The data to represent average test scores for a class of 24 students includes an outlier value of 89. If the mean, including the outlier of 89, equals 77, which statement is always true about the new data when the outlier is removed?

The mean would increase.
The mean would decrease.
The median would increase.
The median would decrease.

By using the Cauchy-Riemann equations on a real-valued function, it can be proven that the function f(z) is constant in the domain D. This is important for understanding analytic functions in complex analysis.

To prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D, let a function f be analytic everywhere in a domain D. We know that a real-valued function is said to be a function whose values lie on the real line. In the case of the complex plane, a function whose values lie on the real line is real-valued.

The Cauchy-Riemann equations, which define the necessary conditions for a function f(z) to be analytic in a domain, say that the imaginary component of f(z) is determined by its real component.

To be more precise, if f(z) is real-valued for all z in D, then we can say that:u(x, y) = f(z),v(x, y) = 0

By definition, the Cauchy-Riemann equations can be stated as:

∂u/∂x = ∂v/∂y∂u/∂y = -∂v/∂x

Taking the first equation, we get:

∂u/∂x = ∂v/∂y => ∂v/∂y = 0

Since v is equal to 0 for all values of x and y, the above equation reduces to ∂u/∂x = 0, which implies u is constant with respect to x.

Similarly, taking the second equation, we get:

∂u/∂y = -∂v/∂x => ∂u/∂y = 0

Since u is equal to a constant for all values of x and y, the above equation reduces to ∂v/∂y = 0, which implies v is constant with respect to y. Since u and v are both constant with respect to their respective variables, u + iv = f(z) is a constant with respect to z throughout the domain D. Thus, we have proved that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D.

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Answer:C

Step-by-step explanation:

Area = 1/2 b h

Area = 1/2 * 9  * 9 = 40.5 sq cm

The area of the right triangle will be 40.5 square cm. Then the correct option is D.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The dimension of the right triangle will be given below.

Height = 9 cm

Base = 9 cm

Then the area of the right triangle will be

Area = 1/2 x 9 x 9

Area = 40.5 square cm

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In the following question, among the given options, The statement "In a meta-analysis, there is a manipulation of variables" is false. hence meaning that the rest of them are stated to be true.

In A meta-analysis is a statistical technique for synthesizing the findings of multiple studies. It involves combining the results from multiple studies, analyzing them, and presenting a summary of the overall evidence. It does not involve manipulating variables or performing a random assignment. In a meta-analysis, any amount of studies can be used, and researchers can look for gaps in the research, based on a statistical analysis.

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Answer:

5.95

Step-by-step explanation:

an increase of 70% on to 100% = 170% - 1.7 multiply the price by 1.7 = 3.50 x 1.7 = 5.95 btw i am on 7 th grade too

The number of digits that are there is 25 digits.

Let the sum of the numbers be x.

Also, let the number of digits there be y

So, we get that:

Average of numbers originally = x / y

Now,

(x + 25) / y = x / y + 1

(x + 25) / y = (x + y) / y

x + 25 = x + y

y = 25

Therefore, we get that, the number of digits that are there is 25 digits.

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Hypothesis testing is a statistical method in which an analyst conducts a hypothesis test on a sample of data to draw inferences about the entire population.
1. Hypothesis tests are one of Inferential statistics. True. Inferential statistics, which deals with generalizing sample data to the population from which the sample was taken, includes hypothesis testing.
2. Mean is a central tendency measurement it is necessary to be one of the raw data. False. The mean measures central tendency calculated by adding all the values and dividing by the number of observations. The mean value does not have to be one of the raw data values. It's just a mathematical calculation used to represent a typical value for a dataset.
3. Calculation of the mean considers all the data, while other measurements do not consider all raw data. True. The mean calculation considers all data points, whereas other measures of central tendency, such as the median and mode, do not. This property makes the mean more representative of the entire data set.
4. Mode, median, and mean are single when that data is normally distributed. False. The mode, median, and mean are distinct when the data is non-normal. The mode, median, and mean are identical when data is normally distributed.
5. Mutually exclusive events can contain common elements. False. If two events are mutually exclusive, they cannot occur simultaneously. They have no elements in common by definition.
6. In the standard normal distribution, μ=1 and σ=0. False. In the standard normal distribution, the mean (μ) is 0, and the standard deviation (σ) is 1.

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All the numbers between 0 and 9 (including 0 and 9) belong to the domain of the function that describes the fare per kilometer.

The function that describes the fare per kilometer in a jeepney ride is:

$$f(x)=\begin{cases}9, & x \in [0,4) \\\ 1.40(x-4)+9, & x \in [4,9]\end{cases}$$

Here, x is the number of kilometers of the jeepney ride.

