write an equivalent expression.

By proving both directions, we have established the equivalence between a language A being Turing recognizable and the existence of a decider V such that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y).

To prove the statement, we need to show both directions of the "if and only if" statement.

First, let's assume that language A is Turing recognizable. This means that there exists a Turing machine M that recognizes A. We will construct a decider V based on M as follows:

V = "On input (x, y):

Simulate M on input x and y.

If M accepts, accept."

Now, let's analyze the behavior of V. If there exists y such that V accepts (x, y), it means that M accepts both x and y as inputs. Since M recognizes language A, this implies that x ∈ A. Therefore, if V accepts (x, y), then x ∈ A.

On the other hand, if x ∈ A, we know that there exists some string y such that M accepts (x, y). In this case, V will also accept (x, y) because it simulates M and accepts when M accepts. Therefore, if x ∈ A, there exists y such that V accepts (x, y).

We have shown that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y). Hence, the existence of the decider V satisfies the condition for language A to be Turing recognizable.

Next, let's assume that there is a decider V such that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y). We will construct a Turing machine M that recognizes A based on V as follows:

M = "On input x:

For each y in Σ∗, do the following:

Simulate V on input (x, y).

If V accepts, accept."

Now, let's analyze the behavior of M. If x ∈ A, then there exists some y such that V accepts (x, y) according to the assumption. In this case, M will eventually simulate V on input (x, y) and accept. Therefore, if x ∈ A, M will accept.

On the other hand, if x ∉ A, it means that for every y in Σ∗, V rejects (x, y). In this case, M will simulate V on all possible pairs (x, y) and reject for each of them. Therefore, if x ∉ A, M will reject.

We have shown that M recognizes language A based on the existence of the decider V.

By proving both directions, we have established the equivalence between a language A being Turing recognizable and the existence of a decider V such that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y).

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Answer:

Step-by-step explanation:

Step1

Definition permutation (order is important):

P(n,r)= n!/(n−r)!

Definition combination (order is not important):

C(n,r) =( n/r )= n!/r!(n−r)!

Step2

a) The order of the students does not matter, because a different order results in the same students being selected, and thus we should use the definition of combination.

We are selecting 3 of the 17 students in the class (of which 3 are math majors and 14 are not math majors).

# of possible outcomes=(17,3)=17!/3!(17−3)!=17!/3!14!=680

There areC(14,3) ways to select 3 of the 14 no math majors.

# of favorable outcomes=C(14,3)= 14!/3!(14−3)! = 14!/3!11! =364

The probability is the number of favorable outcomes divided by the number of possible outcome.

P(no math majors)= # of favorable outcomes/# of possible outcomes

                             = 364/680= 91/170

                             ≈0.5353=53.53%

Step 3

(b) By part (a):

P(no math majors)=91/170≈0.5353=53.53%

Use the Complement rule

Complement rule:

P(E’)=1−P(E)

P(at least one math major)=1−P(no math majors)=1−91/170

=79/170≈0.4647=46.47%

Step 4

(c) The order of the students does not matter, because a different order results in the same students being selected, and thus we should use the definition of combination.

We are selecting 3 of the 17 students in the class (of which 3 are math majors and 14 are not math majors).

# of possible outcomes=C(17,3)= 17!/3!(17−3)!=17! /3!14!=680

There areC(14,1) ways to select 1 of the 14 no math majors and there are

C(3,2) ways to select 2 of the 3 major majors.

# of favorable outcomes=C(14,1)⋅C(3,2)=14⋅3=42

P(2 math majors)= # of favorable outcomes/# of possible outcomes

                           = 42/680= 21/340=approx0.0618=6.18%

​

Answer:

x/2-100=5

Step-by-step explanation:

Answer:

x= -80/77

Step-by-step explanation:

-33x+x+8=-10x

-2.3x+8=-10x

-2.3x=-10-8

-2.3x+10x=-8

7.7x=-8

x=-80/77

Answer:

(3x)/2+14=15-x

2*(3x/2+14)=2*(15-x)

3x+14*2=15*2-x*2

3x-2x=30-28

x=2

Answer:

Option A is the correct answer

Step-by-step explanation:

Where there is + sign it changes to - and where there is - sign it change to + sign for the additive inverse

Answer:

Its the first one <3

Step-by-step explanation:

Because if the exponent is an even number, x can also be -x. For example, -4^2=4^2 but -4^3 isn't the same as 4^3

a. The proportion of days with more than 650 hits is approximately 0.0808.

b. The proportion of days with between 580 and 650 hits is approximately 0.6772.

c. The number of hits such that only 15% of the days will have fewer hits is approximately 406.36.

