Devising recursive definitions for sets of strings.
Let A = {a, b}.
(c) Let S be the set of all strings from A* in which there is no b before an a. For example, the strings λ, aa, bbb, and aabbbb all belong to S, but aabab ∉ S. Give a recursive definition for the set S. (Hint: a recursive rule can concatenate characters at the beginning or the end of a string.)

Answer:

5^9 / 5^3 = 5^6

the answer is 6

Step-by-step explanation:

Let

y ----> total charge in a month

x ----> number of minutes

so

Plan A

y=0.21x+11

Plan B

y=0.10x+20

Equate both equations

0.21x+11=0.10x+20

solve for x

0.21x-0.10x=20-11

0.11x=9

x=9/0.11

x=81.82 minutes

Convert to hours and minutes

81.82 minutes=60+21.82=1 hour 22 min

therefore

Answer: A

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

DJ = 48 units

Step-by-step explanation:

The centroid of a triangle is the point of intersection of its median.

The centroid divides each of the medians in the ratio 2 : 1 .

DJ = \(\frac{2}{3}\) DH

DJ = \(\frac{2}{3}\) × 72 = 48 units

Answer:

Step-by-step explanation:

You want to know how to determine the y-intercepts of a rational function, and their possible number.

A rational function f(x) is the ratio of two polynomial functions p(x) and q(x):

  f(x) = p(x)/q(x)

As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...

  f(0) = p(0)/q(0)

The values of p(0) and q(0) are simply the constant terms in those respective functions.

The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.

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Answer:

brain

Step-by-step explanation:

brain to the fullest

Answer:

Translation down 2 units

Step-by-step explanation:

If a number is added or subtracted like that at the end of a function, it will either lift or put down a function however many units the number says. In this case, the number says 2, so the transformation would be a "Translation down 2 units".

The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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To simplify (9x^3+2x^2-5x+4)-(5x^3-7x+4), we can start by combining like terms.

First, we need to distribute the negative sign to the second set of parentheses:

(9x^3+2x^2-5x+4) - 1(5x^3-7x-4)

= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4 (distributing the negative sign)

= (9x^3 - 5x^3) + 2x^2 - 5x + (4 - 4 + 7x) (grouping like terms)

= 4x^3 + 2x^2 + 2x (combining like terms)

Therefore, the simplified expression is 4x^3 + 2x^2 + 2x.

We cannot factor this expression further as there are no common factors between the terms.

1) Remove parentheses.

\(9x^{3}+ 2x^{2} -5x+4-5x^{3} +7x-4\)

2) Collect like terms.

\((9x^{3}-5x^{3})+2x^{2} +(-5x+7x)+(4-4)\)

3) Simplify.

\(4x^{3}+2x^{2}+2x\)

Answer:

19.71

Step-by-step explanation:

You would add the two values (-5.29) and 25 together

If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch

The area of a triangle is 96 sq. inches

Let base be b

Its altitude is 2 inches greater than five times its base.

a=5b+2

ab/2=A

(5b+2)b/2=96

(5b+2)b=192

5b²+2b=192

5b²2+2b-192=0

On solving the quadrartic equation,

we get

b=6

a=32

Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs

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Answer:

C) 1 ¼

Step-by-step explanation:

.25 = ⁴/⁴ ÷ .25 = ¼

ñññññ

Answer:

The choice C)

\(1 \frac{1}{4} \)

Step-by-step explanation:

\(1.25 = \frac{5}{4} = 1 \frac{1}{4} \)

I hope I helped you^_^

The radius of the middle marble is 12.  To find the radius of the middle marble, we can use the concept of similar triangles and proportions.

Let's denote the radii of the marbles as follows:

r1 = radius of the smallest marble (8)

r2 = radius of the middle marble (unknown)

r3 = radius of the largest marble (18)

Since each marble is in contact with the adjacent marble(s) and with the funnel wall, we can consider the three marbles (smallest, middle, and largest) as forming a triangle within the funnel.

By observing the arrangement of the marbles, we can see that this triangle is similar to a triangle formed by connecting the centers of the marbles.

Now, let's focus on the ratio of the radii of the marbles in the two triangles:

r1 : r2 : r3

We know that r1 = 8 and r3 = 18. To find r2, we can set up the proportion:

r1 / r2 = r2 / r3

Substituting the known values:

8 / r2 = r2 / 18

Cross-multiplying:

(r2)^2 = 8 * 18

Simplifying:

(r2)^2 = 144

Taking the square root of both sides:

r2 = √144

r2 = 12

Therefore, the radius of the middle marble is 12.

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Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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"Answer: 11x - 8y = -9

Step-by-step explanation:

For this exercise you need to remember:

1) The multiplication of signs:

(+) (+) = +

(-) (-) = +

(-) (+) = -

(+) (-) = -

2) By definition, like terms contain the same variables with the same exponent.

Then know this, and given the equations:

8x - 4y = -4 and -3x + 4y = 5

You must subtract the like terms, which means that you must subtract the numerical coefficients of each term.

Then, you get the result is:

8x - 4y = -4

-3x + 4y = 5

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

8x - (-3x) - 4y - 4y = - 4y -5

8x + 3x - 8y  = -9

11x - 8y = -9"

Answer:

after simplifying, we get,

23/6

Step-by-step explanation:

(2/3+5/2-7/3)+(3/2+7/3-5/6)

We simplify,

\((2/3+5/2-7/3)+(3/2+7/3-5/6)\\(2/3-7/3+5/2)+(3/2+7/3-5/6)\\(5/2-5/3)+(9/6+14/6-5/6)\\(15/6-10/6)+((9+14-5)/6)\\(15-10)/6+(23-5)/6\\5/6+18/6\\(5+18)/6\\23/6\)

Answer:

x = 2

Step-by-step explanation:

Since this is an isosceles triangle the unmarked side is also √2

Since this is also a right triangle use the pythagorean theorem to find x.

x² = (√2)² + (√2)²

x² = 2 + 2

x² = 4

x = 2

The value of x is 2.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

H= x, P= √2, B= √2

Now, using Pythagoras theorem

H² = P² + B²

x² = (√2)² + (√2)²

x² = 2 + 2

x² = 4

x = 2

Hence, the value of x is 2.

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Answer:

Step-by-step explanation:

5x - 6y = 27 .......... Equation 1

7x + 6y = 9 ………… Equation 2

To solve using elimination add the second equation to the first one to eliminate y

That's

5x - 6y + 7x + 6y = 27 + 9

12x + 6y - 6y = 36

12x = 36

Divide both sides by 12

x = 3

Substitute it into any of the equations

Using equation 2

That's

7(3) + 6y = 9

21 + 6y = 9

6y = - 12

Divide both sides by 6

y = - 2

The solutions are

x = 3

y = - 2

Hope this helps you

Using the volume of the cylinder we know that 77% of the container B is full when the pumping is complete.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.

In elementary geometry, it is regarded as a prism with a circle as its basis.

A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.

The following is a list of the cylinder's attributes: It has two flat circular faces, two curved edges, and one curved surface.

Its uniform cross-section throughout makes it resemble a prism.

They feature two bases that are circular, flat, and arranged in a straight line.

So, the volume of cylinders A and B:

Formula: V=πr²h

Cylinder A:

V=πr²h

V=π10²20

V = 6283.18531

Rounding off: 6283 ft³

Cylinder B:

V=πr²h

V=π12²18

V=8143.00816

Rounding off: 8143 ft³

Then, contain A is what % of container B:

= 6283/8143 * 100

= 77.15

Rounding off: 77%

Therefore, using the volume of the cylinder we know that 77% of container B is full when the pumping is complete.

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Answer:

B. 4:10

Step-by-step explanation:

A. 3:6 is equal to 1:2, which is our given answer for A.

B. Has no equivalent to 3:6

C. 10:20 can be simplified to 1:2 which 3:6 can also be simplified to… giving our answer.

Finally, D. You can multiply equally by 5 to get 15:30 and divide to get back to 3:6… it’s equal ;)

Hope this helps, good luck!

The limit of the sequence is 0.

To determine the limit of the sequence, we can use the Limit Laws and theorems. We will start by simplifying the expression:

cn=ln((5n-7)/(12n+4))

cn=ln(5n-7)-ln(12n+4)

Now we can use the Limit Laws:

lim n→∞ ln(5n-7) = ∞ (since ln(x) → ∞ as x → ∞)

lim n→∞ ln(12n+4) = ∞ (since ln(x) → ∞ as x → ∞)

Therefore, we have:

lim n→∞ cn = lim n→∞ (ln(5n-7)-ln(12n+4))

= lim n→∞ ln(5n-7) - lim n→∞ ln(12n+4)

= ∞ - ∞ (which is an indeterminate form)

To evaluate this limit, we can use L'Hopital's Rule:

lim n→∞ ln(5n-7) - ln(12n+4) = lim n→∞ [ln((5n-7)/(12n+4))]

= lim n→∞ [(5/12)/(5/n - 3/4n²)]

Since the denominator goes to ∞ and the numerator is constant, we have:

lim n→∞ [(5/12)/(5/n - 3/4n²)] = 0

Therefore, we have:

lim n→∞ cn = 0

So the limit of the sequence is 0.

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The required probability for the given event is given as 0.5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of a door being locked is 70% = 0.7

Total number of keys is 10.

The number of keys being carried is 2.

Thus, there can be two cases for getting through the door.

Case 1: The door is locked.

The probability to open the door by 1 key is 1/10.

Then, the probability to open the door by 2 keys is 2/10 = 1/5.

Case 2: The door is open.

In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,

1 - 0.7 = 0.3.

Now, the overall probability should consider both the cases as,

P(getting through the door) = P(Door is closed and keys open it)

+ P(The door is open)

= 0.3 + 1/5

= 0.3 + 0.2

= 0.5.

Hence, the probability to get through the door without returning for more keys is 0.5.

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The solution to the system of equations is x = 5 and y = -1.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 2x - 6y = 16 and x + y = 4

Let's start with the second equation:

x + y = 4

We can solve for one of the variables, say y, by subtracting x from both sides:

y = 4 - x

Now we can substitute this expression for y into the first equation:

2x - 6y = 16

2x - 6(4 - x) = 16

Expanding and simplifying, we get:

2x - 24 + 6x = 16

Combining like terms, we get:

8x - 24 = 16

Adding 24 to both sides, we get:

8x = 40

Dividing both sides by 8, we get:

x = 5

Now we can substitute this value of x into either of the original equations to find y. Let's use the second equation:

x + y = 4

5 + y = 4

Subtracting 5 from both sides, we get:

y = -1

Therefore, The solution to the system of equations is x = 5 and y = -1.

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Answer:

22) 3 in<x<11 in

23) 8 cm<x<26 cm

24) 0 ft<x<10 ft

25) 9 m<x<31 m

26) 2 km<x<14 km

27) 13 in<x<61 in

Step-by-step explanation:

It has to be greater than the difference and smaller than the sum.

22) 7-4=3, 4+7=11, so the answer is 3<x<11

23) 8<x<26

24) 0<x<10

25) 9<x<31

26) 2<x<14

27) 13<x<61

Answer:

hello!

your answer would be 258, because the y-intercept goes upwards.

:D have a good day <3