Answer:
the numbers are 20, 21 and 22
Step-by-step explanation:
x+(x+1) + (x+2) = 63
3x +3 = 63
3x = 60
x = 20
doing this for ponits
Answer:
the numbers are 20, 21 and 22
Step-by-step explanation:
x+(x+1) + (x+2) = 63
3x +3 = 63
3x = 60
x = 20
Question
Show that a language A is Turing recognizable if and only if 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).
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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In a class of 17 students, 3 are math majors. A group of four students is chosen at random.
(a) What is the probability that the group has no math majors?
(b) What is the probability that the group has at least one math major?
(c) What is the probability that the group has exactly two math majors?
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%
Need Help. 25 Points!
Please Show work, Thanks! :)
Answer:
B
Step-by-step explanation:
We want to find the quadratic regression formula given the table.
So, let's use the quadratic regression function on your graphing calculator. I don't have one on me, but I believe you simply need to enter the data and hit quadratic regression or something similar.
I'm going to use an online quadratic regression calculator by Keisan Casio.
Refer to the screenshot.
Note that it says to use the 24-hour clock to represent time after noon. So, 2 P.M. will just be 14, 4 P.M. will be 16, etc.
Therefore, our quadratic regression equation is, approximately:
[tex]y=-0.511x^2+14.96x-35.8[/tex]
The choice that best represents this is B.
So, our answer is B.
And we're done!
Will give brainiest.
1. At the store, I purchased 3.25 lb of honey crisp apples. The apples cost $15.60. How much does it cost per pound
2. Mr. Santora got 4.3 gallons of gas at Wawa. His bill was $12.47. How much was each gallon of gas?
3. A grocery store sells fruit snacks that come in two different sizes. Box A has 8 snacks for $2.48. Box B has 12 snacks for $3.48. How much does it cost per snack in Box A? How much does it cost per snack in Box B? How much more does Box A cost than Box B?
4. Ashton works at a drop in day care center. She earned $68.25 for working 6 hours and 30 minutes. How much does Ashton make per hour? How many hours would it take Ashton to earn $126
5. The small poster in the gift shop has a width of 12 inches and a height of 15 inches. The largest poster has a width of 32 inches. What is the height of the largest poster?
6. Lauren took 12 hours to read a 360 page book. At this rate, how long will it take her to read a 400 page book? It will take Lauren _____ hours and ____ minutes.
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
What is the length of segment AB with point A and B located at (-4, 1) and (2, 9)
Answer:
The answer is 10 unitsStep-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
10 unitsHope 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
Help me solve this ASAP worth 25 points
202· 87/100 –100· 87/100 –2· 87/100
Answer:
87
Step-by-step explanation:
Answer:
87
Step-by-step explanation:
If 2a-b:2a+b=1:2, find the value of a:b.
Answer:
a:b = 3:2
Step-by-step explanation:
You are given:
2a - b 1
----------- = ------
2a + b 2
Then, through cross-multiplication, we get:
4a - 2b = 2a + b, or
2a = 3b
We want the value of the ratio a:b. To obtain this, divide both sides by b, which results in
2a
------- = 3
b
Finally, we divide both sides by 2, obtaining the desired ratio:
a:b = 3:2
Which function is nonlinear? Y=4x+9 y=7/x-6 y=x-6/7 15 points
Answer:
The answer is y = 7/x -6.
Step-by-step explanation:
A linear function is one where x and y are both to the first power. Using this knowledge, let's look at the options that we are given.
y = 4x + 9
In the above equation, both x and y are raised to the first power, so we know that this equation is linear.
y = 7/x - 6
In the above equation, y is raised to the first power, but x is not. Since x is in the denominator of a fraction, it actually has a power of -1, which makes this equation nonlinear.
y = x - 6/7
In the above equation, both x and y are raised to the first power, making the equation linear.
Therefore, the correct choice is y =7/x - 6.
Hope this helps!
A jeweler had a piece of silver that weighed 196.54 grams. she used 98.6 grams to make some jewelry. How many grams of silver did she have left?
Answer:
97.94
Step-by-step explanation:
Given J(1,4) and the midpoint is M(2, 1), find the other endpoint K.
x=2y-z/4 solve for z
idk how to solve it even though I'm in algebra 1 lol :/
Answer:
z = − 4 x + 2 y
Step-by-step explanation:
SHOW WORK PLEASE!!!!!!!!!!!
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
if f(x, y) = xy, find the gradient vector ∇f(2, 7) and use it to find the tangent line to the level curve f(x, y) = 14 at the point (2, 7).
Equation of tangent line curve: 7x - y = 7
The function f(x, y) = xy . To find the gradient vector ∇f(2, 7) and use it to find the tangent line to the level curve f(x, y) = 14 at the point (2, 7).Gradient vector ∇f(2, 7)We need to find the partial derivative of the function with respect to x and y. Therefore, ∂f/∂x = y and ∂f/∂y = x∴ ∇f = (y)i + (x)j ∴ ∇f(2, 7) = (7)i + (2)j. Hence the gradient vector ∇f(2, 7) = (7)i + (2).j. Tangent line to the level curve f(x, y) = 14 at the point (2, 7)Level curve f(x, y) = 14 is f(x, y) = xy = 14. Therefore, y = 14/x. Then, ∂y/∂x = -14/x²We know that the slope of the tangent line to the level curve is the value of the gradient vector ∇f at the point (2, 7).Therefore, slope = ∇f(2, 7) = 7So, the slope of the tangent line is 7 and it passes through the point (2, 7).Therefore, the equation of the tangent line is given by y-7 = 7(x-2) or y = 7x - 7.
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Work out the product of
work out the product of 3 1/3 and 2 1/6
Give your answer as a mixed number.
