If a = -3, find the value of
a) 2a
b) a2
c) 3a2​

Every element that belongs to the union of the sets also belongs to the intersection of the sets, and vice versa. Therefore, the union and the intersection of the sets are equivalent.

To prove that a1 ∪ a2 ∪ ... ∪ an = a1 ∩ a2 ∩ ... ∩ an, we need to show that every element that belongs to the union of the sets also belongs to the intersection of the sets, and vice versa.

First, let's consider an element x that belongs to the union of the sets, i.e., x ∈ (a1 ∪ a2 ∪ ... ∪ an). By definition, this means that x belongs to at least one of the sets a1, a2, ..., or an. Without loss of generality, let's assume that x belongs to the set a1. Therefore, x ∈ a1.

Now let's consider the intersection of the sets, i.e., x ∈ (a1 ∩ a2 ∩ ... ∩ an). By definition, this means that x belongs to all of the sets a1, a2, ..., and an. Since we have already established that x ∈ a1, it follows that x also belongs to the intersection of the sets.

Therefore, we have shown that if x belongs to the union of the sets, it also belongs to the intersection of the sets.

Next, let's consider an element y that belongs to the intersection of the sets, i.e., y ∈ (a1 ∩ a2 ∩ ... ∩ an). By definition, this means that y belongs to all of the sets a1, a2, ..., and an. Since y belongs to all of the sets, it follows that y must belong to at least one of the sets a1, a2, ..., or an.

Therefore, y ∈ (a1 ∪ a2 ∪ ... ∪ an).

Hence, we have shown that if y belongs to the intersection of the sets, it also belongs to the union of the sets.

In conclusion, we have proven that a1 ∪ a2 ∪ ... ∪ an = a1 ∩ a2 ∩ ... ∩ an.

This result holds for any number of sets, as long as n ≥ 2. It is a fundamental property of set theory and is known as the "duality of union and intersection."

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Answer:

x = - 1/2

Step-by-step explanation:

(3/2 - 6x) + 1 = 3 - 5x

-6x + 5/2 = 3 - 5x

5/2 = 3 - 5x + 6x

5/2 = 3 + x

5/2 - 3 = x

-1/2 = x

x = -1/2

Please mark me the brainliest!?!

\( \frac{3}{2} - 6x +1 = 3 - 5x \\ \)

Plus sides 6x

\( \frac{3}{2} - 6x + 6x + 1 = 3 - 5x + 6x \\ \)

\( \frac{3}{2} + 1 = 3 + x \\ \)

Subtract sides -3

\( \frac{3}{2} + 1 - 3 = 3 - 3 + x \\ \)

\( \frac{3}{2} - 2 = x \\ \)

\( \frac{3}{2} - \frac{4}{2} = x \\ \)

\(x = - \frac{1}{2} \\ \)

Done.....♥️♥️♥️♥️♥️

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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Answer:

D. 578pi

Step-by-step explanation:

Sorry if that's wrong

The probability of selecting a shower gel given item is scented must be the same as grabbing shower gel which is 42%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Juanita has a storage closet at her shop with extra bottles of lotion and shower gel, some are scented and some are unscented.

If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel.

For the events "shower gel" and "scented" to be independent.

P(A|B) = P(A)

P(B|A) = P(B)

P(A∩B) = P(A) × P(B)

We know that the probability she selects a shower gel is 42%. Let this event be A. Then we have

P(shower | scented) = P(shower gel) = 42%

This must be true for the events to be independent.

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Answer:

The answer is

C - P(shower gel | scented) = 42%

Step-by-step explanation:

Hope this helped!

Answer:

Emma traveled on average 315 miles per day.

Step-by-step explanation:

1,890 ÷ 6 = 315

The speed of the train is 1 m/s.

A train travelled along a track for 70 s at a constant speed. What was its speed in metres per second (m/s)?The speed of the train in metres per second is the distance covered by the train in one second. Therefore, to determine the speed of the train, we must first determine the distance it covered during 70 seconds along the track.

