Question 33 of 43
The table shows the number of practice problems
completed in 30 minutes in three samples of 10 randomly
selected math students.
Number of practice problems completed in 30 minutes
Sample 1 12 13 11 10 11 13 12 13 9 13
Sample 2 13 18 17 14 15 14 18 14 15 16
Sample 3 18 14 16 15 16 14 17 16 15 14
Which statement is most accurate based on the data?
Mean = 11.7
Mean = 15.4
Mean = 15.5
A. A prediction based on the data is reliable, because there are no
noticeable differences among the samples.
B. A prediction based on the data is not completely reliable, because
the mean of sample 1 is noticeably lower than the means of the
other two samples.
C. A prediction based on the data is not completely reliable, because
the means of samples 2 and 3 are too close together.
D. A prediction based on the data is reliable, because the means of
samples 2 and 3 are very close together.

There are total 35 students in the class.

Given that,

Vikas ranks 9th in the class,

Assume that there are 'n' number of students in the class  

Therefore,

There are 8 students who have scored better than him.

So, The total number of students with a rank better or equal to Vikas,

= 8 + 1 (Vikas himself)

= 9.

Now, his friend got the 35th rank which is the last rank

This means that there are a total of 35 students in the class.

Also, also given that,

Vikas's rank from the last is 27th,

This means that there are 26 students who have scored lower than Vikas.

So, the total number of students with a rank worse or equal to Vikas,

= 26 + 1 (Vikas himself)

 = 27.

Therefore, The total number of students in the class = 35.

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No, a square matrix with two identical columns is not invertible.

For a square matrix to be invertible (or non-singular), it must have linearly independent columns (or rows). In other words, each column (or row) of the matrix must be unique and not a linear combination of the other columns (or rows).

If two columns of a square matrix are identical, it means that one column is a scalar multiple of the other. This results in linear dependence between the columns, and the matrix does not have full rank.

Since an invertible matrix must have full rank, a square matrix with two identical columns cannot be invertible.

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\(-3s\textless11s+1\\\\\\\\-3s-11s < 1\\\\\\-14s < 1\\\\\\-s < \frac{1}{14} \\\\s > -\frac{1}{14}\)

===========================

\(\textcopyright ELIZA\)

Answer:

If \(r = 1.006\), then it means that dependent variables increases by a factor of 1.006 per decade.

Step-by-step explanation:

Mathematically speaking, the function represents an exponential equation, whose form is:

\(f(t) = a_{o}\cdot r^{k\cdot t}\) (1)

Where:

\(t\) - Independent variable.

\(r(t)\) - Dependent variable.

\(a_{o}\) - Initial value.

\(k\) - Convergence ratio.

\(r\) - Increase rate.

If \(r = 1.006\), then it means that dependent variables increases by a factor of 1.006 per decade.

Poisson arrivals occur on a server with a utilization factor of 13 at a typical rate of 2 per hour. The mean service time in minutes for each arrival unit is 10 if the service time for each unit has an exponential distribution. Here option D is the correct answer.

We can use Little's law to relate the average number of customers in the system to the average time they spend in the system:

L = λW

where L is the average number of customers in the system, λ is the arrival rate, and W is the average time spent in the system.

Since the server utilization factor is 1/3, we know that the service rate is 3 times the arrival rate:

μ = 3λ = 6

We can then use the formula for the expected value of the exponential distribution with rate parameter μ to find the average service time:

E[X] = 1/μ

E[X] = 1/6 hour = 10 minutes

Little's law is used to relate the average number of customers in the system to the average time they spend in the system, and the service rate is calculated from the given utilization factor. The formula for the expected value of the exponential distribution is then used to find the average service time, which is 10 minutes.

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Answer:

Total Surface Area: 65.97 cm²

Lateral Surface Area: 37.70 cm²

Step-by-step explanation:

You can solve for the surface area without the height or you can solve for the height and then find the surface are, either way is easy.

Lets first solve without the height. We will solve the surface area with the radius and slant height.

