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Answer:

B

Step-by-step explanation:

abs value of -9 is still 9, so it should be "="

The standardized data set {} that is derived from {} has mean = 0 and standard deviation = 1.

Let's denote the original dataset {} as X and the standardized dataset {} as Z.

1. Mean of the standardized dataset:

The mean of the standardized dataset Z can be calculated as:

mean(Z) = (mean(X) - μ) / σ

Since we are assuming a population mean of μ = 0 and a known or estimated population standard deviation of σ, the mean of the standardized dataset becomes:

mean(Z) = (mean(X) - 0) / σ

        = mean(X) / σ

Hence, the mean of the standardized dataset Z is equal to the mean of the original dataset divided by the population standard deviation, which in this case, becomes 0.

2. Standard deviation of the standardized dataset:

The standard deviation of the standardized dataset Z can be calculated as:std(Z) = std(X) / σ

Here, std(X) represents the standard deviation of the original dataset, and σ represents the population standard deviation.

Since we are assuming a known or estimated population standard deviation of σ, the standard deviation of the standardized dataset becomes:

std(Z) = std(X) / σ

Therefore, from the definitions and properties related to standardization, it can be concluded that the standardized dataset {} derived from the original dataset {} has a mean of 0 and a standard deviation of 1.

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The Complete Question is

Let {} be a dataset consisting of N real numbers, 1, ..., IN - a. Prove from definitions or proved properties in the textboook that the standardized data set {} that is derived from {} has mean = 0 and standard deviation = 1

Answer:

B) 28.61 > 28.48

Step-by-step explanation:

A is wrong because 28 < 29

B is correct because 0.61 > 0.48

C is wrong because 29 > 28

D is wrong because 29 > 28

I hope this helps!

Answer:

90

Step-by-step explanation:

the forumla of a triangle is base times height, divided by 2 and since it has a height of 12 and a base of 15, and if you multiply that it would give you 180, then divide by 2 since it is half a sqaure, which is 90

Answer:

\(3 \sqrt{41}\)

Step-by-step explanation:

\(12^2 + 15^2 = x^2 \\x = \sqrt{369} = 3\sqrt{41}\)

Answer:

28

Step-by-step explanation:

\(V = b*h = 3.5 * 8 = 28\)

Answer:Using the slope-intercept form, the y-intercept is 1

In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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The approximate value of x in the equation 5 to the power of 2x=20 is 0.93

From the question, we have the following parameters that can be used in our computation:

5 to the power of 2x=20

As an expression, we have

5^(2x) = 20

Take the natural logarithm of both sides

so, we have the following representation

2x = ln(20)/ln(5)

Evaluate the quotients

This gives

2x = 1.86

So, we have

x = 0.93

Hence, the value of x is 0.93

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Answer:

86 & tends to increase

Step-by-step explanation:

Goodluck :)

Answer:

Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.

Step-by-step explanation:

C/3

Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

The simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

The expression cos^2x sin^4x can be simplified by using the trigonometric identity that states sin^2x + cos^2x = 1.

We can rewrite cos^2x sin^4x as cos^2x (sin^2x)^2. Then, using the trigonometric identity sin^2x + cos^2x = 1, we can substitute (1 - cos^2x) for sin^2x.

This gives us cos^2x (1 - cos^2x)^2, which can be expanded using the binomial theorem to give cos^2x (1 - 2cos^2x + cos^4x).

Finally, we can simplify this expression further by distributing the cos^2x term and collecting like terms to get cos^2x - 2cos^4x + cos^6x.

Therefore, the simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

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The probability is 0.1429.

The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:

5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.

The probability that everyone in the group is a girl is 2/7.

Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.

Total number of students in a class = 7

Number of boys students = 2

Number of girls students = 5

The probability that everyone in the group is a girl is;

\(\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}\)

Hence, the probability that everyone in the group is a girl is 2/7.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

is C

Step-by-step explanation:

why are we doing it at school and i did it and it's many solutions

Answer:

slope =x2-x1/y2-y1

= 0-6/4-0

=-6/4

Answer:

x=-3.5 and y=6.25

Step-by-step explanation:

x+2y=9

x=9-2y

-6(9-2y)+4y=46

-54+12y+4y=46

16y-54=46

16y = 100

y = 100/16 = 50/8 = 25/4 = 6.25

x+2(6.25)=9

x+12.5=9

x= -3.5

Based on the zeros and the end behavior of the function, we can choose the graph that matches these characteristics. The graph should have x-intercepts at x = 0 (with multiplicity 3) and x = 1, and it should exhibit a rising behavior on both sides.

