Given the following discrete probability mass function (f(x)): f(x) 1/4 1/8] 1/4 3/8 Find the following probabilities: a) P(x = 3) = b) P(x < 4) = c) P(x > 3) = d) P(2

The set of real numbers with a repeating decimal expansion is countable because it can be mapped to a countable set of unique pairs of rational numbers.

To show that the set of all real numbers with a repeating decimal expansion is countable, we can prove that it is at most countable.

Let's consider a repeating decimal number 0.d1d2d3...dn(dn+1...dn+m-1dn+m...). This can be represented as 0.d1d2d3...dn + (dn+1...dn+m-1dn+m...)/([tex]10^m - 1[/tex]).

We can see that for any repeating decimal number, the part before the repeating block (0.d1d2d3...dn) is a finite decimal representation, which is a rational number.

The part within the repeating block ((dn+1...dn+m-1dn+m...)/([tex]10^m - 1[/tex])) is also a rational number because it can be expressed as a fraction.

Since both the finite decimal part and the repeating block part are rational numbers, we can map each repeating decimal number to a unique pair of rational numbers (finite decimal part, repeating block part).

Now, we know that the set of rational numbers is countable. Therefore, if we can show that the set of unique pairs of rational numbers is countable, then the set of repeating decimal numbers is at most countable.

To show that the set of unique pairs of rational numbers is countable, we can use the fact that the Cartesian product of countable sets is countable.

Since the set of rational numbers is countable, the set of unique pairs of rational numbers (finite decimal part, repeating block part) is also countable.

Thus, we can conclude that the set of all real numbers with a repeating decimal expansion is at most countable.

To know more about a rational number follow

brainly.com/question/1535013

#SPJ4

Answer:

2

Step-by-step explanation:

Subtract the number with the term both sides ( which is 9)

[tex] {x}^{2} + {y}^{2} - 6x + 4y = - 9[/tex]

Complete the square for the x terms and y terms.

( To complete the square divide the coefficient term by 2 and square it, then add that product to both sides.)

[tex] {x}^{2} - 6x + 9 + {y}^{2} +4y + 4 = - 9 + 9 + 4[/tex]

[tex] (x - 3) {}^{2} + (y + 2) {}^{2} = 4[/tex]

Take the square root of the right side to find the radius

[tex] \sqrt{4} = 2[/tex]

The cumulative frequency of the 3rd bin in a frequency distribution table represents the number of data values that are less than the maximum value of the 3rd bin. The correct option is a.

A frequency distribution table, often known as a frequency table, is a table that displays the frequency or amount of occurrences of different values in a dataset. Frequencies may be written as total values or as percentages of the total (relative frequency).

Cumulative frequency is the total frequency of values less than or equal to a given value in a dataset. The cumulative frequency of the 3rd bin in a frequency distribution table represents the total number of data values that are less than or equal to the maximum value of the 3rd bin.

Because it is a cumulative frequency, it contains all the values that came before it as well as its own frequency. The frequency distribution table is used to compute cumulative frequency.

The calculation of cumulative frequency may be done using the data's ascending or descending order.

Thus, the correct option is a.

To know more about frequency distribution table, refer to the link below:

https://brainly.com/question/17114842#

#SPJ11

1. to find angle x:

angles on a straight line add to 180º : 180-92º = 88º

to find angle y:

exterior angle equals opposite interior angles: 88+22=110º

2. to find angle x:

angles on a straight line add to 180º : 180-118 = 62º

to find angle y:

exterior angle equals opposite interior angles: 62+52 = 114º

sorry if i got any of the angles wrong, the picture was a bit blurry and I couldn't tell that well, let me know if i got it wrong and i'll fix it

Answer:

A'=(4,-8)

B'=(4,12)

C'=(-12, -12)

Step-by-step explanation:

Ad 3 to the location you are heading remember first is x then y so (x, y)

X is always left and right

Y is always up or down

Answer:

I DO NOT KNOW

Step-by-step explanation:

I am here for the answers

I am hungry

Pizza

Step-by-step explanation:

the answer is x=-4 ,y=-5

Answer:

Step-by-step explanation:

Unit rate = 26.2 ÷ 4 = 6.55

Answer:

Step-by-step explanation:

4(2x+10)=0

8x+40=0

-40       -40

8x=-40

x=-5

Answer:

-5

Step-by-step explanation:

First you have to distribute 4 to 2x and 10, giving us 8x + 40 = 0. Then subtract 40 from both sides, giving us 8x = -40. Now divide -40 by 8, which gives us -5.

