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Answer:

B.any collection of random variables in a sequence is taken and shifted ahead by htime periods, the joint probability distribution remains unchanged

Step-by-step explanation:

In most of the time series techniques , there is usually a common assumption that data are stationary. A stationary process can be regarded as one that has properties such as variance mean, variance as well as autocorrelation structure not changed over time. The properties is independent as regards the time the series is observed.

✓ Time series that has trends or seasonality cannot be regarded as stationary, because the value of the time series which exist in different times will be affected by the trend and seasonality.

✓A white noise series can be regarded as stationary because the time you observe it does not matter, it will always look much the same at all point in time.

✓ It should be noted that process is stationary if any collection of random variables in a sequence is taken and shifted ahead by htime periods, the joint probability distribution remains unchanged

Hi!

There might be different variations into how anyone would approach this problem but this is by far an easy way for me.

In order to solve fractional relationships with a variable, a perfect way to solve them would be to cross multiply and make them equal to each other.

You see the part '3y+12', and when you criss cross over to the other side of the equation, you get three. Multiply that together.

When you see the part '6', when you glide diagonally, you find '4y'. Multiply this together as well. Make them equal to each other.

(This is how you do cross multiplication.)

You should get something like this:

3(3y+12)=6(4y)              Distribute the three on the left side and multiply. Do the same on the right.

9y+36=24y                    Now, you can combine like terms by subtracting 9y to the other side.

36=15y                           Isolate y and divide it by 15.

y=2.4

I was unclear of the answer, so I plugged in 2.4 into the original equation where the y variable was, and got the right answer, so 2.4 should be the correct one no matter how you got it.

I hope this helped!

Answer:

b

the sqr root should go with the x and the intercept is at -2/3

The initial cost is $12 to enter.

Each ticket is $.50

we want to find out how much it costs for 70 tickets so we multiply the cost by the amount;

70 x .50 = 35

Therefor including the entry fee, it would cost $35 + $12

Which is $47

I hope this helps! :)

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.

Mathematicians use the unitary method, also referred to as the "single unit technique," to answer problems involving proportional relationships between two or more quantities. The unitary technique entails determining the value of a single unit or quantity and using that value to calculate the values of other quantities in relation to that unit or quantity. Problems requiring ratios, proportions, percentages, and other related ideas can be solved using this approach.

given

Shay's age will be denoted by the letter S, and her sister's age will be referred to as "Sister".

The first claim informs us of the following:

Sibling = 2S – 7

And based on the second assertion, we can infer that:

Sibling + S = 80

The result of putting the first equation into the second equation is:

S + (2S - 7) = 80

When we simplify this solution, we obtain:

3S - 7 = 80

7 added to both edges gives us:

3S = 87

When we multiply both parts by 3, we get:

S = 29

Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.

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a. 150 families in the sample earned less than $45,000.

b. We can nοt determine hοw many families earned mοre than $ 55,000 exactly.

The term “incοme” generally refers tο the amοunt οf mοney, prοperty, and οther transfers οf value received οver a set periοd οf time in exchange fοr services οr prοducts.

Here, we have

Given:

Suppοsed yοu study family incοme in a randοm sample οf 300 families. Yοu find that the mean family incοme is $55,000; the median is $45,000; and the highest and lοwest incοmes are $250,000 and $2400, respectively.

a. 150 families in the sample earned less than $45,000 because the median is the middle value in the οrdered data.

Median = 45,000/300

=  150

b. We can nοt determine hοw many families earned mοre than $ 55,000 exactly. It will be less than half. Because $55,000 is the mean value, it is nοt based οn the οrder.

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The expression that models the problem is:

2 and 1/2 pounds + 3 and 3/4 pounds

b. To find the LCD (Least Common Denominator) of the fractions 1/2 and 3/4, we need to find the least common multiple (LCM) of the denominators, which are 2 and 4. The LCM of 2 and 4 is 4. Therefore, the LCD of the fractions is 4.

c. To evaluate the expression, we need to find the sum of the mixed numbers and the fractions separately:

2 and 1/2 pounds = 2 pounds + 1/2 pound = 2 pounds + 2/4 pound

3 and 3/4 pounds = 3 pounds + 3/4 pound = 3 pounds + 3/4 pound

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The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

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Hi!

Since they are the same terms, both \(\frac{-5}{7}\), we can multiply the exponents without any problem.

When multiplying exponents, you just add them together, and that's your new exponent!

\((\frac{-5}{7})^8*(\frac{-5}{7})^9\)

\(8 + 9 = 17\)

Your answer is \(\frac{-5}{7}\)^17

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Step-by-step explanation:

there is nothing to solve as there is no equation.

but we can simplify the expression :

2b - (-4b) = 2b + 4b = 6b

remember :

++ = +

+- = -

-+ = -

-- = +

Answer:

6b

Step-by-step explanation:

2b+4b (- - = +)

The answer is 6b

To minimize the time it takes to get to town, we need to find the point where the time it takes to travel by boat and by car is minimized. Let's assume that the distance the car travels is "x" miles.