Answer:
3⅓×2 1/6
10/3×13/6
5/3×13/3
65/3
21 2/3
-3.3x + 1x + 8 = -10x
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
Which way is better?
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)=$44
Convert 60 mi/hr to feet per second
Answer:
80
Step-by-step explanation:
the easy way to convert mi/hr to feet/s is multiply the speed value by 1.467
[tex]60 \times 1.467 = 88.02 = 88 \: (approx)[/tex]
2.1 = -0.6m
What is the solution to m?
Answer:
m=-3.5
Good Luck!!!
Answer:
Your answer to this is M=-3.5
If m<1 = 88 , find the m<3.
Answer:
use symbolab
Step-by-step explanation:
7. Find two consecutive even integers such that twice the smaller is
26 less than 3 times the larger.
Answer:
20 and 22Step-by-step explanation:
The difference between two consecutive even integers is 2
and even integer is always twice some integer
So:
2x ← smaller of numbers
2x+2 ← larger of numbers
2×2x ← twice the smaller of numbers
3(2x+2) ← three times the larger
3(2x+2)-26 ← 26 less than 3 times the larger
twice the smaller is 26 less than 3 times the larger:
3(2x+2) - 26 = 2×2x
6x + 6 - 26 = 4x
+20 +20
6x - 4x = 20
2x = 20
2x+2 = 20 + 2 = 22
Check: 2×20=40; 40+26 = 66; 66÷3=22
Rhonda decided to invest 15,000 of her retirement fund conservatively . She invested part of this money into one account that pays 4% simple interest and part into another account that pays 2% simple interest . Last year she earned 360$ in intrest . How much did she invest in each type of account ?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Total Planned amount to invest = 15,000
Investment A:
Rate = 4% = 0.04
Principal = a
Investment B:
Rate = 2% = 0.02
Principal = b
Total interest earned = $360
Simple interest = principal * rate * time
Simple interest on A + simple interest on B = $360
a + b = 15,000 - - - (1)
(a * 0.04) + (b * 0.02) = 360
0.04a + 0.02b = 360 - - - (2)
a = 15000 - b
0.04(15000 - b) + 0.02b = 360
600 - 0.04b + 0.02b = 360
-0.02b = 360 - 600
-0.02b = - 240
b = 240 / 0.02
b = $12000
a = 15000 - b
a = 15000 - 12000
a = $3000
Kenny is making a small quilt for his new niece. His pattern calls for 4.5 yards of fabric, and he picks out a plaid fabric that costs $3.90 per yard. How much money does Kenny spend on the fabric?
Answer:
He spends $17.55 on the new fabric.
Step-by-step explanation:
First multiply 3.9 (cost of fabric per yard) by 4 (number of yards) to get 15.6. Then divide 3.9 by 2 (since we need half a yard) to get 1.95. Lastly add 15.6 plus 1.95 to get your answer, $17.55.
Answer:
Kenny spent $17.55 on the fabric.
Step-by-step explanation:
Since it costs $3.90 per yard, we need to multiply 3.90 and 4. The product is 15.60, but we still have half a yard left. Simply divide $3.90 by 2 to get the price of half a yard ($1.95). Now, add them together to get $17.55
Please help!————————
Answer:
°F =(K − 273.15) × 9/5 + 32
Step-by-step explanation:
David's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs David $4.10 per pound, and type B coffee costs $5.25 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $423.40. How many pounds of type A coffee were used?
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
A popular radio station, NPR, transmits a signal that is has a wavelength of 3.38 m. What is the frequency of this signal? Remember that the speed of light is 299,792,458 m.
Answer:
88,695,993.49HertzStep-by-step explanation:
The formula for calculating the velocity of wave is expressed as;
v = fλ
f is the frequency
λ is the wavelength
f = v/λ
Given
v = 299,792,458 m/s
λ = 3.38m
Substitute and get the frequency f
f = 299,792,458 /3.38
f = 88,695,993.49Hertz
Hence the frequency of the signal is 88,695,993.49Hertz
If a ball is thrown upward at 64 feet per second from a height of 8 feet, the height of the ball can be modeled by S = 8 + 64t-16t^2 feet, where t is the number of seconds after the ball is thrown. How long after the ball is thrown is the height 68 feet? It takes___seconds for the ball to reach the height 68 feet.
The ball reaches a height of 68 feet after 1.25 seconds.
To determine the time it takes for the ball to reach a height of 68 feet, we can set the equation S = 68 and solve for t. Substituting the values into the equation S = 8 + 64t - 16t^2, we get 68 = 8 + 64t - 16t^2. Rearranging the equation and setting it equal to zero, we have 16t^2 - 64t + 60 = 0. Factoring this quadratic equation, we get (4t - 6)(4t - 10) = 0. Solving for t, we find two possible values: t = 1.5 and t = 2.5. However, since we are considering the upward motion of the ball, we take the positive value, which is t = 1.25 seconds.
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A coin is tossed three times. Find the probability of the following events:
(1) A: getting at least two heads
(2) B: getting exactly two heads
(3) C: getting at most one head
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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Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
D
Step-by-step explanation:
Just simply plus 3 of the equation then you can get the answer.
Hope my answer can help you
Please mark as brainliest!!
A pelt of 3104 people reveaved that of the respendents that were registered Republicans, 125 aporoved of their representative's job performance, 405 did not, and 733 tad no opinion. of the registered Democrats, 239 approved of their representative's job performance, 433 did not, and 74 had no opinion. of those registered as tindepensents, 117 approved, 107 cd not apprave, and 20 had no opinion, Of the remaining respondents, whe were not registered, 74 approved, 46 did not approve, and 26 had no cpinion. Represent these data in a 3×4 matrix.
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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If f(x) = 3x + 2
Find f(x + 1)
Answer:
use symbolab
Step-by-step explanation:
