What is the median of the data set?

3, 10, 1, 6, 10, 3, 11, 14

Answer: \(a=\frac{9}{2}, b=\frac{15}{2}\)

Step-by-step explanation:

By the geometric mean theorem,

\(\sqrt{8a}=6\\\\8a=36\\\\a=\frac{36}{8}=\frac{9}{2}\)

Using the Pythagorean theorem to solve for b,

\(6^{2}+\left(\frac{9}{2} \right)^{2}=b^{2}\\\\36+\frac{81}{4}=b^{2}\\\\\frac{225}{4}=b^2\\\\b=\frac{15}{2}\)

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

If you know a study does not use a probability sample, a good question to ask to determine if the study has external validity is to inquire whether the findings are applicable to individuals whose location and situation differs from those of participants of the study.

External validity refers to the extent to which the findings of a research study can be generalized to the larger population applicable to other people, situations, settings, and measures. It determines if findings of the study are relevant in a broader context. The objective is to produce generalizable information about the real world. If a random sampling has been used in a study, the sampling methods unbiasedness is strong evidence for external validity.

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The number of tickets purchased for a randomly chosen Olympic event. is the continuous random variable.

y is the number of tickets purchased for a randomly chosen Olympics event. is the random variable y discrete or continuous?

A random variable is a numerical quantity that is generated by a random experiment.

A random variable is called discrete if it has either a finite or a countable number of possible values. A random variable is called continuous if its possible values contain a whole interval of numbers.

A random variable is a number generated by a random experiment.

A random variable is called discrete if its possible values form a finite or countable set.

A random variable is called continuous if its possible values contain a whole interval of numbers.

In Olympics , number of event are there . that are not countable.

therefor, the number of tickets purchased for a randomly chosen Olympic event. is the continuous random variable.

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A random variable is a numerical quantity that is generated by a random experiment.

A random variable is called discrete if it has either a finite or a countable number of possible values. A random variable is called continuous if its possible values contain a whole interval of numbers.

A random variable is called continuous if its possible values contain a whole interval of numbers.

The number of tickets purchased for a randomly chosen Olympic event. is the continuous random variable.

Answer:

x=4 and y=2

Step-by-step explanation:

Quartiles divide data sets in fourths.

In statistics, a quartile is a specific kind of quantile that splits the total number of data points into four roughly equal portions, or quarters. Quartiles are a type of order statistic since they require the data to be arranged from smallest to largest in order to be computed.

Quartiles (Quartiles are the most prevalent percentiles. Data sets are divided into quadruples, or four equal sections, by quartiles. The bottom 25% of the data are separated from the top 75% by the first quartile, abbreviated Q1. The first quartile therefore corresponds to the 25th percentile. The second quartile, or Q2, separates the bottom 50% of the data from the top 50%; it is corresponding to the median or 50th percentile. The third quartile, or Q3, which corresponds to the 75th percentile, separates the bottom 75% of the data from the top 25%.

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Answer:

Step-by-step explanation:

Ratio of side of the 30-60-90 triangle is x : x√3 : 2x

Side opposite to 30° is the shortest leg and it is a

Side opposite to 60° is the longest leg and it is a√3

side opposite to 90° is hypotenuse and it is 2a and it the longest side.

7) a = 8 (Which is opposite to 30°)

 w = 2a = 2*8

w = 16

v = √3a = √3 *8

v = 8√3

8) a√3 = 5√3   (Which opposite to 60°)

   a = 5√3 ÷√3

y = a ⇒y= 5

x = 2a

  = 2*5

x = 10

9) hypotenuse = 10

2a = 10

a = 10 ÷ 2

a = 5

x = a√3

x = 5√3

y = a

y = 5

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

Well to calculate slope you just do

y2-y1/ X2-x1

In this case

9-8/3-2

Which is 1/1

THe slope is 1

Answer:

1

Step-by-step explanation:

The slope is going to be the ratio between the difference of y coordinates, and the difference in x coordinates.

