Kathleen made 29, 38, 45, 42, and 36 points on her assignments. What is the mean number of points Kathleen made?

The probability of exactly 16 students having jobs in the sample is 0.204 and the probability of 16 or more students having jobs in the sample is 0.334.

Let X be the number of KSU students with jobs in a random sample of 20 students. Since each student in the sample can be either employed or not employed, X follows a binomial distribution with parameters n = 20 (the sample size) and p = 0.50 (the probability of a student having a job).

To find the probability of exactly 16 students having jobs in the sample, we can use the binomial probability mass function

P(X = 16) = (20 choose 16) * 0.5^16 * 0.5^(20-16) = 0.204

To find the probability of 16 or more students having jobs in the sample, we can use the cumulative distribution function

P(X ≥ 16) = 1 - P(X < 16) = 1 - ∑(i=0 to 15) (20 choose i) * 0.5^i * 0.5^(20-i) = 0.334

Based on the sample data, it appears that the proportion of KSU students with jobs is higher than the professor's conjectured value of 0.50. However, we cannot conclusively reject the professor's conjecture based on a single sample of 20 students.

We would need to conduct a hypothesis test with appropriate statistical significance level to determine if the difference between the sample proportion and the conjectured value is statistically significant or not.

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ps dont pay attention to the units theyre just there for an example

Hailey had 3/4 feet of a ribbon, she wanted to keep 1/2 of it and give 1/2 of it to her friend. How much does each person get?

The answer is 3/8

Answer:

x=31, x=31, x=21.

Step-by-step explanation:

So for number 33, we see that 2x+28=90 degrees so you just simplify the equation to 2x=62, x=31.

For number 34, we see that 4x+56=180 (flat line), so we simplify the equation again and get 4x=124, x=31 degrees.

For number 35, according to the vertical angle theorem, 43=2x+1, so we simplify that too and we get 42=2x, 21=x, x=21.

The general solution of non-homogeneous system can be written as:

x = xh + xp = [2t + 1, t, -2s - 2] + [-1, -28, 1]

We can now write the augmented matrix of the system as:

[2    -4    5     8]

[-7   14   4   -28]

[3   -6    1      12]

We can use row reduction to determine whether the system is consistent and to find its solutions.

Performing the row reduction, we get:

[1  -2  0  2]

[0   0  1 -2]

[0   0  0 0]

From the last row of the row-reduced matrix, we can see that the system has a dependent variable, which means that there are infinitely many solutions. We can write the general solution as:

x = x1 = 2t + 1

y = y1 = t

z = z1 = -2s - 2

Here, t and s are arbitrary parameters.

To find a particular solution, we can use any method we like. One method is to use the method of undetermined coefficients. We can guess that xp is a linear combination of the columns of A, with unknown coefficients:

xp = k1[2 -7 3] + k2[-4 14 -6] + k3[5 4 1]

where k1, k2, and k3 are unknown coefficients.

We can substitute this into the system and solve for the coefficients. This gives:

k1 = -1

k2 = -2

k3 = 1

Therefore, a particular solution is:

xp = [-1 -28 1]

So the general solution can be written as:

x = xh + xp = [2t + 1, t, -2s - 2] + [-1, -28, 1]

where t and s are arbitrary parameters.

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ANSWER:

38.46%

STEP-BY-STEP EXPLANATION:

Given:

Problems solved by Thazzie: 5 problems

Problems solved by Zhaniyah: 8 problems

Which means that there are 13 problems in total.

Therefore, those 5 represent the following percent:

Therefore, it represents 38.46% of the problems solved by Thazzie

Answer:

2x - 3 = 11

Step-by-step explanation:

"difference" means subtraction, so it is subtraction.

"twice a number" simply means 2x, since you do not know what the specified number is, it is x. and the 2 and just making it twice the number.

"Is 11" just means equals 11.

so, 2x - 3 = 11.

hope this helps!

If Flyer Co. buys back 5102 shares of their $3 par value common stock for $17 per share. The amount debited to the treasury stock account to record the purchase would be $ 86,834.

To calculate the amount debited to the treasury stock account, we need to multiply the number of shares bought back by the price per share.

In this case, Flyer Co. buys back 5102 shares at $17 per share.

The amount debited to the treasury stock account is calculated as follows:

Amount = Number of shares bought back * Price per share

Amount = 5102 * $17

Amount = $86,834

Therefore, the amount debited to the treasury stock account to record the purchase would be $86,834.

