the time series component that reflects the random changes in a time series that are not caused by any other components, and tends to hide the existence of the more predictable components, is called:

The linear equation represented by the table (-2,7) (1,4) (3,2) (6,-1) is y = -x + 5. To find the linear equation represented by the table (-2,7) (1,4) (3,2) (6,-1), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope, which is the change in y over the change in x between any two points. Let's choose the points (1,4) and (3,2):

slope = (y2 - y1) / (x2 - x1)
     = (2 - 4) / (3 - 1)
     = -2 / 2
     = -1

Now that we have the slope, we can plug it in to the slope-intercept form and solve for b using one of the points. Let's use the point (1,4):

4 = (-1)(1) + b
b = 5

So the equation of the line is y = -x + 5.

To check our work, we can plug in the other points and make sure they all satisfy the equation:

-2 = (-1)(-2) + 5 (true)
7 = (-1)(-2) + 5 (true)
2 = (-1)(3) + 5 (true)
-1 = (-1)(6) + 5 (true)

Therefore, the linear equation represented by the table (-2,7) (1,4) (3,2) (6,-1) is y = -x + 5.

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Answer:

The first option

Step-by-step explanation:

2/9 x + 3 > 4 5/9

2/9x > 4 5/9 - 3

2/9x > 14/9

x > 14/9 ÷ 2/9

x > 7

The option that is not characteristic of the t-test is "The Student t distribution has mean of t = 0 and a standard deviation of 5 = 1". The correct answer is option A.

The t-test is a statistical test that uses the Student t-distribution. The Student t-distribution has a mean of 0, but its standard deviation is not equal to 1. The standard deviation of the t-distribution varies depending on the degrees of freedom, which is determined by the sample size. Therefore, the statement in option A is not true. The correct answer is option A.

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The coordinates of P are P(7, 9) such that P partitions the segment AB in the ratio 5:1.

To find the coordinates of point P that partitions segment AB in the ratio 5:1, we can use the concept of section formula. The section formula states that if we have two points A(x1, y1) and B(x2, y2) dividing the segment in the ratio m:n, then the coordinates of the point P(x, y) can be found using the following formulas:

x = (nx1 + mx2) / (m + n)

y = (ny1 + my2) / (m + n)

In this case, A has coordinates A(2, 4) and B has coordinates B(8, 10). We want to find the coordinates of P that divide the segment AB in the ratio 5:1.

Plugging in the values into the formulas, we have:

x = (12 + 58) / (5 + 1) = (2 + 40) / 6 = 42 / 6 = 7

y = (14 + 510) / (5 + 1) = (4 + 50) / 6 = 54 / 6 = 9

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Answer:

Socratic app

Step-by-step explanation:

it will help you

Answer:

3. m1=82, m4=59. m5=98, m6=51, m7=79, m9=51, m10=129

4. m1=36, m2=90, m4=36, m5=90, m6=54, m7=126, m8=54, m9=126, m10=54, m11=36, m12=144, m13=36, m14=144

Step-by-step explanation:

3. m2=98, m3=23, m8=70

by supplementary angles, m1 + m2 = 180, since we know m2, we have m1 = 180 - 98 = 82. by corresponding angles we have m1 = m3 + m4, since we know m1 and m3, we have m4 = 82 - 23 = 59. again by supplementary angles, m3 + m4 + m5 = 180. we know m3 and m4 so m5 = 180 - 23 - 59 = 98. by alternate interior angles m4 = m7, so m7 = 59. by supplementary angles m6 + m7 + m8 = 180 so m6 = 180 - 70 - 59 = 51. by corresponding angles m6 = m9 so m9 = 51. by supplementary angles m9 + m10 = 180 so m10 = 129

4. m3=54

m2 is a right angle so m2=90. by complementary angles m3 + m4 = 90 so m4 = 36. by vertical angles m1=m4 so m1=36. by vertical angles m2=m5 and m3=m6 so m5=90 and m6=54. by corresponding angles m7 = m2+m1 so m7=126. by supplementary angles m7+m8 = m7+m10 = 180 so m8=10=54. by vertical angles m7=m9 so m9=126. by corresponding angles m1=m11 and m3=13 so m11 and m13 = 54. by supplementary angles m12+m13= m11+m14 = 180, so m12 = m14 = 144

Answer:

Step-by-step explanation:

The real square roots of 121/16 are 11/4 and -11/4, because square root of 121 is 11 and square root of 16 is 4.

