1. Here is a polygon. Draw a scaled copy of the polygon using a scale factor of 1/2.
The scale of a map says that 8 cm represents 5 km.
What distance on the map (in centimeters) represents an actual distance of 8 kilometers?
Must show your math thinking on the sketchpad.You may use a calculator, but must show the calculations you used.

The answer is: A) seasonal variations, Seasonal variations in time-series data refer to regularly repeating upward or downward movements tied to recurring events. hese patterns occur over fixed periods, such as daily, weekly, monthly, or yearly cycles.

In time-series data, seasonal variations are regularly repeating upward or downward movements in series values that can be tied to recurring events.

These variations occur over a fixed period, such as daily, weekly, monthly, or yearly cycles. Seasonal variations can be observed in various phenomena, including sales data, weather patterns, and economic indicators.

By identifying and analyzing seasonal variations, patterns and trends can be detected, helping to make predictions and informed decisions.

Seasonal variations are commonly represented using seasonal indices or seasonal adjustment techniques to remove the effects of seasonality and better understand the underlying trends in the data.

Understanding and accounting for seasonal variations are crucial for accurate forecasting and decision-making in various fields.

Hence, the correct option is (A) seasonal variations.

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Alice can be expected to win approximately 5 games out of the 7 games she plays.

If historically Alice wins 70% of the time, we can expect her to win 70% of the games she plays. If Alice and Bob play 7 games of chess, we can calculate how many games Alice can be expected to win by multiplying the total number of games (7) by the probability of Alice winning (70% or 0.7):

Expected number of games Alice wins = 7 * 0.7 = 4.9

Since we cannot have a fraction of a game, we can round the expected number of games Alice wins to the nearest whole number. Therefore, Alice can be expected to win approximately 5 games out of the 7 games she plays.

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Answer:

A

Step-by-step explanation:

(f - g )(x)

= f(x) - g(x)

= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1

= 3x + 2 - 2x + 2 ← collect like terms

= x + 4

The value of the function (f-g)(x) is x+4.

A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).

Given are two functions, f(x) = 3x+2 and g(x) = 2x-2, we need to find the value of (f-g)(x)

So,

(f-g)(x) = f(x) - g(x)

= 3x+2 - (2x-2)

= x+4

Hence, the value of the function (f-g)(x) is x+4.

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A metric can be used to help us determine the extent of how much an outcome is achieved.

A metric is a quantifiable gauge that is employed to assess, scrutinize, and appraise diverse facets of a system, procedure, or outcome. It furnishes a standardized and unbiased approach to gauge and monitor performance or advancement towards particular objectives or goals. Metrics are commonly formulated based on precise criteria or prerequisites and can manifest as numerical or qualitative in essence.

They find application in various domains such as commerce, finance, science, engineering, and myriad others to evaluate performance, facilitate well-informed decisions, and oversee progress over time.

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The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

\(\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}\)

Part b.

Consider V(3X + 2Y)

\(\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}\)

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

\(3 X+2 Y \sim N(18,77)\)

Thus,

\(P(3 X+2 Y < 18)=0.5\)

Part d.

Consider P(3X + 2Y < 28)

\(Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}\)

\(\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}\)

Therefore, the values for the given normal random variables are found.

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The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

Answer:

C. n = 90; p = 0.8

Step-by-step explanation:

According to the Central Limit Theorem, the distribution of the sample means will be approximately normally distributed when the sample size, 'n', is equal to or larger than 30, and the shape of sample distribution of sample proportions with a population proportion, 'p' is normal IF n·p ≥ 10 and n·(1 - p) ≥ 10

Analyzing  the given options, we have;

A. n = 45, p = 0.8

∴ n·p = 45 × 0.8 = 36 > 10

n·(1 - p) = 45 × (1 - 0.8) = 9 < 10

Given that for n = 45, p = 0.8, n·(1 - p) = 9 < 10, a normal distribution can not be used to approximate the sampling distribution

