can consider two cases:

Case 1: The math major who refuses to serve is selected.

In this case, we need to select 3 math majors from the remaining 4 math majors and 2 computer science majors from the 4 computer science majors who are willing to serve together. The probability of this case can be calculated as:

P(case 1) = (4 choose 3) × (4 choose 2) / (9 choose 5)

Case 2: The computer science major who refuses to serve is selected.

In this case, we need to select 3 math majors from the 5 math majors who are willing to serve together and 2 computer science majors from the remaining 3 computer science majors. The probability of this case can be calculated as:

P(case 2) = (5 choose 3) × (3 choose 2) / (9 choose 5)

To find the overall probability, we need to sum up the probabilities of both cases:

P = P(case 1) + P(case 2)

Calculating the probabilities:

P(case 1) = (4 choose 3) × (4 choose 2) / (9 choose 5) = (4 × 6) / 126 = 24 / 126 = 4 / 21

P(case 2) = (5 choose 3) × (3 choose 2) / (9 choose 5) = (10 × 3) / 126 = 30 / 126 = 5 / 21

P = P(case 1) + P(case 2) = 4/21 + 5/21 = 9/21 = 3/7

To know more about probability click here :

https://brainly.com/question/10185463

#SPJ4

Brandon's strong knowledge base of baseball statistics allows him to easily remember and comprehend the new statistics he is reading.

With his deep knowledge of baseball statistics as a foundation, Brandon is better able to recall and comprehend new material.

Brandon has gained a profound understanding of the game, player performance, and statistical patterns from his early study of baseball statistics.

His ability to draw connections between the new numbers and his prior knowledge makes it easier for him to recall and understand the material.

His enthusiasm for baseball is also likely a factor in his drive and engagement, which helps him remember and recall the statistics with ease.

To learn more about knowledge click here:

brainly.com/question/28025185

#SPJ4

The type of survey that is utilized to determine the extent of problems in a certain area and then express the findings as rates affected within the population is known as an epidemiological survey.

What is an epidemiological survey?

An epidemiological survey is a type of survey used to understand the prevalence and incidence of particular health problems in a particular population. In addition, epidemiological surveys are utilized to determine the causes, transmission, and treatment of these problems.

Epidemiological studies are classified according to the types of questions that they are designed to answer. They are as follows:

Descriptive studies: These studies describe the incidence, prevalence, and distribution of diseases in populations.

Analytical studies: These studies are concerned with determining the causative factors of diseases in populations.

Experimental studies: These studies determine the efficacy and safety of new treatments for diseases.

Learn more about epidemiological survey here:

https://brainly.com/question/13497485

#SPJ11

The sum of the series is 1001.

Given,

The first term of the series = 13

The last term of the series = 130

Number of terms in the series = 14

Formula used:

The sum of n terms of an arithmetic series is given by

S = (n/2) * [2a + (n - 1) d]

Where,

S = sum of the series

n = number of terms

a = first term

d = common difference.

Now, to find the sum of the series, we need to find the common difference, d.

To find d, we use the formula for the nth term of an arithmetic series.

Tₙ = a + (n - 1)d

Where

Tₙ = nth term, a = first term, and d = common difference.

We know that the last term of the series is 130i.e,

T₁₄ = 130

Also, the first term of the series is 13i.e, a = 13

Using the above formula,

Tₙ = a + (n - 1)d

T₁₄ = a + (14 - 1)d

130 = 13 + 13d

130 - 13 = 13d

117 = 13d

Dividing by 13 on both sides,

d = 9

So, the common difference is 9.

Now, using the formula for the sum of the series,

S = (n/2) * [2a + (n - 1) d]

S = (14/2) * [2 * 13 + (14 - 1) * 9]

S = 7 * (26 + 117)

S = 7 * 143

S = 1001

Therefore, the sum of the series is 1001.

