A boat travels a straight route from the marina to the beach. The marina is located at point (0,0) on a coordinate plane, where each unit represents 1 mile. The beach is 3. 5 miles east and 4 miles south from the marina. Use the positive y-axis as north. What is the distance the boat travels to get to the beach? Round your answer to the nearest tenth. *

This Turing Machine will accept the language {an bn}, where n is a non-negative integer.

(i) To build a Turing Machine that accepts the language {an bn+1}, we can follow these steps:

1. Start in the initial state, q0.

2. Read the input symbol on the tape.

3. If the symbol is 'a', replace it with 'X' and move to the right.

4. If the symbol is 'b', replace it with 'Y' and move to the right.

5. If the symbol is 'Y', move to the right until you find a blank symbol.

6. If you find a blank symbol, replace it with 'Y' and move to the left until you find 'X'.

7. If you find 'X', replace it with 'Y' and move to the right.

8. If you find 'Y', move to the right until you find a blank symbol.

9. If you find a blank symbol, replace it with 'X' and move to the left until you find 'Y'.

10. If you find 'Y', replace it with a blank symbol and move to the left.

11. Repeat steps 2-10 until all symbols on the tape have been processed.

12. If you reach the end of the tape and the head is on a blank symbol, accept the input.

13. If you reach the end of the tape and the head is not on a blank symbol, reject the input.

This Turing Machine will accept the language {an bn+1}, where n is a non-negative integer.

(ii) To build a Turing Machine that accepts the language {an bn}, we can follow these steps:

1. Start in the initial state, q0.

2. Read the input symbol on the tape.

3. If the symbol is 'a', replace it with 'X' and move to the right.

4. If the symbol is 'b', replace it with 'Y' and move to the right.

5. If the symbol is 'Y', move to the right until you find a blank symbol.

6. If you find a blank symbol, replace it with 'Y' and move to the left until you find 'X'.

7. If you find 'X', replace it with a blank symbol and move to the left.

8. If you find 'Y', move to the left until you find a blank symbol.

9. If you find a blank symbol, replace it with 'X' and move to the right until you find 'Y'.

10. If you find 'Y', replace it with 'X' and move to the left.

11. Repeat steps 2-10 until all symbols on the tape have been processed.

12. If you reach the end of the tape and the head is on a blank symbol, accept the input.

13. If you reach the end of the tape and the head is not on a blank symbol, reject the input.

This Turing Machine will accept the language {an bn}, where n is a non-negative integer.

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(i) To build a TM that accepts the language {anbn+1}, follow the steps below:

Step 1: Input string is obtained on the input tape

Step 2: If the string has an odd length or its second character is a, then it is rejected.

Step 3: The string is divided into two equal halves and compared to each other. If they match, then it is accepted; otherwise, it is rejected.

(ii) To build a TM that accepts the language {anbn}, follow the steps below:

Step 1: Input string is obtained on the input tape.

Step 2: The string is scanned from the left side. For each a seen, it is replaced by A. If a b is seen, then A is replaced by B. If a b or b a is seen, it is rejected. If the string is all a's or all b's, then it is accepted.

Step 3: Repeat step 2 until the whole input string has been processed. If the string is all A's or all B's after processing, then it is accepted; otherwise, it is rejected.

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Answer: \(y=\frac{2}{5}, \frac{6}{5}\)

Step-by-step explanation:

When answering a problem like this, you first isolate the absolute value.  TO do this, first subtract 8 from both sides, to get –2|4–5y|=-4.  Then divide both sides of the equation to get |4–5y|=2.  The next thing you do is split the equation into 4-5y=2 and 4-5y=-2, because the contents of the absolute value could be negative or positive, and simplifying both into y = 2/5, and y = 6/5y.

Hope it helps <3

Answer:

D has the coordinate 17

Step-by-step explanation:

Given

DE  has as the mid point H at 5

D > E

DE = 24

Find the coordinate of D

5 + (24/2) = 5+12 = 17

The correct description is that moon is waxing.

The theory used in this question is the lunar cycle, which is the process by which the moon changes its shape and illumination over the course of a month.

The waxing phase of the lunar cycle is when the moon is gradually getting bigger and more illuminated.

The waning phase is when the moon is gradually getting smaller and less illuminated.

The moon is waxing:

This is an accurate description because when the moon changes from a new moon to a full moon, it is said to be waxing.

This means that the moon is gradually getting bigger, and its illuminated side is increasing.

This process is called the waxing phase of the moon's cycle.

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Answer:

A

Step-by-step explanation:

- 3/4 = - 0.75

- 4.5 - 0.75 = - 5.25 = - 5 1/4

The calculated value of the probability P(yellow) is 0.5 i.e. one half

From the question, we have the following parameters that can be used in our computation:

Sections = 2

Color = yellow, and green

Using the above as a guide, we have the following:

Yellow = 1

When the yellow section is selected, we have

P(yellow) = yellow/section

The required probability is

P(yellow) = 1/2

Evaluate

P(yellow) = 0.5

Hence, the value is 0.5

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Answer:

The answer is the last one.

