Find the median and mean of the data set below?

41,13,49,45,31,16

Answer:

the last option

Step-by-step explanation:

The first choice would only target certain customers who come at a very specific time.

the second choice only surveys customers who spend over ten dollars.

The third only surveys muffin eaters!

The last choice has the most unbiased and random sampling to get a sample of all customers.

We know that the vertex form of a parabola is given.  Therefore, there is no parabola that satisfies these conditions.

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is a constant that determines the shape of the parabola.

We are given the vertex (5, 25), so we can write:

y = a(x - 5)^2 + 25

We are also given two points on the parabola: (0, 0) and (10, 0). Plugging these into the equation, we get:

0 = a(0 - 5)^2 + 25 => 25 = 25a => a = 1

0 = a(10 - 5)^2 + 25 => 0 = 25a => a = 0

We get two different values for a, which means that the given points do not lie on the same parabola. Therefore, there is no unique solution to this problem.

We can also see this geometrically: the points (0, 0) and (10, 0) lie on the x-axis, which means that the parabola would have to open either upwards or downwards. However, the vertex is above the x-axis, which means that the parabola cannot intersect the x-axis. Therefore, there is no parabola that satisfies these conditions.

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Check the picture below.

[tex]\tan(23^o )=\cfrac{\stackrel{opposite}{h}}{\underset{adjacent}{35}} \implies 35\tan(23^o)=h \implies 15\approx h\\[/tex]

Make sure your calculator is in Degree mode.

Answer:  [tex]\frac{-3}{10}[/tex]

Given:

   (b + d) - a

Substitute known values:

   ([tex]\frac{3}{5}[/tex] + - [tex]\frac{1}{5}[/tex]) - [tex]\frac{7}{10}[/tex]

Addition and subtraction becomes subtraction:

   ([tex]\frac{3}{5}[/tex] - [tex]\frac{1}{5}[/tex]) - [tex]\frac{7}{10}[/tex]

Subtract:

   [tex]\frac{2}{5}[/tex] - [tex]\frac{7}{10}[/tex]

Common denominators:

   [tex]\frac{4}{10}[/tex] - [tex]\frac{7}{10}[/tex]

Subtract:

   [tex]\frac{-3}{10}[/tex]

To solve the given initial-value problem, we can separate the variables and integrate both sides. The final answer is Therefore, the solution to the initial-value problem is y = [tex]\frac{-1}{(-14t - 1)}[/tex], where y(0) = 1.

Given: y' = [tex]-(14)y^2\\[/tex]

Initial condition: y(0) = 1

Separating variables:

[tex]\frac{Dy}{y^2 }[/tex]= -14 dt

Integrating both sides:

∫([tex]\frac{1}{y^2}[/tex]) dy = ∫-14 dt

Integrating the left side:

[tex]\frac{-1}{y}[/tex]= -14t + C1

Solving for y:

y = [tex]\frac{-1}{-14t + C1}[/tex]

Using the initial condition y(0) = 1:

1 = [tex]\frac{-1}{C1}[/tex]

C1 = -1

Substituting the value of C1 back into the solution:

y = [tex]\frac{-1}{(-14t - 1)}[/tex]

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The curve given by the equation y = x(t^2/t^2 + t + 9) dt on the interval [0,∞) is concave downward on the interval [3, ∞).

To find where the curve is concave downward, we need to take the second derivative of the function and check where it is negative. Taking the second derivative of the given function with respect to x, we get:

y'' = 2t^2(t^2 + 18)/[(t^2 + t + 9)^3]

To find where y'' is negative, we need to solve the inequality 2t^2(t^2 + 18)/[(t^2 + t + 9)^3] < 0. Factoring the numerator, we get:

2t^2(t^2 + 18) = 2t^2(t+√18)(t-√18)

This is negative when t is between -√18 and 0, and also when t is between 0 and √18. However, we need to consider the interval [0,∞) only, which means we should take the solution from the interval [0, √18]. Therefore, the curve is concave downward on the interval [3, ∞).