To learn more about arithmetic series from the given link.

https://brainly.com/question/6561461

#SPJ11

The probabilities are =

1) Probability ≈ 0.42 or 42%

2) Probability = 0.82 or 82%

3) To maximize the probability of winning, you should bid an amount just above $9,900, which is the lower limit of the range where your bid can win.

4) To maximize the expected profit, you should bid an amount less than $16,000 but as close as possible to maximize your potential profit.

To calculate the probabilities and determine the optimal bidding strategy, we need to analyze the given scenario using probability and expected value concepts.

i. Probability of your bid being accepted when you bid $12,000:

The competitor's bid x is uniformly distributed between $9,900 and $14,900. Since your bid is $12,000, it will be accepted if the competitor's bid is below $12,000.

The range of possible values for x is $9,900 to $14,900, and your bid will be accepted if x < $12,000.

The length of this range is $14,900 - $9,900 = $5,000.

Since the distribution is uniform, the probability of your bid being accepted is the ratio of the length of the range where your bid wins (x < $12,000) to the total length of the range.

Probability = (Length of the range where your bid wins) / (Total length of the range)

Probability = ($12,000 - $9,900) / ($14,900 - $9,900)

Probability = $2,100 / $5,000

Probability ≈ 0.42 or 42%

ii. Probability of your bid being accepted when you bid $14,000:

Using the same approach as before:

Probability = ($14,000 - $9,900) / ($14,900 - $9,900)

Probability = $4,100 / $5,000

Probability = 0.82 or 82%

iii. Bidding amount to maximize the probability of winning:

To maximize the probability of winning, you should bid an amount just above $9,900, which is the lower limit of the range where your bid can win.

iv. Expected profit for different bidding scenarios:

If someone is willing to pay you $16,000 for the property, we can calculate the expected profit for different bidding amounts to determine the optimal bid.

Let's consider the bidding amounts $12,950 and the previously calculated optimal bidding amount.

For a bid of $12,950:

Probability of winning = ($12,950 - $9,900) / ($14,900 - $9,900)

Probability of winning ≈ 0.65 or 65%

Expected profit = (Probability of winning x Offer price) - (Bid amount)

Expected profit = (0.65 x $16,000) - $12,950

Expected profit ≈ $10,400 - $12,950

Expected profit ≈ -$2,550 (negative profit)

For the optimal bid (just above $9,900):

Probability of winning ≈ 1 (since your bid is slightly higher than the competitor's range)

Expected profit = (Probability of winning x Offer price) - (Bid amount)

Expected profit = (1 x $16,000) - (optimal bid amount)

Expected profit = $16,000 - (optimal bid amount)

To maximize the expected profit, you should bid an amount less than $16,000 but as close as possible to maximize your potential profit.

Learn more about probability click;

https://brainly.com/question/31828911

#SPJ4

The function g(x) is defined as 2 times f(x), and we need to find the values of g(2) and g'(2). Given that f(T) = 5, f'(7) = 2, 9'(7) = 3, and g'(7) = 8, we also need to find the values of h(7) and h'(x) where h(x) = 5f(x) + 29x.

To find g(2), we substitute x = 2 into the equation g(x) = 2f(x). Therefore, g(2) = 2f(2). Since we are not given the specific value of f(2), we cannot determine the exact value of g(2) without additional information.

To find g'(2), we need to differentiate g(x) with respect to x. Since g(x) = 2f(x), we have g'(x) = 2f'(x). Therefore, g'(2) = 2f'(2). Again, without knowing the value of f'(2), we cannot calculate the exact value of g'(2).

Moving on to the function h(x) = 5f(x) + 29x, we are asked to find h(7) and h'(x). To find h(7), we substitute x = 7 into the equation. Therefore, h(7) = 5f(7) + 29(7). Given that f(7) = 5, we can calculate h(7) = 5(5) + 29(7) = 25 + 203 = 228.