The speed of the train can be calculated by dividing the distance covered by the train in meters by the time taken in seconds.  Therefore,Speed = Distance/TimeThe formula for distance is;Distance = Speed x TimeThe time taken by the train is 70s.The distance travelled by the train is not given, but we can calculate it using the speed of the train and time taken.

Therefore;Distance = Speed x Time Substituting the values;Distance = Speed x 70To find the speed of the train, we rearrange the formula as shown below;Speed = Distance/TimeNow we can substitute the value of distance to get the speed;Speed = (Speed x 70)/70Simplifying the expression,Speed = Speed

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Answer: the table is proportional and the answer is 2/3

Step-by-step explanation: we can see that the top row goes up by 3 every time the bottom row goes up by 2

this gives us a ratio of 6 : 9

take the 6 and divide it by 3 we get 2

divide 9 by 3 and we get 3

this gives us the fraction 2/3 which is also an answer

gl :)

The difference between distributed vs. distributional representations: Distributed representations use word co-occurrence, while distributional representations use vectors. So, option 1 is the correct answer.

A distributed representation is a model for representing a concept, object, or event in which each entity is defined by a list of factors. These features are usually weighted to reflect their relative importance to the object being modeled.

A distributional representation is a model for representing linguistic meaning in which words are represented by vectors. This approach builds on the observation that words that appear in similar contexts in texts are often semantically similar. As a result, a word's meaning is derived from the distributional information about it that is captured by its context in the text. Distributed representations use word co-occurrence, while distributional representations use vectors. Option 1 is the correct answer.

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Answer:

2.25 dollars per pound

Step-by-step explanation:

Take the cost and divide by the number of pounds

11.25 dollars / 5 pounds

2.25 dollars per pound

Answer:

The cat food costs 2.25 dollars per pound

Step-by-step explanation:

First let's write this like an equation. Let's add a variable instead of pounds and you can name that anything you like. I prefer to use X. And since we have 5 pounds of cat food, we put 5x.

X = 1 Pound of cat food

11.25$ = 5x

Now we want X alone, so we divide both sides by 5

11.25$/5 = 5x/5

Now if we divide we get

2.25$ = X

And if we turn x back into pounds of cat food, we get that, for 2 dollars and 25 cents we have 1 bag of cat food

2.25$ = 1 Pound of cat food

Answer:

The formula in getting the area of the top is πr², because it is a circle, and we are talking about its top.

The smaller cake has the area of 4π

The larger cake has the area of 36π

Therefore, We cannot say that the larger cake is three times as big as the smaller cake since,

4 x 3 = 36

12 ≠ 36

The producer surplus is: Producer surplus = Total revenue - Total variable cost= 57000 - 24000= $33000. Therefore, the producers' surplus is $33,000 (rounded to the nearest dollar).

The producers' surplus can be calculated using the formula given below:

Producer surplus = Total revenue - Total variable cost

The given price of Blu-ray players in the market is given by, p = 100(0.9x + 0.3 / 1+x) dollars.

If the selling price is $190/unit, then we can write:

190 = 100(0.9x + 0.3 / 1+x)

Simplifying the above equation, we get: 1.9 = 0.9x + 0.3 / 1+x

Solving the above equation for x:1.9(1+x) = 0.9x + 0.3

After solving, x = 0.3 (rounded off to nearest thousand)

Thus, the manufacturer will make 300 units available in the market per week.

The total revenue generated by the producer is given by:

Total revenue = selling price × quantity= 190 × 300 = $57000

Total variable cost is the cost of producing these units, which is equal to the amount spent on raw materials, labor costs, and other variable expenses incurred by the producer.

Let's assume that the variable cost is equal to $80/unit.

Hence, the total variable cost of producing 300 units is given by:

Total variable cost = variable cost × quantity= 80 × 300 = $24000

Therefore, the producer surplus is: Producer surplus = Total revenue - Total variable cost= 57000 - 24000= $33000Therefore, the producers' surplus is $33,000 (rounded to the nearest dollar).

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Answer:

Your y intercept is 1.