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Answer:

Thus, the number is equal to x =16 the Answer 16 Basically

The function represented in the table is:

y = 6*cos(x) + 4

Evaluationg this in x = 45 we will get:

y = 3√2 + 4

Here we have the table of the function:

y = a*cos(x) + b

We can see that when x = 0, y = 10, then:

10 = a*cos(0) + b

10  = a + b

And when x = 90, y = 4, then:

4 = a*cos(90) + b

4 = b

Replacing that value in the equation above:

10 = a + 4

10 - 4 = a

6 = a

Then the function is:

y = 6*cos(x) + 4

Evaluating this in x = 45 we will get:

y = 6*cos(45) + 4

y = 6*√2/2 + 4

y = 3√2 + 4

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Thus, a one-way ANOVA test is robust if the data meets the above requirements. It is a powerful statistical tool that can help analyze differences between means of multiple groups.

A one-way ANOVA is a statistical test used to analyze the differences between means of two or more groups. There are certain requirements that need to be met before performing a one-way ANOVA.

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To perform a one-way ANOVA, the observations need to be independent, the data should be normally distributed, and the variances should be equal. However, the test is robust to deviations from these assumptions, particularly if the group sizes are equal.

To perform a one-way ANOVA (Analysis of Variance), there are several requirements you should meet:

The one-way ANOVA is considered robust to deviations from normality and homogeneity of variance, especially when the group sizes are equal. However, if smokes are very unequal or if there are extreme outliers, it might not be as robust.

If these assumptions are not met, a non-parametric alternative like the Kruskal-Wallis test might be a better choice.

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Approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.

Option C is the correct answer.

We have,

To determine the percentage of underclassmen interested in taking a Mandarin course, we need to calculate the ratio of the number of underclassmen interested in Mandarin to the total number of underclassmen.

Looking at the two-way frequency table, we can see that there are 145 underclassmen interested in Mandarin out of a total of 620 underclassmen.

To find the percentage, we divide the number of underclassmen interested in Mandarin by the total number of underclassmen and multiply by 100:

= (145 / 620) x 100

= 23.39%

Therefore,

Approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.

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The probability the student is in drama, given that they are a sophomore is 23%.

What is probability?

Probability is a way of determining how likely something is to happen. Many events are difficult to predict with total certainty. Using it, we can make predictions about the probability of an event happening, or how likely it is.

Total number of students = 20+7+13+20+13+2+25+5+5 = 100

Number of students in sophomore([tex]S_{o}[/tex]) = 20+7+3 = 30

Number of drama students(D) who are in sophomore = 7

To calculate the probability the student is in drama, given that they are a sophomore:

P(drama | sophomore) = [tex]\frac{P(drama \ and \ sophomore)}{P(sophomore)}[/tex] = 23%

Therefore, probability = [tex]\frac{n(D\cap S_{o} )}{n(S_{o} )} =\frac{7}{30} = 23\%[/tex]

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In a two population proportions problem, the use of individual proportions for X and Y (i.e., p_x, q_x, and p_y, q_y) is used for confidence intervals instead of the "common p" used in hypothesis testing.

The reason for this is that in hypothesis testing, we are assuming that the two population proportions are equal (i.e., p_x = p_y = p), which means that we can estimate p using the combined sample proportion. However, in a confidence interval problem, we are interested in estimating the difference between the two population proportions, and using the combined sample proportion to estimate p would not be appropriate. Instead, we use the individual sample proportions for X and Y to construct separate confidence intervals for each population proportion, which we can then use to estimate the difference between them.

In other words, when constructing a confidence interval for the difference in proportions, we are interested in estimating the variability of each population proportion separately, and not the variability of the combined sample proportion. This is why we use the individual sample proportions for X and Y in constructing confidence intervals, rather than the common sample proportion used in hypothesis testing.

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To calculate the standard deviation of hypothetical hours of television watched by high school students per week, we need to use the formula for standard deviation with the given set of numbers.

The standard deviation is a measure of the spread of data around the mean. To calculate the standard deviation of the hypothetical hours of television watched by high school students per week, we need to first determine the mean of the data. Let's say the data set is {10, 8, 12, 6, 14, 10, 8, 16}. The mean is found by adding up all the numbers and dividing by the total number of numbers, which in this case is 10. The sum of the numbers is 84, so the mean is 8.4.

Next, we need to calculate the deviation of each number from the mean. This is done by subtracting the mean from each number. For example, the deviation of the first number (10) is 10 - 8.4 = 1.6. The deviation of the second number (8) is 8 - 8.4 = -0.4 (note that negative deviations indicate values below the mean).

Then, we square each deviation and add up all the squared deviations. This gives us the sum of squared deviations, which is 40.8 for this data set.