Answer:

65

Step-by-step explanation:

all triangles angles equal 180°

180-72-43=65

Using Romberg integration, f(1) = 4.01.

Based on the given information, we can deduce the order of approximation for [tex]R_{33}[/tex] in Romberg integration as h10, h8, h4, h6. Additionally, we are given the values [tex]R_{21} = 7[/tex] and [tex]R_{22} = 7.21[/tex].

Romberg integration typically follows the pattern R(k, m), where k represents the number of iterations and m denotes the number of function evaluations per iteration.

From [tex]R_{21} = 7[/tex], we can determine that the approximation achieved after two iterations is 7.

From [tex]R_{22} = 7.21[/tex], we can conclude that the approximation achieved after two iterations is 7.21.

Since [tex]R_{21}[/tex] and [tex]R_{22}[/tex] represent the same number of iterations (k = 2), we can directly compare the results of these two approximations.

Therefore, the final answer is: f(1) = 4.01.

To know more about Romberg integration, refer here:

brainly.com/question/32622797

#SPJ4

Answer:

51.5 ft^2

Step-by-step explanation:

Given below are the step-by-step solutions to the provided questions:

1. Determine whether 23, 340, 1 is divisible by 341, 341, 11, 77. To prove 23, 340, 1 is divisible by 341, 341, 11, 77:341 is not a prime number since it is equal to 11 * 31, and it is the LCM of 11 and 31.So, 341 is a composite number. To check the divisibility of 23, 340, 1 by 341, we need to find the remainder of 23, 340, 1 when it is divided by 341.Since 341 = 11 * 31, the remainder of 23, 340, 1 when divided by 341 will be the same as the remainder when 23, 340, 1 is divided by 11 and 31, respectively.Remainder of 23, 340, 1 when divided by 11:340 + 23 + 1 = 364364 = 11 × 33Therefore, the remainder of 23, 340, 1 when divided by 11 is 0.Remainder of 23, 340, 1 when divided by 31:10^3 ≡ −1 (mod 31)340 ≡ 12 (mod 31)23 ≡ −8 (mod 31)−8 − 12 − 1 = −21 = −1 × 31Therefore, the remainder of 23, 340, 1 when divided by 31 is 10.Therefore, the remainder of 23, 340, 1 when divided by 341 is 0.Since the remainder is 0, then 23, 340, 1 is divisible by 341, 341, 11, and 77. Hence, the given statement is true.

2. Show that (Zn + nXn) is a commutative ring with unity assuming it is a commutative additive n' group.To prove that (Zn + nXn) is a commutative ring with unity assuming it is a commutative additive n' group:Firstly, we need to prove that Zn is a commutative ring with unity given that it is a commutative additive n' group.Commutativity of addition:a, b ∈ Zna + b = b + aAssociativity of addition:a, b, c ∈ Zna + (b + c) = (a + b) + cExistence of additive identity:n ∈ Zna + n = n + a = aAdditive inverse:For every a ∈ Zn there exists an element -a in Zn such that a + (-a) = (-a) + a = nExistence of multiplication:For a ∈ Zn and b ∈ Zn, their product ab is defined as ab ∈ Zn Multiplication is distributive over addition:For a, b, c ∈ Zna(b + c) = ab + ac and(a + b)c = ac + bcThus, we have proven that Zn is a commutative ring with unity given that it is a commutative additive n' group.Now we need to prove that (Zn + nXn) is a commutative ring with unity given that it is a commutative additive n' group.Zn is a commutative ring with unity and Xn is a commutative additive group. Hence, we have the following:Commutativity of addition:a, b ∈ (Zn + nXn)a + b = b + aAssociativity of addition:a, b, c ∈ (Zn + nXn)a + (b + c) = (a + b) + cExistence of additive identity:n ∈ (Zn + nXn)a + n = n + a = aAdditive inverse:For every a ∈ (Zn + nXn) there exists an element -a in (Zn + nXn) such that a + (-a) = (-a) + a = nExistence of multiplication:For a ∈ (Zn + nXn) and b ∈ (Zn + nXn), their product ab is defined as ab ∈ (Zn + nXn)Multiplication is distributive over addition:For a, b, c ∈ (Zn + nXn)a(b + c) = ab + ac and(a + b)c = ac + bcThus, (Zn + nXn) is a commutative ring with unity assuming it is a commutative additive n' group.