B. n = 90, p = 0.9

∴ n·p = 90 × 0.9 = 81 > 10

n·(1 - p) = 90 × (1 - 0.9) = 9 < 10

Given that for n = 90, p = 0.9, n·(1 - p) = 9  < 10, a normal distribution can not be used to approximate the sampling distribution

C. n = 90, p = 0.8

∴ n·p = 90 × 0.8 = 72 > 10

n·(1 - p) = 90 × (1 - 0.8) = 18 > 10

Given that for n = 90, p = 0.9, n·(1 - p) = 18 > 10, a normal distribution can be used to approximate the sampling distribution

D. n = 45, p = 0.9

∴ n·p = 45 × 0.9 = 40.5 > 10

n·(1 - p) = 45 × (1 - 0.9) = 4.5 < 10

Given that for n = 45, p = 0.9, n·(1 - p) = 4.5 < 10, a normal distribution can not be used to approximate the sampling distribution

A sampling distribution Normal Curve

45 × (1 - 0.8) = 9

90 × (1 - 0.9) = 9

90 × (1 - 0.8) = 18

45 × (1 - 0.9) = 4.5

Now we will investigate the shape of the sampling distribution of sample means. When we were discussing the sampling distribution of sample proportions, we said that this distribution is approximately normal if np ≥ 10 and n(1 – p) ≥ 10. In other words

Therefore;

A normal curve can be used to approximate the sampling distribution of only option C. n = 90; p = 0.8

Step-by-step explanation:

The answer of this equation is x = 3

B:x=3

Step-by-step explanation:

The required equations that are equivalent to each other are,

(A)  2 + x = 5    (B) x + 1 = 4   (E) -5 + x = -2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Given equations,

(A) 2 + x = 5

Simplifying the above expression,

x = 5 - 2

x = 3

Similarly, simplify all the equations,

(B) x = 3

(C) x = -3

(D) x = 11

(E) x = 3

Therefore, equations that give x = 3, after simplification is equivalent equations.

Thus, the requried equations that are equivalent to each other are,

(A)  2 + x = 5    (B) x + 1 = 4   (E) -5 + x = -2.

The mean and the standard deviation of the sampling distribution of the sample mean  is equal to 4.57 and 0.69 respectively.

Population mean  'μ' = 4.57

Sample size 'n' = 7

Population Standard deviation 'σ' =1.82

Mean of the sampling distribution of the sample mean is equal to the population mean,

which is μ = 4.57.

So, μₓ = μ = 4.57.

Standard deviation of the sampling distribution of the sample mean also known as the standard error of the mean.

Using the formula we have,

σₓ = σ / √(n)

Substituting the given values, we have,

⇒ σₓ = 1.82 / √(7)

⇒ σₓ = 1.82 / 2.646

⇒ σₓ = 0.6878

⇒ σₓ ≈ 0.69

This implies,

The standard deviation of the sampling distribution of the sample mean is σₓ ≈ 0.69.

Therefore, the mean of the sampling distribution of the sample mean and

standard deviation of the sampling distribution of the sample mean  is equal to 4.57 and 0.69 respectively.

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The above question is not complete, the complete question is:

Easy Eats Diner is a large restaurant chain. After paying for a meal at Easy Eats Diner, customers are asked to rate the quality of the food as a 1, 2, 3, 4, or 5, where a rating of 1 means "not good" and 5 means "excellent". The customers' ratings have a population mean of μ = 4.57, with a standard deviation of σ=1.82. Suppose that we will take a random sample of n= 7 customers' ratings. Let x represent the sample mean of the 7 customers' ratings. Consider the sampling distribution of the sample mean x.

Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.

(a) Find μₓ(the mean of the sampling distribution of the sample mean).  ?

(b) Find σₓ (the standard deviation of the sampling distribution of the sample mean). ?

Answer:

I, II, III, IV, V, VI, VII, VIII, IX, and X.

