Let S = ∪i∈Z+(Z+)i. S is the set of all nonempty, finite tuples of positive integers; some elements of S include (7), (1000000, 3, 42), and (2, 2, 2, 2, 2, 2, 2). We wish to show that S is countable by finding a one-one (or "injective") function from S into the positive integers.(a) (2 points) What is wrong with the following proof that S is countable: "We can form a 1-1 function from S into the positive integers by mapping each tuple to the sum of its elements. Therefore S is countable."(b) (2 points) What is wrong with the following proof that S is countable: "We can form a 1-1 function from S into the positive integers by treating each tuple as a string and replacing each comma by a 0, so that, for example, (1, 2, 3) → 10203. Therefore S is countable."(c) (6 points) Adapt the proof in part (b) to show that S is countable. (Hint: use a base other than 10.)
Answers
The no two distinct tuples map to the same integer. Thus, S is countable.
(a) The issue with the first proof is that the function mapping each tuple to the sum of its elements is not injective (one-to-one).
Different tuples can have the same sum, e.g., (1, 2) and (3) both map to 3, causing a violation of the injective property.
(b) The problem with the second proof is that the function is not injective either. Tuples like (10, 2) and (1, 02) both map to 1002, which again violates the one-to-one property.
(c) To show that S is countable, we can adapt the proof in part (b) by using a different base. Instead of base 10, let's use base p (a prime number greater than the maximum integer in the tuples). We can map each tuple (a_1, a_2, ..., a_n) to the integer
\( (p^(a_1 - 1)) * (p^(a_2 - 1 + p)) * ... * (p^(a_n - 1 + (n-1)p)).\)
This function is injective because each element in the tuple uniquely contributes to the resulting integer, ensuring that no two distinct tuples map to the same integer. Thus, S is countable.
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Related Questions
The temperature at 6:00p.m. was 7 degrees Celsius. The temperature dropped 2 degrees every hour. What was the temperature at 11:00 p.m.
Answers
Answer:
7 Celsius to Fahrenheit is 44.6.
There is a five hour gap.
The tempature drops two degrees per hour. So, multiply.
2 x 5 = 10.
Subtract 10 from 44.6.
You get 34.6.
34.6 is the answer.
Un tren en marcha acelera a razón de 12 metros por segundo ¿ Cual seria tu masa si la fuerza aplicada fuera de 10N ?
Answers
If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.
The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.
However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.
Substituting the given values, we get:
m = 10 N / 12 m/s²
m = 0.83 kg
So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.
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Complete Question:
A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?
I need the answer ASAP!:/
Answers
Answer:
-2
Step-by-step explanation:
At first, you might think that -5 is bigger than -2 because 5 > 2, right? Actually, no, that's not how it works. The "rules" for numbers are flipped when you are dealing with negative numbers, so therefore, -2 is bigger. Basically, what I'm saying is that the smaller the number after the negative sign, the bigger the number is and vice versa.
Answer:
Answer is - 2
Step-by-step explanation:
Because in case of negative numbers the number which is smaller in negative no is bigger in negative
numbers I hope you understand....Mark me as brainliest
Dave and Sandy hartranft are frequent Flyers with a particular airline they often fly from city A to city be a distance of 828 miles on one particular trip they’re flying to the wind and the flight takes two hours the return trip with the wind behind them only takes one and a half hours find the speed of the wind and find the speed of the plane
Answers
Answer:
dave
Step-by-step explanation:
your welcome
Probability Distributions for Discrete Random Variables
Which of the following are discrete random variables?
Select all that apply
1-The number of CDs that a college student owns
2- The number of dogs you own
3- The amount of gas in your car
4- Number of 6s you get when you throw 5 number cubes
5- The number of dog sleds that a competitor uses in an annual sled dog race
Answers
The discrete random variables from the given options are: 1, 2, 4, and 5.
The number of CDs that a college student owns: This is a discrete random variable because the number of CDs can only be a whole number. You cannot have a fractional or continuous value for the number of CDs.
The number of dogs you own: This is a discrete random variable because you can only own a whole number of dogs. You cannot own a fractional or continuous number of dogs.
Number of 6s you get when you throw 5 number cubes: This is a discrete random variable because the number of 6s can only be a whole number from 0 to 5. You cannot have a fractional or continuous value for the number of 6s obtained.
The number of dog sleds that a competitor uses in an annual sled dog race: This is a discrete random variable because the number of dog sleds can only be a whole number. You cannot have a fractional or continuous value for the number of dog sleds used.
On the other hand, the following option is not a discrete random variable:
The amount of gas in your car: This is a continuous random variable because the amount of gas can be any non-negative real number. It can have fractional or continuous values, such as 10.5 liters or 20.25 gallons. Option 1,2,3,4 and 5
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which is a line of symmetry
Answers
Answer:
is there a pic?