The time it takes to travel by boat is given by t_boat = 8/35 hours, since the boat travels 8 miles at a speed of 35 mph.

The time it takes to travel by car is given by t_car = (48 - x)/45 hours, since the car travels the remaining distance of (48 - x) miles at a speed of 45 mph.

Therefore, the total time it takes to get to town is t_total = t_boat + t_car = 8/35 + (48 - x)/45.

To minimize this expression, we can take its derivative with respect to x and set it equal to zero:

d/dx [8/35 + (48 - x)/45] = -1/45

Setting this equal to zero and solving for x, we get:

48 - x = 315/4

x = 39.4 miles

Therefore, the car should be left at a point about 39.4 miles from town to minimize the time it takes to get to town.

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Answer:

55

Step-by-step explanation:

(after the first "1") You need to add the previous two numbers together to get the next number in the pattern.

Trey will have to add 3 9/16 cups to increase the recipe 1 1/2 times.

To calculate the number of cups needed to add to increase the recipe 1 1/2 times, we have to multiply the original amount of flour by 1 1/2 times. With the help of this method we will be able to find out the number of extra cup of flour that needs to be added when the recipe is increased by 1 1/2 times.

To calculate number of increased cups, we need to:

2 3/8 * 1 1/2

let's convert the mixed fractions into improper fraction:

19/8 * 3/2

To multiple two fractions, multiply the numerators and denominators:

(19 * 3) / (8 * 2)

57 / 16

The mixed fraction would be:

3 9/16

Therefore. number of cups needed to increase the recipe 1 1/2 times is

3 9/16.

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Answer:

n = 2/3

Step-by-step explanation:

3n - 22 = -20

Add 22 to both sides

-20 + 22 = 2

3n = 2

Divide both sides by 3

2 / 3 = 2/3

n = 2/3

Let me know if I've done something wrong :)

Answer:

\(n = \frac{2}{3}\)

Step-by-step explanation:

I hope this helps!

Elina's GPA is greater than 2.0. If this condition is met, the formula returns "OK standing". If neither of the conditions is met, the formula returns "Bad standing".

To determine Elina's standing based on her GPA, you can use the following formula:

=IF(G6 > 3.0, "Good standing", IF(G6 > 2.0, "OK standing", "Bad standing"))

In this formula, we use the IF function to evaluate different conditions. The first condition checks if Elina's GPA (in cell G6) is greater than 3.0. If it is, the formula returns "Good standing". If the first condition is not met, it moves to the second condition, which checks if Elina's GPA is greater than 2.0. If this condition is met, the formula returns "OK standing". If neither of the conditions is met, the formula returns "Bad standing".

By using nested IF statements, we can evaluate multiple conditions and return the corresponding standing based on Elina's GPA.

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Answer:

10. log5625 = 4

12. log1/28 = -3

14. log1010000 = 4

Note: bolded numbers are bases and are written like exponents but at the bottom.

An invertible matrix may have fewer than n linearly independent eigen vectors, making it not diagonalizable. The correct answer is A. The statement is false.

To prove let's consider the definitions and properties of invertible matrices and diagonalizable matrices.

An invertible matrix A is a square matrix that has an inverse, denoted as \(A^(-1)\). A matrix is invertible if and only if its determinant is nonzero. In other words, A is invertible if det(A) ≠ 0.

A diagonalizable matrix is a square matrix A that can be expressed as A = PD\(P^(-1)\), where P is an invertible matrix and D is a diagonal matrix. In this diagonal representation, the diagonal entries of D correspond to the eigenvalues of A.

Now, to determine whether the statement is true or false, we need to consider the relationship between invertible matrices and diagonalizable matrices.

It is true that a diagonalizable matrix is invertible. This is because if A =\(PDP^{-1}\), then\(A^(-1) = (PDP^(-1))^(-1) = PD^(-1)P^(-1),\)and since \(D^{-1}\) is also a diagonal matrix, \(A^{-1}\) is invertible.

However, the converse is not necessarily true. An invertible matrix may not be diagonalizable. This happens when an eigenvalue of the matrix has a geometric multiplicity (the number of linearly independent eigenvectors associated with it) that is less than its algebraic multiplicity (the multiplicity of the eigenvalue as a root of the characteristic polynomial).

For example, consider the matrix A = [1 1; 0 1]. The eigen value of A is 1, and it has only one linearly independent eigenvector, namely [1; 0]. Since the geometric multiplicity is 1 and the algebraic multiplicity is 2, A is not diagonalizable despite being invertible.

In general, for an invertible matrix A, it may or may not have a full set of n linearly independent eigenvectors, making it not necessarily diagonalizable. Therefore, option A is the correct answer: The statement is false.

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The values of y when x is 3, 4, and 5 are 21, 25, and 29, respectively.