Total Surface area of cone formula: πr (r + s)

Curved surface are formula: πrs

Substitute the values in the picture with the formula

Slant height: 4

Radius: 3

πr (r + s)

π(3)(3 + 4)

(3.141593)(3)(3 + 4)

=9.424778(3 + 4)

=(9.424778)(7)

=65.973446

65.973446 rounded to the nearest hundredth is 65.97
TSA = Total Surface Area

TSA = 65.97 cm²

Now to find the curved surface area or some people call it the Lateral Surface Area

Formula: πrs

Radius: 3

Slant Height: 4

π(3)(4)

(3.141593)(3)(4)

=(9.424778)(4)

=37.699112

37.699112 to the nearest hundredth is 37.70

CSA = Curved Surface Area

CSA = 37.70 cm²

If you choose to compute the height (h) the you have to know both the radius (r) and the slant height (s):

Formula: height (h) = √s² - r²

Slant height = s = 4

Radius = r = 3

Height = h = ?

Now substitute the values into the formula

h = √s² - r²

h = √4² - 3²

h = √16 - 9

h = √7

h = 2.64575131

Height: 2.64575131 cm

Now it's time to find the surface area and curved surface area, now that you have the height:

Surface area formula given height and radius: πr(r + √(r² + h²))

Substitute the values

Height: 2.64575131
Radius: 3

πr(r + √(r² + h²))

π(3)(3 + √(3² + 2.64575131²))

TSA = (3.141593)(3)(3 + √(3² + 2.64575131²)

TSA = 9.424778(3 + √(3² + 2.64575131²)

TSA = 9.424778(3 + √(9 + 7)

TSA = 9.424778(3 + √(16)

TSA = 9.424778(3 + 4)

TSA = 9.424778(7)

TSA = 65.973446

TSA = 65.97

Next, time to find the Curved surface area:

Formula: CSA = πr√(r² + h²)

CSA = πr√(r² + h²)

Substitute the values into the formula

Radius: 3

Height: 2.64575131

Slant Height: 4

CSA  = πr√(r² + h²)

CSA = π(3)√(3² + 2.64575131²)

CSA = 9.424778√(3² + 2.64575131²)

CSA = 9.424778√(9 + 7)

CSA = 9.424778√(16)

CSA = 9.424778(4)

CSA = 37.699112

CSA = 37.70

So, we can conclude that the Total Surface Area is 65.97 and the Lateral Surface Area is 37.70.

The final amount you will have in the account after 5 years of continuous compounding at an annual interest rate of 10% is approximately $824.36.

Using the formula for continuously compounded interest, we can calculate the final amount you will have in the account after 5 years:

\(A = P x e^(rt)\)

where:

P = $500 (the initial investment)

r = 0.10 (the annual interest rate as a decimal)

t = 5 (the time period in years)

Substituting the values into the formula, we get:

\(A = $500 x e^(0.10 x 5)\)

\(A = $500 x e^(0.50)\)

A = $500 x 1.6487 (rounded to 4 decimal places)

A = $824.36 (rounded to the nearest cent)

Therefore, the final amount you will have in the account after 5 years of continuous compounding at an annual interest rate of 10% is approximately $824.36.

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If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will have in the account after five years?

Morals are frequently seen as standards of conduct that originate within the individual.

Morals refer to personal beliefs and values that guide an individual's behavior and decision-making. They are often influenced by cultural, social, and religious factors and can vary among individuals. Morals provide a framework for distinguishing right from wrong and can shape an individual's sense of integrity and responsibility. Unlike external standards or ethical frameworks imposed by society or institutions, morals are internalized by individuals and serve as a basis for their ethical judgments and actions.

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The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

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Answer:

7.9

Step-by-step explanation:

7.87400787401

Emika's monthly budget is $60.

A percentage can be described as the fraction of a number multiplied by 100. The sign used to represent percentages is %.

Let Emika's cell phone bill budget be represented with x.

