With a coupon, you get a pair of shoes that normally cost $80.00 for 30% off. How much is the discount?

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

When the equals sign (=) is used to denote equality, an algebraic theorem resembles a rule joining two statements. An algebraic equation is a factual assertion that shows the equivalence of multiple numerical variables. The values ob d + 6 and 12 are separated by an equal sign in the calculation data logger + 6 = 12. The number of syllables that correspond to each side of each letter can be expressed numerically. The message of a symbol is frequently its complete opposite.

Here,

Given :

After a few weeks, you create and calculate an equation

so determine how much money is in your bank account.

M equals -36, as you discover.

Thus,

It mean that you owe 36 amount of money to bank.

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

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The probability that more boys than girls are chosen is 0.4590

as we know,

Probability of any event P(E) = \(\frac{Number of favorable outcomes}{Total number of outcomes}\)

We have to chose five students to do presentations and also number of boys must be greater than the girls.

In classroom there are 12 boys and 13 girls.

So, Possible arrangements can be: B - Boys, G - Girls

(3B, 2G) , (4B, 1G) , (5B, 0G).

Note: nCr = n! / ( (r!) x (n-r)! ) also see the attached figure.

To choose 5 students out of 25 students to do the presentation 25 C 5

25 C 5 = 25! / (5! x 20!) = 53,130

(3B, 2G) :

To chose 3 Boys out of 12 Boys 12 C 3 = 12! / (3! x 9!) = 220

To chose 2 Girls out of 13 Girls 13 C 2 = 13! / (2! x 11!) = 78

(4B, 1G) :

To chose 4 Boys out of 12 Boys 12 C 4 = 12! / (4! x 8!) = 495

To chose 1 Girl out of 13 Girls 13 C 1 = 13! / (1! x 12!) = 13

(5B, 0G) :

To chose 5 Boys out of 12 Boys 12 C 5 = 12! / (5! x 7!) = 792

To chose 0 Girl out of 13 Girls 13 C 0 = 13! / (0! x 13!) = 1

here, 0! is equal to 1.

Now, the probability that more boys than girls are chosen =

\(\frac{(220 *78) + (495 * 13) + (792 * 1) }{53,130}\)

P(E) = 0.4590

Hence, the probability that more boys than girls are chosen is 0.4590.

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In linear equation, 22.5 kilometer  is Shaq from his original starting point.

What is linear equation?

Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2

  then he climbs down = 5 kilometer

Shaq from his original starting point = 9/2 * 5

                                                          = 45/2 = 22.5 kilometer

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a) The reverse-time process {Yr} of a discrete Markov chain {Xt} is a Markov chain. b) The transition matrix of {Yr} is P' = P^T, and {Yr} is reversible if the detailed balance equations are satisfied. c) For a continuous Markov chain, the reverse chain {Yr} has generator matrix Q' = -Q^T, and reversibility is determined by the detailed balance equations.

The reverse-time process {Yr} of a discrete Markov chain {Xt} is defined as {Yr} = {X−t}. Let's address each part of the question:
a) To show that {Yr} is a Markov chain, we need to demonstrate that it satisfies the Markov property, which states that the future states only depend on the current state and not on the past states. In other words, the conditional probability of transitioning to a future state depends only on the current state.

b) Assuming that {Xt} is a stationary Markov chain with distribution π (denoted as π(t) = π for all t), we can compute the transition matrix of the reverse chain {Yr} as follows:

Let P' be the transition matrix of {Yr}. Since {Yr} = {X−t}, the probability of transitioning from state i at time t to state j at time r in {Yr} is equal to the probability of transitioning from state j at time −t to state i at time −r in {Xt}. Therefore, the (i,j) entry of P' is equal to the (j,i) entry of P. In matrix notation, we can express this as P' = P^T, where T denotes matrix transpose.

To show that the Markov chain {Yr} is reversible, we need to prove that the transition matrix P' of {Yr} is the same as the transition matrix P of {Xt}. This is true if and only if the detailed balance equations are satisfied. The detailed balance equations state that for all states i and j, the product of the transition probability from state i to state j and the stationary distribution at state i is equal to the product of the transition probability from state j to state i and the stationary distribution at state j.

c) To repeat parts a) and b) for a continuous Markov chain with generator matrix Q, we can follow a similar approach. The reverse-time process {Yr} will be defined as {Yr} = {X−t}. We need to show that {Yr} is a Markov chain by demonstrating that it satisfies the Markov property.

Assuming that {Xt} is a stationary Markov chain with distribution π (π(t) = π for all t), we can compute the generator matrix Q' of the reverse chain {Yr} as follows:
Q' = -Q^T,
where Q^T denotes the matrix transpose of Q.
To show that the continuous Markov chain {Yr} is reversible, we need to prove that the generator matrix Q' of {Yr} is the same as the generator matrix Q of {Xt}. This is true if and only if the detailed balance equations are satisfied, which are the same as in the discrete case.

Overall, the reverse-time process of a Markov chain can be analyzed by considering the transition matrix (in the discrete case) or the generator matrix (in the continuous case). By showing that the reverse chain satisfies the Markov property and that the detailed balance equations are satisfied, we can conclude that it is indeed a Markov chain and that it is reversible.

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Answer:

-The volume of a sphere:

\(V \approx 5575.279\) \(in ^3\)

     or

\(V \approx 5575.28\) \(in^3\) (Rounded to the nearest hundredth if needed)

Step-by-step explanation:

-Use the formula for the volume of a sphere and use the radius \(11\) \(in\) for that formula:

\(V = \frac{4}{3} \pi r^3\)

\(V = \frac{4}{3} \pi 11^3\)

-Then, you solve the formula:

\(V = \frac{4}{3} \pi 11^3\)

\(V = \frac{4}{3} \times \pi \times 11^3\)

\(V = \frac{4}{3} \times \pi \times 1331\)

\(V = \frac{4}{3} \pi \times 1331\)

\(V = \frac{5324}{3} \pi \approx 5575.279\)

-Round up to the nearest hundredth (if needed):

\(V \approx 5575.28\)

Answer:

One glass of iced tea cost $2.72

Step-by-step explanation:

Let,

x be the amount of gift card.

y be the amount of one glass of iced tea.

According to given statement;

Julie and her friend bought tea and remaining balance was $14.85

x - 2y = $14.85     Eqn 1

All the six members bought tea and remaining balance was $3.97

x - 6y = $3.97      Eqn 2

Subtracting Eqn 2 from Eqn 1

\((x-2y)-(x-6y)=14.85-3.97\\x-2y-x+6y=10.88\\4y=10.88\)

Dividing both sides by 4

\(\frac{4y}{4}=\frac{10.88}{4}\\y=2.72\)

Hence,

One glass of iced tea cost $2.72

The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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Step-by-step explanation:

there are 91 2-digit numbers : 10 ..99

and there are 9 2-digit numbers with identical first and second digit : 11, 22, 33, 44, 55, 66, 77, 88, 99

99 has to be excluded, because there are no 2 2- digit numbers that I can subtract from each other and get 99.

so, e are dealing with 8 possibilities.

88 = 99-11

98-10

77 = 99-22

98-21

97-20

...

78-1

66 = 99-33

98-32

...

67-1

...

11 = 99-88

98-87

...

12-1

all the double- digit numbers are 11 apart. so, by picking 12 numbers, I have to have at least one that I can combine with one of the other 11 to get a double-digit number.

The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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The main answer is √1280x10y7 = 8√10xy³.

The expression √1280x10y7 can be simplified as 8√10xy³. To understand this, let's break it down:

Within the radical, we have √1280. To simplify this, we can factor out perfect squares. The prime factorization of 1280 is 2^7 * 5. Taking out the largest perfect square, which is 2^6, we are left with 2√10.

Next, we have x and y terms outside the radical. These terms can be simplified separately. In this case, we have x^1 and y^7, so we can rewrite them as x and y^6 * y.

Combining these factors, we get the simplified expression 8√10xy³. This means we have 8 times the square root of 10, multiplied by x, and multiplied by y cubed.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

-5 -= -3; 0= 2; 3=5

Step-by-step explanation:

Answer:

No, the student is not correct. The correct expression is 9(n+13).

Step-by-step explanation:

"9 times the sum of a number and 13" means you must multiply 9 by the sum, not just by the number. 9n + 13 would be "the sum of 9 times a number and 13." Slightly different wording.

Answer:

Sample Response: The student is not correct. He should use parentheses like this 9(n+13). Without the parentheses, it means nine times n plus 13, but should be the sum of n plus 13 multiplied by 9.

Answer:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the present balance ($1430.00)

r = the annual interest rate (2% or 0.02)

n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)

t = the number of years (8 years in this case)

Plugging in the values into the formula:

A = 1430(1 + 0.02/1)^(1*8)

Simplifying the equation:

A = 1430(1.02)^8

Using a calculator or performing the calculations manually:

A ≈ 1430(1.171661)

A ≈ 1674.02

the balance after 8 years will be approximately $1674.02.

Step-by-step explanation:

well,

23 < 12 + 0.04×x

11 < 0.04×x

11/0.04 < x

275 < x

x > 275 or x >= 276

so, for more than 275 monthly calls (that means 276 or higher) plan 1 is more economical.

at 275 calls is is plain even between both plans.

for fewer calls than 275 plan 2 is more economical.

Answer:

A rotation 180 clockwise about the origin

Step-by-step explanation:

if you want me to explain, I can in the comments

If in a ping pong tournament consisting of twelve teams, each team plays every other team once, there are 66 games in the ping pong tournament.

In a ping pong tournament consisting of 12 teams, each team will play against all the other teams exactly once. Therefore, each game will involve two teams, and each team will play a total of 11 games (since there are 11 other teams to play against).

To count the total number of games in the tournament, we can use the formula:

total number of games = (number of teams x number of games per team) / 2

Since there are 12 teams and each team plays 11 games, we have:

total number of games = (12 x 11) / 2

total number of games = 132 / 2

total number of games = 66

It is important to divide by 2 at the end of the formula since each game involves two teams, so the total number of games would be counted twice if we simply multiplied the number of teams by the number of games per team.

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Answer:

y = five-halves x, where y is the cost in cents for a book that is x days overdue

Step-by-step explanation:

See attachment

Answer:

y = 5\2 x, where y is the cost in cents for a book that is x days overdue

Step-by-step explanation:

Answer: This is a question which deals with sum total of all angles in a circle. The correct value of x should be 20°

Step-by-step explanation:

As we know the sum total of angle of a complete circle is 360°

which means sum of angles ∠PAR, ∠RAQ and ∠QAP is 360°

∠PAR + ∠RAQ + ∠QAP = 360°

substituting the values of all the angles we get

(x+60)° + (4x+60)° + (2x+100)° = 360°

=> (7x + 220)° = 360°

=> 7x = (360 - 220)°

=> 7x = 140°

=> x = 20°

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Horizontal data is not numerical

A graph is a visual representation of data or information that displays the relationship between different variables or data sets. It is a diagram that uses lines, bars, dots, or other symbols to represent data points or values and displays how they are related to each other. Graphs are commonly used in mathematics, science, economics, and many other fields to represent data in a more accessible and easily understandable way.

In the given graph

The comparison is done between Number of stores and Franchise.

Number of stores is placed in y axis

Franchise is placed in y axis

For comparison, no data is given of Franchise as it showing the non numerical.

hence, Horizontal data is not numerical.

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Answer:

The 54th term is -855

Step-by-step explanation:

Since the sequence is arithmetic, then we have to use the rule of the nth term

\(a_{n}=a+(n-1)d\)

a is the first term

d is the common difference

n is the position

The given sequence is -7, -23, -39

a=-7

d=-23-(-7)=-23+6=-16

We need to find the 54th term

n=54

Substitute them in the rule

\(a_{54}=-7+(54-10)(-16) \)

Solve it:

\(a_{54}=-7+(53)(-16)\\ a_{54}=-7-848\\ a_{54}=-855 \)

The 54th term is -855

Answer:

The characteristic of an arithmetic sequence is:

This difference between consecutive terms is called common difference and is denoted by (d)

(finding the common difference)

As stated above, the common difference is the difference between consecutive terms and, thus, will be found out by subtracting any two consecutive terms.

-7 and -23 are two consecutive terms in the sequence!

Subtracting (-7) from (-23):

\( \implies \mathsf{d = - 23 - ( - 7)}\)

\( \implies \mathsf{d = - 23 + 7}\)

\( \implies \mathsf{ \underline{d = -16}}\)

(Finding the nth term)

The formula used for finding the nth term of an arithmetic sequence is:

\( \boxed{ \mathsf{a _{n} = a + (n - 1)d }}\)

Here,

The question asks us to find the 54th term of the sequence.

Substituting 54 for n:

\( \implies \mathsf{a _{54} = a + (54 - 1)d }\)

substituting -7 for a and -16 for d

\( \implies \mathsf{a _{54} = - 7+ (54 - 1)( - 16)}\)

\( \implies \mathsf{a _{54} = - 7+ (53)( - 16)}\)

\( \implies \mathsf{a _{54} = - 7 - 848}\)

\( \implies \mathsf{ \underline{a _{54} = - 855}}\)

The 54th term of the sequence is -855.

_______________

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The XYZ corporation will receive $1500000 for all the shares sold.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given: Cost of 1 share = $15

To find: Money received on selling 100000 shares.

Finding:

By unitary method,

Money received on selling 1 share = $15

Money received on selling 100000 shares = 15(100000) = $1500000

Hence, The XYZ corporation will receive $1500000 for all the shares sold.

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

C

I think it's C because

Step-by-step explanation:

2x4=8

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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