please help im confused

Non-empty families f and g such that s (f ∩ g) = (s f) ∩ ( s g), we will construct f and g as follows:

In other words, for each A ∈ F, let

A' = {X ∈ F : X ∩ A ≠ ∅}

Then f = {A' : A ∈ F} is a non-empty family. let g be the family of all subsets of G that have at least one element in common. In other words, for each B ∈ G, let

B' = {Y ∈ G : Y ∩ B ≠ ∅}

Then g = {B' : B ∈ G} is also a non-empty family.

Now, we will show that s (f ∩ g) = (s f) ∩ ( s g).

prove that s (f ∩ g) ⊆ (s f) ∩ ( s g). Let x ∈ s (f ∩ g). Then there exists a set C ∈ f ∩ g such that x ∈ C. By definition of f and g, there exist sets A ∈ F and B ∈ G such that A' = C = B'. Then, since x ∈ C, we have x ∈ A ∩ B. Thus, x ∈ s F and x ∈ s G, so x ∈ (s F) ∩ (s G). Therefore, s (f ∩ g) ⊆ (s F) ∩ (s G).

Next, we will prove that (s F) ∩ (s G) ⊆ s (f ∩ g). Let x ∈ (s F) ∩ (s G). Then x ∈ s F and x ∈ s G. By definition of s F, there exists a set A ∈ F such that x ∈ A. Similarly, there exists a set B ∈ G such that x ∈ B. Then A ∩ B is non-empty, so there exists a set C ∈ F ∩ G such that C ⊆ A ∩ B. By definition of f and g, we have C ∈ f and C ∈ g. Therefore, x ∈ C ⊆ (f ∩ g), so x ∈ s (f ∩ g). Hence, (s F) ∩ (s G) ⊆ s (f ∩ g).

Therefore, we have shown that s (f ∩ g) = (s F) ∩ (s G), as required.

To prove that there exist non-empty families f and g such that s(f ∩ g) = (s f) ∩ (s g), we can construct f and g by selecting one element each from F and G, respectively. By doing so, we ensure that both f and g are non-empty.

Let f = {A} and g = {B} be non-empty families constructed by selecting one element each from F and G, respectively. Since F and G are non-empty, f and g are also non-empty. Now, we can observe that the intersection of f and g is given by f ∩ g = {A} ∩ {B} = {} (empty set).

Next, we consider the superset of f, which is s(f) = {A} ⊆ F, and the superset of g, which is s(g) = {B} ⊆ G. The intersection of the supersets is given by (s f) ∩ (s g) = ({A} ∩ F) ∩ ({B} ∩ G) = {A} ∩ {B} = {} (empty set).

Thus, we have s(f ∩ g) = {} = (s f) ∩ (s g). Therefore, we have successfully shown that there exist non-empty families f and g such that their intersection is equal to the intersection of their supersets.

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Solution

For this case we can solve the problem with the following operation:

And rounded the answer we got 3.25 ft

16.24*100 = 1624

5*100 = 500

And we can do this:

1624/500 = 812/250 = 406/125

003

_____

125 / 406

-0

____

-40

-0

____

406

-375

_____

31

Answer:

x=8 (one solution)

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7(x−5)=x+13

(7)(x)+(7)(−5)=x+13(Distribute)

7x+−35=x+13

7x−35=x+13

Step 2: Subtract x from both sides.

7x−35−x=x+13−x

6x−35=13

Step 3: Add 35 to both sides.

6x−35+35=13+35

6x=48

Step 4: Divide both sides by 6.

x=8

Answer:

x = 8 (one solution)

Step-by-step explanation:

7x - 35 = x + 13

-x            -x

6x - 35 = 13

     +35   + 35

6x = 48

divided by six on both sides

x = 8

Answer:

whats the question

Step-by-step explanation:

The value of x in the triangle δhij is 18.2.

Given that in the triangle δhij, the measure of angle h is (x-1)°, the measure of the  angle i is (2x+5)°, and the measure of the angle j is (7x-6)°. We are required to find the value of x.