To solve these questions, we will use the standard normal distribution and the z-score.

a. To find the proportion of days with more than 650 hits, we need to calculate the z-score for 650 and find the area under the standard normal curve to the right of that z-score.

First, calculate the z-score:

z = (x - μ) / σ

z = (650 - 510) / 100

z = 1.4

Using the standard normal table or a calculator, we find the area to the right of the z-score 1.4 is approximately 0.0808.

Therefore, the proportion of days with more than 650 hits is 0.0808 (rounded to four decimal places).

b. To find the proportion of days with between 580 and 650 hits, we need to calculate the z-scores for 580 and 650 and find the area between these two z-scores under the standard normal curve.

First, calculate the z-score for 580:

z1 = (580 - 510) / 100

z1 = 0.7

Next, calculate the z-score for 650:

z2 = (650 - 510) / 100

z2 = 1.4

Using the standard normal table or a calculator, we find the area to the right of z1 (0.7) is approximately 0.7580, and the area to the right of z2 (1.4) is approximately 0.0808. To find the area between these two z-scores, we subtract the smaller area from the larger area:

0.7580 - 0.0808 = 0.6772

Therefore, the proportion of days with between 580 and 650 hits is 0.6772 (rounded to four decimal places).

c. To find the number of hits such that only 15% of the days will have fewer hits, we need to find the z-score that corresponds to the cumulative probability of 0.15 (15%).

Using the standard normal table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.15 is approximately -1.0364.

Now, we can use the z-score formula to find the number of hits:

z = (x - μ) / σ

-1.0364 = (x - 510) / 100

Solving for x:

x - 510 = -1.0364 * 100

x - 510 = -103.64

x = 510 - 103.64

x ≈ 406.36

Therefore, the number of hits such that only 15% of the days will have fewer hits is approximately 406.36.

In summary:

a. The proportion of days with more than 650 hits is approximately 0.0808.

b. The proportion of days with between 580 and 650 hits is approximately 0.6772.

c. The number of hits such that only 15% of the days will have fewer hits is approximately 406.36.

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Answer:

Sorry, no thanks

Step-by-step explanation:

The answer for the equation is A and B... I think

Answer:

A B that is what I think the answer is

Answer:

(Hope I got them correct I may have some mistakes)

1. $4.80 per pound

2. $2.90 per gallon

3. 31 cents or $0.31, 29 cents or $0.29, 2 cents

4. $10.50, 12 hours

5. 40 inches

6. 13 hours and 20 min

Step-by-step explanation:

1. $15.60/3.25=

$4.80 per pound

2. $12.47/4.3=

$2.90 per gallon

3. $2.48/8=

31 cents or $0.31

$3.48/12=

29 cents or $0.29

31 cents- 29 cents= 2 cents

4. $68.25/6hr 30 min=

$68.25/6.5=

$10.50

$126/10.5= 12 hours

5. Hope you are doing a ratio problem

12/32=15/x

15*32= 480

480/12=

40 inches

6. 360/12=

30

400/30=

13 1/3=

13 hours and 20 min

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The distance between two points or a line segment can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 1) and (2, 9)

The length of segment AB is

[tex] |AB| = \sqrt{ ({ - 4 - 2})^{2} + ({1 - 9})^{2} } \\ = \sqrt{( { - 6})^{2} + ({ - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} \: \: \: \: \: \: \: \: \\ = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

Hope this helps you

Answer:

The length of segment AB is 10

Step-by-step explanation:

The distance formula is d=[tex]\sqrt{ (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

With the points (-4,1) and (2,9) you know that [tex]-4=x_{1}, 2=x_{2}, 1=y_{1} ,9=y_{2}[/tex]

Now you put the numbers into the distance formula

d=[tex]\sqrt{(2-(-4))^{2}+(9-1)^2[/tex]

(2-(-4) turns into (2+4) because two negatives equal a positive.

