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The value of the 10% trimmed mean is approximately 1.3027. To calculate the 10% trimmed mean, we need to trim off the lowest and highest 10% of the data and then find the mean of the remaining values.

First, let's sort the data in ascending order:

0.2, 0.21, 0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26, 3.06, 3.24

Next, we calculate the number of values to trim from each end:

10% of 15 (total number of values) = 0.1 * 15 = 1.5

Since we can't remove half a value, we round up to the nearest whole number, which is 2.

Now, we remove the two lowest and two highest values:

0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26

Finally, we calculate the mean of the remaining values:

(0.26 + 0.3 + 0.33 + 0.41 + 0.54 + 0.57 + 1.41 + 1.7 + 1.84 + 2.2 + 2.26) / 11 = 14.33 / 11 ≈ 1.3027

Rounding to four decimal places, the value of the 10% trimmed mean is approximately 1.3027.

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The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)

Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

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Based on the information of an equilateral triangle △STU and the congruence of angles ∠TXU and ∠TVS, it can be concluded that UX is congruent (≅) to SV. The proof involves establishing the congruence of corresponding angles and applying the angle-angle (AA) congruence criterion.

To prove that UX is congruent (≅) to SV using the information, we will utilize the fact that △STU is an equilateral triangle and the congruence of angles ∠TXU and ∠TVS.

We have:

△STU is an equilateral triangle (∠STU = ∠TUS = ∠UST = 60 degrees)

∠TXU ≅ ∠TVS

Proof:

1. Draw a diagram of equilateral triangle △STU.

2. Draw a line segment UX and SV originating from U and S, respectively, towards the interior of the triangle.

3. ∠TXU and ∠TVS are congruent (given).

4. ∠STU = ∠TUS = ∠UST = 60 degrees (equilateral triangle property).

5. Since ∠STU and ∠TUS are both equal to 60 degrees and ∠TXU ≅ ∠TVS, we can conclude that ∠UTX ≅ ∠VTS (angle sum property of triangles).

6. By Angle-Angle (AA) congruence, ∆UTX ≅ ∆VTS.

7. Since corresponding parts of congruent triangles are congruent, we have UX ≅ SV (side UT ≅ side VT).

Therefore, we have proved that UX is congruent (≅) to SV using the information.

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The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.

Here,

The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.

=(1+2+3+4+5+6+7+8)/2

=18

Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.

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The correct statement are:

Based on the given information, we can make the following conclusions:

A. The interquartile range for high school students is smaller than college students.

The statement is False

B. The mean for high school students is smaller than college students.

The statement is False because the mean of College is 25.28 and mean for High school is 30.4.

C. The range for high school students is larger than college students.

The statement is True .

D. The college median is equal to the high school median.

The statement is True because the median for both is 24..

E. The mean absolute deviation is larger for college students than high school students.

The statement is False.

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Answer:

y+1=(x+7)/3

Step-by-step explanation:

slope = (-1-3)/(-7-5) = -4/-12 = 1/3

b = 3-(1/3)×5 = 4/3

y = mx+b

or, y = x/3+4/3

its point slope form,

y = x/3+4/3

or, y=(x+4)/3

or, y+1=(x+4)/3+1

or, y+1=(x+4+3)/7

or, y+1 =(x+7)/3

The equation of the line that pass thought the given points will be y+1 =(x+7)/3.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the data in the question,

Slope = (-1-3)/(-7-5)

= -4/-12

= 1/3

b = 3-(1/3) × 5

b = 4/3

As per the expression for slope,

y = mx+b

y = x/3+4/3

Now, point in slope form

y = x/3+4/3

y=(x+4)/3

y+1=(x+4)/3+1

y+1=(x+4+3)/7

y+1 =(x+7)/3

This is the expression for the line.

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Answer:

First is no solution, second is unique solution (-3,0)

Step-by-step explanation:

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Yes, when multiplying an inequality by a negative, the inequality sign must be flipped.

This is because the negative number changes the direction of the inequality. For example, if the inequality is x > 4, and we multiply both sides by -2, the inequality becomes -2x < -8. The left side is now less than the right side, so the inequality sign must be changed to <. Mathematically, this can be shown as follows:

Let x > 4

Multiply both sides by -2:

-2x > -8

Flip the inequality sign:

-2x < -8

Therefore, when multiplying an inequality by a negative number, the inequality sign must be flipped.

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Initial Perimeter = 2(890+2891)

=> 2781×2

=> 5662 cm

Increase in length = 890+66 => 956 cm

Final Perimeter = 2 (956+2891)

=> 3847×2

Answer:

20%

Step-by-step explanation:

Given/To Find:

A $52.50 screen door is on

sale for $42. Find the percent

of discount on the door.

Solve:

Formula: Value 1 - Value 2 ÷ Original Value × 100

Hence we have:

52.50 - 42 = 10.5

10.5 ÷ 52.50 = 0.20

0.20 × 100

=20%

Check Answer:

52.50 × 20% = 10.5

52.50 - 10.5 = 42

Hence, the percent of discount on the door is 20%

Kavinsky

Answer:

22

Step-by-step explanation:

the terms are counting by 3. making it by adding three to the lest term will give you the answer.

The solution to the equation is -1.5 or -3/2.

We have the equation:

x² + 3-2x= 1+ x² +5

Combine Terms and subtract x² from both sides:

x² - x² + 3 -2x = 1 + 5 + x² - x²

3 -2x = 1 + 5

Add:

3 -2x = 6

Combine Terms and subtract 3 from both sides:

-2x + 3 -3 = 6 - 3

-2x = 3

Dividing by -2 we get:

x = 3/(-2)

x = -3/2

x = -1.5

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Answer:

\( 3,813.33 \: {cm}^{3} \)

Step-by-step explanation:

Volume of the space that is not occupied = Volume of cube shaped box - volume of soccer ball

\( = {20}^{3} - \frac{4}{3} \times 3.14 \times {10}^{3} \\ \\ = 8000 - \frac{4}{3} \times 3.14 \times 1000 \\ \\ = 8000 - \frac{4}{3} \times 3140 \\ \\ = 8000 - \frac{12560}{3} \\ \\ = 8000 - 4,186.66667 \\ \\ = 3,813.33333 \\ \\ = 3,813.33 \: {cm}^{3} \)

Answer:

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

Use the formula for simple interest:

where:

Substituting the given values into the formula, we get:

Therefore, the rate of interest per year is 8%.

Answer:

Larger groups tends to take less time to solve the puzzle.

Step-by-step explanation:

It is given that Vincent gathered few groups from 1 to 8 people and he gave them the same puzzle to solve for each group. The graph is provided which show the relationship between the number of groups and the time taken by each group to solve the puzzle.

From the graph, it cam be seen that, the larger groups is more likely to take less amount of time to solve the puzzle as compared to the smaller groups.

Answer:

B

Step-by-step explanation:

Khan Academy says so

The correct statistical procedure to answer this research question is A one-sample t-test for means.(Option C)

To answer the research question of whether the average heart rate for Canadians who participate in the innovative fitness program is lower than the national average heart rate, the appropriate statistical procedure to use is a one-sample t-test for means.

The reason we use a t-test is that we are comparing the sample mean (68.5 bpm) to a known population mean (72 bpm) with known standard deviation (6 bpm). The t-test is commonly used when the population standard deviation is unknown or when the sample size is small (in this case, n = 26).

The t-test will help determine if the difference between the sample mean and the population mean is statistically significant. It will calculate a t-value by comparing the observed difference with the standard error of the mean, taking into account the sample size and sample standard deviation.

Therefore, the correct statistical procedure to answer this research question is C. A one-sample t-test for means.

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Answer:

DF = 28 units

AC = 64 units

CF = 32 units

Step-by-step explanation:

In the given triangle ABC points D, E and F are the midpoints of the sides AB, BC and AC.

By midsegment theorem,

"Segment joining the midpoints of each side is parallel and measure the half of the opposite side"

DF = \(\frac{1}{2}(BC)\)

     = \(\frac{56}{2}\)

     = 28 units

AC = 2(DE)

     = 2 × 32

     = 64 units

CF = \(\frac{1}{2}(AC)\)

     = \(\frac{64}{2}\)

     = 32 units

A factor in an experiment that changes from the manipulation of the independent variable is the dependent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

The variable being measured or tested in an experiment is known as the dependent variable. 1 The results of the participants' tests, for instance, since that is what is being measured, would be the dependent variable in a study looking at how tutoring affects test scores.

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Answer:

-1

Step-by-step explanation:

-5(-x-4)-3x-5=13

5x+20-3x-5=13

2x+15=13

2x=-2

x=-1

Answer:

205 mins

Step-by-step explanation:

Sentence representing an inequality of a number m is more than -7 2/3 or at most -10 is given by (m>-19/3) ∪(m≤-10).

As given in the question,

Condition for a number m as an inequality is given by:

m is more than -7 2/3

Simplify -7 2/3=-19/3

m>-19/3 __(1)

m at most -10

m≤-10 _(2)

From (1) and (2)

m is more than -7 2/3 or at most -10 is:

'or' represent the symbol of union

(m>-19/3)∪(m≤-10)

Therefore, sentence representing an inequality of a number m is more than -7 2/3 or at most -10 is given by (m>-19/3)∪(m≤ -10).

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Answer:

\(U = x\)

\(V=10\)

Step-by-step explanation:

Given

\((x +3)^2 + 14(x + 3) + 49 = (U + V)^2\)

Required

Find U and V

We have:

\((x +3)^2 + 14(x + 3) + 49 = (U + V)^2\)

Expand

\(x^2 + 6x + 9 + 14x + 42 + 49 = (U + V)^2\)

Collect like terms

\(x^2 + 6x + 14x + 9 + 42 + 49 = (U + V)^2\)

\(x^2 + 20x + 100 = (U + V)^2\)

Expand

\(x^2 + 10x + 10x + 100 = (U + V)^2\)

Group

\([x^2 + 10x] + [10x + 100] = (U + V)^2\)

Factorize each group

\(x[x + 10] + 10[x + 10] = (U + V)^2\)

Factor out x + 10

\([x + 10][x + 10] = (U + V)^2\)

So, we have:

\([x + 10]^2 = (U + V)^2\)

By comparison

\(U = x\)

\(V=10\)

Answer:

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

Step-by-step explanation:

Given:

Which of the relations given by the following sets of ordered pairs is a function?

A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))

C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))

D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}

Solve:

Knowing that; In order to know if a set of ordered pairs is a function or not we must see that if every x value have one or more than one y value that a function. If there is more than one same x value then it isn't a function.

Summary:

x value can't be duplicate but y can - in a working function

Hence, based on what we see in the answer choices;

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6)) is a function. Due to none repeat x values.

[B]((1,2), (2, 3), (3,4), (2, 1), (1, 0)) isn't a function. Due to repeat x -values (1 and 2)

[C] ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3)) isn't a function. Due to repeat x-values (2)

[D]  ((1,3), (1, 1), (1, 1), (1,3), (1,5)} isn't a function. Due to repeat x-values (1)

RevyBreeze

The value given is from a continuous data set because there are infinitely many possible values.

In statistics, a discrete data set is a set of data that can only take certain values, typically whole numbers, that can be counted. A continuous data set is a set of data that can take any value within a certain range, and the values can't be counted as they are infinite in number.

In the given scenario, the weight of a car can take any value within a certain range, and there are infinitely many possible values between any two values. For example, between 1628.3 kg and 1628.4 kg, the car's weight could be an infinite number of values. Hence, the weight of the car is a continuous variable, and the given value of 1628.3 kg is part of a continuous data set.

Hence, the correct answer is d.

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The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

CHINA

Step-by-step explanation:

Answer:

\( \frac{1}{ {5}^{15} } \)

In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.

Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.

The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.

The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.

By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.

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Answer:

a6 = 18,000

Step-by-step explanation:

a1 = 6

an = 5a(n-1)

a2 = 5a(2-1) = 5a1 = 5•6 = 30

a3 = 5a(3-1) =5a2 = 5•30 = 150

a4 = 5a(4-1) = 5a3 = 5•150 = 720

a5 = 5a(5-1) = 5a4 = 5•720 = 3600

a6 = 5a(6-1) = 5a5 = 5•3600 = 18000