Aaden bought a pair of shorts online for $66. He used a coupon code to get a 10% discount. The website also applied a 5% processing fee to the price after the discount. How much was the discount, in dollars and cents?

The rate of the plane in still air is 550 mph, and the rate of the wind is 50 mph.

Let's denote the rate of the plane in still air as "p" and the rate of the wind as "w".

When the plane flies into the wind, its effective speed is reduced by the speed of the wind.

So, the speed of the plane relative to the ground is:

p - w

Similarly, when the plane flies with the wind, its effective speed is increased by the speed of the wind, so its speed relative to the ground is:

p + w

We know that the distance traveled by the plane is 3000 miles in both cases, so we can set up two equations based on the formula:

distance = rate x time

When the plane flies into the wind:

3000 = (p - w) x 6

And when the plane flies with the wind:

3000 = (p + w) x 5

Now we have two equations with two unknowns, which we can solve for "p" and "w".

Let's start by simplifying both equations:

Equation 1: 3000 = 6p - 6w

Equation 2: 3000 = 5p + 5w

We can then solve for one of the variables in terms of the other. For example, we can solve for "p" in terms of "w" by rearranging Equation 2:

5p = 3000 - 5w

p = (3000 - 5w) / 5

We can then substitute this expression for "p" into Equation 1 and solve for "w":

3000 = 6[(3000 - 5w) / 5] - 6w

Multiplying both sides by 5:

15000 = 6(3000 - 5w) - 30w

Distributing the 6:

15000 = 18000 - 30w - 30w

Combining like terms:

15000 = 18000 - 60w

Subtracting 18000 from both sides:

-3000 = -60w

Dividing both sides by -60:

w = 50

Now that we know the rate of the wind is 50 mph, we can substitute this value into either Equation 1 or Equation 2 to solve for "p".

Let's use Equation 2:

3000 = 5p + 5(50)

3000 = 5p + 250

2750 = 5p

p = 550.

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The system of equations are solved and the value of x and y are 6/5 and -14/5 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = x - 4   be equation (1)

y = 6x - 10   be equation (2)

On simplifying , we get

x - 4 = 6x - 10

Subtracting x on both sides , we get

5x - 10 = -4

Adding 10 on both sides , we get

5x = 10 - 4

5x = 6

Divide by 5 on both sides , we get

x = 6/5

So , the value of y = ( 6/5 ) - 4

y = -14/5

Hence , the value of x and y are 6/5 and -14/5 respectively and the equations is solved

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Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

Step-by-step explanation:

From the given information:

Let assume that the invested amount in the investment paying 8% interest is a

Now, since the total amount invested = $3000.

Then, the amount invested in the investment that will be paying 10% interest can be represented as:

= $(3000-a)

Income earned on $a that is being invested in 8% interest = $a × 8/100 = $0.08a

Income earned from $(3000-a)  in the 10% investment is:

= $(3000-a)× 10/100

= $(300 - 0.1a)

Since total income of the two investment = $290;

Then;

0.08a + (300 - 0.1a) = 290

0.08a + 300 - 0.1a = 20-

300 - 0.02a = 290

-0.02a = -10

a = -10/-0.02

x = 500

Thus;

the amount invested in an investment paying 8% interest = $500

the amount invested in an investment paying 10% interest = $(3000 - 500) = $2500

the answer is A explanation is in the picture.

Answer:

False

Step-by-step explanation:

The answer is False

The given statement is false, as the letters are used as keys in the dictionary.

The dictionary used in counting letters examples to keep track of letter frequencies uses the letters as the key and the count as the value. This means that for each letter encountered in a string, the value corresponding to the key (letter) in the dictionary is incremented by 1.

For example, if the string is "hello", the dictionary would initially be empty, and for each letter encountered in the string, the value for the corresponding key in the dictionary would be incremented by 1, resulting in a dictionary like {"h": 1, "e": 1, "l": 2, "o": 1}.

Therefore, the correct answer is false, as the letters are used as keys in the dictionary.

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Answer:

Radius of that cylinder. 

Step-by-step explanation:

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . Simplify.

Answer:

Step-by-step explanation:

Sample Response: The area of the base can be calculated by applying the formula for the volume of a cylinder. First, substitute the known measures for their corresponding variables. Then solve for B by applying the division property of equality.

Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

Please find attached photograph for your answer.

Answer:

The answer is 115.50 sq. mm.

Step-by-step explanation:

Answer:

x = 1/5

Step-by-step explanation:

yeah-ya........ right?

Answer:

59.2592592593 liters

Step-by-step explanation:

First do 320/216 and then multiply by 40

The next letters in the pattern are 6 and -7.The given pattern alternates between positive and negative numbers. By observing the pattern, we can determine the next numbers in the sequence.