After adding and subtracting you get d=[tex]\sqrt{6^2+8^2[/tex]

You then square [tex]6^2[/tex] and [tex]8^2[/tex] to get [tex]\sqrt{36+64[/tex]

After adding 34+64 you get [tex]\sqrt{100[/tex], which is 10

So the length of segment AB is 10

Answer:

Step-by-step explanation:

The difference between two consecutive even integers  is 2

and even integer is always twice some integer

So:

2x   ← smaller of numbers

2x+2  ←  larger of numbers  

2×2x     ←  twice the smaller of numbers

3(2x+2)      ←  three  times the larger

3(2x+2)-26   ← 26 less than 3 times the larger

twice the smaller is  26 less than 3 times the larger:

3(2x+2) - 26 = 2×2x

6x + 6 - 26 = 4x

       +20         +20

6x - 4x = 20

       2x = 20

2x+2 = 20 + 2 = 22        

Check:   2×20=40; 40+26 = 66; 66÷3=22

Given that a pelt of 3104 people revealed that of the respondents that were registered Republicans, 125 approved of their representative's job performance, 405 did not, and 733 had no opinion. Also, of the registered Democrats, 239 approved of their representative's job performance, 433 did not, and 74 had no opinion.

Moreover, of those registered as independents, 117 approved, 107 did not approve, and 20 had no opinion. Lastly, of the remaining respondents, who were not registered, 74 approved, 46 did not approve, and 26 had no opinion.The required matrix can be obtained as follows:Republicans Democrats Independents Not registered Approved12523911774.Did not approve40543310746No opinion7337420Total126910031004

From the given information, we can observe that the pelt of 3104 people is divided into four categories. These categories are registered Republicans, registered Democrats, registered Independents, and the remaining respondents, who are not registered. Further, the data is given in terms of approval, disapproval, and no opinion.Let us tabulate the data for each of these categories. For registered Republicans, 125 people approved, 405 did not approve, and 733 had no opinion. Similarly, for registered Democrats, 239 people approved, 433 did not approve, and 74 had no opinion. Moreover, for registered Independents, 117 people approved, 107 did not approve, and 20 had no opinion. Lastly, for the remaining respondents who were not registered, 74 people approved, 46 did not approve, and 26 had no opinion.Using the above information, we can represent the data in the form of a matrix. The required matrix has four rows and three columns. The first column represents the category, and the remaining three columns represent approval, disapproval, and no opinion for that category. The final matrix is as follows:

RepublicansDemocratsIndependentsNot registeredApproved12523911774Did not approve40543310746No opinion7337420Total126910031004

Thus, we can conclude that a pelt of 3104 people was divided into four categories, and the data was given in terms of approval, disapproval, and no opinion. Using this information, we represented the data in the form of a 3 × 4 matrix, where the first column represents the category, and the remaining three columns represent approval, disapproval, and no opinion for that category.

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Answer:

3⅓×2 1/6

10/3×13/6

5/3×13/3

65/3

21 2/3

Answer:

n is smaller, n + 1 is larger

Step-by-step explanation:

First, make the equation.

2(n + n+1) = 510

Then, simplify.

2(2n + 1) = 510

Distribute.

4n + 2 = 510

Solve.

n = 127

The smaller number is n (127) and the larger number is n + 1 (128).

Answer:

the correct answer is the smaller number is:127 and the bigger number is:128

Step-by-step explanation:

Answer:

x≤4

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−1/4

x≥−1

Step 2: Multiply both sides by 4/(-1).

(4−1)*(−14x)≥(4−1)*(−1)

Answer:

1. multiply both sides of the equality by -4 and flip the equality sign

that makes the problem: -4×x/-4 >_ -4×(-1)

2.since you multiplied -4 the divisor cancels and you are left with : x<_ -4×(-1)

multiplying 2 negatives makes it a positive so now you get x<_4

Answer:

the best way is to follow the law, sales tax is not subject to discount by the seller.

