"Let C be a semialgebra on a set X. Let A = {0} U {U}=1 A; : n E N, {A1, ... , An} C C, disjoint}. = : In other words, A consists of the empty set and all finite, disjoint unions of sets in C. Prove that A is an algebra on X.
"
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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2. A circular patio has a diameter of 18 feet. How
many square feet of tile will it take to cover the
patio?
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
What is the value of x?
Answer. it is 5 or letter i
Answer:
The value of x is 5
Step-by-step explanation:
Using the linear pair theorem, both angles are supplementary and add up to 180 degrees. 180 minus 140 is 40. and 8 times 5 = 40. So x = 5.
Find the area of the shaded sector below.
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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Erin has 5/4 quarts of paint and she needs 2/8 of paint for each stair-step and how much paint can Erin exactly paint
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.
What is division?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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The price of a cup of coffee was $2.10 yesterday. Today, the price rose to $2.45. Find the percentage increase. Round your answer to the nearest tenth of a
percent.
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%.
The speed of light is 3 × 108 meters per second. It take 1.82 × 102 seconds for light to reach Mars. What is the distance, in meters, between the sun and Mars? A 4.82 x 1016 B 4.82 x 1010 C 5.46 x 1016 D 5.46 x 1010
Answer:
D 5.46 x 10^10
Step-by-step explanation:
Recall that speed is the rate of change of distance with time and may be expressed mathematically as
speed = Distance/time
Distance = speed * time
Hence given that the speed of light
= 3 × 10^8 meters per second
Time taken for light to travel between the given distance
= 1.82 × 10^2 seconds
substituting the given values
Distance = 3 × 10^8 * 1.82 × 10^2
= 5.46 * 10^(8+2)
= 5.46 * 10^10 meters
The radius of a circle is 4 feet. What is the area?
r=4ft
Give the exact answer in simplest form.
Experimental Probability is ___________ .
a . our prediction
b. data from our experiment
Answer:
its B
Step-by-step explanation:
Answer:
b. data from our experiment
Step-by-step explanation:
Solve for .
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
43 +4 < 92 +8
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]
Find the value of x. Round to the
nearest tenth.
12
Х
2597
X = ?
Enter
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 )
Solve the initial value problem (2 x-6 xy + xy) dx + (1 - 3x2 + (2 + x?) y) dy = 0, y(1) = -4 and then provide the numerical value of lim y(x) rounded-off to FIVE significant figures. A student rounded-off the final answer to FIVE significant figures and found that the result was as follows (10 points): X+00 (your numerical answer for the limit must be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The implicit solution of the initial value problem is described by the equation as follows (mark a correct variant) (6 points): 3 xy - (x + 1) y2 + 9 x2 = 0 x² + x y + (2x + 10) y2 – 10 = 0; x2 - xy + (2x - 10) y2 + 12 = 0 2x2 – 3xy - (1 + x?)y2 + 19 = 0 x2 - xy + (2x - 10) y2 = 0 x2 + y - 3x"y +(1+) y2 – 33 = 0 2) The explicit solution for the value of y as the function of x is described by the explicit formula as follows (mark a correct variant) (4 points) y -1+3x_v719+8x2 + ** 2+x? y у -*-400-80x+41x2-3x3 40-5+x) -x-41x28x3 4-5+x) x+41x28x? 4-5+x) y = *-480-96x+41x2-3x3 y = 4-5+x) -1+3x2 + 7/1948x2 + x y = 2+x2 -3x - 76+93x2 +8x* у 2(1+x2) 2) The explicit solution for the value of y as the function of x is described by the explicit formula as follows (mark a correct variant) (4 points): y = -1+3x2-77/19+8x2+x 2+x2 y = y = 400-80x+41x2 - 8x? 4-5+x) -x-41x28x3 4(-5+x) x+41x2-8x3 4-5+x) Tut y = X 480-96x+41x2 - 8x3 y = 4-5+x) -1+3x² +17/19+8x2+x+ O y = 2+x2 -3x - 76+93x2 +8x4 y = 2(1+x²) 3x - 14+49x2 +36 x+ y = 2(1+x2)
The implicit solution to the initial value problem (2x − 6xy + xy)dx + (1 − 3x^2 + (2 + x^2)y)dy = 0 with y(1) = −4 is given by the equation:3xy − (x + 1)y^2 + 9x^2 = 0. The explicit solution for y as a function of x is given by the formula: y = (-1 + 3x^2 - 7/19 + 8x^2 + x)/(2 + x^2)The numerical value of lim y(x) rounded off to five significant figures is -1.3152.
Intermediate results obtained during the process include: implicit solution of initial value problem and explicit solution for y as a function of x. The implicit solution of the initial value problem is described by the equation:3 xy - (x + 1) y2 + 9 x2 = 0. The explicit solution for y as a function of x is given by the formula: y = (-1 + 3x^2 - 7/19 + 8x^2 + x)/(2 + x^2).
