A subset A of R has the property that, given ε > 0 and x ∈ R, there exist a, b ∈ R with a ∈ A and b 6∈ A, such that |x − a| < ε and |x − b| < ε. Can A be countable? Can A be uncountable?

The surface area of the pyramid is A = 386.24 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of hexagonal pyramid be represented as A

Surface area of hexagonal pyramid = Area of base + area of lateral surface

Area of the base = 166.3 inches²

Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )

where a = 8 inches

h = 6 inches

Substituting the values in the equation , we get

Area of the lateral surface = ( 3 x 8 ) √ ( 36 + ( 3 x 64 / 4 ) )

On simplifying the equation , we get

Area of the lateral surface = 219.96 inches²

So , Surface area of hexagonal pyramid = Area of base + area of lateral surface

Surface area of hexagonal pyramid A = 166.3 inches² + 219.96 inches²

Surface area of hexagonal pyramid A = 386.24 inches²

Hence , the surface area of hexagonal pyramid is 386.24 inches²

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Answer: 2/3

Step-by-step explanation:

First you multiply both numerators which equals 8

Then, you multiply the denomerators which is 24

This gives you 8/24

Since both 8 and 24 are divisible by 8, you divide them by 8 and you get 1/3

Since two negative numbers equal a positive one, the answer is positive

The correct grouping of the trinomial "-10x² + 13x + 3" is option 4, (-10x² + 0x) + (13x + 3).

To find the correct grouping, we need to factor out the greatest common factor from the first two terms, -10x² + 13x.

The greatest common factor of -10x² and 13x is -x². So, we can factor out -x² and get:

-x² * (10 - 13/x) + 3 = (-x² * 10) + (13/x - x²) + 3 = (-10x² + 7x) + (6x + 3)

Therefore, choice 3 is the correct grouping of the trinomial -10x² + 13x + 3.

A trinomial is a mathematical expression consisting of three terms. It is a polynomial of degree three and has the general form ax³ + bx² + cx + d, where a, b, c, and d are constants and x is a variable.

Complete Question:

'which of the answer choices is a correct grouping of the following trinomial? −10x² 13x 3

1. (-10x² + 5x) - (6x + 3)

2.(-10x² + 2x) +(15x + 3)

3.(-10x² + 7x) +(20x + 3)

4.(-10x² + 0x) +(13x + 3)

5.(-10x² + 0x) - (x + 3)

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Answer:

233.5

Step-by-step explanation:

1) Find the area of the rectangle

2) Find the area of the triangle

3) Find the area of the semicircle

4) Add the results together

5) Round the nearest tenth

Have a lovely day :)

The scale factor of K = 10/3 represents enlargement.

Given is the scale factor of K = 10/3.

For the scale factor of {K} > 1, the dilation is enlargement and for the scale factor of {K} < 1, the dilation is reduction.

Now -

10/3 > 1

So, it represents the enlargement.

Therefore, the scale factor of K = 10/3 represents enlargement.

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Answer:

Below

Step-by-step explanation:

From hour 1 to 2 pay goes from 90 to 120   or 30 dollar increase per hour

slope = rise / run =  (120-90) / (2-1) =  30  dollar/hr

The time that the ferries will leave together next, given the time they leave the jetty would be 12 : 15 pm

The ferries leave at intervals of 8 minutes, 12minutes, and 15 minutes. To find  the time when they will all leave at the same time again, you need to find the lowest common multiple of 8, 12 and 15 as this would show the next time the ferries would be lined up together again.

The lowest common multiple of 8, 12 and 15 is 120 which in minutes is 2 hours.

The next time both ferries would leave together is:

= 10 : 15 + 2 hours

= 12 : 15 pm

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The solution to the system of equations is: D. (-4, -7).

To solve the system of equations, y = (3/2)x - 1 and y = 3x + 5, you can set the two equations equal to each other and solve for one of the variables. For example, setting the two equations equal to each other:

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

Then you can solve for x by isolating it on one side of the equation:

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

-5x/2 = 6

x = -4

Now that you know the value of x, you can substitute it back into one of the equations to find the value of y:

y = (3/2)(-4) - 1 = -6 - 1 = -7

So the solution to the system of equations is x = -4, y = -7.

The solution is: (-4, -7).

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After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

The subject is about finding the joint probability of two independent events: a repair done by Bob being done correctly and a repair done by Carl being done incorrectly.

The answer was determined using the formula for joint probability: P(A and B) = P(A) * P(B), where P(A) is the probability of event A and P(B) is the probability of event B, and A and B are independent events. In this case, event A is a repair done by Bob being done correctly and event B is a repair done by Carl being done incorrectly. The probabilities of each event were calculated by using the number of correctly and incorrectly repaired cars done by each mechanic.

