A right triangle has side lengths of 4 centimeters and 5 centimeters. What is the length of the hypotenuse?

If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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Therefore , the solution of the given problem of unitary method comes out to be 45 copies of the magazine are still available at the bookstore.

Use the tried-and-true core approach, the real variables, nor any useful information you learn from the general and detailed questions to finish the project expression. Customers may be given another chance to taste the products in response. If these improvements don't happen, we'll miss out on significant advancements in programming comprehension.

Here,

Let's figure out how many issues of the magazine are still available in the store.

Given: There were 90 copies in all when the bookstore opened.

1/6 of the total copies were sold at the bookstore yesterday.

=> 15 copies were sold yesterday = (1/6) * 90.

=> Total copies - Copies sold yesterday = 90 - 15 = 75 Remaining copies after yesterday's sale

=> 2/5 of the remaining copies were sold in the bookstore today.

30 copies were sold today, which

=>  (2/5) * 75.

The quantity of copies left after today's sale equals the quantity left after yesterday's sale. - Today's sales of copies:

=>  75 - 30 = 45

45 copies of the magazine are still available at the bookstore.

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Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:

y = 12 - 9.75

Simplifying the right side:

y = 2.25

Therefore, Lin has 2.25 laps left to swim.

Answer:

  -3

Step-by-step explanation:

You want the graphical solution to x² +6x +9 = 0.

The graph of the expression on the left shows it has a value of 0 when x = -3.

The solution is x = -3.

__

Additional comment

A graphing calculator is very helpful when you want a graphical solution.

If you want to graph this by hand, you can rewrite it as ...

  (x +3)² = 0

The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.

True. The Conditional statement is known as the inductive hypothesis.

In mathematical induction, we use this hypothesis to prove that a certain statement or equation is true for all positive integers.

The process involves proving a base case for the smallest possible value of k and then using the inductive hypothesis to prove that the statement is true for the next consecutive value of k.

This process can be repeated infinitely, proving that the statement is true for all positive integers.
Let's say we want to prove that the sum of the first n positive integers is [tex]n(n+1)/2[/tex] for all positive integers n.

We can start by proving the base case for n=1, which states that [tex]1(1+1)/2 = 1.[/tex]

Now, assuming that the statement is true for some positive integer k, we can use the inductive hypothesis to prove that it is also true for k+1.

This involves showing that[tex](k+1)(k+2)/2 = k(k+1)/2 + (k+1)[/tex] which simplifies to the original equation.

By using the inductive hypothesis, we can prove that the statement is true for all positive integers.
Statement "[tex]P(K) - P(k + 1)[/tex] is true for all positive integers k" is indeed the inductive hypothesis. [tex]1(1+1)/2 = 1[/tex]

It is an important concept in mathematical induction, allowing us to prove statements and equations for all positive integers.

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S is a subspace of the vector space V.

For four conditions are satisfied,

The set S is a subspace of C3(1)

The set S is a subspace of Mn(R)

The set S is a subspace of C2(I)

The set S is a subspace of [tex]R^n[/tex]

The set S is not a subspace of P5(R) because it is not closed under scalar multiplication.

If p(x) is a polynomial in S, then 2p(x) may not satisfy the condition. [tex]p(1) > p(0).[/tex]

The set S is a subspace of C3(1).

The differential equation [tex]y\prime\prime\prime + 2y = x^2[/tex] is linear and homogeneous, so the sum of two solutions is also a solution, and a constant multiple of a solution is also a solution.

S is closed under linear combinations.

The set S is a subspace of Mn(R) because it is closed under addition and scalar multiplication.

If A and B are skew-symmetric matrices, then[tex](A + B)^T = A^T + B^T = -A - B = -(A + B), so A + B[/tex]is skew-symmetric. Similarly, if c is a scalar, then [tex](cA)^T = cA^T = -cA, so c A[/tex] is skew-symmetric.

S is a subspace of C2(I) because it is closed under addition and scalar multiplication.

If y1 and y2 are solutions to[tex]y\prime\prime - 4y\prime+ 3y = 0, then y1\prime\prime - 4y\prime + 3y1 = 0[/tex] and [tex]y2\prime\prime - 4y2\prime + 3y2 = 0[/tex].