Since the sum of the measures of the angles in a triangle is always 180°, we have:

m∠h + m∠i + m∠j = 180°

Substituting the given values, we get:

(x-1)° + (2x+5)° + (7x-6)° = 180°

Simplifying the equation, we have:

10x - 2 = 180

10x = 182

x = 18.2

Therefore, we can conclude that the value of x is 18.2.

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Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

Answer:

C.)

Step-by-step explanation:

You need at least 6 employees to generate 7,300 dollars in revenue because 7300-5500=1800 and 1800/300=6. Hope this helps

Answer:

see below

Step-by-step explanation:

There are two points where y = -3

   at x = -2   and x = 1

   when x = 0    f(0) = 1

The descriptive statistics results will be displayed in the Output window in Minitab, which can be viewed by selecting “Analyze > Descriptive Statistics > Descriptive”. This will provide information such as the mean, median, standard deviation, and other summary statistics.

1. Launch Minitab and open the data set that contains the observations for the ESL students in John Adams Elementary School.

2. Select the “Analyze” tab at the top of the screen.

3. Select “Descriptive Statistics” from the drop-down menu.

4. Select “Descriptive” from the sub-menu.

5. Select the variables of interest and click “OK”.

6. The descriptive statistics results will appear in the Output window.

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Download

GET

Algebra

Factor

Factor the polynomial.

(

x

+

3

)

(

x

+

5

)

Tap to view FREE steps...

()|[]√≥

789≤

456/^×>∩∪

123-+÷<π∞

,0.%=

Factor

x

2

+

8

x

+

15

+

0

Regroup terms.

x

2

+

0

+

8

x

+

15

Add

x

2

and

0

.

x

2

+

8

x

+

15

Factor

x

2

+

8

x

+

15

using the AC method.

Tap for fewer steps...

Consider the form

x

2

+

b

x

+

c

. Find a pair of integers whose product is

c

and whose sum is

b

. In this case, whose product is

15

and whose sum is

8

.

3

,

5

Write the factored form using these integers.

(

x

+

3

)

(

x

+

5

)

Answer:

(x+3)(x+5)

Step-by-step explanation:

The absolute value equation which correctly represents the situation as described is; | x- 3.5 | = 0.8.

The values which are 0.8 units from 3.5 as given are therefore; 4.3 and 2.7.

It follows from the task content that the numbers which are 0.8 units away from 3.5 on the number line be determined.

On this note, the correct representation of the situation above involves an absolute value equation such that;

| x- 3.5 | = 0.8

Hence, to solve the equation; (x- 3.5) = 0.8 OR (x- 3.5) = -0.8.

x = 0.8 + 3.5. OR. x = -0.8 + 3.5

x = 4.3 OR x = 2.7.

Ultimately, the required values are; 4.3 and 2.7.

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Answer:

Answer:

Permutation:

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Formula:

\(nPr=\frac{n!}{(n-r)!}\)

Example:

Permutations are the different ways in which a collection of items can be arranged. For example, the different ways in which the alphabets A, B and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different.

Combination:

In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.

Formula:

\(nCr=\frac{n!}{r!(n-r)!}\)

Example:

Combination: Picking a team of 3 people from a group of 10.

C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is 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 certainty.

Formula:

Conditional Probability P(A | B) = P(A∩B) / P(B)

Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)

Example:

Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and its being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.

~permutation~

Permutation is a term that in mathematics refers to several different meanings in different areas.

Permutation can be permutation with repetition and permutation without repetition.

nPr=

(n−r)!

n!

~Permutation without repetition~

Permutation means to combine the default elements in all possible ways so that each group contains all the default elements.

The number of permutations of a set of n different elements is equal Pn=n×(n-1)×...×2×1=n!

~Permutation with repetition~

If between n given elements there are k1 equals of one kind, k2 equals of another kind,..., ky equals of rth kind, we speak of permutations with repetition.

~combinations without repetition~

In many counting problems, the order of the selected elements is not important.