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Answer:

well the volume of a sphere is V = 4/3 x pie x r3 so the radius is half of the diameter so that would be 8 not going to show work but the answer is 2144.66

Answer in order:

False

True

False

False

False

False

False

True

True

Step-by-step explanation:

All of the solutions to the equation\(3x^2 - 12 = 0\)are x = 12 and x = -12

Solve:

Common factor - \(3(x^2-4)=0\)

Divide both sides

\(x^2-4=0\)

Use the quadratic formula

\(x=\sqrt{4,x}=\sqrt{-4\)

x = 2, x = -2

Thus, This is false..

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There are two unique solutions to the equations (x-3)^2 = 16

one variable in matrix = one possible value.

Therefore, x = 7, x = -1

Hence this is True

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The solutions for the equation 2(x-3)^2-18 = 0 are x = 6 and x = 0

\(2x^3-18x^2+54x-72=0\)

\(x=5.080084\)

Hence this is false

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The solutions for the equation 2(x-5)^2-8=0 are x = 7 and x = -7

Add both sides by 8

2(x-5)^2-8+8=0+8

2(x-5)^2=8

(x-5)^2=4

x = 7, x = 3

Hence, this is false

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The solutions for the equation (x + 3)^2-25 = -8 are x = 2 and x = -8

\((x+3)^2=17\)

\(x=\sqrt{17-3,}=-\sqrt{17}-3\)

Hence this is false.

-------------------------------------------------------------------------------------------------------------

The solutions for the equation 2(2x-1)^2=18 are x = 5 and x = -4

\((2x-1)^2=9\)

x=2, x = -1

Hence this is false.

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The only solution for equation (2x-1)^2-49=0 is x = 4

\((2x-1)^2=49\)

x = 4, x = -3

Hence, this is false

-------------------------------------------------------------------------------------------------------------

The solutions for the equation 3(x+2)^2 - 3 = 0 are x = -3 and x = -1

\(3(x+2)^2=3\)

\((x+2)^2=1\)

x = -1, x = -3

Hence, this is true

-------------------------------------------------------------------------------------------------------------

The solutions for the equation 5x^2 - 180 = 0 are x = 6 and x  = -6

Add 180 to both sides

\(5x^2-180+180=0+180\)

\(5x^2 = 180\)

\(x^2 = 36\)

\(x=\sqrt{36},x=-\sqrt{36}\)

x = 6, x = -6

Hence, this is true.

-------------------------------------------------------------------------------------------------------------

[RevyBreeze]

The total number of intervals in a frequency distribution for a numerical variable can vary depending on the range and nature of the data, typically ranging from a minimum of 5 to a maximum of 20 intervals.

A frequency distribution is a representation of data that organizes values into intervals or bins and shows the number of occurrences or frequencies within each interval. The choice of the number of intervals depends on the characteristics of the data and the desired level of detail in the distribution. Generally, it is recommended to have at least five intervals to capture the overall pattern of the data. Too few intervals may oversimplify the distribution, while too many intervals may result in excessive detail and difficulty in interpretation.

The maximum number of intervals, often around 20, is determined by the data range and the desired level of granularity. When the range of values is large or the data contains outliers, more intervals may be needed to capture the variations accurately. On the other hand, if the range is small or the data is relatively homogenous, a smaller number of intervals may suffice. Balancing the level of detail with the readability and interpretability of the distribution is essential to effectively communicate the information contained in the data.

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A frequency distribution for a numerical variable is a statistical tool that groups the data into intervals and counts the frequency of observations within each interval. The total number of intervals typically ranges from 5 to 20. However, the choice of how many intervals to use depends on the total number of observations in the dataset and the need to balance detail with complexity.

In the realm of statistics, creating a frequency distribution for a numerical variable is a common task. In a frequency distribution, data is grouped into intervals or classes, and the frequency of observations within each interval is counted. When determining the number of intervals, it often depends on the total number of observations in the dataset.

Typically, the total number of intervals in a frequency distribution may range from 5 to 20. These are rough guidelines though, and the number of intervals you decide upon should best represent the data and make it easier to interpret.  

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Answer: Small Campground: 15 garbage cans

Large Campground: 45 garbage cans

Step-by-step explanation: If there are 40 picnic tables in a small campground, there should be 15 garbage cans. Because 40/8=5 and 5*3=15. If there are 120 picnic tables in a large campground, there should be 45 garbage cans. Because 120/8=15 and 15*3=45

Answer: A. removing 1 x-tile from each side

Step-by-step explanation: To solve the equation represented by the model, we need to remove 3 unit tiles from the right side, since each unit tile represents a value of 1. Then, we need to arrange the tiles into equal groups to match the number of x-tiles. We can see that there are 2 x-tiles and 2 unit tiles on the left side, which means that each x-tile represents a value of 1.