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How to multiply fractions
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.
Please help me find the value of x for this trig question
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
Plz help is it the same?
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:
Examine the number pattern below. 1,203, 1,624, 2,045, 2,466 ... What rule does this pattern follow? Write the next three numbers in the pattern. If the pattem continues, what will the 10 number in the sequence be? Examine the number pattern below. 10,000, 9,899, 9,798, 9,697 ... What rule does this pattern folow? Write the next three numbers in the pattern if the patter continues, what will the 11" number in the sequence be? 3. Examine the number pattern below. 5,554, 5,274, 4,994, 4.714 ... What rule does this pattern follow? Write the next three numbers in the pattern. It the patter continues, what will the 12 number in the sequence be?
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.
How to continue these number patterns?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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In an independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each treatment. If all three treatments have the same total. T1 T2 T3, what is SSbetween?
a. 0
b. 100
c. 10(3)
d. This cannot be determined from the information given.
The value obtained for SSbetween is 20. The correct answer is (b) 20.
To calculate the sum of squares between (SSbetween) for an analysis of variance (ANOVA), we need to determine the variation between the sample means of the different treatment conditions. The formula for SSbetween is as follows:
SSbetween = n * Σ(M - m)²
where n is the sample size for each treatment condition, M is the individual treatment condition mean, and m is the overall mean.
In this case, the sample size for each treatment condition is n = 10, and the treatment condition means are M1 = 1, M2 = 2, and M3 = 3.
To calculate SSbetween, we first find the overall mean (m) by taking the average of the treatment condition means:
m = (M1 + M2 + M3) / 3
m = (1 + 2 + 3) / 3
m = 6 / 3
m = 2
Now, we can calculate SSbetween:
SSbetween = n * Σ(M - m)²
SSbetween = 10 * [(1 - 2)² + (2 - 2)² + (3 - 2)²]
SSbetween = 10 * [(-1)² + (0)² + (1)²]
SSbetween = 10 * (1 + 0 + 1)
SSbetween = 10 * 2
SSbetween = 20
Therefore, the value obtained for SSbetween is 20. The correct answer is (b) 20.
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Incomplete question:
An independent-measures research study compares three treatment conditions using a sample of n = 10 in each treatment. For this study, the three sample means are M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?
a.30
b.20
c.10
d. 2
HELP ASAP PLEASE ILL MARK BRAINLIEST AND RATE 5 STARS PLEASEEE
A survey about the student government program at a school finds the following results:
190 students like the program
135 students think the program is unnecessary
220 students plan on running for student government next year.
If a circle graph were made from this data, what would the measure of the central angle be for the group that likes the program? Round your answer to the nearest whole number. Make Sure To Show Your Steps
Answer: 126 degrees
there are 360 degrees in a circle.
sooooooooo
technically i've neevr lost a fight with a tiger
Answer:
oh thats cool
Step-by-step explanation:
A matched pairs experiment compares the taste of instant coffee with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study, 14 prefer the instant coffee and the other 26 prefer fresh-brewed. Take p to be the proportion of the population that prefers fresh-brewed coffee. You might find a table of critical values useful. You can use table A or the bottom row of table D, but table D is easier.
Find a 95% confidence interval for p. 95% CI:_________
The 95% confidence interval for p is (0.47, 0.83)
Total subjects = 40
People preferring fresh brewed = 26
Calculating the sample proportion -
Sample proportion = Number of subjects preferring fresh brewed coffee / Total number of subjects
= 26 / 40
= 0.65
It is required to establish crucial values depending on chosen confidence level in order to generate the confidence interval. The z-value associated with a 97.5% cumulative probability to obtain a 95% confidence range is to be found. This is because the remaining 5% by 2 is divided to determine middle 95% of the standard normal distribution. The z-value for a 97.5% cumulative probability is around 1.96 using Table D or any other approach.
Using the formula for confidence interval -
[tex]CI = p + z x \sqrt ((px (1 - p) / n)[/tex]
Substituting the values -
[tex]CI = 0.65 ± 1.96 \sqrt{x} ((0.65 * (1 - 0.65)) / 40)[/tex]
[tex]= 0.65 ± 1.96 x \sqrt(0.2275 / 40)[/tex]
= 0.65 ± 1.96 x 0.0921
= 0.65 ± 0.1802
Rounding to two decimal places, the 95% confidence interval will be 0.47, 0.83)
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-48+6
+(-3)(-4) (-2)
-7
Answer:
-73
Step-by-step explanation:
-48+6-24-7 = -73
2. kiran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite?
a. 9√3 feet
b. 9 feet
c. 18/√2 feet
d. 18/√3 feet
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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If A = {3, 7, 9, 13, 22}, B = {5, 7, 14, 23, 31}, and C = {8, 9, 15, 23, 25, 31, 33}, then what is (A∪B)∩C?