The first 4 kilometers cost Php 9 per kilometer. Thus, the fare for the first 4 kilometers is fixed at Php 9 per kilometer. For the distance from 4 to 9 kilometers, the cost is Php 1.40 per kilometer. So, the fare per kilometer in this interval is $1.40(x-4)$.

However, we have to add Php 9 since the first 4 kilometers already cost Php 9. Therefore, the fare function for this interval is $1.40(x-4)+9$.

To determine the domain of this function, we have to consider only the values of x that fall between 0 and 9 kilometers since the jeepney's route is at most 9 kilometers. Thus, the domain of the function is:

$$D=\{x \in \mathbb{R} : 0 \leq x \leq 9\}$$

Therefore, all the numbers between 0 and 9 (including 0 and 9) belong to the domain of the function that describes the fare per kilometer.

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Obtuse angle is the name of the angle m<CEB

The point where two lines meet is known as an angle. rom the given diagram, the sum of angles on a straight line is 180 degrees.

<CEB + 88 = 180 degrees

<CEB = 180 - 88

<CEB = 92 degrees

Since an obtuse angle is an angle greater than 90 but less than 180 degrees, hence the measure of angle <CEB is obtuse angle

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Answer:

12.5% increase

Step-by-step explanation:

Take the new price minus the original

36000-32000 = 4000

Divide by the original

4000/32000 = .125

Multiply by 100%

.125*100%

12.5% increase

Answer:

12.5%

Step-by-step explanation:

There is an 1/8 increase and 1/8 as a percent is 12/5%

Answer:

I am pretty sure it is 5/8 because it is perpendiculiar

Step-by-step explanation:

The required scale factor with respect to the pre-image and image is equal to 2.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.

In Mathematics, the scale factor of any geometric figure can be calculated by using this mathematical expression:

Scale factor = Dimension of image/Dimension of pre-image

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = -10/-5 = -4/-2

Scale factor = 2.

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There are two conditions :

1) If data consumed is less than or equal to 2 GB.

2) if data consumed is more than 2 GB.

Change in 1st condition is constant i.e $50.

Now, charge in 2nd condition is given by :

\(C=15x+50\)

So, money she have to pay in a month where she used ent over by x GB is :

\(C(x) = \$50\ , \ 0 \leq x \leq 2\\or\\C(x ) = \$\ (50+15x )\ ,\ x \geq 3\)

Hence, this is the required solution.

The value of x is 10.

Given triangle is a right-angled triangle.

Let the lengths of not mentioned lengths be 2p(hypotenuse) and 2q (other side).

There are two triangles in the given picture.

Consider the smaller triangle.

Apply Pythagoras theorem to that i.e.,

\(p^{2}\) = \((3x)^{2} + q^{2}\)

(Here, total hypotenuse is 2p length and the smaller triangle has half of its length. So, length is p. Similarly in case of q)

\(p^{2} = 9x^{2} + q^{2}\)  (Equation 1)

Now, consider the large triangle.

Apply Pythagoras theorem to that i.e.,

\((2p)^{2} = (4x + 20)^{2} + (2q)^{2}\)

\(4p^{2} = (16x^{2} + 160x + 400) + 4q^{2}\)

Substitute \(p^{2}\) from Equation 1

\(4(9x^{2} + q^{2} ) = 16x^{2} + 160x + 400 + 4q^{2}\\\)

\(36x^{2} + 4q^{2} = 16x^{2} + 160x + 400 + 4q^{2}\)

\(36x^{2} = 16x^{2} + 160x + 400\)  (\(4q^{2}\) from both sides got cancelled)

\(20x^{2} - 160x - 400 = 0\)

Solving the quadratic equation,

\(20x^{2} - 200x + 40x - 400 = 0\)

\(20x(x - 10) + 40(x - 10) = 0\)

\((20x+ 40)(x - 10) = 0\)

So, 20x + 40 = 0 or x - 10 = 0

i.e., x = -2 or 1o

But \(x \neq -2\) because angles cannot be negative.

So, x is 10.

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Answer:

200, 160

Step-by-step explanation:

if perimeter is 240 it means sides are 40 by 80.

if he does not need to place fencing on one side, they remove one 80 or 40,

40+80+80=160 or 40+40+80=200

Boom Awser

Answer:

200 160

Step-by-step explanation:

if the perimeter is 240, the length is 80 and width is 40.

40+80+80=200

80+40+40=160

Answer:

Step-by-step explanation:

Perimeter

Area

1) The lower class limits: 100, 200, 300, 400, 500, 600 .

2) The upper class limits:  199, 299, 399, 499, 599, 699.