Step-by-step explanation:

slope is y2-y1 over x2-x1, or 2.

slope intercept formula is y=mx+b, and if you plug values into formula you get 3=2(1)+b

and if you solve that, 2x1=2, 3-2=1.

then you get 1 as your y intercept.

Answer:

Imaginary 0= 18

I think it will help you

Answer:

4:22 6:33

Step-by-step explanation:

These two ratios simplify down to 2:11

Answer:

Step-by-step explanation: uhm maybe 4/3 idrk-

Based on the information given, the annual dollar difference will be C. $5600.

Based on the information given, the annual dollar difference will be calculated as follows:

= (13% × $112000) - (8% × $112000)

= (0.13 × $112000) - (0.08 × $112000)

= $14560 - $8960

= $5600

In conclusion, the correct option is $5600.

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The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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Answer:

53 degrees

Step-by-step explanation:

If r is 25 and s is 102, and if there are 180 degrees in a triangle, then you can just add to get 53.

Answer:

53

Step-by-step explanation:

Hello There!

So in this problem they give us two angles of a triangle and want us to find the missing angle

Remember the sum of all of the angles in a triangle is 180

So to find the missing angle we subtract the given angles from 180

180-25-102=53

so we can conclude that the answer is 53

Answer:

3=3x+3

4=2x+8

Step-by-step explanation:

Answer:

The area of a rectangle with length 4 cm and width 6 cm is 24 square cm. To find the area of a semi-circle, we use the formula for the area of a circle and divide by 2. The formula for the area of a circle is πr^2, where r is the radius. The radius of the semi-circle is half the width of the rectangle, so r = 6/2 = 3 cm. Thus, the area of the semi-circle is π(3^2) = 9π square cm.

The total area of the figure would be the sum of the area of the rectangle and the semi-circle, so the answer would be 24 + 9π square cm.

Step-by-step explanation:

using Pythagoras theorem.

37,

x² = 6² + 8²

x = √6²+8² = 10ft

38.

13²=12²+x²

169 = 144 + x²

√169 - 144 = x = 5cm

hope it helps. :)

Answer:

x = 10 and x = 5

Step-by-step explanation:

using Pythagoras' identity

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

(36)

x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

x = \(\sqrt{100}\) = 10

(38)

13² = x² + 12²

169 = x² + 144 ( subtract 144 from both sides )

25 = x² ( take square root of both sides )

\(\sqrt{25}\) = 5 = x

x = 5

The expected rate of return on the common stock of CrisisGreat is 4.43%.

To calculate the expected rate of return on the stock of CrisisGreat, we need to use the formula:

Expected rate of return = (Probability of recession * Rate of return in recession) + (Probability of normal economy * Rate of return in normal economy) + (Probability of boom * Rate of return in boom)

Let's plug in the given values:

Therefore, the expected rate of return on the common stock of CrisisGreat is 4.43%.

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Step-by-step explanation:

l = w-6

w-6 * w = 60

w^2 - 6w - 60 = 0

w^2 - 12w + 5w - 60=0

w(w-12)+5(w-12) = 0

(w+5) (w-12) = 0

w = -5

w=12

since width can't be negative, its 12 yds

length = 5 yds

Answer:

\(\tt 18\: m^3\)

Step-by-step explanation:

Volume ⇒ (Area of base) height

\(\tt (\cfrac{1}{2} \times4\times.5)\times 6=\boxed{18}\)

~

Therefore your answer is C)18 m³

Answer:

19.66

Step-by-step explanation:

Let x represent our unknown number

Okay so it's basically saying that 30 is greater than 3x by 89

We would represent that mathematically by:

30 - 89 = 3x

So then we just solve this like we usually would

30 - 89 = -59

-59 \(\div\) 3 = 19.666. . .

Hope this helps:)

Answer:

14. 2 RAISE TO POWER 15

3×5 = 15

B

( 20 - 16 / 16 ) × 100 =

( 4 / 16 ) × 100 =

( 1 / 4 ) × 100 =

100/4 =

% 25

Answer:

y=-4x+1 is the answer to your question.