\(m= \frac{\Delta y}{\Delta x} = \frac{3-2}{9-8} = \frac11 = 1\)

The similarity lies in the fact that both lists contain the same set of numbers, but their order is determined by different criteria - one based on magnitude and the other based on distance from zero.

Let's order the numbers -3, 5, -10, and 16 as requested.

From least to greatest:

-10, -3, 5, 16

The ordered list from least to greatest is: -10, -3, 5, 16.

Now let's order the same numbers from closest to zero to farthest from zero:

-3, 5, -10, 16

The ordered list from closest to zero to farthest from zero is: -3, 5, -10, 16.

Regarding the similarity between the two lists, both lists contain the same set of numbers: -3, 5, -10, and 16. However, the ordering criteria are different in each case. In the first list, we order the numbers based on their magnitudes, whereas in the second list, we order them based on their distances from zero.

By comparing the two lists, we can observe that the ordering changes since the criteria differ. In the first list, the number -10 appears first because it has the smallest magnitude, while in the second list, -3 appears first because it is closest to zero.

Overall, the similarity lies in the fact that both lists contain the same set of numbers, but their order is determined by different criteria - one based on magnitude and the other based on distance from zero.

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The correct answer is: A. The radius of convergence is finite and at least 4.

To find the minimum value for the radius of convergence of a power series solution, we need to consider the coefficients of the differential equation.

The given differential equation is:

(x^2 - 9x + 20)y" - 3xy' - y = 0

The coefficients of the differential equation are polynomial functions of x. In this case, the coefficients are:

a(x) = x^2 - 9x + 20

b(x) = -3x

c(x) = -1

To determine the minimum value for the radius of convergence, we need to find the point where the coefficient functions a(x), b(x), and c(x) have a singularity or a point where they become infinite.

Let's solve for the roots of a(x) = 0:

x^2 - 9x + 20 = 0

Using the quadratic formula, we find:

x = (9 ± √(9^2 - 4120))/(2*1)

Simplifying further, we get:

x = (9 ± √(81 - 80))/2

x = (9 ± 1)/2

So the roots of a(x) = 0 are x = 5 and x = 4.

The minimum value for the radius of convergence occurs at the closest singularity to the expansion point x = 0. In this case, the closest singularity is x = 4. Therefore, the minimum value for the radius of convergence is 4.

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The average speed is the ratio of the total distance to the total time. Then the average speed of the airplane will be 698.19 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

An airplane files 867 miles with a constant speed of 612 mph and then another 1984 miles with a constant speed of 744 mph.

Then time taken for the first trip will be

t₁ = 867 / 612

t₁ = 1.4167 hours

Then time taken for the second trip will be

t₂ = 1984 / 744

t₂ = 2.6667 hours

Then the average speed is the ratio of the total distance to the total time.

The total distance will be

Total distance = 867 + 1984

Total distance = 2851 miles

The total time will be

Total distance = 1.4167 + 2.6667

Total distance = 4.0834 hours

Then the average speed will be

Average speed = 2851 / 4.0834

Average speed = 698.19 mi/h

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The greatest rate of change can be seen in a straight line plotted using the coordinates of the tabular data in part [B].

The slope of a straight line is the measure of the tangent of the angle that the line makes with the + x axis. The intercept of a straight line is -

y = mx + c

from this we can write slope [m] as -

mx = y - c

m = (y - c)/x

If y - intercept [c] is zero, then -

m = y/x

Given is a equation, tabular data and a graph representing a straight line

Slope of a line also tells us about the rate of change of [y] value with respect to the [x] value.

[A]

For the equation -

D = 55t

The slope will be [m] = 55.

[B]

For the tabular data, take two coordinates -

(1, 475) and (2, 535)

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

The slope will be -

[m] = (535 - 475)/(2 - 1)

[m] = 60

[C]

For the graph we have a straight line that passes through the coordinates as follows -

(0, 100)

(1, 150)    

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (150 - 100)/(1 - 0)

[m] = 50

The slope of the line is maximum for the tabular data [B].