Step-by-step explanation:

ik the numerals

Answer:

2n^4

Step-by-step explanation:

462⋅−2

*

Cancel terms that are in both the numerator and denominator.

*

4n6

-----   ⋅ n−2

2  

*

26 ⋅ −2

*

Combine exponents.

*

2n^4

Hope this helped:D

Answer:

2,4

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

Given

9(3x - 5) = - 9(- 5x - 3) ← distribute parenthesis on both sides )

27x - 45 = 45x + 27 ( subtract 45x from both sides )

- 18x - 45 = 27 ( add 45 to both sides )

- 18x = 72 ( divide both sides by - 18 )

x = - 4

Answer:

36.5

Step-by-step explanation:

y= -x²+73x-520

which can be represented as ax²+bx+c

a= -1, b= 73, c = -520

for maximum value of y,

the formula is

c - (b² / 4a)

= -520 - (73² / 4×(-1))

= -520 - (5329 / -4)

= -520 + 1332.25

= 812.25

Solving for x,

812.25 = -x²+73x-520

or, x²-73x+ 1332.25 = 0

Solving,

x= 36.5

The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]

Solving the given question:

We know that the formula for Margin of error is:

Margin of error = z-score * (standard deviation) / root (sample size)

E = z * σ / √(n), where

E = Margin of error

z = z-score

n = Sample size

σ = standard deviation

Therefore, sample size = ( z – score * standard deviation / margin of error)²

n = ( z * σ / E )²

First, calculate the z-score for the 99% confidence level.

From the normal distribution curve, the area under 99% confidence level is given as:

Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995

From the z-score table, we find the value of z with the corresponding area of 0.995

We find the value of the z-score corresponding to 0.995 is 2.58

Also given sample mean is one unit of the population. So the margin of error is 1

E = 1

And given Standard deviation = 13.8

σ = 13.8

Putting the values in the given formula of sample size n =

n = (2.58 * 13.8 / 1 )²

n = 1267.64

n = 1268

Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )

Answer:-3

Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry

The correct option is (C) The graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Option (C) gives a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

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Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

Answer:

x = 1  and x = -3

Step-by-step explanation:

if y = f(x) and f(x) = -5, this means y = -5

draw a horizontal line at y = -5 and see write the x values for where the line intersects with the graph.

The x values are:

x = 1  and x = -3

Answer:

to find the slope of any graph

use this equation

Step-by-step explanation:

\(m = \frac{y2 - y1}{x2 - x1} \\ \frac{8 - 0}{2 - 0} \\ m = 4\)

Answer:

-4.9

Step-by-step explanation:

the dot is on -4.9

Answer:

359.19

Step-by-step explanation:

Using the formula V=(πr^2) * h/3 and plugging in the given values we get 359.19.

I estimated pi at about 3.14

a) The two events A and B are mutually exclusive and the probability of A occurring is P(A) = 0.2, and the probability of event B occurring is

P(B) = 0.5.

The probability of A or B happening is given by the following formula:

P(A or B) = P(A) + P(B) – P(A and B)

Since the two events are mutually exclusive, it means they cannot happen at the same time, so

P(A and B) = 0.

Thus,

P(A or B) = P(A) + P(B)

= 0.2 + 0.5

= 0.7

b) The events C and D are independent of each other and the probability of event C happening is

P(C) = 0.3,

while the probability of event D occurring is

P(D) = 0.6.

The probability of C and D happening is given by:

P(C and D) = P(C) x P(D)

= 0.3 x 0.6

= 0.18

Answer: a) P(A or B) = 0.7,

b) P(C and D) = 0.18

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The provided algorithm assigns classrooms to courses while minimizing the total number of classrooms required with a time complexity of O(n log n).

To solve the problem of assigning classrooms to courses while minimizing the total number of classrooms required, we can use the Interval Scheduling algorithm based on the concept of greedy approach. The algorithm has a time complexity of O(n log n), where n is the number of courses.