To find h'(x), we need to differentiate h(x) with respect to x. Using the sum rule and the constant multiple rule of differentiation, we have h'(x) = 5f'(x) + 29. Therefore, h'(7) = 5f'(7) + 29(1). Given that f'(7) = 2, we can calculate h'(7) = 5(2) + 29 = 10 + 29 = 39.

Finally, we cannot determine the exact values of g(2) and g'(2) without additional information about f(x). However, we can calculate h(7) = 228 and h'(7) = 39 using the given values for f(T), f'(7), 9'(7), and g'(7).

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

To determine the height the ball will reach on the third bounce, we need to consider the pattern of the ball's bounces.

The ball is initially dropped from a height of 128 cm. On the first bounce, it reaches a height equal to the height of the previous bounce, which is 128 cm. On the second bounce, the ball again reaches a height equal to the height of the previous bounce, which is 128 cm. Therefore, we can observe that the height of each bounce remains constant at 128 cm. Since the question asks for the height the ball will reach on the third bounce, we can conclude that the third bounce will also reach a height of 128 cm.

Hence, the height reached on the third bounce will be 128 cm, or three-quarters of the original height.

To learn more about height click here:brainly.com/question/29131380

#SPJ11

There are 75,287,520 ways to select a subset of 9 from 100 applicants for a shortlist.

The number of ways to select a subset of 9 from 100 applicants can be calculated using the formula for combinations, which is:

n C r = n! / r!(n-r)!

Where n is the total number of applicants and r is the number of applicants to be selected for the shortlist.

Substituting n = 100 and r = 9, we get:

100 C 9 = 100! / 9!(100-9)!

= (100 x 99 x 98 x ... x 92) / (9 x 8 x ... x 2 x 1)

= 75,287,520

To know more about subset refer here:

https://brainly.com/question/31739353#

#SPJ11

The correct answer is option c. 18.952. The deseasonalized value for the second quarter of 2008 can be calculated by dividing the actual value by its corresponding seasonal index.

1. In this case, the actual value for the second quarter of 2008 is given as 17. Using the seasonal index for the second quarter (0.897), we can compute the deseasonalized value as:

Deseasonalized value = Actual value / Seasonal index

Deseasonalized value = 17 / 0.897 ≈ 18.952

2. Therefore, the deseasonalized value for the second quarter of 2008 is approximately 18.952. Hence, the correct answer is option c. 18.952.

Learn more about deseasonalized here: brainly.com/question/14378549

#SPJ11

The time taken to paint the room by both April and Alma is 4.44 hours.

Given that :

April can paint a room in 10 hours.

Alma can paint the same room in 8 hours.

Let t be the time taken by both April and Alma to paint the room.

Rate at which Alma paint the room is 1/8.

Rate at which April paint the room = 1/10.

So we can write this as :

Rate at which both paint the room = 1/t.

So,

1/8 + 1/10 = 1/t

(10 + 8) / 80 = 1/t

Cross multiply.

18t = 80

t = 4.44 hours.

Hence they both will complete the work in 4.44 hours.

Learn more about Rate here :

https://brainly.com/question/29334875

#SPJ4

The probability that Betty gets an A in math based on a coin flip decision is 0.8.

The given information states that Betty estimates her probability of receiving an A grade in a math course to be 0.8. However, her decision-making process is based on flipping a fair coin. In this case, the coin flip does not affect the probability of Betty's performance in the math course. Therefore, the probability of her getting an A in math remains the same as her initial estimation, which is 0.8.

In other words, the outcome of the coin flip is independent of Betty's ability or performance in the math course. It does not affect the probability she assigned to receiving an A grade. The coin flip simply serves as a random decision-making mechanism, and regardless of the coin flip's outcome, the probability of her getting an A in math remains 0.8.

Learn more about Probability

brainly.com/question/29381779

#SPJ11

John is 10 years old and Marcus is 15 years old.

Let the present age of John be j years.