Step-by-step explanation:
we are able to see
it is given
the
\ABC = \FDE and AB = 4cm, \B-40 and
\E=60 then which of the following is true
LA DE=4 cm, ZA = 60°
(A)D F = 4cm , \A = 80° (B)DE =4cm. \C=80°(C)df=4cm\a=80°
(D) Df=ucm LC=80°
Answers
Answer:
(C) DF=4 cm, ∠A=80⁰Step-by-step explanation:
Question It is given the ∆ABC≅∆FDE and AB=4 cm, ∠B=40⁰ and ∠E=60⁰, then which of the following is true. (A) DE=4cm, ∠A=80⁰ (B) DE=4 cm, ∠C=80⁰ (C) DF=4 cm, ∠A=80⁰ (D) DF=4cm, ∠C=80⁰SolutionCorresponding sides and angles are:
AB ≅ FD∠A≅∠F, ∠B≅∠D, ∠C≅∠EGiven:
AB = 4 cm, so FD = 4 cm ∠B = 40⁰ and ∠E = 60⁰, so ∠D = 40⁰ and ∠C = 60⁰and
∠A = ∠F = 180⁰ - (40⁰ + 60⁰) = 80⁰Considering all above we see that correct answer option is (C)
The kids' pool in Ben's neighborhood is rectangular-shaped and covers an area that
can be represented by 169x2 - 64 units. Write expressions to represent the dimensions of the
pool.
Answers
Explanation:
Factor using the difference of squares rule
\(a^2 - b^2 = (a-b)(a+b)\\\\(13x)^2 - (8)^2 = (13x-8)(13x+8)\\\\169x^2 - 64 = (13x-8)(13x+8)\)
The rectangular pool has dimensions of 13x-8 units by 13x+8 units.
.Write the product of 4x104
Answers
Answer:
416
Step-by-step explanation:
The measurement of a rectangular room on a scale drawing are 8cm x 6cm. If the scale use is 1 : 400, calculate the actual area of the room in m².
Answers
Answer:
768 m²
Step-by-step explanation:
8 x 400 = 3200 cm = 32 m
6 x 400 = 2400 cm = 24m
32 x 24 = 768 m²
The model below has an area of 16 square units which expression represents the side length of the model in units /64 /4 /16 /8
Answers
Answer:
4
Step-by-step explanation:
the area of a square = length²
16 = length²
find the square root of both sides of the equation
length = 4
Have i done this right, why did i not get the third mark
Answers
Answer:
because you are good with math
Step-by-step explanation:
not every linearly independent set in set of real numbers r superscript ℝn is an orthogonal set. T/F?
Answers
The given statement is true.
Consider linearly independent vectors of \(R_{n}\)
Where n = 2
\(V = \[\begin{array}{ccc}4&\\2\end{array}\right]\)
\(U = \[\begin{array}{ccc}5&\\6\end{array}\right]\)
Now product of these vectors
UV = 4x5 + 2x6
= 32
Hence these vectors are not orthogonal.
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Item 4
Write the word sentence as an inequality.
A number b minus 4.2 is less than −7.5.
An inequality is
.
Answers
Answer:
b-4.2 < -7.5
Step-by-step explanation:
Here, we want to write an inequality
A number b minus 4.2
b - 4.2
is less than -7.5
< -7.5
The inequality is:
b-4.2 < -7.5
Cuantos Gigabytes (GB) es un Terabyte (TB)?
Answers
1,024 GB un TB es 1024 GB espero que te ayude esto
help please ASAP!!! Got a lot of math to do here comes an all nighter :(
Answers
Answer:
110
Step-by-step explanation:
2 ( wl+hl+hw ) = 2 (7·1+6·1+6·7 ) = 110
Here Enjoy :)
Please can you help me with this
Answers
9514 1404 393
Answer:
85°
Step-by-step explanation:
The sum of arcs in a circle is 360°.
FG +140° +80° +55° = 360°
FG = 360° -275°
FG = 85°
to prepare for a downhill skiing competition ,roman completed three training sessions. the table shows his average time and distance to each session. did romans rate in miles per hour increase from session to session write an agurement that can be used to defend your solution
Answers
Answer:
no
Step-by-step explanation:
Apparently, the three runs are ...
(hours, miles) = (2/125, 9/10), (3/200, 11/12), (3/250, 17/30)
The speed in miles per hour is found by dividing miles by hours for each run. Of course dividing by a fraction is the same as multiplying by its inverse.
session 1 speed = (9/10)(125/2) = 56.25
session 2 speed = (11/12)(200/3) ≈ 61.11
session 3 speed = (17/30)(250/3) ≈ 47.22
Roman's speed increased from the first session to the second, but decreased for the third session.