The first number, 2, is positive. The second number is obtained by taking the negative of the previous number and subtracting 1. Therefore, -2 - 1 = -3.The third number is positive and is obtained by taking the absolute value of the previous number and adding 1. Therefore, |-3| + 1 = 4.

The fourth number is negative and is obtained by taking the negative of the previous number and subtracting 1. Therefore, -4 - 1 = -5.

Following this pattern, the next number will be positive and obtained by taking the absolute value of the previous number and adding 1. Therefore, |-5| + 1 = 6.

The next number after 6 will be negative and obtained by taking the negative of the previous number and subtracting 1. Therefore, -6 - 1 = -7.

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Answer:

A is the answer

\(x = \frac{1}{48} \)

Answer:

840

Step-by-step explanation:

To find the LCM of a set of numbers, we can use different methods such as prime factorization method or listing multiples method 1.

In this case, we can use the listing multiples method to find the LCM of the first eight positive integers 1. We list out the multiples of each number until we find a common multiple that is divisible by all of them.

Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, ...

Multiples of 2: 2, 4, 6, 8, ...

Multiples of 3: 3, 6, ...

Multiples of 4: 4, 8, ...

Multiples of 5: 5, ...

Multiples of 6: 6, ...

Multiples of 7: 7, ...

Multiples of 8: 8, ...

We can see that the smallest common multiple that is divisible by all of them is 840.

I hope this helps!

Answer:

D

Step-by-step explanation:

Answer:

=48x2^+3097x+12

Step-by-step explanation:

3(4x+9)(4)x+2712x+277x+12

Distribute:

=48x2+108x+2712x+277x+12

Combine Like Terms:

=48x2+108x+2712x+277x+12

=(48x2)+(108x+2712x+277x)+(12)

=48x2+3097x+12

Answer:

Hello~

12x+3×9

12x + 27

Ary~

The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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Answer:

see explanation

Step-by-step explanation:

given (x - 5) is a factor of f(x) then x = 5 is a zero

dividing f(x) by (x - 5) using synthetic division

5 | 1   - 8   17   - 10

    ↓    5   - 15    10

    ----------------------

     1   - 3    2       0 ← remainder = 0 indicates (x - 5) is a factor

quotient = x² - 3x + 2 = (x - 1)(x - 2)

then

f(x) = (x - 5)(x - 1)(x - 2) ← in factored form

to find the x- intercepts let f(x) = 0 , that is

(x - 5)(x - 1)(x - 2) = 0

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

the x- intercepts are x = 1, x = 2, x = 5

to find the y- intercept let x = 0 , then

f(0) = (0 - 5)(0 - 1)(0 - 2) = (- 5)(- 1)(- 2) = 5 × - 2 = - 10

the y- intercept is y = - 10

Answer:

the x- intercepts are x = 1, x = 2, x = 5

AND

the y- intercept is y = - 10

Step-by-step explanation:

given (x - 5) is a factor of f(x) then x = 5 is a zero

dividing f(x) by (x - 5) using synthetic division

5 | 1   - 8   17   - 10

   ↓    5   - 15    10

   ----------------------

    1   - 3    2       0 ← remainder = 0 indicates (x - 5) is a factor

quotient = x² - 3x + 2 = (x - 1)(x - 2)

then . .

f(x) = (x - 5)(x - 1)(x - 2) ← in factored form

to find the x- intercepts let f(x) = 0 , th

(x - 5)(x - 1)(x - 2) = 0

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

the x- intercepts are x = 1, x = 2, x = 5

to find the y- intercept let x = 0 , then

f(0) = (0 - 5)(0 - 1)(0 - 2) = (- 5)(- 1)(- 2) = 5 × - 2 = - 10

the y- intercept is y = - 10

Answer: −

7p^4 + 2p^3 + 10p^2

Step-by-step explanation:

Answer:

6/27

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

5/27+1/27=6/27

reduced to lowest denominator

(divide top & bottom by 3)

2/9

Answer:

x = 4.5

Step-by-step explanation:

The attached figure shows the diagram of this problem. Here, line m is intersected by line l and m. We need to find the value of x.

In this case, 6x+42 =18x-12 as they form alternate interior angles

So,

6x+42 =18x-12

taking like terms togther

6x-18x=-42-12

-12x = -54

x = 4.5

So, the value of x is 4.5

The Pearson correlation coefficient for these data is 0.1. This suggests a weak, positive linear relationship between X and Y variables.