Finally, we divide the sum of squared deviations by the total number of numbers minus one, and then take the square root of this value. In this case, the calculation would be:

sqrt(40.8 / (10 - 1)) = 2.31

So the standard deviation of the hypothetical hours of television watched by high school students per week is 2.31 hours. This means that the data is relatively tightly clustered around the mean of 8.4 hours, with most values falling within 2.31 hours of the mean.

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The measure of arc BC in a circle where the two chords, chord AD and chord AC are equal in measure, is 146°. Therefore, the correct option is option C.

The measure of arc made by parallel chord in a circle are equal in measure.

arc BC=8x-46°                

arc AD=5x+26°                

arc BC=arc AD

8x-46°=5x+26°

x=24°

arc BC=8x-46°

arc BC=8(24°)-46°

arc BC=192°-46°

arc BC=146°

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

The smallest integer value of x that satisfies the inequality 3x+4>=14 is 4.

To find the smallest integer value of x that satisfies the inequality 3x+4>=14, we need to isolate x on one side of the inequality sign.

First, we subtract 4 from both sides of the inequality to get:

3x >= 10

Next, we divide both sides of the inequality by 3 to get:

x >= 10/3

So any value of x that is greater than or equal to 10/3 will satisfy the inequality 3x+4>=14. However, since x is an integer, we need to round up to the smallest integer value that satisfies the inequality.

The smallest integer that is greater than or equal to 10/3 is 4, so the smallest integer value of x that satisfies the inequality is 4.

To check this, we can substitute x=4 back into the original inequality:

3(4) + 4 >= 14

12 + 4 >= 14

16 >= 14

Since 16 is indeed greater than or equal to 14, we have verified that x=4 is a valid solution to the inequality.

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The quadratic function for the graph in this problem is given as follows:

y = 2(x + 1)(x - 2).

The roots for the quadratic function in this problem are given as follows:

Hence the linear factors of the function are given as follows:

Considering the factor theorem, the function is given by the product of it's linear factors and the leading coefficient a, hence:

y = a(x + 1)(x - 2)

When x = 0, y = -4, hence the leading coefficient a is obtained as follows:

-2a = -4

2a = 4

a = 2.

Hence the function is:

y = 2(x + 1)(x - 2).

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Check the picture below.

The exact length of the polar curve described by r=4e^(-theta) on the interval 7/6pi ≤ theta ≤ 5pi is approximately 36.60 units.

To find the length of the polar curve, we can use the formula: L = ∫(a to b) sqrt[r^2 + (dr/d theta)^2] d theta. Applying this formula to the given polar curve, we get L = ∫(7/6pi to 5pi) sqrt[(4e^(-theta))^2 + (-4e^(-theta))^2] d theta. Simplifying this expression, we get L = 8∫(7/6pi to 5pi) e^(-theta) dtheta. Evaluating this integral, we get L = 8[e^(-7/6pi) - e^(-5pi)] ≈ 36.60 units.

Therefore, the exact length of the polar curve described by r=4e^(-theta) on the interval 7/6pi ≤ theta ≤ 5pi is approximately 36.60 units. This formula can be used to find the length of any polar curve, given its equation and the interval in which it is being evaluated. It is important to note that the formula for the length of a polar curve is derived using calculus, specifically the arc length formula. The arc length formula is used to find the length of a curve in the Cartesian coordinate system, while the formula for the length of a polar curve is used to find the length of a curve in the polar coordinate system.

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The answer is option D, which is 1 and 8.To find the values of x where f has a removable discontinuity, we need to check if there are any values of x that make the denominator of f(x) equal to zero.

If this occurs, the function will have a vertical asymptote at that point, and if the limit of the function as x approaches that point exists, then the function has a removable discontinuity at that point.

In this case, we can see that the denominator of f(x) is (2x-1)(4x+8), which equals zero at x=1/2 and x=-2. However, we need to check if these values of x result in a removable discontinuity. At x=1/2, the function f(x) is undefined, and the limit as x approaches 1/2 is -1/3. Therefore, f(x) has a removable discontinuity at x=1/2. At x=-2, the function f(x) is also undefined, but the limit as x approaches -2 does not exist. Therefore, f(x) does not have a removable discontinuity at x=-2. Thus, the answer is option D, which includes the value 1 where f has a removable discontinuity, and the value 8 where f does not have a removable discontinuity.

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The probability that it is not raining if the flight leaves on time is 0.9.