Roman's speed did not increase from session to session.
What is the equation of a line perpendicular to y-2=-2/3(x+1) and passing through the point (4,1)
PLS HELP
Answers
Answer: y = (1/3)*x - 5
Step-by-step explanation: Hope this helps!
What is the area of this polygon?
Answers
Answer:
39 unitsSolution,
Total area=Area of ABCD+ Area of triangle ADE
\((ab \times bc) + \frac{1}{2} \times ad \times ef \\ = (5 \times 6) + \frac{1}{2} \times 6 \times 3 \\ = 30 + 9 \\ = 39 \: {units}^{2} \)
hope this helps...
Good luck on your assignment...
The circle graph shows how a family spends its annual Income. If $25,200 is used for Food, Savings, and Insurance combined, what is the total annual income?
housing 21%
food 18%
clothing 17%
auto 14%
entertaining 12%
insurance 11%
savings 7%
Answers
Answer:41,328
Step-by-step explanation:
18+7+11=36 36%
100-36=64 64%
25,200 x 164%=41,328
Solve each equation in the interval from 0 to 2 π . Round your answers to the nearest hundredth.
6 tan 2θ=1
Answers
The solutions to the equation 6tan(2θ) = 1 in the interval from 0 to 2π (0 to 360 degrees) rounded to the nearest hundredth are θ = 0.19 radians (10.87 degrees) and θ = 2.95 radians (169.05 degrees).
To solve the equation 6tan(2θ) = 1, we need to isolate θ. First, divide both sides of the equation by 6 to obtain tan(2θ) =\(\frac{1}{6}\) Next, take the inverse tangent (arctan) of both sides to find the value of 2θ. This gives us 2θ = arctan(\(\frac{1}{6}\)).
Now, to solve for θ, divide both sides of the equation by 2, yielding θ = (\(\frac{1}{2}\)) * arctan(\(\frac{1}{6}\)). By evaluating this expression, we find that θ is approximately equal to 0.19 radians or 10.87 degrees. However, this gives only one solution within the given interval.
To find the other solution, we need to consider the periodic nature of the tangent function. Adding π (180 degrees) to the previous solution, we get θ = 0.19 + π ≈ 3.32 radians or 190.87 degrees. Since this solution is outside the given interval, we subtract 2π (360 degrees) to bring it back within the range. Thus, the second solution is θ = 3.32 - 2π ≈ 2.95 radians or 169.05 degrees.
In summary, the solutions to the equation 6tan(2θ) = 1 in the interval from 0 to 2π rounded to the nearest hundredth are θ = 0.19 radians (10.87 degrees) and θ = 2.95 radians (169.05 degrees).
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Simplify for a = 3, b = -4 and c = -1.
2a(b−c)
Answers
Answer:
your answer would be -18
PLZ HELP ASAP NEED HW
Answers
Answer:
\(m=\frac{x}{7k} -n\)
Step-by-step explanation:
Step 1: Write equation
\(x=7k(n+m)\)
Step 2: Solve for m
Divide both sides by 7k: \(\frac{x}{7k} =n+m\)Subtract n on both sides: \(\frac{x}{7k} -n=m\)Rewrite: \(m=\frac{x}{7k} -n\)PLEAS HELP ASAP 50 POINTS IF RIGHT: A landscaper is creating a bench for a pool deck. A model of the bench is shown in the image.
A rectangular prism with dimensions of 7 feet by 3 feet by 4.8 feet.
Part A: Find the total surface area of the bench. Show all work. (6 points)
Part B: The landscaper will cover the bench in ceramic tiles except for the bottom that is on the ground. If the tiles cost $0.89 per square foot, how much will it cost to cover the bench? Show all work. (6 points)
Answers
Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.
Given dimensions:
Length = 7 feet
Width = 3 feet
Height = 4.8 feet
Surface Area of each face:
Front and back faces: Length * Height
= 7 feet * 4.8 feet
= 33.6 square feet
Top and bottom faces: Width * Length
= 3 feet * 7 feet
= 21 square feet
Side faces: Width * Height
= 3 feet * 4.8 feet
= 14.4 square feet
Total Surface Area:
2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)
= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet
= 67.2 square feet + 42 square feet + 28.8 square feet
= 137 square feet
Therefore, the total surface area of the bench is 137 square feet.
Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.
Cost per square foot = $0.89
Total Surface Area = 137 square feet
Total cost to cover the bench:
= Cost per square foot * Total Surface Area
= $0.89 * 137 square feet
= $121.93
Therefore, it will cost $121.93 to cover the bench with ceramic tiles.
Construct B so that B = A.
