hey guys i rlly need help i don't understand rational numbers

The set A, defined as A = {∅} ∪ {⋃_{i=1}^n Ai : n ∈ ℕ, {Ai} ⊆ C, disjoint}, is proven to be an algebra on a set X.

To prove that A is an algebra, we need to show that it satisfies three conditions: (1) X ∈ A, (2) for any set A ∈ A, its complement X\A also belongs to A, and (3) for any sets A, B ∈ A, their union A ∪ B also belongs to A.

First, the empty set ∅ is included in A by definition. Second, let A be any set in A, represented as A = ⋃_{i=1}^n Ai, where {Ai} is a collection of disjoint sets from C. Then, the complement of A is X\A, which can be represented as X\A = ⋃_{i=1}^n (X\Ai). Since each Ai is in C, their complements X\Ai are also in C, implying X\A is a disjoint union of sets from C and therefore belongs to A.

Lastly, let A and B be two sets in A, represented as A = ⋃_{i=1}^n Ai and B = ⋃_{j=1}^m Bj. The union of A and B is A ∪ B = ⋃_{i=1}^n Ai ∪ ⋃_{j=1}^m Bj. Since Ai and Bj are disjoint sets from C, their union Ai ∪ Bj is also in C. Thus, A ∪ B is a disjoint union of sets from C and belongs to A.

By satisfying all three conditions, A is proven to be an algebra on X.

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Answer:  So to cover the patio it would take 255 whole tiles.  254.469 if you want to be exact.

Step-by-step explanation:

When finding flooring needed we are finding for area.  We know the formula for finding the area of a circle is A=[tex]\pi r^{2}[/tex] so we plug in our known variables...

we know r because radius is half of diameter and diameter was given in problem.  So half of 18 is 9.

r=9

A=[tex]\pi 9^{2}[/tex]

A=[tex]\pi[/tex]81

A=254.469

Answer:

12.054 < 12.54

Step-by-step explanation:

12.054 is less than 12.54 because it has a zero in the tenths place, and 12.54 has a five in the tenths place! Always check the first spot after the decimal first. Best of luck<3

Answer:

12.054 < 12.54

Step-by-step explanation:

Answer:

x ≈ 5.1

Step-by-step explanation:

Using the sine ratio in the right triangle

sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] ( multiply both sides by 12 )

12 × sin25° = x , that is

x≈ 5.1 ( to the nearest tenth )

Ответ:​

Объяснение:

Probability of an event happening = Number of ways it can happen / Total number of outcomes

Number of ways it can happen: 1 (there is only 1 group with french team in it)

Total number of outcomes: 4 (there are 4 groups)

So the probability = 1/4

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Вероятность возникновения события = Количество способов которыми это может произойти / Общее количество исходов

Количество способов которыми это может произойти: 1 (есть только 1 группа с французской командой в ней)

Общее количество исходов: 4 (есть 4 группы)

Таким образом вероятность = 1/4

Я надеюсь, что это было полезно ^^

Answer:

32 degrees.

Step-by-step explanation:

Answer:

11.330

Step-by-step explanation:

Answer:

x=11.3

Step-by-step explanation:

Hello There!

We can use trigonometry to solve for x

Remember these are the trigonometric ratios

SOHCAHTOA

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

We can use the angle that has a measure of 31 degrees

We are given the hypotenuse and we need to find its opposite side

hypotenuse and opposite corresponds with sine so we will use sine to create an equation

(remember sin = opposite over hypotenuse)

[tex]sin(31)=\frac{x}{22}[/tex]

now that we have created an equation we solve for x

step 1 multiply each side by 22

[tex]sin(31)*22=22sin(31)\\\frac{x}{22} *22=x\\x=22sin(31)\\sin(31)=0.5150380749\\0.5150380749*22=11.33083765\\x =11.33083765[/tex]

finally we round to the nearest tenth and get that x = 11.3

This statement is false because the sample variance is always greater than or equal to the sample standard deviation.

Variance and standard deviation are both measures of variability or dispersion within a dataset. The sample variance is defined as the average of the squared differences between each data point and the mean of the dataset. On the other hand, the sample standard deviation is the square root of the variance.

Since variance involves squaring the differences, it accounts for the spread of the dataset more effectively than the standard deviation. As a result, the sample variance tends to be larger than or equal to the sample standard deviation.

Mathematically, this relationship can be expressed as follows:

Sample Variance = [tex]\[\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}\][/tex]

Sample Standard Deviation = [tex]\[\sqrt{\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}}\][/tex]

Where x represents each data point, [tex]\(\overline{x}\)[/tex] represents the mean, and n is the sample size.

Therefore, it is not possible for the sample variance to be smaller than the sample standard deviation.