Present age of Marcus = (j + 5) years

Five years ago: Age of John = (j - 5) years

Age of Marcus = ((j + 5) - 5) years = j years

According to the given statement, five years ago he was 2 times older than John. i.e.

j = 2(j - 5)

j = 10

So, present age of John = j = 10 years

Present age of Marcus = (j + 5) = 15 years

Thus, John is 10 years old and Marcus is 15 years old.

Learn more about "Age relationship" refer to the link : https://brainly.com/question/28480994

#SPJ11

In the given scenario, it is established that JKLM is a rectangle. The explanation shows that due to the presence of right angles, certain angles and sides of the rectangle are congruent, leading to the conclusion that JL¯¯¯¯¯ is congruent to MK¯¯¯¯¯¯¯.

Given that JKLM is a rectangle, we know that all four angles of the rectangle are right angles. Since ∠JML and ∠KLM are both formed by the intersection of two perpendicular lines, they are right angles. Furthermore, since all right angles are congruent, ∠JML and ∠KLM are congruent as well.

Using the definition of a rectangle, we can determine that JM¯¯¯¯¯¯≅KL¯¯¯¯¯. This is because in a rectangle, opposite sides are congruent. Similarly, ML¯¯¯¯¯¯ is congruent to itself, as any segment is congruent to itself.

By applying the response area, we can conclude that △JML≅△KLM. This means that the two triangles formed by the congruent angles and sides are themselves congruent.

Finally, we can use the property that corresponding parts of congruent triangles are congruent. Since △JML≅△KLM, we can state that JL¯¯¯¯¯≅MK¯¯¯¯¯¯¯, as JL¯¯¯¯¯ and MK¯¯¯¯¯¯¯ are corresponding sides of the congruent triangles.

To learn more about angles click here: brainly.com/question/31818999

#SPJ11

The rate of the current is 1.5 mph, and the length of the course is 9 miles.

Let's assume the rate at which Ben paddles in still water is represented by r (in mph), and the rate of the current is represented by c (in mph).

When paddling upstream, Ben is paddling against the current, so his effective speed is reduced. The time it takes him to complete the course is 6 hours, and the distance he covers is represented by d (in miles). Using the formula d = (r - c) * t, we have d = (r - c) * 6.

When paddling downstream, Ben is paddling with the current, so his effective speed is increased. The time it takes him to complete the course is 2 hours. Using the same formula, we have d = (r + c) * 2.

We can solve these two equations to find the values of r and c. By dividing the second equation by the first equation, we get (r + c)/(r - c) = 1/3.

Solving this equation, we find r = 4 mph and c = 1.5 mph.

Therefore, the rate of the current is 1.5 mph, and the length of the course is determined by substituting r and c into either of the original equations. The length of the course is 9 miles.

To learn more about “distance” refer to the https://brainly.com/question/26550516

#SPJ11

The size of the box, as well as the length of the whiskers, indicates the spread of the dataset. Overall, box plots are an excellent tool to present statistical data and identify potential outliers.

The median of the data is represented by a vertical line inside the box. It is the midpoint of the dataset, i.e., 50% of the data lies below and 50% lies above it.

The lower quartile is shown on the left side of the box plot. It indicates the 25th percentile of the data, i.e., the point at which the bottom 25% of the data lies.

The upper quartile is shown on the right side of the box plot. It indicates the 75th percentile of the data, i.e., the point at which the top 25% of the data lies.

The minimum value is the smallest value in the dataset, shown as the bottom end of the whisker.

The maximum value is the largest value in the dataset, shown as the upper end of the whisker.

Q. Use the box plot to complete the sentences.

The median of the data is

The lower quartile is

The upper quartile is

The minimum value is

The maximum value is

Learn more about Box Plot from :

https://brainly.com/question/14277132

#SPJ11

The initial founder population for the given function is equal to 5 million.