To find the square roots of 121/16, we need to take the square root of both the numerator and the denominator separately. The square root of 121 is 11, and the square root of 16 is 4. Therefore, the simplified fraction becomes √121/√16.

Now, let's calculate the square root of 121. Since the square root of a positive number is always positive, the positive square root of 121 is 11. Therefore, we have 11/√16.

Next, we calculate the square root of 16. The positive square root of 16 is 4, so we have 11/4.

To find the other square root, we take the negative value of 11/4, giving us -11/4.

The real square roots of 121/16 are 11/4 and -11/4.

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Therefore,  subscript indices must be either positive integers or logical. True

Explanation: The statement "subscript indices must be either positive integers or logicals" is true. Subscript indices are used to identify elements in an array. A positive integer subscript identifies a particular element in an array, while a logical subscript identifies a subset of elements based on a logical condition. For example, if we have an array A, then A(1) would identify the first element of the array, while A(A > 0) would identify all elements in the array that are greater than zero. Subscript indices cannot be negative or non-integer values.

Therefore,  subscript indices must be either positive integers or logical. True

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Answer:

Step-by-step explanation:

4x-8y

Answer: the equivalent system of equations is:
                       x = 17/37
                       y = -16/37

To determine the equivalent system for the given system of equations:
5x + 3y = 1
4x - 5y = 4

We can use the method of elimination. Here are the steps:

1. Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations equal:

  5(5x + 3y) = 5(1)  -->  25x + 15y = 5
  3(4x - 5y) = 3(4)  -->  12x - 15y = 12

2. Add the resulting equations together to eliminate the variable y:

  (25x + 15y) + (12x - 15y) = 5 + 12
  25x + 12x + 15y - 15y = 17
  37x = 17

3. Divide both sides of the equation by 37 to solve for x:

  x = 17/37

4. Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:

  5x + 3y = 1
  5(17/37) + 3y = 1
  85/37 + 3y = 1
  3y = 37/37 - 85/37
  3y = -48/37
  y = -16/37

Therefore, the equivalent system of equations is:

x = 17/37
y = -16/37

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Answer: Choice D)

6 unit cubes and 18 smaller cubes of volume 1/27 cubic inches

=========================================================

Explanation:

Block A = unit cube that has side length of 1 inch

Block B = cube that has side length 1/3 inch

Block B has a volume of (1/3)*(1/3)*(1/3) = 1/27 cubic inches

If we have 180 of block B, then

180*(1/27) = 180/27 = 6.6667 approximately

The first 6 before the decimal point tells us we have 6 block A's. This is the same as saying that we have 6 cubic inches so far.

The 0.6667 at the end means we have 0.6667*27 = 18.0009 = 18 block B's

So we have 6 unit cubes (block A) and 18 smaller cubes (block B) that have a volume of 1/27 cubic inches

--------------

Another way to look at it

180/27 = (162+18)/27

180/27 = 162/27+18/27

180/27 = 6+18/27

180/27 = 6 remainder 18

The last line can also be found through using long division.

The 6 refers to 6 unit cubes and the remainder 18 is the left over 18 smaller blocks.

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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The expected number of times that they will end up flipping the coin \(\boxed{N}$.\)

Let P be the probability that Alpha goes bankrupt before either player reaches 2N dollars. We can calculate this probability using a recursive approach. Let p_i be the probability that Alpha goes bankrupt given that Alpha has i dollars and Beta has 2N-i dollars. Then we have:

\($p_i = \frac{1}{2}p_{i-1} + \frac{1}{2}p_{i+1}$\)

The first term represents the probability that Alpha loses the next flip and ends up with i-1 dollars, while the second term represents the probability that Alpha wins the next flip and ends up with i+1 dollars. The boundary conditions are\(p_0 = 1\) (Alpha is already bankrupt) and \($p_{2N} = 0$\) (Alpha has reached 2N dollars). We can solve this system of equations to find:

\($p_i = \frac{i}{2N}$\)

This result can be verified by induction.