Answers
Answer:
make it the same except the letter b
Step-by-step explanation:
6.1.d.i. reduce the number of predictors: which predictors are likely to be measuring the same thing among the 13 predictors? discuss the relationships among indus, nox, and tax.
Answers
There should be training and validation sets as both of them have respective contribution in developing the multiple linear regression model.
There are many variables that measure levels of industrialization that have positively correlated. In
There is a positive relationship between the INDUS, NOX and TAX as Boston has high proportion of non-retail businesses and this would lead to high taxes and pollution levels in the region.
How to explain the relationshipThe relationship between the dependent and independent variables is shaped in part by the two data sets.
The model is fitted using the training data, and the regression coefficients (β0, β1, …, βp.) are estimated. This will assist us in forecasting the coefficients necessary to establish the relationship between the variables.
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6.1 Predicting Boston Housing Prices
a. Why should the data be partitioned into training and validation sets?
Which predictors are likely to be measuring the same thing among the 14 predictors? Discuss the relationships among INDUS, NOX, and TAX.
Is there a unique way of filling in the missing probabilities in the transition diagram shown to the right? If so, complete the transition diagram and write the corresponding transition matrix. If not, explain why. 0.1 0.4 0.5 0.4 0.1 0.3 Is there a unique way of filing in the missing probabilities in the transition diagram? If so, identify the missing probabilities. If not necessary, fill in the answer boxes to complete your choice. Yes. The probability of transition from A to A is Type integers or decimals.) No. At least one of the missing probabilities is needed to find the other two. the probability of transition from B to C is and the probability of t O B. Click to select and enter your answer(s).
Answers
The probability of transition from A to A: 0.5
The probability of transition from B to C: 0.4
The probability of transition from B to B: 0.1
The corresponding transition matrix is as follows:
| 0.1 0.4 0.5 |
| 0.4 0.1 0.3 |
| 0.4 0.0 0.6 |
What is Probability?
Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates a certainty
To determine if there is a unique way of filling in the missing probabilities in the transition diagram, let's analyze the given information.
The transition diagram is not explicitly shown, but we can infer the following structure based on the provided probabilities:
0.1 0.4 0.5
A ----> B ----> C ----> A
\ ↑ ↑
\ 0.4 | 0.1 | 0.3
V | |
B ----' |
0.4 |
↑ |
| 0.1 |
'----------'
0.3
From the given probabilities, we can fill in the missing probabilities as follows:
The probability of transition from A to A is 0.5 (since it is the only missing probability in that row).
The probability of transition from B to C is 0.4 (since it is the only missing probability in that row).
The probability of transition from B to B is 0.1 (since it is the only missing probability in that row).
Therefore, there is a unique way to fill in the missing probabilities, and the missing values are:
The probability of transition from A to A: 0.5
The probability of transition from B to C: 0.4
The probability of transition from B to B: 0.1
The corresponding transition matrix is as follows:
| 0.1 0.4 0.5 |
| 0.4 0.1 0.3 |
| 0.4 0.0 0.6 |
Please note that the transition matrix represents the probabilities of transitioning from each state to another state.
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What is 1/2sq miles - 1/3 sq miles
Answers
Answer: 431 664.685 m2
Step-by-step explanation:
Evaluate the expressiin when a=6, b=3, and c=2: c(b+a)-a= please help
Answers
Answer:
\( \huge{ \fbox{ \tt{12}}}\)
Step-by-step explanation:
\( \underline{ \sf{Given}} : \sf a=6, \: b=3 \: and \: c=2\)
\( \underline{ \sf{To \: find }} : \sf{Value \: of \: the \: given \: expression}\)
\( \underline{ \underline{ \mathfrak{Let's \: solve}}} : \)
\( \bigstar{ \tt{ \: c \: ( \: b \: + \: a \: ) - \: a}}\)
\( \text{Step \: 1 \: } : \) Plug the values of a , b and c
\( \mapsto{ \tt{ \: 2 \: ( \: 3 \: + \: 6 \: ) \: - \: 6}}\)
\( \text{Step \: 2} : \sf{ \: Add \: the \: numbers : 6 \: and \: 3}\)
\( \mapsto{ \sf{ \: 2 \: * \: 9 \: - \: 6 \: }}\)
\( \text{Step \: 3 \: } : \sf{ \: Multiply \: the \: numbers : 9 \: and \: 2}\)
\( \mapsto{ \sf{18 - 6}}\)
\( \text{Step \: 4 \:} : \sf{Subtract \: 6 \: from \: 18}\)
\( \mapsto{ \sf{ \: 12}}\)
Note : Just follow the PEMDAS rule ( See attached picture )
Hope I helped!
Best regards! :D
~\( \sf{TheAnimeGirl}\)