3) The class width: 100.

4) Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5, 649.5.

5) Class boundaries : 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5.

6) The number of individuals included in the summary : 155

The lower class limit in each class: 0,100, 200, 300, 400, 500, 600.

The upper-class limit is the biggest value in each class.

so the upper-class limit is:  99, 199, 299, 399, 499, 599, 699.

As we know the class width is the difference between the lower limit of one class and the lower limit of the previous class.

For example, 300 is the lower limit of one class and the lower limit of the previous class is 200 , so 300 - 200 = 100.

We know that, the class midpoints are the average of the limits of a class.

So, using midpoint formula the class midpoints are:

\(\frac{100+199}{2} = 149.5\\\\\frac{200+299}{2} = 249.5\\\\\frac{300+3199}{2} = 349.5\\\\\frac{400+499}{2} = 449.5\\\\\frac{500+599}{2} = 549.5\\\\\frac{600+699}{2} = 649.5\\\)

We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.

So, the class boundaries for the first class = (99.5, 199.5)

the class boundaries for the second class = (199.5, 299.5)

the class boundaries for the third class = (299.5, 399.5)

the class boundaries for the fourth class = (399.5, 499.5)

the class boundaries for the fifth class = (499.5, 599.5)

The total of individuals is equal to the sum of all the frequencies of each class: 3 + 54 + 76 + 21 + 0 + 0 + 1 = 155

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The complete question is:

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males ​(1000 ​cells/mu​L) Frequency 0​-99 3 100​-199 54 200​-299 76 300​-399 21 400​-499 0 500​-599 0 600​-699 1 Identify the lower class limits​ (in 1000 ​cells/mu​L).

Answer: x=5

Step-by-step explanation: isolate the variable by dividing each side by factors that don't contain the variable

Answer:

x=5

i don't know why the "infinite solution" is in the question but there is one solution.

Step-by-step explanation:

-3x+5 = -2(x+7)+2x+4

Distribute

-3x+5 = -2x-14+2x+4

Combine like terms

-3x+5 = -10

Apply inverse operations

-3x = -15

x=5

Answer:

b

Step-by-step explanation:

you need to round 2.51 to 3 because it was the correct answer

Answer:

Step-by-step explanation:

Add the 21 then divide by 2

Answer:

x = 16, x = -7

Step-by-step explanation:

The question is;

35 * 4 = ( x - 7 ) ( x - 3 )

Combine like terms on one side;

140 = ( x - 7 ) ( x - 3 )

Distribute, remember to multiply every term with one another;

140 = \(x^{2}\) - 3x - 7x + 21

Combine like terms;

140 = \(x^{2}\) - 10x + 21

Inverse operations;

140 = \(x^{2}\) - 10x + 21

-21                  -21

119 = \(x^{2}\) - 10x

Factor;

119 = x ( x - 10 )

At this point it is fairly obvious that;

x = 16, x = -7

Note; One could have used a multitude of methods to solve this problem, one could have factored, completed the square, or used the quadratic formula, this method was simply chosen because it is easy to explain

Answer:

58°

Step-by-step explanation:

A right triangle is a type of triangle with exactly one angle equal to 90°. The other two angles sum up to 90°.

A triangle measures 180°. We plug in the given information from the question above…

90° + 32° = 122°

Applying the Triangle Sum Property…

180° - 122° = 58°

After considering the given data we conclude that the correct answer which is the correct option is b which is 3/28, regarding the conditional probability.

We are given that an urn contains 3 green balls and 5 red balls. Let Rᵢ be the event that the i-th ball without replacement is red. We need to find \(P(R_3| R_2 \cap R_1).\)
Using the conditional probability formula, we have:
\(P(R_3| R_2\cap R_1) = P(R_3 \cap R_2 \cap R_1) / P(R_2 \cap R_1)\)
Since we are drawing balls without replacement, the probability of drawing a red ball on the first draw is 5/8. The probability of drawing a red ball on the second draw given that the first ball was red is 4/7. Similarly, the probability of drawing a red ball on the third draw given that the first two balls were red is 3/6 = 1/2. Therefore, we have:
\(P(R_3 \cap R_2 \cap R_1) = (5/8) * (4/7) * (1/2) = 5/56\)
To find P(R₂ ∩ R₁), we can use the law of total probability:
\(P(R_2 \cap R_1) = P(R_2 \cap R_1 | R_1) * P(R_1) + P(R_2 \cap R_1 | R_1') * P(R_1')\)
where R₁' is the complement of R₁ (i.e., the event that the first ball drawn is not red). Since we are drawing balls without replacement, the probability of drawing a red ball on the second draw given that the first ball was not red is 5/7. Therefore, we have:
\(P(R_2 \cap R_1) = (5/8) * (5/7) + (3/8) * (3/7) = 29/56\)
Substituting these values into the conditional probability formula, we get:
\(P(R_3| R_2 \cap R_1) = (5/56) / (29/56) = 5/29\)
Therefore, the answer is (b) 3/28.
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The complete question is
An urn contains 3 green balls and 5 red balls. Let R, be the event the i-th ball without replacement is red. Find P(R3| R2 \cap R₁).
a) 1/56
b) 3/28
c) 1/2
d) 5/8

The probability of a family having three males and two females can be calculated using the concept of binomial probability.