Now, let\($E_i$\)be the expected number of flips required to reach the endpoint of the game (either bankruptcy or 2N dollars) starting from the state where Alpha has i dollars and Beta has \($2N-i$\)dollars. Then we have:

\($E_i = 1 + \frac{1}{2}E_{i-1} + \frac{1}{2}E_{i+1}$\)

The first term represents the flip that is about to be made, while the second and third terms represent the expected number of flips required to reach the endpoint starting from the new state after the next flip. The boundary conditions are \($E_0 = E_{2N} = 0$\)(we have already reached an endpoint). We can solve this system of equations to find:

\($E_i = 2N\left(1 - \frac{i}{2N}\right)^2$\)

Therefore, the expected number of flips required to reach the endpoint of the game starting from the initial state where both players have N dollars is:

\($E = E_N = 2N\left(1 - \frac{1}{2}\right)^2 = \boxed{N}$\)

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The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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Answer:

400000000 dollar

Step-by-step explanation:

because why not

The statement is false. The assumptions of discharge and friction head loss in series and parallel pipes are the same, not different. In pipes in series, the total discharge is equal to the individual discharge in each pipe. This means that the flow rate remains the same as it passes through each pipe in series. For example, if Pipe A has a discharge of 10 liters per second and Pipe B has a discharge of 5 liters per second, the total discharge in the series will be 10 liters per second.

In pipes in parallel, the total friction head loss is equal to the individual friction head loss in each pipe. This means that the pressure drop across each pipe is independent of the others. For example, if Pipe A has a friction head loss of 20 meters and Pipe B has a friction head loss of 30 meters, the total friction head loss in the parallel pipes will be 50 meters. Therefore, the correct statement would be: For pipes in series, the total discharge equals the individual discharge in each pipe, and for pipes in parallel, the total friction head loss equals the individual friction head loss in each pipe.

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Answer:

45.5

Step-by-step explanation:

66+3x+8=5x+50

3x+74=5x+50

75=2x+50

2x=25

x=12.5

3×+8=45.5

Answer:

Second Data Set

Step-by-step explanation:

The mean absolute deviation describes the average distance between each data point. Let's consider both data sets. In data set one, classmate ages are recorded. Because most of Jordan's classmates are close together in age, the amount of deviation is small. In data set two, teach ages are recorded. Because teacher's ages can range from 23-99, the deviation in this set is expected to be larger than set one.

Answer:

6 and -6

Step-by-step explanation:

you multiply them together you get -36 and then you add them and get 0

-6 and 6

-6x6=-36

-6+6=0

Answer:

Step-by-step explanation:

1. A

2. C

3. B

The statement holds true for the base case and it holds true for any k=n assuming it holds true for k=n, we can conclude that the statement holds true for all positive integer values of k. Hence, if we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in k binomial trees of the smaller orders.

The statement to be proven is: "If we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{k}$\) binomial trees of the smaller orders."

We will prove this statement by mathematical induction.

Base case k=1 :

Inductive step:

Suppose the statement holds true for some \($\mathbf{k}=\mathbf{n}$\), i.e., if we remove the root of an \($\mathbf{n}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{n}$\) binomial trees of the smaller orders. We need to show that it also holds true for \($\mathbf{k}=\mathbf{n}+1$\)

using definition of mathematical induction.

Consider a \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, which can be formed by joining two \($\mathrm{n}^{\text {th }}$\) order binomial trees. If we remove the root of this \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, we are left with two nth order binomial trees. By the induction hypothesis, each of these \($\mathbf{n}^{\text {th }}$\) order binomial trees will result in n binomial trees of the smaller orders. Hence, the result of removing the root of the \($(n+1)^{\text {th }}$\) order binomial tree will be n + n = 2n binomial trees of the smaller orders, which implies that the statement holds true for \($\mathrm{k}=\mathrm{n}+1$\) as well.