The Pearson correlation coefficient, also denoted as r, is a measure of the strength and direction of the linear relationship between two variables. In this case, we have a set of 5 pairs of X and Y values, with SSx = 16, SSy = 4 and SP = 2.
The sample standard deviations (Sx and Sy) for the X and Y variables. The sample covariance is defined as:
Sxy = (SP/n) - (SX/n)(SY/n)
Sxy = (2/5) - (sqrt(16)/5)(sqrt(4)/5) = 0.2

Next, we can calculate the sample standard deviations for X and Y using the formulas:
Sx = sqrt(SSx/(n-1)) = sqrt(16/4) = 2
Sy = sqrt(SSy/(n-1)) = sqrt(4/4) = 1
Finally, we can calculate the Pearson correlation coefficient using the formula:
r = Sxy/(SxSy) = 0.2/(2*1) = 0.1

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Answer:

AB=13

Step-by-step explanation:

1/2AC^2+1/2BD^2=AB^2

AB=13

The dimensions and area of Sergio's garden are 5 yards and 25 square yards respectively

The given parameters are

Perimeter = 20 yards

For the rectangle to have the greatest are, the rectangle must be a square

So, the dimension is

Length = Perimeter/4

This gives

Length = 20/4

Evaluate

Length = 5

The area of Sergio's garden is

Area = 5 * 5

Evaluate

Area= 25

Hence, the dimensions and area of Sergio's garden are 5 yards and 25 square yards respectively

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The output on the tape after following these transitions starting with a blank tape will be a sequence of alternating 1s and 0s, ending with a 0, depending on the value of n.

Starting with a blank tape and following the given instructions of the Turing machine TM, let's analyze the transitions step by step:

1. Initial configuration: q₀0

2. Transition from q₀ with input 0: (q₁, 1, R)

  - The machine moves to state q₁ and writes a 1 on the tape.

3. Transition from q₁ with input 1: (q₁, 1, L)

  - The machine remains in state q₁, reads the 1 from the tape, and moves one position to the left.

4. Transition from q₁ with input 0: (q₂, 0, R)

  - The machine moves to state q₂ and writes a 0 on the tape.

5. Transition from q₂ with input 0: (q₂, 1, L)

  - The machine remains in state q₂, reads the 0 from the tape, and moves one position to the left.

6. Transition from q₂ with input 1: (q₃, 1, L)

  - The machine moves to state q₃, writes a 1 on the tape, and moves one position to the left.

7. Transition from q₃ with input 1: (q₃, 1, L)

  - The machine remains in state q₃, reads the 1 from the tape, and moves one position to the left.

8. Transition from q₃ with input 0: (q₄, 0, R)

  - The machine moves to state q₄ and writes a 0 on the tape.

9. Transition from q₄ with input 0: (q₄, 1, L)

  - The machine remains in state q₄, reads the 0 from the tape, and moves one position to the left.

10. Transition from q₄ with input 1: (q₅, 1, L)

   - The machine moves to state q₅, writes a 1 on the tape, and moves one position to the left.

11. Transition from q₅ with input 1: (q₅, 1, L)

   - The machine remains in state q₅, reads the 1 from the tape, and moves one position to the left.

12. Transition from q₅ with input 0: (q₆, 0, R)

   - The machine moves to state q₆ and writes a 0 on the tape.

13. Transition from q₆ with input 0: (q₆, 1, L)

   - The machine remains in state q₆, reads the 0 from the tape, and moves one position to the left.

14. Transition from q₆ with input 1: (q₇, 1, L)

   - The machine moves to state q₇, writes a 1 on the tape, and moves one position to the left.

15. Transition from q₇ with input 0: (q₇, 1, L)

   - The machine remains in state q₇, reads the 0 from the tape, and moves one position to the left.

16. Transition from q₇ with input 1: (q₈, 0, R)

   - The machine moves to state q₈ and writes a 0 on the tape.

17. Transition from q₈ with input 0: (q₈, 1, L)

   - The machine remains in state q₈, reads the 0 from the tape, and moves one position to the left.

18.

Transition from q₈ with input 1: (q₉, 1, L)

   - The machine moves to state q₉, writes a 1 on the tape, and moves one position to the left.

19. Transition from q₉ with input 0: (q₉, 1, L)

   - The machine remains in state q₉, reads the 0 from the tape, and moves one position to the left.

20. Transition from q₉ with input 1: (q₁₀, 0, R)

   - The machine moves to state q₁₀ and writes a 0 on the tape.

This pattern of transitions continues until reaching state q₁₁, q₁₂, ..., qₙ, and finally qₙ₊₂, where the machine writes 0 on the tape and halts.

Therefore, the output on the tape after following these transitions starting with a blank tape will be a sequence of alternating 1s and 0s, ending with a 0, depending on the value of n.

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The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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Answer: m=0.5

Step-by-step explanation:

Let's find the slope between your two points.

(7,9.5);(2,7)

(x1,y1)=(7,9.5)

(x2,y2)=(2,7)

Use the slope formula:

m=Let's find the slope between your two points.

(7,9.5);(2,7)

(x1,y1)=(7,9.5)

(x2,y2)=(2,7)

Use the slope formula:

y2−y1/y2−y1

7−9.5/2-7

2.5/-5  m=0.5

Answer:

\(\displaystyle m=0.5\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (7, 9.5)

Point (2, 7)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m