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Answer:

240000000

Step-by-step explanation:

2.4x100000000=240000000

Answer:

343 meters per second (3 sf)

Step-by-step explanation:

1236km/h is basically 1236km per hour.

1km = 1000 meters

1h = 60 minutes

1m = 60 seconds

Using these rules, we can convert the kilometers and hour to meters and minutes and then to seconds.

---

1236km = 1236*1000

             = 1 236 000m

---

1h --> 1 236 000m

60m --> 1 236 000m

1m --> 1 236 000/60 = 20 600m

60s --> 20 600m

1s --> 20 600/60 = 343m (3 sf)

There are 343 (3 sf) meters per second.

Answer:

The probability of not being the same temperature would be 100% - (55% + 25%) = 20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

so the probability of whole is 100%

which means the un same day is 55%+25%=80%

so we just use 100% to minus 80%=20%

i hope this helps

Based on the information we can infer that 25 km is equivalent to 7.5 cm on the map.

To find the relationship between centimeters and kilometers on the map we must take into account the following information:

3cm = 10km

According to the above, we must make a rule of three to find the equivalence of kilometers. Below is the procedure:

According to the above, 7.5 centimeters would represent the 25 kilometers distance on the map.

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THE ANSWER IS 33$ BECAUSE YOU JUST ADD THE BEADS PLUS PENDANT PLUS CHAIN

Answer:

x = 2

Step-by-step explanation:

3x + 5 = 11

Let x = 1. Let's substitute the value of x into the equation to check if it's correct.

3(1) + 5 = 3 + 5

            = 8

8 ≠ 11

x is not 1.

---

Let x = 3. Let's substitute the value of x into the equation to check if it's correct.

3(3) + 5 = 9 + 5

            = 14

14 ≠ 11

x is not 3.

---

Let x = 2. Let's substitute the value of x into the equation to check if it's correct.

3(2) + 5 = 6 + 5

            = 11

11 = 11 so you can see that the value of 2 for x satisfies the equation!

x = 2.

---

When solving an equation, it is important to check for extraneous solutions.

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A better score is the SAT score of 2100 which has an average of 1500 with an SD of 325.

- SAT score of 2100

Now, According to the question:

"Information available from the question"

An ACT score of 28 or a combined SAT score of 2100 when

ACT: μ = 21 and σ = 5;

SAT: μ = 1500 and σ = 325

In order to determine which is a better score, we compare the scores in standard deviation units.

We can convert the score to standard deviation units by subtracting the mean and dividing by the standard deviation.

ACT: (28-21)/5 = 1.2

SAT: (2100-1500)/325 = 1.38

As we see SAT score is better than ACT score as it is 1.38 standard deviation units above the mean, while the ACT score is only 1.2 standard deviation units above the mean.

Hence, SAT score of 2100

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The required longest hike executed by the family is 2 hours.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
From the table,
Hike 1 took 1 2/4 hours which is equivalent to 1.5 hours.
Similarly
Hike 2 = 1.75 hours
Hike 3 = 2 hours
Hike 4 = 1.75 hours
Hike 5 = 1.5 hours
Hike 6 = 1 hours

Thus, the required longest hike executed by the family is 2 hours.

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Answer:

2. 5/4

Step-by-step explanation:

The constant of proportionality in this proportional relationship is the ratio of y to x for any given pair of values. To find it, we can divide the y value by the x value for one of the pairs. For example, using the first pair (x = 2, y = 5/2), we can divide 5/2 by 2 to get the constant of proportionality:

(5/2) / 2 = 5/4

Alright, so they want you to find the probability of landing on 4 or 2.

There are 8 numbers total so that will be our denominator x/8

There are two outcomes we are finding the probability, that gives us 2/8

We must simplify the fraction into its lowest form.

2/8=1/4

Your answer would be 1/4

The expression after multiplying the factors in the form is -573.21.

The provided expression is (-√36)(-√22)(-√415).

We have to multiply the factor and express in the radical form.

Let us solve this step by step and one by one,

(-√36) = -6

Now, for -√22,

-√22 = -4.69

Now, for -√415,

-√415 = -20.37

Now, we have to simply multiply these three values and that will be the radical form,

So,

(-√36)(-√22)(-√415) = -6 x -4.69 x -20.37

(-√36)(-√22)(-√415) = -573.21

So, the expression after simplification is -573.21.

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The measure of the length AD will be 4cm.

What is are of triangle?