To find the values of y when x is 3, 4, and 5 using the equation y = 4x + 9, we substitute the respective values of x into the equation and solve for y.

For x = 3:

y = 4(3) + 9

y = 12 + 9

y = 21

For x = 4:

y = 4(4) + 9

y = 16 + 9

y = 25

For x = 5:

y = 4(5) + 9

y = 20 + 9

y = 29

So, the values of y when x is 3, 4, and 5 are 21, 25, and 29, respectively.

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Answer:

a

Step-by-step explanation:

in y intercept x = 0 so the choice a become the answer

The length on the blueprint is approximately 0.2667 units.

To find the length on the blueprint, we can set up a proportion using the given information.

Let's denote the length on the blueprint as "x".

According to the blueprint, the width is 4 inches, and the actual length is 20 feet. We can set up the following proportion:

Width on Blueprint / Actual Width = Length on Blueprint / Actual Length

Plugging in the values:

4 inches / 20 feet = x / 16 feet

Now, we need to convert the units to be consistent. Since we have feet in the denominator on both sides, we can convert inches to feet by dividing by 12:

(4 inches / 12 feet) / 20 feet = x / 16 feet

Simplifying:

1/3 / 20 = x / 16

Now, we can cross multiply:

(1/3) × 16 = 20 ×x

Simplifying further:

16/3 = 20x

To solve for x, we can divide both sides by 20:

(16/3) / 20 = x

Simplifying:

16 / (3 × 20) = x

16 / 60 = x

Now, we can simplify the fraction:

4/15 = x

So, the length on the blueprint is 4/15 of a unit.

Alternatively, if you want to convert the fraction to decimal form, you can divide 4 by 15:

4 ÷ 15 ≈ 0.2667

Therefore, the length on the blueprint is approximately 0.2667 units.

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Answer: where is the figure tot he right???

Step-by-step explanation:

The equation that can be used to find the value of x is 120 = (x + 5) × (120/x - 1/3).

Carmen's first trip was 120 miles, and she traveled at an average of x miles per hour. We can use the formula:

distance = rate × time, which can be written as:
120 miles = x miles/hour × time

where, time is the time for outgoing.

For the return trip, Carmen traveled at a rate that was 5 miles per hour faster, so her speed was (x + 5) miles/hour. The time for the return trip was one-third of an hour less than the time for the outgoing trip, so we can represent the return trip time as (time - 1/3) hours. Using the distance formula again for the return trip:
120 miles = (x + 5) miles/hour × (time - 1/3) hours

Now, let's express both times in terms of x. From the first equation, we can find the time for the outgoing trip as:
time = 120 miles / x miles/hour

Substitute this expression for time in the return trip equation:
120 miles = (x + 5) miles/hour × (120/x - 1/3) hours

Now you have an equation that can be used to find the value of x:
120 = (x + 5) × (120/x - 1/3)

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The probability that four of the five digits are the same is 0.036.

There are 10,000 (10*10*10*10) possible sequences. There are 4C3 ways, 4, of having exactly three digits be the same value. The differing digit can be any of the four positions. There are 10P2 ways, 90 (10*9), to choose the digits of the sequence since we have 10 choices for the digit to be repeated, then 9 more options or the differing digit. The product of the combination arrangements and permutation selection, 4*90, shows there are 360 sequences with three of the same digit. Thus the probability is 360/10,000 or 0.036 or 3.6%.

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Answer:

18.66 minutes or 18 minutes 39.6 seconds

Step-by-step explanation:

23 x .19 = 4.37

23 - 4.37 = 18.66 minutes

The best linear prediction of Y 2​ conditional on X=1 under the MSE criterion is Y = 1. 

The question is about calculating the best linear prediction of Y2 given the value of X. The conditional expectation of Y2 given X is

E(Y2|X) = E(X+W)

= E(X) + E(W)

= 0.

Therefore, the best linear prediction of Y2 given X is

Y1 = E(Y2|X)

= 0.

If we condition on X = 1, the best linear prediction is Y = 1, which has a mean squared error (MSE) of 1 since

Var(X+W) = Var(X) + Var(W) = 1 + 1 = 2.

Thus, the best linear prediction of Y2 conditional on X=1 under the MSE criterion is Y = 1.

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Using positive integers between 1 and 9 and each positive integer at most once,

2 x+ 9 < 3 x + 1

6x+ 4 > 5 x+ 8

To get two constraints so that x = 7 is the only integer that will satisfy both constraints at the same time. Upon analysing it can be seen that to the coefficients of x in eaxh equation shouch be two consecutive number. The coefficient on the lesser than side should be lower than the coeffiecient present on the greater than side.

To make the equation in such a way that only 7 satisfy it, the lesser than sides are added with numbers higher than 7 that is 8 and 9.

Therefore, Using positive integers between 1 and 9 and each positive integer at most once,

2 x+ 9 < 3 x + 1

6x+ 4 > 5 x+ 8

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Answer: 4135 over 1 or 8270 over 2

Step-by-step explanation: