What happens to standard deviation when outliers are removed?; How does outliers affect standard deviation?; When the outliers are removed How does this mean change?; How will a high outlier affect the mean and median?; Which data set has an outlier?

It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

Given that

Ted can remove the trash from a football field in three hours. The same field may be cleared by Jacob in two hours. The scenario can be represented by the equation when they cooperate, where t is the total number of hours needed to clear the field.

We have to find how long will it take ted and jacob to clear the field together.

We know that,

Let the number of hours = t

Ted can clear the field = t/3

Jacob can clear the field = t/2

Together they can clear the field = t/3 + t/2 = 1

3t+2t/6 = 6/6

2t + 3t = 6

5t = 6

t = 6/5

t = 1.2 hours.

Converting

1.2 hours = 1 hour 12 minutes.

Therefore, It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

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In an isosceles triangle, the angle opposite the base is referred to as the vertex angle.

A triangle refers to a two-dimensional shape which comprises of three sides and three angles. The isosceles triangle is a type of triangle in which two sides are congruent i.e., they are the same length. The third side of an isosceles triangle is of different length and is referred to as the base. The three angles of any triangle add up to a sum of 180°. In isosceles triangles, the two angles located along the base are referred to as the base angles which are always congruent, or equal. The angle opposite the base is referred to as the vertex angle and is different value from the two base angles. The value for the vertex angle can always be calculated by subtracting the base angles from 180° using the general formula: 180° - 2B = A, where B refers to the base angle and A is the vertex angle.

Note: The question is incomplete. The complete question probably is: Which is the vertex angle of an isosceles triangle.

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Answer:

1.3 to the twenty-eighth power over 1.2 to the twenty-first power

Step-by-step explanation:

The equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven is 1.3 cubed over 1.2 raised to the fourth power.

To find the equivalent expression, we need to use the rule that x^a / x^b = x^(a-b) for any value of x except 0.

In this case, we have 1.2^3 / 1.3^4 raised to the power of -7. Applying the rule, we get:

(1.2^3 / 1.3^4)^-7 = (1.2^(-4) / 1.3^3)^7

Since the exponent of a number raised to a power is the same as the power, we can rewrite the expression as:

1.2^(-47) / 1.3^(37)

Simplifying, we get:

1.2^(-28) / 1.3^(21)

Which is the same as:

1.3^(21) / 1.2^(28)

This is the same as the expression 1.3 cubed over 1.2 raised to the fourth power. Therefore, the equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven is 1.3 cubed over 1.2 raised to the fourth power.

The volume of the tissue box is 85⅓ cubic inches.

The correct answer option is option D

Volume of the tissue box = Base area of the rectangular prism × Height of the rectangular prism

= 16 square inches × 5⅓ inches

= 85⅓ cubic inches

Therefore, the rectangular prism has a volume of 85⅓ cubic inches

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The equation in slope-intercept form would be; y = 5x + 33

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given that line passes through points (-8, – 7) and (-6, – 3).

Now we will write in slope-intercept form,

y = m x + b .

Now to find m, we use the formula;

m = y₂ - y₁ / x₂ - x₁

Then,

m = { -3 - (-7)} / { 6 - (-8)}

m = 4 / 14

m = 2/7

Thus, y = 5x +33

Therefore,  its equation in slope-intercept form would be; y = 5x + 33

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Answer: She could make those two changes to save money for her trip. Also, she could save a little bit of her salary to have enough money to go.

Step-by-step explanation:

This is just a guess but PLEASE GIVE ME BRAINLIEST if you're pleased with my answer.

Yes, it is possible that one-to-one function and its inverse are true. If f(f(x)) = x then function and its inverse coincide.

If each x-value corresponds to exactly one y-value, the function is said to be one-to-one.  Inverse function graphs are reflections of the y = x line. This indicates that there can be only one y-value for each x-value. One-to-one functions are those that fit this description.

Inverse of function is represented by [tex]f^{-1} (x)[/tex].

Test to check inverse function: If and only if no horizontal line intersects the graph of f at more than one location, then the function f is one-to-one and possesses an inverse function.

Example: f(x) = 5-x

f(f(x))= 5- (5-x) = x

So above function is one to one and inverse of itself.

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The given

Incidence of multiple chronic conditions is connected to frailty, a condition marked by a lack of resilience to physiological changes and an elevated risk of poor health outcomes.

It is TRUE.

"Information available from the question:"

In the question:

Incidence of multiple chronic conditions is connected to frailty, a condition marked by a lack of resilience to physiological changes and an elevated risk of poor health outcomes.

It is TRUE / FALSE

Now, According to the question:

Let's know:

What is Frailty?