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The probabilities using Binomial Expansion is

A) P(X = 4) = C(160, 4)  p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾

B) P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾

C) P(X = 2) = C(160, 2)  p² (1 - p)⁽¹⁶⁰⁻²⁾

D) P(X = 1) = C(160, 1)  p¹ (1 - p)⁽¹⁶⁰⁻¹⁾

E) P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾

To determine the theoretical probability of the five possible combinations between females and males in the 160 families, we can use the binomial expansion formula:

P(X = k) = C(n, k) [tex]p^k(1-p)^{n-k}[/tex]

Where:

C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!).

p is the probability of success

(1 - p) is the probability of failure.

Let's calculate the probabilities for each combination:

A) 4 males, 0 females:

P(X = 4) = C(160, 4)  p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾

B) 3 males, 1 female:

P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾

C) 2 males, 2 females:

P(X = 2) = C(160, 2)  p² (1 - p)⁽¹⁶⁰⁻²⁾

D) 1 male, 3 females:

P(X = 1) = C(160, 1)  p¹ (1 - p)⁽¹⁶⁰⁻¹⁾

E) 0 males, 4 females:

P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾

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Answer:

16.6667% increase

Step-by-step explanation:

Percentage Increase=Final Value−Starting Value|Starting Value|×100  

Answer:

17%

Step-by-step explanation:

The increase is calculated as the difference between yesterday's price and today's price, hence $2.45 - $2.10 = $0.35

As a fraction of yesterday's price, the fraction is [tex]\frac{0.35}{2.10}[/tex], which reduces to [tex]\frac{1}{6}[/tex].  Expressed as a decimal fraction, this is 0.16...  Shift the decimal point two places to the right to get the percentage increase of 16.6...%.

Since it said to round to the nearest tenth, rounding it makes the answer of 17.0% or 17% because since 6 is bigger than 10, we needed to round up and thus the answer is 17%.

Given:

The shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.

Radius of the circle = 3 cm

To find:

The area of the sector in terms of π.

Solution:

The area of a circle is

[tex]A=\pi r^2[/tex]

Substituting [tex]r=3[/tex], we get

[tex]A=\pi (3)^2[/tex]

[tex]A=9\pi[/tex]

It is given that the shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.

The area of shaded sector [tex]=\dfrac{1}{3}A[/tex]

                                             [tex]=\dfrac{1}{3}(9\pi)[/tex]

                                             [tex]=3\pi[/tex]

Therefore, the area of shaded sector is 3π sq. cm.

if x+y=19

and

x-y=1

now solve it by adding the equations together

x+x , y+[-y] and 19+1

2x=20

x=10, y=9

Answer:

answer is 16

good day mate

Answer:

1/3

Step-by-step explanation:

15/(15+18+12)=15/45=1/3

Answer:

5 steps

Step-by-step explanation:

Turn 5/4s into 10/8s and it becomes really easy

The number of steps Erin could paint if he has 5/4 parts of paint, and she needs 2/8 of paint for each stair step, is 5.

It is a basic operation of mathematics in which you divide a number into smaller parts.

Given:

Erin has 5/4 quarts of paint,

2/8 of paint for each stair-step,

Calculate the number of steps painted as shown below,

Number of steps = total paint / paint required for each step

Number of steps = 5/4 / 2/8

Number of steps =

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Answer:

ZX

Step-by-step explanation:

Answer:

[tex]x > -\frac{24}{19}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{3}x + 4 < \frac{9}{2}x + 8[/tex]

Required

Solve for x

Collect like terms

[tex]\frac{4}{3}x - \frac{9}{2}x < 8-4[/tex]

[tex]\frac{4}{3}x - \frac{9}{2}x < 4[/tex]

Take LCM

[tex]\frac{8x - 27x}{6} < 4[/tex]

[tex]\frac{-19x}{6} < 4[/tex]

Multiply by 6

[tex]6 * \frac{-19x}{6} < 4 * 6[/tex]

[tex]-19x < 24[/tex]

Divide by -19

[tex]x > -\frac{24}{19}[/tex]

Answer:

c maybe

Step-by-step explanation:

4n(6n+2m)

24n²+8mn

Answer: C, 24n²+8mn

Step-by-step explanation:

So because 4n is on the outside of the bracket, you have to times everything on the inside of the bracket by 4n.

So, you do:

4n×6n=24n² (4×6=24 and n×n=n²)

4n×2m=8mn (4×2=8 and n×m=mn)

Then you add 24n² to 8mn like this:

24n²+8mn

Hope this helps :)

The researcher can conclude that there is a statistically significant difference in the mean number of complaints between people living on the West Coast and those living in the Northeast.

To determine if there are geographical differences in how much people complain between the Northeast and the West Coast, we can conduct a hypothesis test.

Null hypothesis (H0): There is no difference in the mean number of complaints between the Northeast and the West Coast.

Alternative hypothesis (H1): There is a difference in the mean number of complaints between the Northeast and the West Coast.

Given the sample statistics, we can perform a two-sample independent t-test to compare the means of the two groups.

Let's calculate the test statistic and compare it to the critical value at a significance level of α = 0.05.