In order to determine his monthly budget, divide $60 by 120%

x = $60 / 120%

x = $60 / 1.20

x = $50

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Answer:

3:2

Step-by-step explanation:

42:28

21:14

3:2

Answer:180

Step-by-step explanation: i am in collge

Answer:

The Great Gatsby by F. Scott Fitzgerald

Step-by-step explanation:

Answer:

Step-by-step explanation:

HOPE IT HELPS

The nurse manager approves two staff nurses to attend a national conference.

The nurse manager has given their authorization or consent for two staff nurses to participate in and attend a national conference. This decision indicates that the nurse manager recognizes the value and relevance of the conference for professional development and sees the benefit of the staff nurses' participation. By approving their attendance, the nurse manager demonstrates support for their growth, learning, and exposure to new knowledge, experiences, and networking opportunities available at the conference.

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The value of f(0) is -1

A function can be defined as an expression, law or rule that explains the relationship between two variables; a dependent and an independent variable.

Given the function;

f(x)= -x - 1

To determine f(0), we substitute the value of x as 0 in the function

So, we have;

f(0) = -(0) - 1

f(0) = -0 - 1

f(0) = -1

Thus, the value of f(0) is -1

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To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13

So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.

So, by dividing both sides of the equation by 3, we get:

3x/3 = 6.4/3

x = 2.13

Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer: Screenshot below!

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

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1. The variable is qualitative or quantitative is the variable is qualitative because it is an attribute characteristic (option d). 2. The quantitative variable is discrete or continuous is the variable is discrete because it is countable (option d).

The variable "Hair color" is qualitative because it represents an attribute characteristic rather than a numerical measure. It refers to the different categories or qualities of hair color, such as blonde, brown, black, or red. It is not based on a numerical scale or measurement. Therefore, the correct answer is D) The variable is qualitative because it is an attribute characteristic.

The variable "Number of members present at a meeting" is discrete because it is countable and takes on distinct, separate values. It cannot take on any value between the integers, and there are no fractions or decimals involved. The number of members present can only be whole numbers, such as 0, 1, 2, 3, and so on. Therefore, the correct answer is D) The variable is discrete because it is countable.

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Step-by-step explanation:

Let the distance between them be y

sin20° =

=> 0.342 =           [  sin20° = 0.342]

=> y =  33/ 0.342

=> y = 96.5 ft

So, the distance between them is 96.5 ft

Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

\(\frac{tan(59)}{1} = \frac{h}{45}\)

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.

Answer:

5500m..................

The coordinates of the two closest points on the cone z^2 = x^2 + y^2 to the point (4, 6, 0) are (4, 6, sqrt(52)) and (4, 6, -sqrt(52)).

To find the points on the cone z^2 = x^2 + y^2 that are closest to the point (4, 6, 0), we need to minimize the distance between the point and the cone.

Express the distance: The distance between the point (x, y, z) on the cone and the point (4, 6, 0) can be calculated using the distance formula as d = sqrt((x - 4)^2 + (y - 6)^2 + z^2).

Substitute the equation of the cone: Since the point lies on the cone, we can substitute z^2 = x^2 + y^2 into the distance formula to obtain d = sqrt((x - 4)^2 + (y - 6)^2 + x^2 + y^2).

Minimize the distance: To find the closest point, we need to minimize the distance function d. This can be done by finding the critical points of the distance function by taking the partial derivatives with respect to x and y and setting them equal to zero.

Solve for the critical points: By taking the partial derivatives and setting them equal to zero, we obtain the following equations: 2x - 8 = 0 and 2y - 12 = 0. Solving these equations gives x = 4 and y = 6.

Calculate the coordinates of the closest point: Substituting the values of x and y into the equation of the cone, we find that z^2 = 4^2 + 6^2 = 52. Taking the square root, we get z = ±sqrt(52), so the two points on the cone closest to (4, 6, 0) are (4, 6, sqrt(52)) and (4, 6, -sqrt(52)). The coordinates of the two closest points on the cone z^2 = x^2 + y^2 to the point (4, 6, 0) are (4, 6, sqrt(52)) and (4, 6, -sqrt(52)).

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Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.

The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.

P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.

There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.

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Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)