Step-by-step explanation:

f(x) = 3/2 x  - 1  If you plug in -2 for x

f(-2) = 3/2 (-2) -1

f(-2) = -3 - 1

f(-2) = -4

This function works for every input given.

Helping in the name of Jesus.

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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To clear the old codes in the garage door and reprogram it access the doors motor and reprogram the remote afterwards.

Most individuals do not consider the garage door opener remote control to be a particularly valuable feature unless something goes wrong. Using the remote, the garage door can be opened from the outside.

You can unlock it by entering a PIN on the keypad outside the garage. The PIN can be activated or deactivated when you enter a personal identification number.

The door code may occasionally need to be changed. This has a number of advantages, such as improving security or getting access to your garage when you forget the code.

You could be considering how to modify the garage door code. You might try to do it yourself or ask a professional for help.

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Step-by-step explanation:

n³/m²

remember, x^-n = 1/(x^n)

Answer:  between $42 and $54 including both endpoints.

In symbolic form we can say \(42 \le p \le 54\) where p is the final price after the discount is applied.

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

Explanation:

10% off means you save 10% but pay the remaining 90%

Then convert 90% to decimal form to get 0.90

If the original price is $60, then the final price is 0.90*60 = 54 dollars.

In other words,

10% of 60 = 0.10*60 = 6 dollars saved

60-6 = 54 is the final price

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

If the discount is 30% then you pay the remaining 70%

0.70*60 = 42

Or you can think of it like this

30% of 60 = 0.30*60 = 18 dollars saved

60-18 = 42 dollars is the final price

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

Let's summarize with this chart:

\(\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}\)

Therefore, the final price after the discount is between $42 and $54 including both endpoints.

Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.

Answer:

m∠JKI: 43°

Explanation:

As its an isosceles triangle, m∠JKI = m∠JIK

m∠JKI:

\(\hookrightarrow \sf \dfrac{( 180 - 94 )}{2}\)

\(\hookrightarrow \sf \dfrac{ 86 }{2}\)

\(\hookrightarrow \sf 43\)

Answer:

43.

Step-by-step explanation:

The function f(x) that has a local minimum at (0,0) and a local maximum at (1,3) is f(x) = 2x³ - 3x².

From the information, we can set up a system of equations as follows:

f'(x) = 3ax² + 2bx + c = 0 (at x=0)

f'(x) = 3ax² + 2bx + c = 0 (at x=1)

Plugging in x=0, we get:

f'(0) = c = 0

Plugging in x=1, we get:

f'(1) = 3a + 2b + c = 0

3a + 2b = -c = 0

3a + 2b = 0 (since c=0)

Solving the system of equations, we get:

a = 2

b = -3

c = 0

d = 0

The function is f(x) = 2x³ - 3x²

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Answer:

2 5/12

Step-by-step explanation:

You put it so that the denominators are the same so in this case I used 12 as the denominator and used the rule for each. Next I subtracted 3 9/12 minus 1 4/12 and got 2 5/12

The probability that at least one bit is received incorrectly is 2.96%

Incorrect measure = 0.001

There are just two possible outcomes for each bit. Either it's understood properly or it's not. Since each bit is received independently of the others, this problem can be solved using the binomial probability distribution. Using the binomial probability distribution, where X can only have two outcomes, the likelihood of precisely x successes on n repeated trials

Therefore,

P ( X = x) = Cn,x.px ( 1 - p)^n-x

Here, P = 0.001 and n = 30 ( since the message is 30-bit)

Therefore, calculating the incorrect bit -

P ( X≥1) = 1 - P ( X = 0)

P (X =x) = Cn,x.px ( 1 - p)^n-x

P ( X = 0)  = C30 (0.001). (0.999)^30

= 0.9704

Thus,

P ( X≥1) = 1 - P ( X = 0)

= 1 - 0.9704

= 0.0296 or 2.96%

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Answer:

=3

Step-by-step explanation:

5b/c

=5*6/10

=30/10

=3

Answer:

If b = 6 and c = 10, the value of an expression is 3.

Step-by-step explanation:

Given the expression

\(\frac{5b}{c}\)

We have to evaluate the expression if b = 6 and c = 10.

Important Tip:

In order to evaluate the expression  \(\frac{5b}{c}\), all we need to do is to substitute the value of b and c in the expression.

As the expression is

\(\frac{5b}{c}\)

substitute b = 6 and c = 10 in the expression

\(\frac{5b}{c}=\frac{5\left(6\right)}{10}\)

     \(=\frac{30}{10}\)

      \(=3\)       ∵ \(\frac{30}{10}=3\)

Therefore, if b = 6 and c = 10, the value of an expression is 3.