Frailty is most often defined as an aging-related syndrome of physiological decline, characterized by marked vulnerability to adverse health outcomes.

Incidence of multiple chronic conditions is connected to frailty, a condition marked by a lack of resilience to physiological changes and an elevated risk of poor health outcomes.

Hence, The above statement is TRUE.

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g(x) is shifted 4 units left and -8 units down from f(x).

when y=f(x)

When y = f (x + a), the function is either shifted to the right by a units (a 0) or to the left by a units (a > 0).

g(x)=(x+4)-2⇒f(x−8)

This causes f (x) to be moved by 8 units to the right.

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Answer:

Step-by-step explanation:

A rectangle measures 75 cm by 15 cm.Find the length of the perimeter?

P = (75 + 15) x 2

P = 90 x 2

P = 180 cm

Answer:

reflection across the line y=x

Step-by-step explanation: the point (-2,1) would turn into (1,-2) which the other figure shows

One of the proofs below and use one of the indirect proof techniques presented in Chapter 8 to demonstrate the validity of the argument .

Given :

The proofs below may use any of the rules of inference or replacement rules given in Chapter 8.

( G � P ) → K, E → Z, ~P → ~ Z, G → ( E v L ), therefore, ( G � ~L ) → K

( S v T ) ↔ ~E, S → ( F � ~G ), A → W, T → ~W, therefore, ( ~E � A ) → ~G

( S v T ) v ( U v W ), therefore, ( U v T ) v ( S v W )

~Q → ( L → F ), Q → ~A, F → B, L, therefore, ~A v B

~S → ( F → L ), F → ( L → P ), therefore, ~S → ( F → P )

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Answer:

  the Pythagorean theorem was used

Step-by-step explanation:

You want to know the missing side in a right triangle with hypotenuse 15 cm and one side 9 cm.

The Pythagorean theorem tells you the relationship between sides 'a' and 'b' and hypotenuse 'c' in a right triangle is ...

  a² +b² = c²

  9² +?² = 15² . . . . use the given values

  ?² = 225 -81 = 144 . . . . subtract 9²

  ? = √144 = 12 . . . . . . . take the square root

The length of the missing side is 12 cm.

__

Additional comment

The little green square in the upper corner tells you that is a right angle, and the triangle is a right triangle.

All units of length are in cm.

Therefore ,the true bearing of the plane and its speed is ∝=-71.9° and 324.31 mph

A thing with both magnitude and direction is called a vector. A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector. From the vector's tail to its head is the direction of motion. According to the definition of a resultant vector, a single vector is one that has the same result as several other vectors taken together.

Here,

To find the true bearing of the plane and its speed.

We find the vector component,

Since  N75°W is same as 95°+90°=165°

Thus,

f(x)=300cos100 +50cos165 = -100.39

f(y)=300sin100 +50sin165= 308.38

next we find resultant

R=[tex]\sqrt{f(x)^{2}+f(y)^{2} }[/tex]

R=[tex]\sqrt{(-100.39)^{2}+(308.38)^{2} }[/tex]

R=[tex]\sqrt{105178.35}[/tex]

R=324.31 mph

The bearing of the plane=> ∝=[tex]tan^{-1}[/tex](308.38/-100.39)

So  ∝=-71.96°

Therefore ,the true bearing of the plane and its speed is ∝=-71.96° and 324.31 mph

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By using proportionality theorem, the equation that expresses the statement is written as

1) T = kx

2) w = kyz

3) x = ks/t

4) A = kt²/y³

Proportionality

In math, a proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.

Given,

Here we have to find the equation that expresses the statement by using the k as the constant of proportionality.

Here we know that the value of the constant of proportionality is k.

Then the equation for the statement are,

1- T varies directly as x. And it can be written based on the constant proportionality,

=> T = kx

2- w is jointly proportional to y and z

Then the statement is written as,

=> w = k x y x z

=> w = kyz

3- x is proportional to s and inversely proportional to t.

Here we have to use the inverse proportional to write the statement,

=> x = k x s x 1/t

=> x = ks/t

4- A is proportional to the square of t and inversely proportional to the cube of y

Here first we have to take the square on t, then we get t² and then have to take cube on y, then we get y³,

then the equation is written as,

=> A = kt²/y³

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The non-zero orthogonal vector to the plane is 486i + 243j + 162j and the area of the triangle is 4374 unit squares.

The vertices of the triangle are P(9, 0, 0), Q(0, 18, 0), and R(0, 0, 27).