Each choice of r different elements of an n-member set determines one of its subsets that has r elements, we call it a combination of r-th class without repetition of n elements.

nCr=

r!(n−r)!

n!

~combinations with repetition~

Repetition combinations are combinations in which elements can be repeated.

~Variations without repetition~

A variation of the r-th class in an n-membered set is each ordered r-torque of different elements.

(We can determine this number using the principle of consecutive counting).

~Variations with repetition~

If the elements in ordered r-tuples can be repeated we are talking about variations with repetition.

(We can determine this number using the principle of consecutive counting).

Answer:

180

Step-by-step explanation:

The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

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letter B

I'v just substitute 1, 2, 3, etc in each equation

Ex. when n = 2 a2 = -4(2) + 5

a2 = -8 + 5

a2 = -3

or when n = 3

a3 = -4(3) + 5

a3 = -12 + 5

a3 = -7

Doing this we obtain the values of the sequence 5, 1, -3, -7

Jack jogs for 30 minutes and rides his bike for 45 minutes and the pair of linear equations that shows the relationship between the number of minutes he jogs (x) and the number of minutes he rides his bike (y) every day are:y = (1/3)x + 35 and y = (-1/3)x + 40

Let's assume that Jack jogs for x minutes. According to the question, he rides his bike for 15 minutes more than he jogs.Therefore, the number of minutes he rides his bike is (x + 15).He spends a total of 75 minutes every day exercising.

So, x + (x + 15) = 75

Now, we'll solve this equation for x:2x + 15 = 75 or 2x = 75 - 15, 2x = 60 or x = 30

So Jack jogs for 30 minutes.

Therefore, he rides his bike for x + 15 = 30 + 15 = 45 minutes.

To write a pair of linear equations that shows the relationship between the number of minutes Jack jogs (x) and the number of minutes he rides his bike (y) every day, we can use the slope-intercept form:

y = mx + b

Here, m is the slope and b is the y-intercept. For the first equation, the slope is the ratio of the rise (y) to the run (x).

Since Jack jogs for 30 minutes and rides his bike for 45 minutes, the slope is:

y/x = (45-30)/45 = 15/45 = 1/3

Hence, the first equation is:y = (1/3)x + b

We can use either of the two points (30,45) or (45,30) on the line to find the value of b.

Let's use the point (30,45).

y = (1/3)x + b45 = (1/3)(30) + b45 = 10 + bb = 35

So, the first equation is:y = (1/3)x + 35Similarly, we can find the second equation:

y = (-1/3)x + 40

To verify, substitute x = 30 in both equations:

y = (1/3)(30) + 35 = 45

y = (-1/3)(30) + 40 = 30

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The correct answer would be -3/8 or in decimal form -0.375 :)

Percentage decrease is 17.29 .

Given :

In 2006, 65.2 million people subscribed to cable television.

In 2013, that number had decreased to 54.2 million.

To Find :

The percent decrease in the number of cable TV subscribers from 2006 to 2013.

So,

Decrease in the number of cable TV subscribers from 2006 to 2013 is :

Percentage decrease = Decrease in subscribers / initial subscribers * 100

% decrease = 63.6 - 52.6 / 63.6 * 100

% decrease = 17.29

Hence the percentage decrement in the tv subscribers are 17.29 .

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Rounding to the nearest thousandth, x ≈ 2.345

One or more variables or numbers are combined with one additional action to form an expression.

To solve this equation, we can start by adding 3 to both sides:

\(4^x - 3 + 3 = 18 + 3\)

Simplifying:

\(4^x = 21\)

Now, we can take the logarithm base 4 of both sides:

\(log4(4^x) = log4(21)\)

Simplifying:

x = log4(21)

Using a calculator, we can approximate:

x ≈ 2.345

Rounding to the nearest thousandth, we get:

x ≈ 2.345

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Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Both rational expressions' least common denominator is 6\(y^{3}\)

The denominator of a group of fractions with the lowest common multiple is known as the lowest common denominator (Lowest Common Multiple, or LCD for short). For many denominators in the collection, LCD is the smallest positive integer. In writing fractions, as 3/4, a fraction bar is used.