Therefore, the solution is x = 1. Answer choice A.

There are 42 subsets of size two that contain at least one of the elements of {1, 2, 3}.

There are \(${8\choose2}=28$\) subsets of size two that can be formed from the set {1, 2, 3, 4, 5, 6, 7, 8}.

To count the number of subsets of size two that contain at least one of the elements of {1, 2, 3}, we can use the principle of inclusion-exclusion.

Let A be the set of subsets of size two that contain 1, B be the set of subsets of size two that contain 2, and C be the set of subsets of size two that contain 3. We want to count the size of the union of these three sets, i.e., the number of subsets of size two that contain at least one of the elements of {1, 2, 3}.

By the principle of inclusion-exclusion, we have:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

To calculate the sizes of these sets, we can use combinations. For example, |A| is the number of subsets of size two that can be formed from {1, 2, 3, 4, 5, 6, 7, 8} with 1 as one of the elements. This is equal to \(${3\choose1}{5\choose1}=15$\), since we must choose one of the three elements in {1, 2, 3} and one of the five remaining elements.

Similarly, we have:

|A| = \(${3\choose1}{5\choose1}=15$\)

|B| = \(${3\choose1}{5\choose1}=15$\)

|C| = \(${3\choose1}{5\choose1}=15$\)

|A ∩ B| = \(${2\choose1}{5\choose0}=2$\), since there are two elements in {1, 2} that must be included in the subset, and we can choose the other element from the remaining five.

|A ∩ C| = \(${2\choose1}{5\choose0}=2$\)

|B ∩ C| = \(${2\choose1}{5\choose0}=2$\)

|A ∩ B ∩ C| = \(${3\choose2}=3$\), since there are three elements in {1, 2, 3} and we must choose two of them.

Substituting these values into the inclusion-exclusion formula, we get:

|A ∪ B ∪ C|\(= 15 + 15 + 15 - 2 - 2 - 2 + 3 = 42\)

Therefore, there are 42 subsets of size two that contain at least one of the elements of {1, 2, 3}.

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Answer:

x = 7.2

Step-by-step explanation:

\(5(x - 3) = 21\)

\(x - 3 = 4.2\)

\(x = 7.2\)

Okay, it seems like you want to analyze a sample of 16 babies based on their weight.

The information you provided states that the Center for Disease Control and Prevention reports that 25% of baby boys aged 6-8 months in the United States weigh more than 20 pounds.

However, you haven't mentioned the specific question or analysis you want to perform on the sample. Could you please clarify what you would like to know or do with the given information?

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Answer:

JT = 29

Step-by-step explanation:

CT=CJ+JT

69= (4x+8)+ ( 3x+5)

69= 7x +13

7x= 69-13

7x= 56

x=56/7

x=8

JT=3x+5=3(8)+5= 24+5=29

I hope I helped you^_^

Answer:

Δy = 5  Δx = 1

slope = \(\frac{5}{1}\) = 5

Step-by-step explanation:

The width of the garden is 18 feet. In this case, the length of the diagonal of the rectangular garden is the hypotenuse, and the length and width of the garden are the other two sides. Let's denote the width of the garden as "w".

Given:

Length of the garden = 24 feet

Diagonal of the garden = 30 feet

Using the Pythagorean theorem, we can set up the following equation:

\(24^2\) + \(w^2\) = \(30^2\)

Simplifying:

576 + \(w^2\) = 900

Subtracting 576 from both sides:

\(w^2\) = 900 - 576

\(w^2\) = 324

Taking the square root of both sides:

w = √324

w = 18

So, the width of the garden is 18 feet.

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we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324 Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

Using the Pythagorean theorem, we can find the width of the garden. If the length is 24 feet and the diagonal is 30 feet, then the width can be found by taking the square root of (30^2 - 24^2), which is approximately 18.97 feet.

Therefore, the garden is about 18.97 feet wide. We can use the Pythagorean theorem to find the width of the rectangular garden.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal across the garden is the hypotenuse, and the length and width of the garden are the other two sides.

The diagonal is 30 feet, and the length is 24 feet. We need to find the width (w).

The Pythagorean theorem formula is:a² + b² = c²Where 'a' and 'b' are the two shorter sides, and 'c' is the hypotenuse.

In this case, we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

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Answer:

the answer is a. 2cos2(x) - 1) 2 -1

Step-by-step explanation:

an easy way to check is to graph every equation and see which ones line up. i did this and a was the right answer :)   (edge 2020)

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is B.

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.

Cos2x is a double angle trigonometric identity because the angle under consideration is a multiple of 2, or the double of x.

Therefore, The expression that is equivalent to cos(4x) is 2cos²(2x) – 1.

Hence, the correct option is B.

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The population parameter will always be between lower and upper bounds of the confidence interval. - True, whereas sample statistic will always be between lower and upper bounds of the confidence interval - False

With a certain degree of certainty, the population parameter is anticipated to lie between the lower and higher limits of the confidence interval. The confidence interval, which gives an interval estimate of the unidentified population parameter, is created based on the sample data. The interval's level of confidence shows the amount of ambiguity we are prepared to accept when determining the actual population parameter.

The confidence interval's lower and upper limits may or may not be met by the sample statistic used to compute them. A single point estimate, the sample figure is susceptible to sampling error. On the other hand, based on the observed sample data and the selected degree of confidence, the confidence interval is a range of values that we can be fairly confident includes the true population parameter.

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The probability that the number of 0's in a randomly generated bit string of length 8 is different from the number of 1's is 56/256, or 7/32.

To understand why, let's consider the possible combinations of 0's and 1's in an 8-bit string. There are a total of 2^8 = 256 possible outcomes. Out of these, we need to determine the number of outcomes where the number of 0's and 1's is different.

One way to approach this is by counting the number of strings with 4 zeros and 4 ones, and then subtracting it from the total number of outcomes. The number of ways to arrange 4 zeros and 4 ones is given by the binomial coefficient C(8,4) = 70. Thus, there are 70 outcomes where the number of 0's and 1's is equal.

Subtracting this from the total number of outcomes, we get 256 - 70 = 186 outcomes where the number of 0's and 1's is different. Therefore, the probability of having an unequal number of 0's and 1's is 186/256, which simplifies to 7/32, or approximately 21.9%.

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Yes, the mysteries equal 0.06 of the total books.

Marcella said that the mysteries equal 0.06 of the total books.

To check the mysteries equal 0.06 of the total books is correct or not.

We can follow these steps:

1. Identify the total number of books and the number of mysteries: Marcella read 100 books, and 60 of them were mysteries.

2. Calculate the fraction of mysteries: Divide the number of mysteries (60) by the total number of books (100) to find the fraction of mysteries.

3. Compare the fraction with Marcella's claim: If the calculated fraction equals 0.06, then she is correct.

Now let's perform the calculations:

60 mysteries ÷ 100 total books = 0.6

Since 0.6 ≠ 0.06, Marcella's claim that the mysteries equal 0.06 of the total books is incorrect. In reality, mysteries make up 0.6 or 60% of the total books she read.

A model to support this answer could be a pie chart, where the circle represents the 100 books, and the mysteries portion is shaded in. By dividing the circle into 10 equal sections, the mysteries would fill 6 of those sections, which represents 60% of the total books.

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To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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Answer:

5/7+3/8=40/56+21/56

=61/56=1/5/56

1/6+5/6=6/6=1

5/6+1/3=5/6+2/6

=7/6=1/1/6

3/4/5+7/1/2=19/5+15/2

=38/10+75/10

=113/10=11/3/10

3/3/4+5/1/3=15/4+16/3

=45/12+64/12

=109/12=9/1/12

2/3-5/8=16/24-10/24

=6/24=1/4

3/7-1/6=18/42-7/42

=11/42

2/3-2/4=8/12-6/12

=2/12=1/6

16/2/3-12/2/5=50/3-62/5

=250/15-186/15

=64/15=4/4/15

7/5/6-3/1/4=47/6-13/4

=94/12-39/12

=55/12=4/7/12

Answer:

\(m=-2\)

Step-by-step explanation:

\(\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(2,\:-2\right)\)

Answer:

-2 is the answer .

Step-by-step explanation:

Good luck ^^

The shift of the function y = log(x+4) -3 is 4 units left and 3 units down

From the question, we have the following parameters that can be used in our computation:

y = log(x + 4)

The above equation is a logarithmic equation

So, the parent function is

y = log(x)

When the parent function is compared to the given function, we have

3 units down and 4 units left

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Answer:

A

I believe because p→q

q→p

Answer:

answer is »»»4. 3

Step-by-step explanation:

Use a factor tree to express 60 as a product of prime factors. So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2 2 × 3 × 5. The actual prime factors of 60 are 2, 3, and 5.