Know more about commutative ring here:

https://brainly.com/question/32556076

#SPJ11

Answer:

286 Degrees

Step-by-step explanation:

A circle is 360 degrees, and from the question, we know that it is asking for ACB, so it would be 360 - 74, which is 286 degrees

Brainliest Maybe?

Let T: R² → R³ be a linear mapping, satisfying T(1, 2) = (1, 0, 1) and T (2,5) = (0, 1, 1). T(0, 1) is option (b) (-2, 1, -1)

Let T: R² → R³ be a linear mapping, and T(1, 2) = (1, 0, 1) and T (2,5) = (0, 1, 1).

To calculate T(0, 1), we must first determine the matrix A of T with respect to the standard basis of R² and R³.

Using the values of T(1, 2) and T(2, 5), we can create an augmented matrix with the standard basis vectors of R²:1 2 1 0 01 2 0 1 1

Using Gaussian elimination to solve this augmented matrix, we get:A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \\ -1 & 1 \end{bmatrix}

Now, we can apply T to (0, 1) as follows: T(0, 1) = A(0, 1) = \begin{bmatrix} 1 & 2 \\ 0 & 1 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 0 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}

Therefore, the answer is option (b) (-2, 1, -1).

Know more about linear mapping here,

https://brainly.com/question/32560791

#SPJ11

Answer:

12z-32

Step-by-step explanation:

-4z-12-20+16z

The mean housing cost for the given cities is $20.42.

The standard deviation of housing costs for the given cities is 1.91.

The mean is calculated by summing up all the values in the dataset and dividing the sum by the total number of values. In this case, we have the following data for housing costs in different cities:

Comparative City Housing Cost

NY $16.00

Coors $20.00

Los Angeles $22.05

Santa Barbara $18.70

Oceanside $22.90

Porterville $20.50

New York $21.40

To calculate the mean, we add up all the values:

Sum = $16.00 + $20.00 + $22.05 + $18.70 + $22.90 + $20.50 + $21.40 = $141.55

Next, we divide the sum by the total number of values, which is 7 in this case:

Mean = $141.55 / 7 = $20.42

Therefore, the mean housing cost for the given cities is $20.42.

The standard deviation is a measure of the spread or variability in the dataset. It tells us how much the individual values deviate from the mean.

The formula for calculating the standard deviation is:

σ = sqrt[(Σ(x - μ)^2) / N]

Where:

σ is the standard deviation

Σ represents the sum of

x represents each individual value

μ is the mean

N is the total number of values

Using the given data, we substitute the values into the formula:

σ = sqrt[((16 - 20.42)^2 + (20 - 20.42)^2 + (22.05 - 20.42)^2 + (18.70 - 20.42)^2 + (22.90 - 20.42)^2 + (20.50 - 20.42)^2 + (21.40 - 20.42)^2) / 7]

Simplifying the expression within the square root:

σ = sqrt[(5.2364 + 0.0016 + 0.0264 + 2.7164 + 0.0524 + 0.0064 + 0.0064) / 7]

σ = sqrt[8.0456 / 7]

σ = sqrt(1.1494)

σ ≈ 1.07

Therefore, the standard deviation of housing costs for the given cities is approximately 1.07.

These calculations provide a measure of the average and spread of the housing costs across the different cities.

To learn more about standard deviation visit : https://brainly.com/question/475676

#SPJ11

1. The participants would be a member of all four groups. In a within-subjects ANOVA, participants are exposed to all levels of the factor, so they experience each group.