So, firstly we should find the vector PQ and PR,

Now,

PR = (0)i + (-18)j + (27)k

PR = -18j + 27j

And PQ,

PQ = (-9)i + (18)j + (0)k

PQ = -9i + 18j

Now, the normal vector which is also a non-zero orthogonal vector,

n = PQ x PR

n = 486i + 243j + 162j

Now, the area of the ΔPQR will be,

Ar(PQR) = [tex]\left[\begin{array}{ccc}9&0&0\\0&18&0\\0&0&27\end{array}\right][/tex]

Solving further,

Ar(PQR) = 4374 unit square.

So, the area of the triangle is 4374 unit square.

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For two-sample t-tests, results cannot be compared between studies. The test statistic is given, as well as a p-value. This test is also known as a matched sample or paired t-test. It is assumption of normal distribution.

The paired-samples t-test, also known as the dependent-samples t-test, is a statistical technique used to determine whether the mean difference between two sets of observations is zero. In a paired-samples t-test, each subject or entity is measured twice to obtain a pair of observations. Common uses of the paired-samples t-test are case-control studies or repeated measures designs.

A normal distribution is a type of continuous probability distribution in which most data points cluster toward the middle of the range and the rest decrease symmetrically toward one extreme. The middle of the range is also called the mean of the distribution.

The normal distribution is also known as the Gaussian distribution or probability bell curve. It is symmetrical about the mean, indicating that values ​​close to the mean occur more frequently than values ​​far from the mean.

Assumption:

The Normalization Assumption is cautioned because so many experiments are based on the assumption of a normal distribution. is required. In most cases, the assumption of normality makes sense.

However, there is an important special case where this is not the case. Understanding the normal distribution assumptions helps researchers understand the limitations of their experiments and understand their own research and where it went wrong.

The assumption of normal distribution can be relaxed in some situations, but the analysis is more complicated. The simplest analysis is obtained when the physical process can be approximated by a normal distribution. However, even if the distribution is non-normal, it retains some basic properties. For example, you can assume symmetry, such as the t distribution, even if the distribution is not truly normal.

In fact, many different non-normal distributions are just variations of the normal distribution. For example, there are distributions with long tails that represent variations in a normal distribution. Such distributions are also common.

The reason for the normal distribution assumption is that it is usually the simplest mathematical model available. Moreover, it is remarkably ubiquitous, found in most natural and social phenomena. So the assumption of normality is usually a good first approximation.

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Answer:

Step-by-step explanation:

Solving for X in Other Triangles In any triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the longest side. This is known as the Pythagorean theorem.

a) The hypotheses are given as follows:

b) The test statistic is given as follows: [tex]\chi^2 = 37.79[/tex]

c) The p-value is given as follows: 0.61

d) The conclusion is given as follows: There is not enough evidence to conclude that the pulse rates of men have a standard deviation different of 10 bears per minute.

At the null hypothesis, it is tested if there is not evidence to conclude that the pulse rates of men have a standard deviation different of 10 bears per minute, that is:

[tex]H_0: \sigma = 10[/tex]

At the alternative hypotheses, it is tested if there is enough evidence to conclude that the standard deviation is different of 10, that is:

[tex]H_1: \sigma \neq 10[/tex]

The equation for the test statistic is given as follows:

[tex]\chi^2 = \frac{(n - 1)s^2}{\sigma^2}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]n = 42, s = 9.6, \sigma = 10[/tex]

Hence the test statistic is calculated as follows:

[tex]\chi^2 = \frac{(n - 1)s^2}{\sigma^2}[/tex]

[tex]\chi^2 = \frac{41 \times 9.6^2}{10^2}[/tex]

[tex]\chi^2 = 37.79[/tex]

Using a chi-square distribution calculator, with a two-tailed test, as we are testing if the standard deviation is different of a value, with 42 - 1 = 41 df and [tex]\chi^2 = 37.79[/tex], the p-value is given as follows:

0.61.

As the p-value is greater than the significance level of 0.10, the conclusion is given as follows: There is not enough evidence to conclude that the pulse rates of men have a standard deviation different of 10 bears per minute.

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Answer:the answer is 8070

Step-by-step explanation:

because it is

Answer:

25. y = 36

26. w = -4

Explanation:

25.

74 + 74 = 148

360 - 148 = 212

212 ÷ 2 = 106

106 = 2y + 34

106 - 34 = 2y

72 = 2y

72 ÷ 2 = (2y) ÷ 2

y = 36

26.

72 = 2w + 80

72 - 80 = 2w

-8 = 2w

-8 ÷ 2 = (2w) ÷ 2

w = -4

Assuming the Dodgers sign more quality players from the free agent market in a year, they will have a better chance of winning when they play the Angels. The odds of the Dodgers winning four of a possible seven games in a series are in probability  0.2097.