To determine the initial flounder population (P(0)) from the  function

Function is equal to,

P(t) = 6t + 5(0.3t² + 1),

Substitute t = 0 into the function P(t) = 6t + 5(0.3t² + 1) we get,

⇒ P(0) = 6(0) + 5(0.3(0)² + 1)

Simply the above expression we get,

⇒ P(0) = 0 + 5(0 + 1)

⇒ P(0) = 5(1)

⇒ P(0) = 5

Therefore, the initial flounder population is 5 million.

learn more about population here

brainly.com/question/32658669

#SPJ4

The required sample size is 22.

Given, We want to estimate the population mean within 20, with a 90% level of confidence. The population standard deviation is estimated to be 57. We need to find how large a sample is required.

The formula for the sample size is given by,

Sample size formula n = ((z * σ) / E)^2

Where z is the z-value,σ is the population standard deviation, and E is the maximum error between the sample mean and population mean.

From the given information, The level of confidence is 90%. The maximum error between the sample mean and population mean is 20. The population standard deviation is 57. The level of confidence for a 90% confidence interval is 0.90, which means the alpha level (α) is 0.10.

Therefore, the z-value for a 90% confidence interval is 1.645.

Using the given values in the sample size formula,n = ((z * σ) / E)^2n = ((1.645 * 57) / 20)^2n = (93.765 / 20)^2n = 4.688^2n = 22.0072 ≈ 22

Hence, the required sample size is 22. The answer is 22.

To learn more about sample size refer to:

https://brainly.com/question/31734526

#SPJ11

(1) (4.17 x 10⁻³) (4 x 10⁻²), the simplified expression is 1.67 x 10⁻⁴

(2) [tex]\frac{2 \times 10^{-6} }{8.38 \times 10^{-2}}[/tex] , the simplified expression is 2.39 x 10⁻⁵.

(3) [tex]\frac{7.72 \times 10^{2} }{4.39 \times 10^{3}}[/tex], the simplified expression is 0.176.

(4) [tex]\frac{4 \times 10^{3} }{2 \times 10^{4}}[/tex],  the simplified expression is 0.2.

(5) [tex]\frac{8.96 \times 10^{-5} }{4.6 \times 10^{-4}}[/tex], the simplified expression is 0.195.

(7) (7.4 x 10⁻³)⁻², the simplified expression is 1.826 x 10⁴.

(8) (5 x 10²) (3.5 x 10³), the simplified expression is 1.75 x 10⁶.

(9) (3.2 x 10²)³, the simplified expression is 3.28 x 10⁷.

(10) (7 x 10⁻⁴) (6.29 x 10⁻⁴), the simplified expression is 4.403 x 10⁻⁷.

(11) (4.95 x 10² ) ( 7.29 x 10⁴), the simplified expression is 3.609 x 10⁷.

The simplification of the expressions is calculated by applying the following method.

(1) (4.17 x 10⁻³) (4 x 10⁻²)

The expression is simplified as follows;

= (4.17 x 4 ) x 10⁻³ ⁻ ²

= 16.7 x 10⁻⁵

= 1.67 x 10⁻⁴

(2) [tex]\frac{2 \times 10^{-6} }{8.38 \times 10^{-2}}[/tex]

The expression is simplified as follows;

= (2/8.38) x 10⁻⁶ ⁺ ²

= 0.239 x 10⁻⁴

= 2.39 x 10⁻⁵

(3) [tex]\frac{7.72 \times 10^{2} }{4.39 \times 10^{3}}[/tex]

The expression is simplified as follows;

= 0.176

(4) [tex]\frac{4 \times 10^{3} }{2 \times 10^{4}}[/tex]

The expression is simplified as follows;

= (4/2) x 10⁻¹

= 2 x 10⁻¹

= 0.2

(5) [tex]\frac{8.96 \times 10^{-5} }{4.6 \times 10^{-4}}[/tex]

The expression is simplified as follows;

= 0.195

(7) (7.4 x 10⁻³)⁻²

The expression is simplified as follows;

= (1000/7.4)²

= 1.826 x 10⁴

(8) (5 x 10²) (3.5 x 10³)