The mathematical expressions are -8/y^2 and 3/6^y.

Let's factorize the denominators right now.

\(y^{2}\) = y,y

6y = 6,y

To locate the common component among the terms, we must now group them.

y,y and 6,y

We now need to determine which fraction has the lowest common denominator.

We must first take the common and missing components, then combine them to obtain the least common factor in order to discover the least common denominator.

The common factor in both denominators is equal to y.

The first rational expression's missing element is equal to 6.

The second rational expression's second missing element is y.

Thus, the rational expression's least common denominator is equal to 6\(y^{3}\).

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The area of the concave hexagon is 24/√2

Given that,

Having radii of 2 and 4, respectively, and being externally tangent, are circles with centers O and P. The circle with the center at O has points A and B, while the circle with the center at P has points C and D, so that

AD and BC are frequent tangents to the outside of the circles.

To find : What is the hexagon's area?

ADPO and OPBC are congruent right trapezoids with legs 2 and 4 and with OP equal to 6. Draw an altitude from O to either DP or CP,

Creating a rectangle with width 2 and base x, and a right triangle with one leg 2, the hypotenuse 6, and the other aa Using the Pythagorean theorem, \($x$\) is equal to \($4\sqrt{2}$\) , and x is also equal to the height of the trapezoid. The area of the trapezoid is thus

Area = 1/2 * (4+2).4√2 = 12√2

and the total area is two trapezoids, or 24/√2

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Answer:

cos 32° = 12/x

x = 14.15

Step-by-step explanation:

Number of hours spent by Monica on TV is 45 minutes , the time spent by Becky is in mixed fraction.

What is mixed fraction?

A mixed fraction is one that has each its quotient and remainder delineated.

Main Body:

Number of hours spent by Becky on TV = 1 1/2 hours

This is a mixed fraction.

Converting into decimal form,

1 1/2 can be written as 1.5 hours

Converting hours into minutes ,

⇒1.5 * 60 = 90 minutes

Time spent by Monica = (1/2)* Becky's time

⇒Time spent by Monica = (1/2)*90

⇒ 45 minutes

Hence time spent by Monica is 45 minutes.

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The required answer is the series ∑ln(6k)4k diverges.

determine whether the series ∑ln(6k)4k converges or diverges.

To analyze the convergence or divergence of the given series, we can use the Ratio Test:

1. Find the ratio of consecutive terms: a_(k+1)/ask
  In this case, a_k = ln(6k)4k.

2. Compute the limit as k approaches infinity: lim(k->∞) (a_(k+1)/a_k)
  a_(k+1) = ln(6(k+1))4(k+1) and a_k = ln(6k)4k

3. Compute the ratio: (ln(6(k+1))4(k+1))/(ln(6k)4k)

4. Find the limit as k approaches infinity: lim(k->∞) [(ln(6(k+1))4(k+1))/(ln(6k)4k)]

5. Apply L'Hopital's rule for indeterminate forms (0/0 or ∞/∞) if needed.

If limit exist and partial sum converges or individual term approaches zero then series is convergent otherwise divergent and further checked by methods explained below.
In this case, however, we notice that the terms in the series do not go to zero, since ln(6k)4k will always grow larger as k increases. This implies that the series does not converge.

Thus, the series ∑ln(6k)4k diverges.

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step 1: convert fractions to decimals to make it easier to solve

3.1s=6.2

step 2: subtract 3.1 from both sides of the equation to isolate the variable

s=3.1

I hope this helps, good luck!

This may be wrong I am not sure so let me know... (edited)

h(4)=−28

Explanation:

If h(n)=−2n2+4

then h(4)=−2(4)2+4

=−2×16+4

=−32+4

=−28

No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

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If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

Answer:

Step-by-step explanation:

To find the distance traveled, we need to subtract the starting odometer reading from the ending odometer reading.

In this case:

Journey distance = 12714 km - 12138 km = 576 km

So the journey was 576 kilometers.