Ethen bought a jacket that was on sale for 25% off.The jacket was originally priced at $69.99 . About how much change would he get from $100.00 bill if he also pays 6% tax

The sequence \(an=6ne^{(-5n)}\) is decreasing and bounded.

To determine whether the sequence \(an=6ne^{(-5n)}\)  is increasing, decreasing, or not monotonic and whether it is bounded or not, follow these steps:

1. Analyze the sequence's formula:
[tex]an=6ne^{(-5n)}\) can be rewritten as \(an=6n \frac{1}{e^{(5n)} }\)

2. Examine the factors in the formula:
The first factor, 6n, is increasing as n increases. The second factor, \(\frac{1}{e^{5n} }\), is decreasing as n increases since the exponent in the denominator is increasing, causing the overall value to decrease.

3. Determine the overall trend of the sequence:
The sequence an is a product of an increasing factor and a decreasing factor. To determine the overall trend, we can examine the limit of the sequence as n approaches infinity.

4. Calculate the limit:
As n approaches infinity, the decreasing factor \(\frac{1}{e^{5n} }\) dominates the sequence, causing the limit of the sequence to approach 0. This indicates that the sequence is decreasing.

5. Determine if the sequence is bounded:
Since the sequence is decreasing and approaches 0 as n approaches infinity, it has a lower bound of 0. Additionally, the sequence is positive for all values of n, so it is also upper-bounded. Therefore, the sequence is bounded.

The sequence \(an=6ne^{(-5n)}\) is decreasing and bounded.

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the correct answer is a. likely to be due to true differences between the groups.

If we say we have statistically significant results, it means that the results are likely to be due to true differences between the groups. Statistical significance is a term used in hypothesis testing to determine if the observed differences between groups are likely to be real and not due to chance.

When conducting a statistical analysis, researchers compare the data from different groups or samples to see if there is a significant difference between them. This involves calculating a p-value, which represents the probability of obtaining the observed results if there were no true differences between the groups.

If the p-value is less than a predetermined threshold, typically 0.05, then the results are considered statistically significant. This means that the likelihood of obtaining the observed results by chance alone is very low, and it is more likely that the differences between the groups are due to a real effect.

For example, let's say we conduct a study to compare the effectiveness of two different treatments for a medical condition. If we find that the p-value is less than 0.05, we can conclude that there is a statistically significant difference between the treatments, and the observed improvement in one group is likely to be due to the treatment itself rather than random chance.

In summary, when we say we have statistically significant results, it means that the observed differences between groups are likely to be due to true differences rather than chance. This provides evidence for the presence of a real effect or relationship between the variables being studied.

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Answer:

6x+9y

Step-by-step explanation:

first, 4y-y is 3y

3(2x)+3(3y)

6x+9y

Answer:

6x + 9y

Step-by-step explanation:

\(3(2x + 4y - y)\)

\(4y - y = 4y - 1y = (4 - 1)y = 3y\)

\(3(2x + 3y)\)

\( = 6x + 9y\)

Step-by-step explanation:

61 degree

180 _ 58 =122

122 is the sum of the two angles

If we divide 122 by 2 we'll get 61

Answer:

61°

Step-by-step explanation:

hope this helps! :D

The solution of the given system of linear equations is

x₁ = 3/2, x₂ = –2, x₃ = –1/2.

Given system of linear equations are 2x1-2x2+6x3 = 10x1+2x2-3x3 = 8-2x₁ x3 = -11

To solve the given system of equations, we have to compute A¹ and then use it to find x.To compute A¹, we have to follow these steps:

Step 1: Find the determinant of A:

Now we have matrix A:2 -2 6 1 2 -3 -2 0 1

So, we can find the determinant of A using the formula det(A) = (2×2) [(2×1)×(–3×1) + (6×2)×(1×–2) + (–2×2)×(2×–3)]  

= 4(–8 + (–24) + 24) = 4(–8) = –32

So, det(A) = –32

Step 2: Find the inverse of A:

We can find the inverse of matrix A using the formula A⁻¹ = adj(A) / det(A)

Here adj(A) is the adjoint matrix of A.