The given function f(x) = (x^3)(x^2)(x - 1) is a polynomial function. By analyzing the factors of the function, we can determine its zeros, which are the x-values where the function equals zero.

The zeros of the function occur when any of the factors equal zero. Setting each factor to zero, we find the following zeros:

x^3 = 0  --> x = 0

x^2 = 0  --> x = 0

x - 1 = 0  --> x = 1

Therefore, the zeros of the function are x = 0 (with multiplicity 3) and x = 1.

Now, let's consider the end behavior of the graph. As x approaches negative or positive infinity, we can determine the behavior of the function.

Since the highest power of x in the function is x^3, we know that the end behavior of the graph will match that of a cubic function. If the leading coefficient is positive, the graph will rise to the left and rise to the right. If the leading coefficient is negative, the graph will fall to the left and fall to the right.

In the given function, the leading coefficient is positive (since the coefficient of x^3 is 1). Therefore, the graph of the function will rise to the left and rise to the right as x approaches negative or positive infinity.

Based on the zeros and the end behavior of the function, we can choose the graph that matches these characteristics. The graph should have x-intercepts at x = 0 (with multiplicity 3) and x = 1, and it should exhibit a rising behavior on both sides.

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The predicted gold-medal-winning distance of 26.25 meters is just a prediction, and the actual gold-medal-winning distance may vary is the answer.

The long jump is one of the track and field events that have been in the Olympics since the inception of the modern Olympics in 1896. In men's long jump, Bob Beamon's jump of 8.90 meters at the 1968 Mexico City Olympic Games is considered the longest. This was achieved at an altitude of 2,240 meters, which implies that the rarefied atmosphere made it simpler for him to cover a long distance. Since 1968, no athlete has been able to jump as far as Beamon did. The men's long jump has seen a general increase in performance over the years. Athletes are now jumping considerably further than they were 100 years ago. The Olympic long jump record progression chart is shown below. Analyzing the trendline reveals that long jump performances have increased at a rate of roughly 0.14 meters every four years since 1896.

Therefore, to predict the gold-medal-winning distance at the 2020 Tokyo Olympics, we will use the following model: 8.89 + 0.14(2020 - 1896) = 8.89 + 0.14(124) = 8.89 + 17.36 = 26.25 meters.

The above analysis is built on the assumption that long jump performances will continue to improve at the same rate they have since 1896. This is a significant assumption because other variables, such as the participants' age, body type, climate, and so on, may influence long jump performance.

As a result, the predicted gold-medal-winning distance of 26.25 meters is just a prediction, and the actual gold-medal-winning distance may vary.

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Answer:

length is 36

Step-by-step explanation:

perimeter=2L+2W

Answer:

Step-by-step explanation:

Discussion and Correction

The algrebra  itself is fine. The exclusions are not so good. The difficulty comes in the denominator. It factors into (2x)(x - 3). x cannot take on a value of 0 (that was pointed out and that is correct). The problem comes in the plus/minus 3. Plus 3 is correct. x - 3 will come 0 if x = 3. Nothing bad will happen if x = - 3

Answer: So the exclusions in the denominator should be modified to x = 3.

Answer:

The excluded values are x-values that make the denominator of the original expression zero, since \(\dfrac{a}{0}\) is undefined.

\(x = -3\) is not an excluded value since this x-value does not make the  denominator zero.

\(x = -3\) makes the numerator zero, but as \(\dfrac{0}{a}=0\) it is not an excluded value.

Therefore, step 3 of her work should read:

\(\textsf{Finding excluded values}:x\neq 0\:\textsf{and}\:x\neq 3\)

Answer:

Option C

Step-by-step explanation:

Given expression in the question is,

y = \(7(2)^{\frac{t}{30}}\)

To get the value of t,

\(\frac{y}{7}=2^{\frac{t}{30}}\)

Take the log on both the sides of the expression,

log(\(\frac{y}{7}\)) = \(\text{log}[(2^{\frac{t}{30}})]\)

log(\(\frac{y}{7}\)) = \(\frac{t}{30}(\text{log2})\)

t = \(30(\frac{\text{log}\frac{y}{7}}{\text{log}2} )\)

t = \(30[\text{log}_2(\frac{y}{7})]\) [Since, \(\frac{\text{loga}}{\text{logb}}=\text{log}_a(b)}\)]

Therefore, Option C will be the answer.

Answer:

225

Step-by-step explanation:

Answer:

the answer is 221.1

Step-by-step explanation:

The volume of the rectangular prism is 221.1 in³.

The volume of any object defined the capacity of it, how much it can hold something is called its volume.

Given is rectangular prism, we need to find the volume of the same,

So, we know that the volume of a rectangular prism is the product of its dimensions.

V = length × width × height.

\(V = 16\frac{3}{4} \times 4\frac{2}{5} \times 3\)

\(V = \frac{67}{4} \times \frac{22}{5} \times 3\)

V = 4422/20

V = 221.1

Hence, the volume of the rectangular prism is 221.1 in³.

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The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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A key problem faced by poorer inner-city neighborhoods in America due to their geographical position is a lack of quality food options.

One of the significant challenges faced by poorer inner-city neighborhoods in America is the limited availability of quality food options, commonly referred to as "food deserts." Food deserts are areas where residents have limited access to fresh, nutritious, and affordable food. These neighborhoods often lack grocery stores, farmers markets, and other sources of healthy food, leaving residents with few choices but to rely on convenience stores and fast food outlets that predominantly offer processed and unhealthy food options.

The geographical positioning of these neighborhoods plays a crucial role in this interest. Many low-income inner-city neighborhoods are located in areas that are underserved by grocery stores and supermarkets.

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The frequency of the allele for non-tasting PTC in the population is 0.09 or 9%.

To determine the frequency of the allele for non-tasting PTC in a population where the frequency of PTC tasters is 91%, we can use the Hardy-Weinberg equation. The Hardy-Weinberg principle describes the relationship between allele frequencies and genotype frequencies in a population under certain assumptions.

Let's denote the frequency of the allele for taster individuals as p and the frequency of the allele for non-taster individuals as q. According to the principle, the sum of the frequencies of these two alleles must equal 1, so p + q = 1.

Given that the frequency of PTC tasters (p) is 91% or 0.91, we can substitute this value into the equation:

0.91 + q = 1

Solving for q, we find:

q = 1 - 0.91 = 0.09

Therefore, the frequency of the allele for non-tasting PTC in the population is 0.09 or 9%.

It's important to note that this calculation assumes the population is in Hardy-Weinberg equilibrium, meaning that the assumptions of random mating, no mutation, no migration, no natural selection, and a large population size are met. In reality, populations may deviate from these assumptions, which can affect allele frequencies. Additionally, this calculation provides an estimate based on the given information, but actual allele frequencies may vary in different populations or geographic regions.

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The required equation of the line is represented by x + 2y = 10 in standard form.

A linear equation is written in the standard form as Ax + By = C, where A, B, and C are integers and x and y are variables.

The equation is given in the question

⇒ y = 5 - 1/2 x

We have to determine the standard form of the given linear equation

⇒ y = 5 - 1/2 x

⇒ 1/2 x + y = 5

Multiply by 2 into both sides of the above equation,

⇒ 2(1/2 x + y) = 2(5)

⇒ x + 2y = 10

Therefore, the required equation of the line is represented by x + 2y = 10 in standard form.

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Answer:

its d i just the test

Step-by-step explanation:

StartRoot 4 Superscript 5 EndRoot expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared.

Definition of equivalent

1: equal in force, amount, or value also: equal in area or volume but not superposable a square equivalent to a triangle.

2a: like in signification or import. b: having logical equivalence equivalent statements. 3: corresponding or virtually identical especially in effect or function.

The definition of equivalent is something that is essentially the same or equal to something else. An example of an equivalent is (2+2) and the number 4. Since 2+2= 4, these two things are equivalent. adjective.

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