The following data represent the dividend yields of a random sample of 28 pubicly traded stocks.

Answer:

6

Step-by-step explanation:

3x-4=14

3x=14+4

3x=18

x=6

Answer:

x = 6

Step-by-step explanation:

\(x+(-4)+2x=14\\\\ \text{Distribute '+' into '-4' : }\\ x-4+2x=14\\\text{Combine Like Terms: }\\x+2x-4=14\\3x-4=14\\\text {Add 4 to Both Sides: }\\3x-4+4=14+4\\3x=18\\\text{Divide both sides by 3: }\\\frac{3x}{3}=\frac{18}{3}\\\huge\boxed{x=6}\)

1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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Step-by-step explanation:

for this we need to know the conversion rate between miles and kilometers :

1 mile = 1.60934 km

which means

1 km = 0.621371 miles

so,

70 m/h = 70×1.60934 km/h = 112.6538 km/h

compared to the 120 km/h limit in Canada, it is clear that the speed limit in Canada is higher.

the difference is

7.3462 km/h = 7.3462×0.621371 = 4.56471564 m/h

The answer is 143.90. We used the formula for the standard error of the mean to find the expected value of the sample mean, then added 1.5 standard deviations to that value to find the answer.

To begin, we can use the formula for the standard error of the mean to calculate the expected value of the sample mean. The formula is as follows:

standard error of the mean = standard deviation / √(sample size)

In this case, the standard deviation is 8 minutes and the sample size is 40, so we can plug those values into the formula:

standard error of the mean = 8 / √(40)
standard error of the mean = 1.2649

Next, we can use the formula for the mean of the means to find the expected value of the sample mean:
mean of the means = average

In this case, the average is given as 142 minutes, so the mean of the means is also 142 minutes.

Now we can find the value that is 1.5 standard deviations above the expected value of the sample mean:

1.5 standard deviations = 1.5 * standard error of the mean
1.5 standard deviations = 1.5 * 1.2649
1.5 standard deviations = 1.8974

Finally, we add this value to the mean of the means to find the answer:

\(\bar{X} + 1.5\; standard \; deviations = 142 + 1.8974\)

\(\bar{X} + 1.5 \;standard \;deviations = 143.8974\)

Rounding to 2 decimal places, the answer is 143.90.

In summary, we used the formula for the standard error of the mean to find the expected value of the sample mean, then added 1.5 standard deviations to that value to find the answer. This calculation helps us understand the range of values we might expect to see in a sample of runners in this category.

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Answer:

The cost of Ticket = £63Booking Fee = 3% = 63*(3/100) = 1.89 = £ 1.89The total price of the ticket = £63 + £1.89 = £64.89. Therefore, the total price of the ticket is £64.89.

Answer:

A & B

Step-by-step explanation:

4x²- 12x + 9 = 5

4x²- 12x + 4 = 0

devided by 4

x²-3x+1=0

x = (3 ± √9-4)/2 = (3±√5)/2

x = (√5+3)/2 or x= (-√5+3)/2

The value that is added on the left-hand side to make the equation equal is -1/100.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows: multiplication, division, addition, and subtraction.

Given [1/-2  - 3/4  of -8/15],

to add a number so the sum equals the product of -7/50 and 11/14

let the number be x

according to the question,

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

taking LHS

[1/-2  - 3/4  of -8/15] = -1/2 - (3(-8)/60)

[1/-2  - 3/4  of -8/15] = -1/2 + 24/60

[1/-2  - 3/4  of -8/15] = (-30 + 24)/60

[1/-2  - 3/4  of -8/15] =-6/60 = -1/10

RHS

-7/50*11/14 = -77/700 = -11/100

substitute the values

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

-1/10 + x = -11/100

x = -11/100 + 1/10

x = (-11 + 10)/100

x = -1/100

Hence -1/100 is added to make the equation equal.

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Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857\)

\(P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429\)

Hence:

\(p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286\)

0.4286 = 42.86% probability of getting 2 of the same colour.

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Answer:

9

Step-by-step explanation:

By BODMAS rule,

45 ÷ 15 + 2 ⋅ 3

= ( 45 ÷ 15 ) + ( 2 ⋅ 3 )

= 3 + ( 2 ⋅ 3 )

= 3 + 6

= 9

Note : -

B - Bracket

O - Of

D - Division ( step 1 )

M - Multiplication ( step 2 )

A - Addition ( step 3 )

S - Subtraction ( step 4 )

Answer:

the answer is 9

Step-by-step explanation:

45/15 = 3

2*3=6

3+6=9

The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer:

D

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the y- intercept is the value of the constant term c

A

y = (x + 1)(x - 3)

  = x² - 2x - 3 ← y- intercept = - 3

B

y = x² - 9 ← y- intercept = - 9

C

y = 3x(x - 3)

  = 3x² - 9x ← y- intercept = 0

D

y = (x + 1)(x + 3)

  = x² + 4x + 3 ← with y- intercept 3

To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.

Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.

Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.

When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.

Hence the unit of analysis is objective of the section.

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Answer:

Thus there are 3150 ways to select the 2 faculty members and 4 students for the committee.

Step-by-step explanation:

Answer:

  (b)  y = -7x -27

Step-by-step explanation:

When x and y in the equation y = f(x) are replaced by (x-h) and (y-k), the function graph is translated h units right and k units up. The translated function can be written as ...

  y -k = f(x -h)

  y = f(x -h) +k . . . . . . add k

__

Your function is ...

  y = -7x

and you want to translate it by (h, k) = (-5, 8). That makes it ...

  y' = -7(x -(-5)) +8 = -7x -35 +8

  y' = -7x -27

Answer:

(3) The slope of BD is 1/3.