Therefore, the greatest rate of change can be seen in a straight line plotted using the coordinates of the tabular data in part [B].

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The probability of event F given that event E has occurred is approximately 0.5850.

The conditional probability of an event F given that event E has occurred is the probability that both events E and F occur, divided by the probability that event E occurs. It is denoted as P(F|E).

In this problem, Here,  P(E) = 0.326, P(F) = 0.298, and P(E ∩ F) = 0.191. We want to calculate P(F|E).

Using the conditional probability formula, we have:

P(F|E) = P(E ∩ F) / P(E)

Substituting the given probabilities, we get:

P(F|E) = 0.191 / 0.326

Simplifying the expression, we get:

P(F|E) ≈ 0.5850

Therefore, the probability of event F given that event E has occurred is approximately 0.5850.

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Answer:

4) Dmytro drank more juice

5) Henrietta is older

Step-by-step explanation:

4)

Dmytro drank 7/4 bottles which is 1.75 bottles

Jitka drank 1 1/2 bottles which is 1.5 bottles

So, Dmytro drank more juice

5)

Henrietta is 7 2/3 years old which is 7.66

Jagdeep is 65/12 years old which is 5.41

So, Henrietta is older

Answer:

edgar

Step-by-step explanation:

edgar - 5.75 times 3 = 17.25

fiona - 7.50 times 5 = 37.50

edgar payed least since he has the smallest value

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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Answer: 15/14

Step-by-step explanation:

Use the slope formula: y2-y1/x2-x1

Apply that:

-15-0/-11-3 = -15/-14 = 15/14

Answer:

Step-by-step explanation:

Accurate estimation of 33% of 146.7

A) Round the percent and find 30% of 146.7

B) Round the number and find 33% of 150

C) Use benchmark percent and find 50%

of 146.7

D) Round the percent and number and

find 30% of 150

E) All of them would be an accurate  estimation

Answer:

14, square root of 200, 15

Step-by-step explanation:

square root of 200=14.14

Answer:

im positive it would be 2

Step-by-step explanation:

Answer: The slope is -2x. The slope intercept form is Y = -2x - 4

Step-by-step explanation:

Get y by itself just like you are solving for it, all you need to do is subtract 2x

y = -2x - 4

Answer:

x = 8

Step-by-step explanation:

Answer: Jina bought 5 pounds of coffee by spending a total of $38.60.

Step-by-step explanation:

According to this problem, Jina has an $80 gift card for a coffee store and when she bought some pounds of coffee, she had $41.40 left.

To solve this equation you will need to rephrase this equation to

80 - 41.40 = x

When you subtract the problem, you should get $38.60.

80 - 41.40 = 38.60

Now since Jina bough coffee that costs $7.72 per pound, you will need to divide that by the amount you have just subtracted.

38.60 ÷ 7.72

When you divide "38.60 ÷ 7.72", you should get the number 5.

Therefore, Jina bought 5 pounds worth of coffee, making her total on her gift card $38.60. Hope this helps!

-From 5th Grade Honors Student

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

Step-by-step explanation:

Given:

n= Total number of random sample of people taken=400

x= Number of people who provided yes responses= 124

P= The point of estimate of the sample of the population portion taken=?

Now,

P=x/n

P=124/400

P= 124/4×100

P= 32/100

P= 0.32 or 32%

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0.31 or 31% is the point estimate of the proportion of the population that would provide yes responses

Estimate of Proportion: If we divide the random variable, the mean, and the standard deviation by n, we get a normal distribution of proportions with P′, called the estimated proportion, as the random variable. (Recall that a proportion as the number of successes divided by n.)

a simple random sample of 400 individuals provides 124 yes responses

The point estimate of individuals that would provide yes responses is the sample proportion.

n= Total number of random sample of people taken=400

x= Number of people who provided yes responses= 124

P= The point of estimate of the sample of the population portion taken

The sample proportion is calculated by dividing number of yes responses by sample size

p = x/n = 124/400= 0.31 or 31%

0.31 or 31% is the point estimate of the proportion of the population that would provide yes responses

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