2. The within-groups sums of squares is only found in a one-way within-subjects ANOVA. This represents the variability within each group or condition.

3. In this case, you would typically conduct a post-hoc analysis to determine which specific groups or conditions differ significantly from each other. Common post-hoc tests for within-subjects ANOVA include the Bonferroni or Tukey tests. These tests help identify pairwise differences between the groups.

4. True. Eta-squared, partial eta-squared, and R-squared are all measures of effect size that indicate the proportion of variance explained within a study. They provide information about the strength and magnitude of the effect being studied.

5. When conducting a two-way between-subjects ANOVA, you would typically run two F-tests: one for each main effect and one for the interaction effect. The main effects assess the effects of each independent variable separately, while the interaction effect examines whether the combined influence of the variables is significant.

6. The between-groups sums of squares is only found in a two-way between-subjects ANOVA. It represents the variability between the different groups or levels of the independent variables.

To learn more about independent variables

https://brainly.com/question/3764906

#SPJ11

For the CDF of a continuous real function, the answers are as follows:

(i) P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive

(ii) P(exist i < j with Xi = Xj) = 0 which is a contradiction.

(i) Suppose the CDF F is a continuous real function and note that this does not imply F is differentiable. Assume for simplicity that F(0) = 0 and F(1) = 1 (this does not change the major statements below but makes the proof a bit cleaner). If X, Y are independent F-distributed RVs, then for any n in N, we have; P(X ≤ Y) = P(X ≤ Y, Y ≤ X) = P(X ≤ Y|Y ≤ X) P(Y ≤ X) = P(Y ≤ X|X ≤ Y) P(X ≤ Y) = P(X ≤ Y|X ≤ Y) P(X ≤ Y) = P(X = Y). Hence, P(X = Y) = P(X ≤ Y)P(Y ≤ X) = P(X ≤ Y)P(X ≤ Y) = P²(X ≤ Y).Since F is continuous, P(X ≤ Y) = P(X < Y) = P(X ≤ Y) - P(X = Y). Therefore, P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive.

(ii) Conclude that P(X = Y) = 0 (remember that you cannot assume F has a density). As for the sample case, we show that P(exist i < j with Xi = Xj) = 0. Suppose, for the purpose of contradiction, that we have X1, . . . , Xn in F such that P(exist i < j with Xi = Xj) > 0. Then, there must be some distinct i < j such that Xi = Xj. Without loss of generality, we may assume i = 1 and j = 2. Then, the probability that this event occurs is; P(X1 = X2, X3 ≠ X1, . . . , Xn ≠ X1) = P(X2 ≤ X1, X3 ≠ X1, . . . , Xn ≠ X1) + P(X1 < X2, X3 ≠ X1, . . . , Xn ≠ X1)Since Xi are independent F-distributed RVs and P(X = Y) = 0, it follows that the probability of the first term in the sum above is zero. Therefore, P(exist i < j with Xi = Xj) = 0 which is a contradiction.

To know more about CDF, visit the link : https://brainly.com/question/30402457

#SPJ11

Comparing the two z-scores, we can conclude that the student performed better relative to the other testers on the first exam because the z-score of 1 is closer to the mean (0) than the z-score of 2.5 on the second exam.

Given that the national mean and standard deviation were 475 and 100, respectively for the first test, and 40 and:8, respectively for the second test and the student scored 575 on the first test and 60 on the second test, we are to use z-scores to determine which exam the student performed better relative to the other testers.

A z-score is a numerical measure of a value's relationship to the mean of a group of values, measured in terms of the number of standard deviations from the mean. It can be calculated using the formula; z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For the first exam;z-score = (x - μ) / σ = (575 - 475) / 100 = 1For the second exam;z-score = (x - μ) / σ = (60 - 40) / 8 = 2.5

To Know more about z-scores visit:

https://brainly.com/question/31871890

#SPJ11

Given that a student took two national aptitude tests. The national mean and standard deviation were 475 and 100, respectively for the first test, and 40 and:8, respectively for me second test the student scored 575 on the test and 60 on the second test. The student performed better relative to other test-takers on the second test as the z-score of the second test is higher than the z-score of the first test.