Adding these equations gives [tex](y1 + y2)\prime\prime - 4(y1 + y2)\prime + 3(y1 + y2) = 0,[/tex] so [tex]y1 + y2[/tex]is also a solution.

Similarly, if c is a scalar, then [tex](cy)\prime\prime - 4(cy)\prime + 3(cy) = c(y\prime\prime - 4y\prime+ 3y) = 0[/tex], so cy is also a solution.

The set S is a subspace of [tex]R^n[/tex]because it is the null space of a fixed matrix A.

The null space of a matrix is always closed under addition and scalar multiplication.

The set S is not a subspace of [tex]R^n[/tex]because it is not closed under addition. If (1, 1, 0) and (0, 2, 1) are in S, then their sum (1, 3, 1) is not in S because. [tex]1 - 4(3) + 1 \neq 3.[/tex]

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(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.

(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.

(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.

In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is

E[N] = λW = 25 x 0.025 = 0.625 vehicles

So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).

P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5

= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5

= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)

Using a calculator or software, this probability is found to be approximately 0.0176.

(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is

W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes

So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.

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Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.

Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.

GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.

Seasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.

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The amount of their pay per hour is $55.5

The given parameters that will help us to get the amount are.

Louise repaired a computer for each hour she works and we're paid 1165.50

The question reads that if Carla work for 12 hours and Louise work for nine hours

this implies that 12x + 9x = 1165.50

This implies that 21x = 1165.50

Dividing both sides of the equation by 2 to get

21x/21 = 1165.50/21

x = 55.5

So, their  their pay per hour is $55.5

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a. A best-fit line is close to most of the data points.

Best-fit lines help show trends or correlations in data

Best-fit Lines

Best-fit lines attempt to create a line that is close to most data points. This line is a function that can be used to estimate data points that are not a part of the original data set. Additionally, best-fit lines will show the trend of the data. For example, if the slope of the best-fit line is constant, then the data points are directly proportional.

Common Misconceptions

Although best-fit lines can be extremely accurate and helpful, they are not perfect. A best-fit line will attempt to minimize the distance between the line and data points, but it will rarely be perfect. In most cases, there is no way to write a line that will perfectly describe the exact coordinates of each data point.

Additionally, data sets can have any type of correlation. It does not need to be proportional or positive. This means that the slope of a best-fit line can be anything.

Finally, as aforementioned, best-fit lines try to fit the data as much as possible. However, this does not mean that the line has to go through any data points. It is possible for best-fit lines to not go through any data points at all.

The leg measurement will make a right triangle is 21 cm.

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

= 400 + 441 = 841

i.e. p = √(841) = 29

Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.

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Answer:2/3

Step-by-step explanation:

its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD

Answer: 2/3

Step-by-step explanation:

The corresponding side of AD is A'D'.

AD = 30

A'D' = 20

Scale factor = 2/3 because AD * 2/3 = A'D'

If I'm wrong, please tell me.

Answer:

Eleven below Zero

Step-by-step explanation:

Every number below zero (less than zero) is a negative number.

The sampling distribution in this case is positively skewed. This is due to the fact that the mean is greater than the median, and the data is spread out further to the right than to the left, resulting in a long right tail on the histogram.

Data is information that has been collected, organized, and presented in a meaningful way. It can include facts, figures, observations, and other information, such as survey responses, images, and videos. Data is used to inform decision-making, inform research and analysis, and generate insights. Data can be qualitative or quantitative, and it is often gathered from multiple sources. Data can be collected through surveys, experiments, observational studies, or other methods. When combined with analytical tools, data can be used to identify patterns and trends, generate insights, and develop strategies.

The best description of the shape of the sampling distribution in this case would be positively skewed. Positively skewed distributions occur when the mean is greater than the median, and the data is spread out further to the right than to the left. This results in a long tail on the right side of the histogram that skews the data in a positive direction. To determine if this is the case, we can calculate the mean and median of the data.