In a family with five kids, each child has a 50% chance of being male or female. The probability of having three males and two females can be calculated by considering the different ways this combination can occur.

There are a total of 10 possible outcomes when arranging three males and two females in a sequence of five children (i.e., 5C3, where 5C3 represents the binomial coefficient "5 choose 3").

The probability of having three males and two females is given by the number of favorable outcomes divided by the total number of possible outcomes, which is 10/32 or 0.3125. Therefore, the probability of a family having three males and two females is approximately 31.25%.

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Given differential equation is, `y′′ + y′ − 2y = 0`.Here, we are going to substitute `y = erx` into the given differential equation to determine all values of the constant `r` for which `y = erx` is a solution of the equation.

We are given a differential equation `y′′ + y′ − 2y = 0`.Here, we are to determine all values of the constant `r` for which `y = erx` is a solution of the equation.We know that the differentiation of `erx` with respect to `x` is `rerx` and the differentiation of `rerx` with respect to `x` is `r2erx`.

By substituting `y = erx` in the given differential equation, we get`y′′ + y′ − 2y = 0``

⇒ y′′ + y′ − 2(erx) = 0``

⇒ r2erx + rerx − 2(erx) = 0``

⇒ erx (r2 + r − 2) = 0`

For this equation to be true for all values of `x`, we must have `(r2 + r − 2) = 0`.

This is a quadratic equation in `r`.Solving the above quadratic equation, we get`(r + 2)(r − 1) = 0`

⇒ r = −2 or r = 1

Therefore, the given differential equation has two solutions: `y1 = e−2x` and `y2 = e^x`.Thus, the values of the constant `r` are `r = −2` and `r = 1`.

We can conclude that for the given differential equation `y′′ + y′ − 2y = 0`, the values of the constant `r` are `r = −2` and `r = 1`.

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Answer:

The bottom option(C)

Step-by-step explanation:

The answer to your question is that the only way to demonstrate causation is to conduct a controlled experiment. This domain involves manipulating one variable and measuring the effect it has on another variable while holding all other variables constant.

correlation simply shows a relationship between two variables, but it doesn't prove that one variable causes the other. There could be other factors at play that are influencing both variables. For example, there may be a correlation between ice cream sales and crime rates, but this doesn't mean that ice cream causes crime or vice versa. It's possible that a third variable, such as temperature, is influencing both ice cream sales and crime rates.

further into the complexities of establishing causation, such as the need for random assignment in experimental studies, the importance of replicating findings, and the challenges of applying experimental findings to real-world situations. However, the key point is that a controlled experiment is the most reliable method for establishing a causal relationship between variables.

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Answer:

You cannot tell which number is greater, we need more information.

"multi-digit" does not imply how many digits each number has, therefore both numbers could be greater, for example:

3005 vs 60

OR

30 vs 645

Answer:

If you were to multiply the percentages by the numberws your using to the AB formula you can get the answer 252 B

Step-by-step explanation:

The number of cups of each ingredient Kwame and Olivia could have used is 6 cups and 10 cups respectively.

In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter. For example, the combination of three fruits from a basket containing apples, oranges, and bananas would be the set {apple, orange, banana}, {apple, banana, orange}, {orange, apple, banana}, {orange, banana, apple}, {banana, apple, orange}, and {banana, orange, apple}. The number of possible combinations is often represented using the combination formula, which is often written as "nCr", where "n" is the total number of items in the collection.

It's not possible to give an exact example of the number of cups of each ingredient each person used, as there are infinitely many ways that Kwame and Olivia could have combined orange juice and mango juice to make 12 and 20 cups respectively.

However, one example of the number of cups of each ingredient each person could have used is:

Kwame: 6 cups orange juice, 6 cups mango juice Olivia: 10 cups orange juice, 10 cups mango juice

This satisfies the constraints that Kwame uses less orange juice than Olivia and his orange-mango juice tastes more like oranges than hers does.

This is an example of the possible combination, but it might not be the only one. Also, it's possible that there are other combinations that could satisfy the given information, but this is one example.

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