The area of a triangle is the region enclosed by its sides. The area of a triangle differs from one triangle to another depending on the length of the sides and the internal angles. Triangle areas are expressed using square measurements like m2, cm2, and in2. One right angle or two perpendicular sides are both acceptable for right triangles. They may also be known as orthogonal triangles, right-perpendicular triangles, or originally rectangular triangles. Trigonometry's foundation is formed by the relationship between the sides and other angles of a right triangle.

2 / 1= AD / 2

AD=4 cm

Hence The measure of the length AD will be 4cm.

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The missing entries for f(x) are 20, 30, and 40, and the missing entries for g(x) are 40, 80, and 160.

The missing entries for f(x) can be found by knowing that f is a linear function and using the values given. A linear function has the form f(x) = ax + b, where a is the slope and b is the y-intercept. Since f(0) = 10 and f(1) = 20, we can use these two points to find a and b.

Putting x = 0 in the equation, we get:

f(0) = 10 = a(0) + b

Putting x = 1 in the equation, we get:

f(1) = 20 = a(1) + b

Solving these two equations simultaneously, we find:

a = 10

b = 0

So, the equation for f is:

f(x) = 10x + 0 = 10x

Using this equation, we can find the missing entries for f(x) in the table:

f(2) = 10x = 10(2) = 20

f(3) = 10x = 10(3) = 30

f(4) = 10x = 10(4) = 40

So the missing entries for f(x) are 20, 30, and 40.

To find the missing entries for g(x), we need to know the form of the exponential function g. A common form for exponential functions is g(x) = ab^x, where a is the y-intercept and b is the growth factor. Since g(0) = 10 and g(1) = 20, we can use these two points to find a and b.

Putting x = 0 in the equation, we get:

g(0) = 10 = a(1)^0 = a

So, a = 10.

Putting x = 1 in the equation, we get:

g(1) = 20 = 10b

Solving for b, we find:

b = 2

So, the equation for g is:

g(x) = 10(2^x)

Using this equation, we can find the missing entries for g(x) in the table:

g(2) = 10(2^2) = 10(4) = 40

g(3) = 10(2^3) = 10(8) = 80

g(4) = 10(2^4) = 10(16) = 160

So the missing entries for g(x) are 40, 80, and 160.

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--The given question is incomplete; the complete question is

"The table below shows some values of a linear function f and an exponential function g. find exact values (not decimal approximations) for each of the missing entries.                                                                                    x      0  1  2  3 4                                                                                                                                             f(x)  10 _ 20 _ _                                                                                                                                 g(x) 10 _ 20 _ _"--

Step-by-step explanation:

0.3333333333.... = 1/3

0.2222222222... = 1/3 / 3 × 2 = 2/9

so, we now know all the involved fractions.

(1/3 - 1)² - sqrt(1 - 3/2/2) + 2/9

(-2/3)² - sqrt (1 - 3/4) + 2/9

4/9 - sqrt(1/4) + 2/9

6/9 - 1/2

2/3 - 1/2

to calculate that we need to bring both fractions to the same denominator (6).

2/2 × 2/3 - 3/3 × 1/2 = 4/6 - 3/6 = 1/6

so, the complete result is 1/6.

Max's next step after swinging arcs on either side of the segment is to place the compass on the other endpoint and swing another arc that intersects the previous arcs.

After swinging arcs on either side of the segment, Max's next step is to place the compass on the other endpoint of the segment.

He needs to make sure the compass width remains the same as before.

Then, he swings another arc that intersects the previous arcs.

The point where the new arc intersects the segment is the midpoint of the segment.

By connecting this point with the endpoints of the segment, Max will have successfully bisected the segment.

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Answer:

Yes, it is possible to have a triangle with angles 60°, 70°, and 50°. The sum of the angles must equal 180° in order for a triangle to be formed.

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

To create any possible triangle, all three angle measurements should add up to 180° and the exterior angle should also be equal to the sum of two interior opposite angles!

Answer:

x = 6

Step-by-step explanation:

6x-9=51-4x

10x - 9 = 51

10x = 60

x = 6

Let's check

6(6) -9 = 51 -4(6)

36 - 9 = 51 - 24

27 = 27

So, x = 6 is the correct answer.

The length of the fabric which Brandon formed a rectangle, is 11 inches.

To find the length of the fabric, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the fabric is one of the other two sides, and the diagonal cut is the hypotenuse. So, we can write the equation:

[tex]L^2 + 5^2 = 13^2[/tex]

where L is the length of the fabric.

Solving for L, we get:

[tex]L^2 = 144 - 25 = 119, and L =\sqrt{119} = 11.[/tex]

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