Step-by-step explanation:

Answer:

the answer for this one is A

Step-by-step explanation:

mostly because for this you're only looking for H and not the rest of them so if you reflect is itll be in the same spot just on the opposite side

We can see that the name of shape A on the centimetre grid is: Trapezium.

A centimeter grid is a grid made up of squares, where each square represents one square centimeter of area. The grid is often used in mathematics for graphing, geometry, or measurement activities.

The horizontal and vertical lines on the centimeter grid are spaced one centimeter apart, with thicker lines often used to denote every fifth or tenth line. The grid is numbered along the edges to make it easier to locate specific points on the grid.

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Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

Answer:

The distance between -12 and -15 is 3.

Step-by-step explanation:

hope this helps

The likelihood that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

To compute the probability for the a data point, we must first get the value's z-score.

Mean = μ = 15 points

SD = σ = 3 points

When calculating the likelihood that a score will be higher than 24, the z-score for 24 is:

z-score = (x-μ)/σ

z = (24-15)/3

z = 9/3

z = 3

The chance of z3 must now be determined using the z-score table, and it will be deducted from 1 to determine the likelihood of z>3.

P(z < 3) = 0.9987

P(z > 3) = 1 - P(z < 3)

P(z > 3) = 1 - 0.9987

P(z > 3) = 0.0013 = 13%

Thus, the probability that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

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Answer:

it is b or 20,000 or it is the base salary, you can put all 3 to be safe since they are all technichaly the same.

Step-by-step explanation:

so y=mx+B is the equation right here m the slope which is rise over run or y/x=.1 and B is the y inercept and 20,000 it is the starting point on the graph. where it overlaps with the y axis, in this case 20,000 which as it says earlier is his base salary

When peers at work offer suggestions to correct a weakness, it is important for the person to respond in a thoughtful and constructive manner.

Here are some guidelines for effectively addressing such suggestions:

Listen and be open-minded: Actively listen to the suggestions without becoming defensive or dismissive. Remember that your peers are offering their perspectives to help you improve. Keep an open mind and be willing to consider their viewpoints.

Express gratitude: Appreciate the effort and willingness of your peers to provide feedback. Thank them for their suggestions and acknowledge their input. Demonstrating gratitude fosters a positive and collaborative work environment.

Seek clarification, if needed: If you need further clarification on any of the suggestions, ask your peers for more information. This shows your commitment to understanding their feedback and ensures you can address the weakness effectively.

Reflect on the feedback: Take some time to reflect on the suggestions offered. Evaluate their validity and consider whether they align with your own self-assessment. Honest self-reflection is crucial in recognizing and addressing weaknesses.

Develop an action plan: Once you have understood the suggestions and reflected on them, create an action plan to address the weakness. Break down the steps you need to take to improve and set realistic goals for yourself. This proactive approach demonstrates your commitment to personal growth and professional development.

Seek support if necessary: If you require additional resources or assistance to address the weakness, don't hesitate to ask for help. Reach out to mentors, supervisors, or relevant professionals who can provide guidance or training. Collaborating with others can accelerate your progress in overcoming the weakness.

Communicate progress: Keep your peers informed about the steps you are taking to improve. Sharing your progress demonstrates your commitment to growth and allows them to see your efforts. It also encourages ongoing support and accountability from your colleagues.

Show resilience: Addressing weaknesses takes time and effort. Be prepared for setbacks and challenges along the way. Stay resilient and maintain a positive mindset, focusing on continuous improvement rather than being discouraged by temporary obstacles.

Remember, accepting and addressing weaknesses is a part of personal and professional growth. Embrace the feedback from your peers as an opportunity to enhance your skills and become a stronger professional.

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The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.

Let x be the number of square feet of carpet and y be the number of square feet of hardwood.

The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:

x + y <= 2000

The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:

4.50x + 8.25y <= 10000

So the system of inequalities is:

x + y <= 2000

4.50x + 8.25y <= 10000

This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.

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Answer:

-13 is less than zero in the options

The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

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Given that

Hence,

Similarly,

Therefore,

The first partial derivatives of the function f(x, y, z) = xyz + 9yz are:

To find the first partial derivatives of the function f(x, y, z) = xyz + 9yz, we need to differentiate the function with respect to each variable (x, y, z) one at a time while treating the other variables as constants.

Let's start with finding the partial derivative with respect to x (fx):

fx(x, y, z) = ∂/∂x (xyz + 9yz)

Since y and z are treated as constants when differentiating with respect to x, we can simply apply the power rule:

fx(x, y, z) = yz

Next, let's find the partial derivative with respect to y (fy):

fy(x, y, z) = ∂/∂y (xyz + 9yz)

Again, treating x and z as constants, we differentiate yz with respect to y:

fy(x, y, z) = xz + 9z

Finally, let's find the partial derivative with respect to z (fz):

fz(x, y, z) = ∂/∂z (xyz + 9yz)

Treating x and y as constants, we differentiate yz with respect to z:

fz(x, y, z) = xy + 9y

Therefore, the first partial derivatives of the function f(x, y, z) = xyz + 9yz are:

fx(x, y, z) = yz

fy(x, y, z) = xz + 9z

fz(x, y, z) = xy + 9y

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Answer:

While it was true that the cotton gin reduced the labor of removing seeds, it did not reduce the need for slaves to grow and pick the cotton. In fact, the opposite occurred. Cotton growing became so profitable for the planters that it greatly increased their demand for both land and slave labor.

Step-by-step explanation:

Pretty sure this isnt math tho

The solution for b is y-mx in the equation y=mx+b.

The given equation is y=mx+b

y equal r=to m times of x plus b

We need to solve for b in the equation

To solve we have to isolate b from the equation

Subtract mx from both sides

y-mx=b

Hence, the solution for b is y-mx in the equation y=mx+b.

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The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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