The West Coast sample has a mean (x1) of 9.5 and a standard deviation (s1) of 2.8, with a sample size (n1) of 20.

The Northeast sample has a mean (x2) of 15.5 and a standard deviation (s2) of 3.8, with a sample size (n2) of 20.

Using the formula for the pooled standard deviation (sp), we can calculate the test statistic (t):

sp = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

t = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2))

Calculating the test statistic:

sp = sqrt(((19 * 2.8^2) + (19 * 3.8^2)) / (20 + 20 - 2)) ≈ 3.273

t = (9.5 - 15.5) / (3.273 * sqrt(1/20 + 1/20)) ≈ -4.63

Using a t-table or a statistical calculator, we can find the critical value for a two-tailed t-test with α = 0.05 and degrees of freedom (df) = n1 + n2 - 2 = 38. The critical value is approximately ±2.024.

Since the absolute value of the test statistic (4.63) is greater than the critical value (2.024), we reject the null hypothesis.

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1. Next three numbers: 2,887, 3,308, 3,729. Tenth number: 5,905.

2. Next three numbers: 9,596, 9,495, 9,394. Eleventh number: 9,293.

3. Next three numbers: 4.434, 4.154, 3.874. Twelfth number: 3.594.

Let's examine each number pattern one by one:

1. Pattern: 1,203, 1,624, 2,045, 2,466 ...

  Rule: Each number in the pattern is obtained by adding 421 to the previous number.

  Next three numbers: 2,887, 3,308, 3,729

  Tenth number: 5,905

2. Pattern: 10,000, 9,899, 9,798, 9,697 ...

  Rule: Each number in the pattern is obtained by subtracting 101 from the previous number.

  Next three numbers: 9,596, 9,495, 9,394

  Eleventh number: 9,293

3. Pattern: 5,554, 5,274, 4,994, 4.714 ...

  Rule: Each number in the pattern is obtained by subtracting 280 from the previous number.

  Next three numbers: 4.434, 4.154, 3.874

  Twelfth number: 3.594

Therefore, based on the given patterns, the next three numbers and the specified numbers in the sequences would be as follows:

1. Pattern: 2,887, 3,308, 3,729 ... 5,905 (10th number)

2. Pattern: 9,596, 9,495, 9,394 ... 9,293 (11th number)

3. Pattern: 4.434, 4.154, 3.874 ... 3.594 (12th number)

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Answer:

I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.

Step-by-step explanation:

There could be a multitude of rules, but let's try to find a simple one.

I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:

a - flat fee for a vehicle

b - fee per person

then a car with x people in it would be charged

a + bx

Let's see if the fees fit this assumption:

for x = 2

a + b*2 = $14

for x = 4

a + b*4 = $20

for x = 8

a + b*8 = $32

If so, we can subtract the second equation from the first and get

a + b*4 - a - b*2 = $20 - $14

b*2 = $6

b = 3$

a + b*2 = $14

a + $3*2 = a + $6 = $14

a = $8

so the first 2 equations gave us a = $8 and b = $3.

Let's see if these values fit the 3rd equation

a + b*8 = $32

$8 + $3*8 = $32

$8 + $24 = $32

$32 = $32

It fits!

That tells us that the rule is indeed very likely.

Answer:

Answer Below:

Step-by-step explanation:

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

(a) If A is an invertible matrix, then A is an invertible matrix. - True

Explanation:

If A is invertible, then A has an inverse matrix A^(-1).

(b) If A is an invertible matrix, then A+ A is an invertible matrix. - False

Explanation:

A+ A = 2A is invertible if and only if A is invertible.

Therefore, this statement is false.

(c)

If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. - False

Explanation:

Even if AB is invertible, it is not always true that B is invertible.

For instance, if A = [1 0], B = [0 1],

then AB = [0 1] which is invertible, but B is not invertible.

(d)

If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix. - False

Explanation:

If A = [2 0], B = [0 1], then both A and B are invertible, but A - B = [2 -1] is not invertible.

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Answer:

9.07571212

Step-by-step explanation:

To solve this we first need to find the area of the circle, r squared times pi

4 x 4 x pi = 50.2654825

Now we multiply this by 65/360, 50.2654825 x 65/360 = 9.07571212

The shaded sector covers 9.07571212 square inches.

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If kite is on a string that is 18 feet long, then the height of kite is (b) 9 feet.

In order to find the height of the kite, we use trigonometry. We know that the length of the string is 18 feet and the angle with the ground is 30 degrees, we use the Sine function to determine the height of the kite.

The formula to find the height is:

Height = (Length of string) × Sin(Angle),

Substituting the values,

We get,

Height = (18 feet) × Sin(30 degrees),

Using the value of Sine of 30 degrees as (0.5), we can calculate the height as :

Height = (18 feet) × (0.5),

= 9 feet

Therefore, the correct option is (b) 9 feet.

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