Answer:

$159.1

Step-by-step explanation:

Given that:

Original price of surfboard = $199

Reduction of price done = 10%

Then a coupon is used by a customer for $20 off.

To find:

How many dollars were paid by the customer?

Solution:

First of all, let us find the price after the reduction of 10% from the original price.

10% of $199 = \(\frac{10}{100}\times 199 = \$19.9\)

This price is reduced from the original price.

Price after reduction = $199 - $19.9 = $179.1

Now, again there is coupon of $20.

Therefore, final price that the customer had to pay = $179.1 - $20 = $159.1

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

Let Length= x, Width= y

A.t.c.

3x-2=y ...(1)

Area = length × width

= xy = 40

from (1)

\(x(3x - 2) = 40 \\ 3 {x}^{2} - 2x = 40 \\ 3 {x}^{2} - 2x - 40 = 0 \\ 3 {x}^{2} - 12x + 10x - 40 = 0 \\ 3x(x - 4) + 10(x - 4) = 0 \\ (3x + 10)(x - 4) = 0 \\ x = - \frac{10}{3} \: or \: 4\)

neglecting -10/3

length = 4

width = 3(4)-2=12-2

= 10

The family buys around 19 cases of sparkling water in 30 days.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let the total number of sparkling cans of water used in a day be = x

Now, As mentioned, the family uses more than 15 cans each day so inequality becomes,

x > 15

As they buy cases of water with 24 cans in each case. So less than 1 case is used in a day.

Number of cans used in a day is more than 15, so approx number of cans used in 30 days will be is,

30 × 15 = 450

As each case contains 24 cans, so the number of cases that will contain 450 cans will be,

450 / 24

= 18.75  cases.

Hence, Rounding this off to nearest whole number, we get 19 cases.

Thus, The family buys around 19 cases of sparkling water in 30 days.

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Given information:Position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds.

To determine the position at the following times. a. t = 3.30 s, b. t = 3.30 s + Δt xf and c. Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 3.30 s. a. To find the position when t = 3.30 s, substitute t = 3.30 s in x = 3t².x = 3t² = 3(3.30)² = 32.67 metersTherefore, the position at t = 3.30 s is 32.67 meters.

b. To find the position when t = 3.30 s + Δt, substitute t = 3.30 s + Δt in x = 3t².x = 3t² = 3(3.30 s + Δt)² = 3(10.89 + 6.6Δt + Δt²) = 32.67 + 19.8Δt + 3Δt²Therefore, the position when t = 3.30 s + Δt is 32.67 + 19.8Δt + 3Δt².c. Velocity is given by Δx/Δt.Δx/Δt = [x(t + Δt) - x(t)]/ΔtBy substituting the given values, we have;Δx/Δt = [x(3.30 + Δt) - x(3.30)]/Δt= [3(3.30 + Δt)² - 3(3.30)²]/Δt= 19.8 + 6ΔtTaking the limit of Δx/Δt as Δt → 0, we have;Δx/Δt = 19.8 + 6(0)Δt = 19.8Therefore, the velocity at t = 3.30 s is 19.8 m/s.

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Answer:

- 3p + 10

Step-by-step explanation:

- p + 2 - 2p + 8 ← collect like terms

= (- p - 2p) + (2 + 8)

= - 3p + 10

Answer:

12xy+14x

Step-by-step explanation:

12xy+14x

Hope this helps :3

Answer:

12xy + 14x

Step-by-step explanation:

I believer this is correct

Answer:

y = 1x+b

Step-by-step explanation:

\( \large \mathfrak{Solution : }\)

Degree of a polynomial is the highest exponential power in the expression.

i.e 9 here

so, degree of the given expression is 9

Answer:

1.) 27a^11 + 18a^9 -72a^7

2.) 6p^4q^3 - 10p^3q + 4p^2q3

Step-by-step explanation:

1.) Distribute and do the math

-9a^5 x (-3a^6) - 9a^5 X (-2a^4) - 9a^5 x 8a^2

27a^11 + 18a^9 -72a^7

2.)  Distribute and do the math

2pq^2q x 3p^2q^2 - sp^2q x 5p + 2p^2q x 2q^2

6p^4q^3 - 10p^3q + 4p^2q3

Answer:

A. 5, 7, 9

Step-by-step explanation:

in a regular triangle the sum of any 2 sides must always be greater than the third side.

A.

5+7 = 12 > 9

5+9 = 14 > 7

9+7 = 16 > 5

yes, this can be a triangle.

B.

1+8 = 9 = 9

that violates the condition. both sides together are equally long as the third side, so the triangle would be only a flat line with the top vertex being squeezed flat onto the baseline.

no triangle.

C.

5+5 = 10 < 12

that violates the condition. the sides cannot even connect all around.

no triangle.

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = \(\frac{2-(-4)}{2-(-1)}\) = \(\frac{2+4}{2+1}\) = \(\frac{6}{3}\) = 2

I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05