Here's the step-by-step explanation of the algorithm:

Now, let's prove the correctness of the algorithm:

The algorithm is based on the greedy approach, which involves making locally optimal choices at each step. In this case, we choose the classroom with the earliest available time slot for each course.

By sorting the courses based on their end times, we ensure that for each subsequent course, its start time is compared only with the end times of the courses already assigned to classrooms. If the start time is after the end time of any classroom's last course, we assign the course to that classroom.

If the start time is before or overlapping with the end time of all classrooms' last courses, a new classroom is created. This ensures that no conflicts arise and that each course is assigned to a compatible classroom.

Since the courses are sorted based on their end times, the algorithm guarantees that each course is assigned to a classroom with the earliest available time slot, minimizing the need for additional classrooms.

Now, let's analyze the time complexity:

Therefore, the provided algorithm assigns classrooms to courses while minimizing the total number of classrooms required with a time complexity of O(n log n).

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Answer:

D) The expression equals 0

Step-by-step explanation:

-8 + 8 = 0

the negative and positive cancel eachother out

Answer:

An impossible event has a probability of 0. A certain event has a probability of 1.

Answer:

A. b+5

B.3(b+5)

C.b+5+8b=9b+5

Step-by-step explanation:

The sum of the given series, 6+12+24+...+15366+12+24+...+1536, is approximately -6291450.

To find the sum of the given series, we need to determine the first term (a₁), the common ratio (r), and the number of terms (n).

The first term (a₁) is 6.

The common ratio (r) is 2 because each term is double the previous term.

The number of terms (n) can be calculated by finding the number of terms in the first part and the number of terms in the second part separately.

First part:

The last term in the first part is 15366.

We can find the number of terms (n₁) in the first part using the formula for the nth term of a geometric sequence: an = a₁ * r^(n-1).

15366 = 6 * 2^(n₁ - 1)

2561 = 2^(n₁ - 1)

By testing different values, we find that n₁ = 12.

Second part:

The last term in the second part is 1536.

We can find the number of terms (n₂) in the second part using the same formula.

1536 = 12 * 2^(n₂ - 1)

128 = 2^(n₂ - 1)

By testing different values, we find that n₂ = 8.

The total number of terms (n) is n = n₁ + n₂ = 12 + 8 = 20.

Now, we can calculate the sum of the series using the formula for the sum of a finite geometric series:

Sn = a₁ * (1 - r^n) / (1 - r)

Sn = 6 * (1 - 2^20) / (1 - 2)

Sn = 6 * (1 - 1048576) / (-1)

Sn = -6291450

Therefore, the sum of the given series is -6291450.

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The best way to describe the center of the data represented in a line plot is by using measures of central tendency.

- Measures of central tendency include mean, median, and mode.
- Mean is calculated by adding up all the data points and dividing by the total number of data points. It gives an idea of the average value of the data.
- Median is the middle value of the data set when arranged in order. It is not affected by extreme values or outliers and gives an idea of the middle value of the data.
- Mode is the value that appears most frequently in the data set. It is useful when the data has repeated values.

To describe the center of the data represented in a line plot, one can use measures of central tendency. The three most commonly used measures of central tendency are mean, median, and mode. Mean is calculated by adding up all the data points and dividing by the total number of data points. It gives an idea of the average value of the data. For example, if a line plot represents the number of hours spent studying for an exam, the mean could give an idea of the average number of hours studied by the students. Median is the middle value of the data set when arranged in order. It is not affected by extreme values or outliers and gives an idea of the middle value of the data. For example, if a line plot represents the salaries of employees in a company, the median could give an idea of the salary earned by the middle-ranked employee. Mode is the value that appears most frequently in the data set. It is useful when the data has repeated values. For example, if a line plot represents the favorite color of a group of people, the mode could give an idea of the color that is most commonly preferred. Therefore, by using these measures of central tendency, one can describe the center of the data represented in a line plot.

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