The expression is simplified as follows;

= (5 x 3.5) x 10²⁺³

= 17.5 x 10⁵

= 1.75 x 10⁶

(9) (3.2 x 10²)³

The expression is simplified as follows;

= 3.28 x 10⁷

(10) (7 x 10⁻⁴) (6.29 x 10⁻⁴)

The expression is simplified as follows;

= (7 x 6.29) x 10⁻⁴⁻⁴

= 44.03 x 10⁻⁸

= 4.403 x 10⁻⁷

(11) (4.95 x 10² ) ( 7.29 x 10⁴)

The expression is simplified as follows;

= ( 4.95 x 7.29) x 10²⁺⁴

= 36.09 x 10⁶

= 3.609 x 10⁷

Learn more about simplification of expressions here: https://brainly.com/question/723406

#SPJ1

Probability of the first child being a girl and the second child being a boy (GB): 0.5 x 0.5 = 0.25 or 25%The sum of these probabilities is 1, which means that one of these four outcomes is guaranteed to occur when a family has two children.

When a family has two children, there are four possible outcomes that could occur with regards to the genders of the children. These outcomes are:Both children are boys (BB)Both children are girls (GG)The first child is a boy, and the second child is a girl (BG)The first child is a girl, and the second child is a boy (GB)The probability of each of these outcomes can be calculated using the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Probability of both children being boys (BB):

0.5 x 0.5 = 0.25 or 25%

Probability of both children being girls (GG):

0.5 x 0.5 = 0.25 or 25%

Probability of the first child being a boy and the second child being a girl (BG):

0.5 x 0.5 = 0.25 or 25%.

To know more about Probability visit:-

https://brainly.com/question/31828911

#SPJ11

The 95% confidence interval for the difference in the proportion of adults who smoke in 1990 and 2010 is (0.0132, 0.0688).

In the given question, we have the following information:

In 1990, 551 out of 1500 randomly sampled adults indicated they smoked.

In 2010, 652 out of 2000 randomly sampled adults indicated they smoked.

To calculate the confidence interval, we can use the formula:

CI = p1 – p2 ± z√(p1(1-p1)/n1 + p2*(1-p2)/n2)

where:

p1 = 551/1500 = 0.367

p2 = 652/2000 = 0.326

n1 = 1500

n2 = 2000

z = 1.96 (for a 95% confidence level)

Now, let’s plug in these values into the formula and calculate the confidence interval:

CI = 0.367 – 0.326 ± 1.96√(0.367(1-0.367)/1500 + 0.326*(1-0.326)/2000)

CI = 0.041 ± 0.0278

CI = (0.0132, 0.0688)

Therefore, the 95% confidence interval for the difference in the proportion of adults who smoke in 1990 and 2010 is (0.0132, 0.0688).

Interpretation:

This means that we are 95% confident that the true difference in the proportion of adults who smoke in 1990 and 2010 is between 0.0132 and 0.0688. Since the interval does not contain zero, we can conclude that there is a significant difference in the proportion of adults who smoke between 1990 and 2010.

Learn more about confidence interval

https://brainly.com/question/32546207

#SPJ11

To determine the convergence or divergence of the series Σ(n^2)/(n+1) as n goes from 1 to 10, let's consider the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. If the limit is greater than 1 or does not exist, the series diverges. Let's apply the ratio test to the given series: |((n+1)^2)/((n+1)+1)| / |(n^2)/(n+1)| = ((n+1)^2)(n+1) / (n^2)(n+2). Taking the limit as n approaches infinity: lim (n -> ∞) (((n+1)^2)(n+1)) / ((n^2)(n+2)) = 1.  Since the limit is equal to 1, the ratio test makes no claims about the convergence or divergence of the series.

Therefore, we cannot conclude whether the series is convergent or divergent based on the ratio test alone.

To learn more about ratio test click here: brainly.com/question/31700436

#SPJ11