(A∪B)∩C = {9, 23, 31}.
To find the intersection of the sets (A∪B) and C, we first need to determine the union of sets A and B. The union of two sets consists of all the unique elements present in both sets.
A∪B = {3, 5, 7, 9, 13, 14, 22, 23, 31}
Next, we find the intersection of the obtained union (A∪B) and set C. The intersection of two sets contains the elements that are common to both sets.
(A∪B)∩C = {9, 23, 31}
Therefore, the intersection of the sets (A∪B) and C is {9, 23, 31}. These are the elements that are present in both (A∪B) and C.
In summary, (A∪B)∩C = {9, 23, 31}.
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pleas help thanks
5. Which term of the geometric sequence 1, 3,9, ... has a value of 19683? 14
The term of the geometric sequence 1, 3,9, ... which has a value of 19683 is :
To find which term of the geometric sequence has a value of 19683, we can use the formula for the nth term of a geometric sequence.
Here's the formula:
an = a₁ * r^(n - 1)
where an is the nth term of the sequence
a₁ is the first term of the sequence
r is the common ratio of the sequence
Given the sequence 1, 3, 9, ..., we can see that a₁ = 1 and r = 3.
To find the value of n that gives the term with a value of 19683, we can substitute these values into the formula and solve for n:
19683 = 1 * 3^(n - 1)
19683/1 = 3^(n - 1)
3^9 = 3^(n - 1)
Now we can equate the exponents:
9 = n - 1
n = 9 + 1
n = 10
Therefore, the 10th term of the geometric sequence 1, 3, 9, ... has a value of 19683. Thus, the answer is 10.
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Triangle Sums***GRADED 1 of 51 of 5 Items #1 Triangle RST is shown. What is the measure of ∠T? Record your answer and fill in the bubbles on the grid. Be sure to use correct place value.
Answer:
[tex]\angle T = 70[/tex]
Step-by-step explanation:
Given
[tex]\angle T= 2x[/tex]
[tex]\angle S= 75[/tex]
[tex]\angle R= x[/tex]
See attachment for triangle
Required
Calculate [tex]\angle T[/tex]
First, we add up the angles in the triangle;
[tex]\angle R + \angle S + \angle T = 180[/tex]
[tex]x + 75 + 2x = 180[/tex]
Collect like terms
[tex]x + 2x = 180 - 75[/tex]
[tex]3x = 105[/tex]
Solve for x
[tex]x = \frac{105}{3}[/tex]
[tex]x = 35[/tex]
Given that:
[tex]\angle T= 2x[/tex]
[tex]\angle T = 2 * 35[/tex]
[tex]\angle T = 70[/tex]
[tex] {2x}^{2} - 5x + 3[/tex]
which of the following segments is a diameter of 0?
Answer:
ZX
Step-by-step explanation:
If
y=∑n=0[infinity]cnxny=∑n=0[infinity]cnxn
is a solution of the differential equation
y′′+(3x−1)y′−1y=0,y″+(3x−1)y′−1y=0,
then its coefficients cncn are related by the equation
cn+2=cn+2= cn+1cn+1 + cncn .
The coefficients cn are related by the equation:
cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn
To begin, we can substitute the expression for y into the differential equation and see if it satisfies the equation. Taking the first and second derivatives of y with respect to x, we find:
y' = ∑n=0[infinity]cnxn-1
y'' = ∑n=0[infinity]cn(n-1)xn-2
Substituting these expressions into the differential equation yields:
∑n=0[infinity]cn(n-1)xn-2 + (3x-1)∑n
=> 0[infinity]cnxn-1 - ∑n=0[infinity]cnxn+1 = 0
We can rearrange this equation to get:
∑n=0[infinity]cn(n+2)xn+1
=> ∑n=0[infinity]cn(n-1)xn-2 + (3x-1)∑n=0[infinity]cnxn
Now, we can compare the coefficients of xn+1 on both sides of the equation to get:
cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn
This is a recurrence relation for the coefficients cn. To see how it relates to the equation given in the question, we can substitute n+1 for n and simplify:
cn+3 = (n+2)(n+3)cn+2 + (3n+2)cn+1
Now we can substitute cn+1 from the original recurrence relation:
cn+3 = (n+2)(n+3)(n+1)cn+1 + (n+2)(n+3)cn + (3n+2)cn+1
Simplifying gives:
cn+3 = (n+2)(n+3)cn+2 + [(n+2)(n+3)(n+1) + 3n+2]cn+1
This is exactly the same recurrence relation as the one given in the question. Therefore, we can conclude that the coefficients cn are related by the equation:
cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn
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i don't understand. please help
Answer: 5m
Step-by-step explanation:
The Initial water level means that level amount when the time equal to 0hrs, which is 5m.
A survey of 879 supermarket employees revealed that 239 workers felt they were overqualified for the position. What is the best way to characterize the 879 employees?
Answer:
they doubt if they're qualified or not