The probability for the Dodgers to win a game when playing against the Angels is 2/3 (doubling the chance vs Angels).

So the probability for the Dodgers to win a seven game series against the Angels is (2/3)^7. That is, the probability for the Dodgers to win four games out of a seven game series is (2/3)^4.

Therefore, the probability for the Dodgers to win four games out of a seven games series is (2/3)^4 = 0.2097.

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Answer: anything between -3 and 3, inclusive (meaning-3 and 3 are answers)

Step-by-step explanation:

6≤-x+9≤12(-x is just x times 1)

The population in the year 2000 is 395.808

Exponential Function

Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria. Some bacteria double every hour

Where t is the number of months since the population was first recorded. And the population after 36 months so we need to replace t=36 months into the function

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

So then can conclude that after 38 months the population of mouse is between 1963 and 2000.

A(t)=336e^(0.031t)

The population can be represented with this formula:

A(38)=336e^(0.031*38)

Where t is the number of months since the population was first recorded. And  the population after 38 months so we need to replace t=38 months into the function and we got:

A(38)=336e^(0.031*38)

A(38)=336e^(1.178)

       =395.808

So then can conclude that after 38 months the population of mouse is between 1963 and 2000.

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Answer:

  55.5°

Step-by-step explanation:

You want the angle in a right triangle that has opposite side 16 and adjacent side 11.

The tangent relation is ...

  Tan = Opposite/Adjacent

In this geometry, that means ...

  tan(x) = 16/11

Taking the inverse tangent, we have ...

  x = arctan(16/11) ≈ 55.49° ≈ 55.5°

The angle x is about 55.5°.

The perimeter of the square will be equal to 31.96 meters.

The perimeter of the square is defined as the sum of all the sides of the square. The perimeter of the square when the diagonals of the square are given will be calculated by the product of 2√2 with the diagonal magnitude.

Given that the diagonal of the square is 11.3 meters. The perimeter of the square will be calculated as,

P = 2√2 x d

P = 2√2 x 11.3

P = 31.96 meters

Therefore, the perimeter of the square will be equal to 31.96 meters.

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As per the given line segments, the work done by the particle is 78N.

Line segments:

In meth, then bounded by two distinct points on a line is called as line segment.

Given,

Here we have a particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field below.

And we need to find the work done.

While we have the function in the given question as,

=> F(x,y,z) = z²i + 3xy j + 4y²k

Here we have consider that, If C is the path the particle follows, then work done is ∫ₓᵃ F dx.

Then according to the question the force F(x,y,z) = z²i + 3xy j + 4y²k and all four points are in the plane is written as,

z = 1/4 y

So, if S is the at surface with boundary C, so that S is the portion of the plane  over the rectangle is calculated as,

=> D=[0,2] x [0,4].

Then as per the stroke's theorem,

=> ∫∫[2z(0) + 3z(1/4) + 4y]

=> ∫∫3z/4 + 4y

=> [39]₀²

=> 78

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The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 324.

The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 326.   This is calculated using the 1/2-value correction (de Moivre-Laplace Approximation). The 1/2-value correction assumes the normal distribution is symmetric, with the mean in the middle of the distribution. This means that the probability of being above the mean is equal to the probability of being below the mean.  Since the airline wants to be 99% confident that all ticket holders who do show up will be able to board the plane, this means that the airline needs to sell enough tickets such that the probability of being above the mean (300 tickets sold) is 99%.   Using the 1/2-value correction, the airline needs to sell 326 tickets to achieve this confidence level.

This is calculated as follows:   P(x > 300) = 0.99  P(x < 300) = 0.01  Using the 1/2-value-correction:

P(x = 300 + 0.5) = 0.99

Therefore,   x = 300 + 0.5=>  x = 300.5 => x = 326

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False, that is if the number of data observations is even, the median is generally considered to be the average of middle values not the first and last values.

The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

At least half of the observations are equal to or smaller than the median, and at least half of the measurements are equal to or greater than the median. The median divides the bottom half of observations from the upper half.

Even Number of Observations :

Suppose we have the monthly wages of 4 employees of a company. How would you find the median wage?

wages are 120,240,500,400

we have arranged their wages above from lowest to highest. This ranking will help us to determine the median. Using the method introduced earlier, the median is computed by taking the simple average of the (n/2)ᵗʰ = (4/2)ᵗʰ = 2ⁿᵈ and

(n/2 + 1)ᵗʰ = (2+1)ᵗʰ = 3ʳᵈ observations.

Therefore, the median is 240+500/2

= 370.

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Complete question

True/false

if the number of data observations is even, the median is generally considered to be the average of the first and last values