Step-by-step explanation:

both ways result in the same outcome:

improper way, discount after tax

$50+$5(tax)=$55, after discount $55-$11(20%)=$44

proper way, discount before tax

$50-$10(20%)=$40+$4(tax)=$44

Answer:

uhmmm try to search on google ‍♂️

Answer:

Katrina = 0.8

Susan = 0.833

Gabrielle = 0.85

Savannah = 0.9

Step-by-step explanation:

Change to decimal

Gabrielle = 85%

= 85/100

= 17/20

= 0.85

Savannah = 0.9

= 9/10

= 0.9

Katrina = 4/5

= 0.8

Susan = 5/6

= 0.833

Arrange from least to greatest

Katrina = 0.8

Susan = 0.833

Gabrielle = 0.85

Savannah = 0.9

Given, the coin is tossed three times.

Sample space: {HHH, HTH, THH, TTH, HHT, HTT, THT, TTT}

Number of positive outcomes = 8

Probability of

(1) A: Getting at least two heads

P(A) = P(Getting 3 heads) + P(Getting 2 heads)

        = [tex]\frac{3}{8} +\frac{1}{8}[/tex]                           Since, P(event) = [tex]\frac{No. of favourable outcomes}{Total no. of possible outcomes}[/tex]

P(A)  = [tex]\frac{1}{2}[/tex]            

(2) B: Getting exactly two heads

P(B) = [tex]\frac{3}{8}[/tex]

(3) C: Getting at most one head

P(C) = P(Getting zero head) + P(Getting 1 head)

       = [tex]\frac{1}{8} + \frac{3}{8}[/tex]

       = [tex]\frac{4}{8}[/tex]

P(C) = [tex]\frac{1}{2}[/tex]

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The given statement when calculating the standard error for p-hat, we use the p-hat not the p under h null is false.

When calculating the standard error for p-hat (the sample proportion), we use the value of p under the null hypothesis (p₀) rather than the observed sample proportion (p-hat). This is because the standard error is an estimate of the variability or uncertainty in the sample proportion compared to the population proportion assumed under the null hypothesis.

The standard error formula for p-hat is:

SE(p-hat) = sqrt[(p₀ * (1 - p₀)) / n]

Here, p₀ represents the hypothesized population proportion under the null hypothesis, and n is the sample size. We use p₀ because it represents the proportion assumed to be true in the population when there is no evidence to reject the null hypothesis.

Using p-hat (the observed sample proportion) instead of p₀ would not accurately reflect the assumptions made under the null hypothesis and could lead to incorrect inference and conclusions.

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Separate the inequalities by part.

[tex]8<12+c\\12+c<12[/tex]

We'll do 8 < 12+c first then 12+c<12 next.

[tex]8-12<c\\-4<c\\c>-4[/tex]

Then 12+c<12

[tex]12+c<12\\c<12-12\\c<0[/tex]

Then mix c<0 and c>-4 as we'll get [tex]-4<c<0[/tex] #

Answer:

18

X + 12 = 30

-12. -12. Subtract 12

X = 18. Answer

Answer:

42

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

f(6)=-2(6)+2

f(6)=-12+2

f(6)=-10

Answer:

 f(6) = - 10

Step-by-step explanation:

-2(6)+2

-12+2

= -10

Answer:

use symbolab

Step-by-step explanation:

Answer:

29 pounds of type A coffee was used

Step-by-step explanation:

David's shop makes a blend that is a mixture of 2 coffee

Type A costs $4.10

Type B costs $5.25

Let a represent the number of pounds of type A coffee used

Since this month's blend used twice as many pound of type B coffee as type A

a + 2a

The total cost is $423.40

Therefore the amount of pounds of type A coffee used can be calculated as follows

4.10a + 5.25(2a)= 423.40

4.10a + 10.5a= 423.40

14.6a= 423.40

a= 423.40/14.6

a= 29

Hence 29 pounds of type A coffee was used