Now, we have to find the adjoint matrix of A.

Adjoint of A is given as:adj(A) = (cof(A))T

where cof(A) is the matrix of cofactors of the matrix A and (cof(A))T is the transpose of cof(A).

Now we can find cof(A) as:

cof(A) =   [[(-6) (-12) (-2)] [(6) (2) (2)] [(4) (8) (2)]]

Then transpose of cof(A), cof(A)T, is  

[[(-6) (6) (4)] [(-12) (2) (8)] [(-2) (2) (2)]]

So, adj(A) = cof(A)T

=  [[(-6) (6) (4)] [(-12) (2) (8)] [(-2) (2) (2)]

Now we can find A⁻¹ as:

A⁻¹ = adj(A) / det(A)

A⁻¹ = [[(-6) (6) (4)] [(-12) (2) (8)] [(-2) (2) (2)]] / (-32)

A⁻¹ =   [[(3/16) (-3/8) (-1/16)] [(3/4) (-1/4) (-1/4)] [(1/16) (-1/8) (1/16)]]

So, A¹ = A⁻¹ = [[(3/16) (-3/8) (-1/16)] [(3/4) (-1/4) (-1/4)] [(1/16) (-1/8) (1/16)]]

Then the given system of linear equations can be written as AX = B, where

X = [x₁ x₂ x₃]T and B = [10 8 –11]TAX = B  

⟹   X = A-¹B

Substituting the value of A-¹, we get X as   [[(3/16) (-3/8) (-1/16)] [(3/4) (-1/4) (-1/4)] [(1/16) (-1/8) (1/16)]] .

[10 8 -11]T= [3/2 -2 -1/2]T

So, the solution of the system is:

x₁ = 3/2x₂ = –2x₃ = –1/2

Therefore, the solution of the given system of linear equations is

x₁ = 3/2, x₂ = –2, x₃ = –1/2.

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Answer:

the correct answer is 65 degrees

Step-by-step explanation:

The angle is 65 degrees

Answer:

it is 75°

Step-by-step explanation:

so do you see the red line? it is in between 70° and 80° which means it's 75°

P2, P3, P1 is a safe sequence according to the banker's algorithm.

The banker's algorithm gets its name from the fact that it determines whether or not a person should be granted a loan amount in order to assist the bank system in securely simulating resource allocation. In this part, we'll go through the Banker's Algorithm in depth. The Banker's Algorithm is primarily used in the banking system to avoid stalemate. It assists you in determining whether or not a loan will be granted. This procedure is used to assess the allocation for securely replicating the maximum amount available for all resources.

Here,

According to the banker's algorithm, the sequence P2, P3, P1 is secure.

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Answer:

Hence 27 cubes can be obtained.

Step-by-step explanation:

Volume occupied by one cube of side 2cm = 2*2*2 = 8cm^3

Volume of cube of side 6cm = 216cm^3

Number of cubes of side 2cm which would fit in a cube of side 6cm = 216/8 = 27 cubes

The distance between the third traffic light from the second traffic light is 35 yards.

Three traffic lights on a street span 120 yards.

If the second traffic light is 85 yards away from the first.

Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.

This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.

Thus, the distance between the third traffic light from the second traffic light is 35 yards.

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The coordinates of the point that is 2/5 of the way from A to B is (-1,-2).

Given, points are A = (-4, -2) and B = (11, -2).

We want to find the coordinates of the point that is 2/5 of the way from A to B.

According to distance rule,

Now distance of A and B =

\( \sqrt{ {( - 4 - 11)}^{2} + {( - 2 + 2)}^{2} } = \sqrt{ {15}^{2} } = 15 \: unit\)

Now required co-ordinate is away 2/5 th distance

from A to B.