Let's define the events:

A: It is raining

B: The flight is delayed

We have,

P(A) = 0.19 (probability that it will rain)

P(B) = 0.1 (probability that the flight will be delayed)

P(A ∩ B) = 0.07 (probability that it will rain and the flight will be delayed)

Using the formula for conditional probability, we have:

P(A' | B') = P(A' ∩ B') / P(B')

Since A' and B' are complementary events (if it's not raining, then the flight is leaving on time), we can rewrite the formula as:

P(A' | B') = P(B' | A') x P(A') / P(B')

We know that P(A) + P(A') = 1, so P(A') = 1 - P(A).

Now, let's substitute the given values into the formula:

P(A' | B') = (P(B' | A') x (1 - P(A))) / P(B')

P(B' | A') represents the probability that the flight is leaving on time given that it's not raining.

We know that:

P(B') = 1 - P(B) = 1 - 0.1 = 0.9

we can estimate P(B' | A') as:

P(B' | A') ≈ P(B') = 0.9

Now we can substitute the values into the formula:

P(A' | B') ≈ (0.9 x (1 - 0.19)) / 0.9

P(A' | B') ≈ 0.81 / 0.9

P(A' | B') ≈ 0.9

Therefore, the probability that it is not raining if the flight leaves on time is 0.9.

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The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

In Mathematics and Geometry, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

According to the Linear Pair Postulate which states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair, we have:

m∠5 + m∠6 =180°.

As a general rule in geometry, the sum of all the angles that are formed by a triangle is equal to 180º and this gives:

m∠2 + m∠3 + m∠5 = 180°.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The variation in assembly times within each assembly method the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.

To determine the degrees of freedom (df1) for the treatment sum of squares, we need to consider the number of groups (assembly methods) being compared.

In this case, there are three different ways of assembling the part. Since there are three groups, the degrees of freedom for the treatment sum of squares is calculated as:

df1 = number of groups - 1

= 3 - 1

= 2

To calculate the degrees of freedom (df2) for the error sum of squares, we need to consider the total number of observations and the number of groups.

In this case, there are 5 people assigned to each assembly method, and there are 3 assembly methods in total. so the total number of observations is 5 * 3 = 15.

df2 = total number of observations - number of groups

= 15 - 3

= 12

Therefore, the degrees of freedom (df1) for the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.

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The Fourier series for the function f(x) = { -1, -1 ≤ x < 0; 1, 0 ≤ x ≤ 1 } in the interval [−1, 1] is (4/π) ∑n=1∞ [sin((2n−1)πx)/(2n−1)]. This represents an odd function and is known as a Fourier sine series.

The Fourier series for the function f(x) = { −1, −1 ≤x < 0; 1, 0 ≤x ≤1 } in the interval [−1, 1] can be expressed as follows:

f(x) = ∑n=0∞ (a0/2 + an cos(nπx) + bn sin(nπx))

where a0, an, and bn are the Fourier coefficients, given by:

a0 = (1/2) ∫−1^1 f(x) dx = 0

an = (1/π) ∫−1^1 f(x) cos(nπx) dx = 2(1−cos(nπ))/nπ

bn = (1/π) ∫−1^1 f(x) sin(nπx) dx = 0

Therefore, the Fourier series for f(x) in the interval [−1, 1] is:

f(x) = ∑n=1∞ [2(1−cos(nπ))/nπ] sin(nπx)

This series can also be written as:

f(x) = (4/π) ∑n=1∞ [sin((2n−1)πx)/(2n−1)]

This is an example of a Fourier sine series since the function f(x) is odd (i.e., f(−x) = −f(x)).

In summary, the Fourier series for f(x) = { −1, −1 ≤x < 0; 1, 0 ≤x ≤1 } in the interval [−1, 1] is given by:

f(x) = (4/π) ∑n=1∞ [sin((2n−1)πx)/(2n−1)]

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The probability of rolling an odd number given you have spun a red section is 1/3 or approximately 33.33%.

The probability of getting a sum of 7 is 20%.

There are three equally likely outcomes when you spin a red section: roll an odd number, roll an even number, or roll a 1. Of these three outcomes, only one corresponds to rolling an odd number. The probability will be:

= 1/3

= 33.33%

There are 5 possible outcomes when you spin the spinner and 6 possible outcomes when you roll the die, so there are 5 x 6 = 30 equally likely outcomes when you play this game. Therefore, the probability of getting a sum of 7 is 6/30 = 1/5 or 20%.

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The box plot that represents the data is the third option.

A box plot is a graph that is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.

The first whisker represents the minimum number and the end of the second whisker represents the maximum number. On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.

The numbers arranged in ascending order : 64, 68, 68, 74, 76, 82, 84, 86, 90, 90, 92,  94,

The minimum number is 64 and the maximum number is 94.

First quartile = 1/4(n + 1)

1/4 x (12 + 1) = 3.25 number = 71

Third quartile =  3/4(n + 1)

3/4 x (12 + 1) = 9.75 number = 90

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Answer:

6

Step-by-step explanation:

£5 - £1.45 = £3.55

£3.55 ÷ 0.53p = 6.698

since you cant have .6 of a pencil, the maximum number of pencils Rio can buy is 6

Answer:

6

Step-by-step explanation:

call £5 500p.

£1.45 =145p

500 - 145 = 355.

355/53 = 6.7

so the maximum number of pencils he can buy is 6.

you can check this by inputting those numbers.

£1.45 + 6 X £0.53

= £1.45 + £(3.18)

=£4.63

Rio still has 37p left. not enough for another pencil

The system of linear equations is not necessarily inconsistent just because its 3x5 augmented matrix has a non-pivot column in the fifth position.

It is possible that the system has infinitely many solutions. However, it is also possible that the system has no solutions. The key factor that determines whether the system is consistent or not is whether the corresponding coefficient matrix has full row rank (i.e., has three pivot rows).

If the coefficient matrix has full row rank, then the system is consistent, regardless of the structure of the augmented matrix. If the coefficient matrix does not have full row rank, then the system is inconsistent.

If the system is consistent, we can use row operations to reduce the augmented matrix to row echelon form or reduced row echelon form, and then use back substitution to find the solutions.

If the system is inconsistent, we can use row operations to derive a contradiction (e.g., a row of the form [0 0 ... 0 b], where b is a nonzero constant), which means that the system has no solutions.

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The sampling method described in which the population is first divided into groups and then random samples are drawn from each group is called stratified sampling. In this sampling method, the population is divided into homogeneous subgroups called strata, based on some characteristic of interest such as age, gender, income level, or geographic location. Random samples are then drawn from each stratum, and the data collected from each sample are combined to form the final sample.

Stratified sampling is often used when the population is heterogeneous, meaning that it has distinct subgroups with different characteristics that may affect the outcome of the study. By dividing the population into homogeneous subgroups, stratified sampling increases the precision of the estimates and reduces the sampling error, compared to simple random sampling. Stratified sampling also ensures that each subgroup of the population is represented in the sample, which may be important for making inferences about the entire population. However, stratified sampling can be more complex and time-consuming than simple random sampling, especially if the population has many subgroups.

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The standard error of the sample mean is 1.25.

The formula for the standard error of the sample mean is s/√n, where s is the standard deviation of the sample and n is the sample size. In this case, s=5 and n=16, so the standard error of the sample mean is 5/√16=1.25.

The standard error measures the variability of sample means that could be obtained from the population, and it decreases as the sample size increases. A smaller standard error means that the sample mean is a more precise estimate of the population mean.

In this example, the standard error of 1.25 indicates that the sample mean of 74 is relatively precise, but without additional information, we cannot determine how accurately it estimates the population mean.

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Answer:

Step-by-step explanation:

Yes, the Student Council advisor's sample method is valid.

In this scenario, the sample method used by the Student Council advisor is known as systematic sampling. The process of selecting every nth element from a population is known as systematic sampling. The advisor in this case polled every tenth student in the lunch line. This method is valid because it guarantees that every student in the population has an equal chance of being chosen and provides a representative sample of the entire student body.

The advisor obtained a sample distribution of their preferred contact methods for school news by surveying 36 students. The advisor discovered that 16 students preferred email, 12 preferred newsletters, 5 preferred announcements, and 3 preferred phone contact from this sample. The proportion of students in the sample who preferred email can be used to estimate the number of students who prefer email among the entire student population.

In this case, 16 of 36 students preferred email, representing 44.44 percent (16/36 * 100). We can estimate the number of students who prefer email by applying this percentage to the total student population if we assume that this proportion remains constant across the entire student population. Given that the school has 684 students, we can expect approximately 303 students (684 * 44.44 percent) to prefer email as their preferred method of communication for school news.

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