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The z-scores for the data values 560, 690, 500, 470, and 290 are 0.6, 1.9, 0, -0.3, and -2.1, respectively.

To calculate the z-scores for the given data values, we use the formula:

z = (x - μ) / σ

where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation.

Mean (μ) = 500

Standard deviation (σ) = 100

Let's calculate the z-scores for each data value:

For x = 560:

z = (560 - 500) / 100 = 0.6

For x = 690:

z = (690 - 500) / 100 = 1.9

For x = 500:

z = (500 - 500) / 100 = 0

For x = 470:

z = (470 - 500) / 100 = -0.3

For x = 290:

z = (290 - 500) / 100 = -2.1

Therefore, the z-scores for the given data values are:

560: 0.6

690: 1.9

500: 0

470: -0.3

290: -2.1

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Complete Question:

Consider a sample with a mean of 500 and a standard deviation of 100. what are the z-scores for the following data values: 560, 690, 500, 470, and 290?

The equivalent expression is seven-fifths squared times one-third cubed. Then the correct option is D.

The equivalent is the expression that is in different forms but is equal to the same value.

Five-sevenths squared times one-third raised to the power of negative three all raised to the power of negative one.

Convert the sentence into numerical form.

\(\rm \rightarrow \left [ \left (\dfrac{5}{7} \right )^2 \times \left ( \dfrac{1}{3}\right )^{-3} \right ] ^{-1}\)

Simplify the expression, then we have

\(\rm \rightarrow \left [ \left (\dfrac{7}{5} \right )^{2} \times \left ( \dfrac{1}{3}\right )^{3} \right ]\)

The equivalent expression is seven-fifths squared times one-third cubed. Then the correct option is D.

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The points that the program connects to make the last N are (-7, 6), (-7, 8), (-5, 6), and (-5, 8).

The coordinates of the points that form the original N are (1, 0), (1, 2), (3, 0), and (3, 2). We need to perform two transformations as given in the rules. The type of transformations consist of translation operations.

The first rule for the translation is (x, y) → (x + 2, y + 5). The translated points are (3, 5), (3, 7), (5, 5), and (5, 7).

The second rule for the translation is (x, y) → (x - 10, y + 1). The translated points are (-7, 6), (-7, 8), (-5, 6), and (-5, 8).

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Answer: x=-6

Step-by-step explanation:

Add 5 to both sides to get 2x by itself

Yes, subtract 1 from both sides to get 3x by itself so you can subtract 2x as to not get a negative x value

One common mistake would be to accidentaly adding or subtracting 1 or 5 when they are supposed to be added/subtracted. To avoid this just go back and check your awnser by plugging it in.

Step-by-step explanation:

Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649

Angle = arctan(-4/-12) = 198 degrees

The Magnitude: 12.649 and Direction: 18° (option c).

To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:

Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)

Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)

where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.

Let's calculate:

Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)

Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°

Since we need to round the direction to the nearest degree, the direction is approximately 18°.

So, the correct answer is:

Magnitude: 12.649 (rounded to the thousandths place)

Direction: 18° (rounded to the nearest degree)

The correct option is: 12.649; 18°

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The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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Answer:

f = -6g/5

Step-by-step explanation:

6f + 9g = 3g + f

combine like terms

6f -f = 3g - 9g

5f = -6g

divide both sides of the equation by 5

f = -6g/5

Answer:

f= -6/5.      aka].  answer B

Step-by-step explanation:

Answer:

2.5 years

Step-by-step explanation:

Given data

Principal= Rs 24000

Final amount A= Rs 30000

Rate r= 10%

The simple interest expression is

A=P(1+rt)

substitute

30000=24000(1+0.1*r)

30000=24000+2400t

30000-24000=2400t

6000=2400t

t= 6000/2400

t=2.5

Hence the time is 2.5 years

Answer:

b) 1.82n

Step-by-step explanation:

n + n - 0.18n

2n - 0.18n (combine like terms)

1.82n

Hope this helps!