So, the distance

\( = 15 \times \frac{2}{5} = 3 \: unit\)

Let, required co-ordinate be (x,y)

Now, distance between (x,y) and (-4,-2) = 3

\( \sqrt{ {(x + 4)}^{2} + {(y + 2)}^{2} } = 3....(1)\)

We are putting first point (5,0) in equation (1) and get \( \sqrt{ {(5 + 2)}^{2} + {(0 + 2)}^{2} } \ne3\)

Again putting (-1,-2) in equation (1), and get \( \sqrt{ {( - 1 + 4)}^{2} + {( - 2 + 2)}^{2} } = 3\)

Therefore, it is clear that required co-ordinate is (-1,-2).

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Correct question is;

Factor out the GCF from the given polynomial. 10x³ + 16x² - 18x. (Type your answer in factored form.)​

Answer:

GCF = 5x² + 8x - 9

Step-by-step explanation:

The given polynomial is;

10x³ + 16x² - 18x

First thing is to inspect the coefficients and see the greatest number that all three can be divided by evenly without remainder.

The greatest number is 2.

Secondly let's inspect the variables to see what we can factor out.

They all contain x. Thus, x is a factor.

Thus, we will divide each term by 2x to obtain the GCF of the polynomial.

GCF = (10x³/2x) + (16x²/2x) - (18x/2x)

GCF = 5x² + 8x - 9

Answer:

72.13

Step-by-step explanation:

If you bought a stock last year for a price of $79, and it has gone down 8.7% since then, how much is the stock worth now, to the nearest cent?​

The conjugate is -7+6i. The correct option is third.

When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.

Given:

On a coordinate plane,

the y-axis is labeled imaginary and the x-axis is labeled real.

Point z is at (negative 7, negative 6).

Z(-7, -6)

So, the equation,

-7-6i

So, the conjugate of the equation is,

-7+6i

Therefore, -7+6i is the conjugate of the points.

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The Laplace transformation of sin(Wt+a) is given by the equation L{sin(Wt+a)}=e^(-as)W/(s^2+W^2).

To find the Laplace transformation of sin(Wt+a), we can use the formula for the Laplace transformation of sin(Wt), which is L{sin(Wt)}=W/(s^2+W^2). Then, we can use the shifting property of Laplace transformations to find the Laplace transformation of sin(Wt+a).

The shifting property of Laplace transformations states that if L{f(t)}=F(s), then L{f(t-a)}=e^(-as)F(s).

Therefore, the Laplace transformation of sin(Wt+a) is given by L{sin(Wt+a)}=e^(-as)L{sin(Wt)}=e^(-as)W/(s^2+W^2).

In conclusion, the Laplace transformation of sin(Wt+a) is L{sin(Wt+a)}=e^(-as)W/(s^2+W^2).

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Step-by-step explanation:

1. 400-144 = 256

unknown side = 16 cm

2.

√10 = 3.16

the biggest side is hypotenuse. assuming 6cm is the hypotenuse.

4+10= 14, which is different From hypotenuse. so it's not a triangle

In the given information, we can see that the populace of the United States has expanded consistently over time, with a few variances.

 Here is a chronological chart of the US population data:

Year   Population (millions)

1790  3.9

1800  5.3

1810   7.2

1820   9.6

1830   12.9

1840   17.1

1850   23.2

1860   31.4

1870   38.6

1880   50.2

1890   63.0

1900   76.2

1910   92.2

1920   106.0

1930   123.2

1940   132.2

1950   151.3

1960   179.3

1970   203.3

1980   226.5

1990   248.7

2000  281.4

2010  308.7

From the time chart, we can see that the populace of the United States has expanded consistently over time, with a few variances.

The slant is up, with the populace developing quicker in later a long time.

The time chart moreover permits us to see the rate of populace development over time. We can see that the population has expanded from less than 4 million in 1790 to more than 300 million in 2010.

We are able moreover to see the rate of populace development over diverse periods, such as fast populace development. within the middle of the twentieth century.

In general, the time chart of US populace information gives a visual representation of statistic patterns over time and permits us to effortlessly distinguish designs and changes within the populace.

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Step-by-step explanation:

is this what you were looking for?

The length of side LJ in triangle JKL is approximately 12.27 centimetre .

To determine the length of side LJ in triangle JKL, we can use the concept of similarity between triangles. When two triangles are similar, their corresponding sides are proportional.

Length of side XY in triangle XYZ: 8.7

Length of side XZ in triangle XYZ: 8.2

Length of side YZ in triangle XYZ: 7.8

Length of side JK in triangle JKL: 13.05

Let's set up the proportion using the corresponding sides:

XY / JK = XZ / LJ = YZ / KL

Substituting the given values:

8.7 / 13.05 = 8.2 / LJ = 7.8 / KL

Now, we can solve for LJ:

8.2 / LJ = 8.7 / 13.05

Cross-multiplying:

8.2 * 13.05 = 8.7 * LJ

106.71 = 8.7 * LJ

Dividing both sides by 8.7:

LJ = 106.71 / 8.7

LJ ≈ 12.27

Therefore, the length of side LJ in triangle JKL is approximately 12.27cemtimetre .

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Answer and Step by Step:

Alrighty people. Time to do some math!

So to find the first problem we basically need to combine all the functions and multiply them. Ugh I know I know it may seem a little complicated.

f ((-4x + 3)(5x))

(is this the final answer?)

Hmm maybe not so complicated. Oh well on the the next one. By the way let me know if the first problem is not finished.

We basically do the same thing here

(-4x+3)(f(5x))

Hope you have a good day and luck in finding good memes!

The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne in the simplest form, will be 4:3

The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 28:21.

To simplify this ratio, we can divide both numbers by their greatest common factor (GCF). The GCF of 28 and 21 is 7.

So, the simplified ratio is 28/7: 21/7 = 4:3

So the ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 4:3 in simplest form.

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In a scatter plot, if all data points were aligned along a 44º angle, the correlation would be 0. The correct answer is D.

In a scatter plot, the correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

When all data points are aligned along a 44º angle, it means that the points are distributed randomly and do not follow a clear linear pattern. There is no consistent increase or decrease in one variable as the other variable changes. Therefore, the correlation between the variables is 0, indicating no linear relationship or strength of association.

In other words, the angle of 44º suggests that the variables are unrelated and have no linear dependency on each other.

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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Answer: \(y-2=3(x-4)\\y=3x-12+2\\-3x+y=-10\\3x-y=10\)

Step-by-step explanation:

I showed the steps to find the equation. In case you need to know, I used point-slope form, which involves using the formula y-y1=m(x-x1), in which you use a point like (4,2) and the slope, which we know is 3x since it's parallel to the original line. Simplifying and bringing it to standard form such as Ax+By=C. Ax has to be positive, which is why -3x went to positive, and y and -10 switched signs.

Answer:

Step-by-step explanation:

See the attachment for derivation of the equation.

y = -(6/7)x + 20 6/7

The y-intercept of the equation is 20 6/7, which means there is 20 6/7 hours of setup time required.  When Anna arrives, she has not yet done any setup, so she would not have done any work yet.

In any event, the graph does not tell us how much time Anna really worked.  Did Anna spend 6 or 9 hours on the setup?  We don't know.  

Answer:

b or d

c

Step-by-step explanation:

i hope work

yon lang kaya ko

There are 120 people in a theatre. 72 are female and 48 are male. 12 females purchase an ice cream and 31 males purchase an ice cream.

Frequency trees display the real frequency of certain events. They can display the same data as a two-way table, but frequency trees are more readable since they illustrate the frequency hierarchy. Probability trees depict the likelihood of a series of occurrences.

Solution:

From the question, we can see the there are 120 people in the theatre.

Since, there are 72 females in the theatre we can find the total number of males by 120-72 = 48

Also, the male who purchased Ice Cream were 36 therefore, the males who did not purchased Ice Cream are 48-36 = 12

And, the females who purchased Ice Cream are 41. So, the female who did not purchased Ice Cream are 72 - 41 = 31

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complete question"

there are 120 people in a theatre 72 are female of these 41 purchase an ice cream 36 males purchase and ice cream use this information to compete the frequency tree

Answer:

65536

Step-by-step explanation:

=(642)(42)

=4096(42)

=(4096)(16)

i hope this helps if u need me to explain more i will be happy too <3