To calculate the mean, we will use the formula for the population mean: $$\mu = \frac {\sum_{i=1}^n x_i} n$$

where $\mu$ is the population mean, $\sum_{i=1}^n$ represents the sum of all the data points, and $n$ is the sample size.

For the median, we can use the formula for the population median: $$Median = \frac{n+1}{2}th \ \ term$$

where $n$ is the sample size.

In this case, the sample size is 36, so the median would be the 18.5th term.

Now that we have the formulas, we can calculate the mean and median of the data.

The mean of the data is $46,408.89$.

The median of the data is $25,000.

Since the mean is greater than the median, it indicates that the data is positively skewed. This is further confirmed by examining the histogram of the data, which shows a long right tail on the right side of the histogram.

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Answer: Using the given information and the formula ab = cd, we can write:

d = (ab) / c

We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

where a is the unknown length we want to find. Substituting the given values, we get:

a^2 + 12^2 = 6^2

a^2 + 144 = 36

a^2 = -108 (which is not a possible solution)

This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.

Step-by-step explanation:

Yes, the situation is a linear function as y = 30 + 5x is representing the standard form of a linear equation y = mx + b where m is the slope and b is the y-intercept.

Function is equal to ,

y = 30 + 5x

General form of the linear function is written as

y = mx + b

Here, the slope of the equation is 5,

This implies that for every additional service bought the cost increases by $5.

The y-intercept of the equation is 30.

This represents the initial cost of getting the dog groomed without any additional services.

The graph of this function will be a straight line.

And the relationship between the cost and the number of extra services bought will be linear.

When the number of extra services bought increases the cost of grooming the dog will increase by a constant amount .

Here the constant amount is equals to $5 per service.

Therefore, the function y = 30 + 5x is representing a linear function with slope 5 and y-intercept 30.

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The above question is incomplete, the complete question is:

The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x extra services. Does this situation represent a linear function? Explain​

The correct option is (a) i.e. The translation direction is downward, and the number of units is 8.

What is translation?

In mathematics, translation refers to the process of moving a geometric object from one location to another, without changing its size, shape, or orientation.

To determine the translation direction and number of units, we need to find the vector between the original point Q(4,3) and the new point Q'(4,-5).

The vector between two points is found by subtracting the coordinates of the initial point from those of the final point. Therefore, we have:

Q'Q = (4,-5) - (4,3) = (0, -8)

This tells us that the new point Q' is 8 units down (in the negative y-direction) from the original point Q. Therefore, the translation direction is downward, and the number of units is 8.

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The combination of angle measures that could form a triangle are (a) 22, 140, 18 degrees and (c) 55, 67, 58 degrees.

In a triangle, the sum of the three interior angles is always equal to 180 degrees. Therefore, if the sum of the given angle measures is equal to 180 degrees, they could form a triangle.

For option a) 22 + 140 + 18 = 180, so the given angles could form a triangle.

For option b) 72 + 92 + 46 = 210, which is greater than 180, so the given angles could not form a triangle.

For option c) 55 + 67 + 58 = 180, so the given angles could form a triangle.

Therefore, the correct options are (a) 22,140,18 degrees and (c) 55,67,58 degrees

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The given question is incomplete, the complete question is:

Identify the combination of angle measures that could form a triangle

a) 22,140,18 degrees

b) 72,92,46 degrees

c)  55,67,58 degrees

The result of the operation 3a²-ab-2b² and 2a² +5ab "-3b² is

4a² + 7ab - b².

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

Let's simplify the expressions and then perform the given operation:

3a² - ab - 2b² + 2a² + 5ab - 3b² - (a² - 3ab - 4b²)

Combining like terms within parentheses:

3a² - ab - 2b² + 2a² + 5ab - 3b² - a² + 3ab + 4b²

Combining like terms outside parentheses:

4a² + 7ab - b²

Therefore, the result of the operation is 4a² + 7ab - b².

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Answer:

40.8°

Step-by-step explanation:

SohCahToa

use tan

tan^-1(19/22)

=40.81508387

=40.8

Answer:

Step-by-step explanation:

Here,

Opposite side is 19

Adjacent side is 22

To find : The value of Angle A, that is X°.

Formula

Tan X° = Opposite side/Adjacent side

Tan X° = 19/22 = 0.863 ( approximately )

X° = Tan inverse (0.863)

X° = 40.79° ~ 40.8°

Rounding off this to nearest tenth is 41°.

Hence,

X° = 41°

That is,

Angle A is 45°.

To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.

Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.

To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the binomial probability formula to calculate these probabilities:

P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^(n-k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we get:

P(X = 2) = (5 choose 2) * [tex](1/2)^2[/tex] * [tex](1/2)^3[/tex] = 10/32

P(X = 3) = (5 choose 3) * [tex](1/2)^3[/tex] * [tex](1/2)^2[/tex] = 10/32

P(X = 4) = (5 choose 4) * [tex](1/2)^4[/tex] *[tex](1/2)^1[/tex] = 5/32

P(X = 5) = (5 choose 5) * [tex](1/2)^5[/tex] * [tex](1/2)^0[/tex] = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at least two goals is 13/16.

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The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

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There are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.

There are two ways to divide 5 people into two groups where the first group has 2 people and the second has 3. The first way is to choose 2 people out of the 5 for the first group, which can be done in 5C2 ways, and then the remaining 3 people form the second group. The second way is to choose 3 people out of the 5 for the second group, which can be done in 5C3 ways, and then the remaining 2 people form the first group. Therefore, the total number of ways to divide 5 people into two groups with a group of 2 people and a group of 3 people is 5C2 + 5C3, which equals 10 + 10, or 20.
The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

where C(n, r) is the number of ways to choose r items from a set of n items, n! represents the factorial of n, and r! represents the factorial of r.

In this case, you want to choose 2 people from a set of 5. So, n = 5 and r = 2. Plug the values into the formula:

C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = 5! / (2!3!)
C(5, 2) = 120 / (2*6)
C(5, 2) = 120 / 12

So, there are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.

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Possible translations such that the graph passes through the point (1,2) are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Two possible translations for the function to pass through the point (1,2) are given as follows:

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The proof that the Quadrilateral WXYZ is a rectangle is shown below

To prove that Quadrilateral WXYZ is a rectangle, we need to show that it has four right angles.

First, we can find the slopes of each pair of opposite sides to determine if they are perpendicular.

The slope of WX is:

m(WX) = (y2 - y1)/(x2 - x1) = (-2 - 1)/(2 - (-1)) = -1

The slope of YZ is:

m(YZ) = (y2 - y1)/(x2 - x1) = (6 - 3)/(4 - 7) = -1

Since the slopes of WX and YZ are equal , we know that they are opposite sides.

Now we can use the distance formula to check if the sides of the quadrilateral are congruent. The length of WX is:

√((2 - (-1))^2 + (-2 - 1)^2) = √18

The length of YZ is:

√((7 - 4)^2 + (3 - 6)^2) = √18

The length of WY is:

√((7 - (-1))^2 + (3 - 1)^2) = √68

The length of XZ is:

√((4 - 2)^2 + (6 - (-2))^2) = √68

We can see that opposite sides WX and YZ have the same length, as do opposite sides WY and XZ.

So, the quadrilateral is a rectangle

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The coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).

The picture M', whose coordinates are in the fourth quadrant and created when point M is mirrored in the x-axis, is (h, -k). As a result, we deduce that when a point is reflected along the x-axis, the x-coordinate stays constant while the y-coordinate changes to the negative.

As a result, M'(h, -k). is the image for point M (h, k)

Given data:

coordinates of the vertices before reflection:

B(1,7), D(1,6) and C(10, 7).

Reflection about x = 1.

As Point B and D lies on the line x = 1, their coordinates will  not change.

C is 9 units to the right of the line x = 1 at (10, 7)

Thus, after reflection C will be 9 units to the left of the line x = 1 at (-8, 7).

Therefore, the coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).

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There are  [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.

The problem you are describing is a classic example of a combination problem, specifically choosing a certain number of items from a larger set without regard to the order in which they are arranged.

The formula to calculate the number of ways to choose "r" items from a set of "n" items without replacement is given by the combination formula, also known as "n choose r" or denoted as C(n, r). The formula is:

[tex]C(n, r) = n! / (r! \times (n - r)!)[/tex]

where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

In your case, you are choosing 4 members from a family of 5 for a photo shoot, and the order in which they line up does not matter. So you need to find C(5, 4).

Plugging the values into the formula:

[tex]C(5, 4) = 5! / (4! \times (5 - 4)!) = 5! / (4! \times 1!) = (5 \times 4 \times 3 \times 2 \times 1) / ((4 \times 3 \times 2 \times 1) \times 1) = 5[/tex]

Therefore,  there are  [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.

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The standard form expression that represents the amount of border material Jessica will need is 2L + 2W - 2x - 2y = -2B

To create this expression, we need to consider a few things. Firstly, we need to know the length and width of the solar panels. Let's say the length of the solar panel is L and the width is W. We also need to know the width of the border that Jessica wants to add. Let's call this value B.

The total amount of material needed for the border will be the sum of the material needed for the four sides of the solar panel. Each side will need a length of B, so the total length of the material needed will be 2B + 2L + 2W.

However, we can simplify this expression by putting it into standard form. Standard form expressions are written in a specific way that makes them easier to read and work with. In standard form, the expression is written as Ax + By = C, where A, B, and C are constants and x and y are variables.

To put the expression 2B + 2L + 2W into standard form, we need to group the variables together and move the constants to the other side of the equation. This gives us the expression 2L + 2W - Ax - By = -2B, where A and B are both equal to -2, and C is equal to -2B.

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Answer:

8c^2 + 24c - 6

Step-by-step explanation:

I got it right on edmentum

To calculate the odds ratio of being diabetic for older adults compared to adults while controlling for glucose levels in a logistic regression model, we exponentiate the coefficient estimate for Age. For example, if the estimate is 0.05, the odds ratio is 1.65.

To obtain the odds ratio for older adults compared to adults while controlling for glucose levels in a logistic regression model predicting diabetic status based on age and glucose levels, we would need to look at the coefficient estimate for the age variable. Let's say the logistic regression model is

logit(P(Diabetic)) = β_0 + β_1Age + β_2Glucose

where P(Diabetic) is the probability of being diabetic, Age is the age in years, and Glucose is the glucose level in mg/dL. β_1 represents the coefficient estimate for Age.

To calculate the odds ratio for older adults (e.g., those who are 10 years older than the average age in the sample) compared to adults while controlling for glucose levels, we can exponentiate the coefficient estimate for Age and round to 0.01. That is

OR = exp(β_1*10)

For example, if the coefficient estimate for Age is 0.05, then:

OR = exp(0.05*10) = 1.65

This means that for every 10-year increase in age, the odds of being diabetic compared to non-diabetic increase by a factor of 1.65 while holding glucose levels constant.

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the Princess Resort is the best deal with a total cost of $657 for a four-night stay.

What is Total fixed cost?

Total fixed cost refers to the cost of all fixed assets which incur a fixed cost irrespective of the level of production in a company.

The Contemporary Resort costs $239 per night, so the total cost for four nights would be:

$239 × 4 = $956.

The Fun Times Resort costs $189 per night, so the total cost for four nights would be:

$189 × 4 = $756.

The regular cost is $219 per night, so the total cost for three nights would be:

$219 × 3 = $657. But since they get the fourth night free, the total cost for four nights would be:

$657 + $0 = $657.

Comparing the three options, the Princess Resort is the best deal with a total cost of $657 for a four-night stay.

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Both computers working together can process the payroll in 2.4 hours.

Let's denote the time it takes for both computers working together to process the payroll as "t".

We can use the formula:

work done = rate x time

where "work done" is the same in both cases, as they are processing the same payroll. Therefore, we can set up an equation using the rates :

1/6 + 1/4 = 1/t

We can simplify the left-hand side of the equation:

2/12 + 3/12 = 1/t

5/12 = 1/t

Multiplying both sides by 12t:

5t = 12

t = 12/5

t = 2.4

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