In order to determine which test the student performed better on relative to other test-takers, we need to calculate the z-score for each test.

For the first test, the national mean is 475 and the standard deviation is 100.

The student's score is 575.

The z-score is calculated as:

z = (x - μ) / σ

z = (575 - 475) / 100

z = 1

For the second test, the national mean is 40 and the standard deviation is 8.

The student's score is 60.

The z-score is calculated as:

z = (x - μ) / σ

z = (60 - 40) / 8

z = 2.5

Since the z-score is a measure of how many standard deviations an observation is above or below the mean, a higher z-score indicates that the student performed relatively better compared to other test-takers.

Therefore, the student performed better relative to other test-takers on the second test as the z-score of the second test is higher than the z-score of the first test.

To know more about z-score, visit:

https://brainly.com/question/31871890

#SPJ11

The Economic Stimulus Act of 2008 focused on providing tax relief, while the American Recovery and Reinvestment Act of 2009 focused on a combination of tax cuts, government spending, and investments for economic growth.

the Economic Stimulus Act of 2008 was enacted in response to the economic downturn that occurred during the Great Recession. Its main objective was to provide immediate relief to the economy by implementing tax incentives and rebates for individuals and businesses. The act aimed to encourage consumer spending and investment by putting more money into people's pockets and reducing the tax burden on businesses.

On the other hand, the American Recovery and Reinvestment Act of 2009 was a broader and more comprehensive economic stimulus package. It included a mix of tax cuts, grants, loans, and direct government spending on infrastructure projects, renewable energy, healthcare, education, and other areas. The goal was to not only provide short-term economic relief but also to make long-term investments that would promote sustainable economic growth and job creation.

Overall, while both acts were aimed at stimulating the economy, the focus of the Economic Stimulus Act of 2008 was primarily on tax relief, while the American Recovery and Reinvestment Act of 2009 encompassed a wider range of measures to boost the economy and address various sectors affected by the recession.

Learn more about recession here:

https://brainly.com/question/31926163

#SPJ11

Thus, the adult male foot length of 31.6 cm is significantly high since it falls outside the range of values considered normal for adult male foot length.

Range rule of thumb:The range rule of thumb is a formula used to calculate the range of the data that's spread around the mean. The range is the difference between the maximum and minimum data values. The range rule of thumb estimates the expected range for a normally distributed dataset by taking the difference between the maximum and minimum values, then multiplying that difference by 4. This estimate is usually only useful for datasets with more than 15 data points. Thus, using the range rule of thumb, the range of a normally distributed data set is approximately four times the standard deviation. Thus, the range of the adult male foot length is as follows:Range = 4 × Standard deviation= 4 × 1.41 cm= 5.64 cmWe can then identify the limits separating values that are significantly low or high as follows:Significantly low values are cm or lower: 28.48 - 2 x 1.41 = 25.66 cmSignificantly high values are cm or higher: 28.48 + 2 x 1.41 = 31.3 cmThus, the adult male foot length of 31.6 cm is significantly high since it falls outside the range of values considered normal for adult male foot length.

To know more about range rule of thumb,

https://brainly.com/question/11069423

#SPJ11

Answer:

64y^2

Step-by-step explanation:

its a           .......................................Step-by-step explanation:

Answer:

Air

Step-by-step explanation:

You can't really measure air

Answer:

Air

Step-by-step explanation:

You cannot measure air because it is invisible.

Answer:

first circle is radius= 12.5 inches and diameter= 25 inches

second circle is radius=2 feet and diameter=4 feet

Step-by-step explanation:

radius is the point halfway down the circle. diameter is full length straight across the whole circle.

further analysis;

in the first circle it gives you the diameter which is 25 inches. in order to get the radius you cut 25 in half which is 12.5 inches.

in the second circle it gives you the radius which is 2 feet. in order to get the diameter you need to double 2 feet which is a total of 4 feet.

Answer:

Answer

Step-by-step explanation:

for 4. I think sports?

for 5. I think sports also.

Not sure though.. sorry if it's wrong.

Answer:

Step-by-step explanation:

Answer:

14

Step-by-step explanation: