Let X be a topological space and A ⊂ X. The closure of A, denoted
A¯, is the intersection of all closed sets containing A.
(a) Show that A¯ is the smallest closed subset of X containing A, in
the following sense: if A ⊂ F ⊂ X and F is closed, then A¯ ⊂ F.

Answer:

Negative

Step-by-step explanation:

When an even number of negatives are multiplied together, the product will be positive (because two negatives cancel out). When an odd number of negatives are multiplied together, the product will be negative.

In the given expression, there is also a singular (1) at the end, which we can ignore since anything multiplied by 1 is itself. The other numbers are all negative and there are 3 of them, and since 3 is an odd number, the product will be negative.

I hope this helps!

Answer:

The third choice

Step-by-step explanation:

Negative, because the product (–7)(–2) is positive, and the product (–5)(1) is negative and the product of a positive and a negative number is negative,

pls mark as brainliest hope you have a nice day!

Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

According to the statement

We have given that the two rectangles EFGH and ABCD and we have show that the these rectangles Are dilation at origin or not.

So, According to the given diagram

Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation of rectangle at the origin.

Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.

The scale factor could be calculated by the ratio of the sides of the image to the pre-image rectangle.

According to the diagram In Rectangle ABCD:

Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).

Now consider rectangle EFGH:  

Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).

Hence the scale factor is becomes from these values is:

EF/AB = EH/AD = FG/BC = HG/DC = 4/3.

Hence the scale factor becomes 4/3.

Also

∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°

( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).

So, Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

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Perimeter formula: p = 2(w + l)

The perimeter is 62.

p = 62

The width of a rectangle is 5 feet less than the length.

w = l - 5

Substitute and solve.

62 = 2[(l - 5) + l)]

62 = 2l + 2l - 10

62 = 4l - 10

72 = 4l

18 = l

Substitute and solve for the width

w = 18 - 5

w = 13

Therefore, the length is 18 and the width is 13.

Best of Luck!

Answer:

see below and attached.

Step-by-step explanation:

Perimeter (P) = 2 L (Length) + 2 W (Width)

where P = 62

          W = L - 5

P = 2L + 2W

62 = 2L + 2(L -5)

62 = 2L + 2L - 10

72 = 4L

L = 72/4

L = 18

W = L - 5

W = 18 - 5

W = 15

Variables :                           P, L, W

Model equation:                 P = 2L + 2W

Length of the rectangle:    18

Width of the rectangle:      13

The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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Answer:

13.89

Step-by-step explanation:

Answer:13

Step-by-step explanation:

1. The Taylor polynomial at x = -0.34. 10^-5 ≤ |Pn(-0.34)| ≤ 0.34^n / n!

2. The minimum order of the Taylor polynomial is n = 4.

1. To find the minimum order of the Taylor polynomial centered at 0 for cos(x) required to approximate cos(-0.34) with an absolute error no greater than 10^-5, we can use the error bound formula for Taylor polynomials.

The error bound formula states that for a function f(x) and its nth-degree Taylor polynomial Pn(x) centered at a, the absolute error between f(x) and Pn(x) is bounded by:

|f(x) - Pn(x)| ≤ M * |x - a|^n / (n!)

where M is the maximum value of the (n+1)th derivative of f(x) on the interval of interest.

For cos(x), the maximum value of the (n+1)th derivative is 1 for all n.

Let's solve the inequality:

10^-5 ≤ |cos(-0.34) - Pn(-0.34)| ≤ |0 - Pn(-0.34)|

Since cos(0) = 1, we only need to consider the error of the Taylor polynomial at x = -0.34.

10^-5 ≤ |Pn(-0.34)| ≤ 0.34^n / n!

2. To find the minimum value of n, we can start with a small value of n and increase it until the right side of the inequality is less than or equal to 10^-5.

Let's calculate the right side for n = 1, 2, 3, ...

For n = 1: 0.34^1 / 1! ≈ 0.34

For n = 2: 0.34^2 / 2! ≈ 0.057

For n = 3: 0.34^3 / 3! ≈ 0.006

For n = 4: 0.34^4 / 4! ≈ 0.001

We can see that for n = 4, the right side is less than 10^-5.

Therefore, the minimum order of the Taylor polynomial is n = 4.

So, the answer is n = 4.

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The correct answer is 3.

The probability that the student answers exactly 1 question correctly is

                            \($\frac{135}{243}=\boxed{\frac{5}{9}}$\)

What is the binomial coefficient?

In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.

There are a total of \($3^5=243$\) possible ways that the student can answer the quiz. To count the number of ways that the student can answer exactly 1 question correctly, we can use the binomial coefficient formula:

      \(\binom{5}{1}=5\)

This counts the number of ways that the student can choose which 1 question to answer correctly.

For each of these 5 ways, there are 3 ways to choose the incorrect answer for each of the other 4 questions, so the total number of ways that the student can answer exactly 1 question correctly is

\($5\cdot 3^4=135$\).

Therefore, the probability that the student answers exactly 1 question correctly is

              \($\frac{135}{243}=\boxed{\frac{5}{9}}$\)

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To determine the total charge we first need to calculate how much we pay of taxes. This can be done by using a rule of three:

Then we have:

Hence charge for the tax is $3.8.

Therefore the total charge of the meal is $51.3

Answer:

O.225

Step-by-step explanation:

Two negatives = positive

Answer:

.255

Step-by-step explanation:

.255

Step-by-step explanation:

x<-5 is the answer

1.

6x=-30

2.

x=-5

3.

x<-5

Answer:

range

Step-by-step explanation:

The difference between the lowest and the highest number is called the range. The middle value is the median (it's in the "mid"dle, median) The mean is the average. And the mode is the most frequent value.

Answer:

Q11: x = 3

Q12: x = -4

Step-by-step explanation:

Q11
We have the equation as
\(\:64^{2x\:+\:4}=16^{5x}\)

Convert the bases in terms of the common base 4

64 = 16 x 4 = 4 x 4 x 4  = 4³

16 = 4 x 4 = 4²

Therefore the original equation becomes:
\(\mbox {\large 4^{3\left(2x+4\right)}=4^{2\cdot \:5x}}\)

Since the bases are the same in this equation, the exponents must also be the same

Equation the two exponents we get

3(2x + 4) = 2·5x

==> 6x + 12 = 10x

Move 12 to the right side

6x = -12 + 10x

Move 10x to the left:

6x - 10x = -12

-4x = -12

x = -12/-4 = 3

Answer to Q11

-------------------------------------------------------------

Q12

We can solve this in a similar manner to Q12

27 = 3 x 3 x = 3³

9 = 3 x 3 = 3²

Plugging these in we get

\(\mbox {\large 27^x = 3^{3(x)} = 3^{3x}}\)

\(\mbox {\large 9^ {(x - 2)} = 3^{2(x-2)} = 3^{2x -4} }\\\\\)

Thus we get

\(\mbox {\large 3^{3x} = 3^{2x -4} }\\\\\)

Equating the exponents we get

\(3x = 2x - 4\\\\3x - 2x = -4\\\\x = -4\)

ANSWER to 12

It's is b cause it is and yeah

Answer:

a

Step-by-step explanation:

Answer:

90, 91, 92, 93, 94, 95, 96

The length of KI is 10 cms.

The skill of measuring the lengths of objects and understanding the units of length is very crucial as it helps us to interact with our environment in a more organized manner.

Here, ΔRJS ≈ Δ IJK

then JR / JI = SR/KI

         1/2   =5 /ki

         kI = 5 X 2

        kI = 10 units.

Thus, The length of KI is 10 cms.

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The mass of the population of bacteria after 30 hours is 9.6×10⁻⁴ grams in expressions.

What does a math expression mean?

Mass of 1 bacterium =2×10-¹². Then the mass after 30 hours will be calculated as below:-

Mass of 480,000,000 bacteria = 2×10-¹²×480,000,000

Mass of 480,000,000 bacteria =0.00096

Mass of 480,000,000 bacteria =9.6×10⁻⁴

Therefore, the mass of the population of bacteria after 30 hours is 9.6×10⁻⁴ grams.

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Using improper fractions we know that Jerry took 3/4 hours longer than Rhonda to complete the homework.

To find out how much longer Jerry took than Rhonda to complete the homework, we need to subtract Rhonda's time from Jerry's time. Here's a step-by-step explanation:

1. Convert the mixed numbers to improper fractions:
  Rhonda: 1 1/2 = (1 * 2 + 1)/2 = 3/2
  Jerry: 2 1/4 = (2 * 4 + 1)/4 = 9/4

2. Find a common denominator for both fractions, which in this case is 4.

3. Convert both fractions to have the common denominator:
  Rhonda: 3/2 * 2/2 = 6/4
  Jerry: 9/4 (already has the common denominator)

4. Subtract Rhonda's time from Jerry's time:
  9/4 - 6/4 = 3/4

So, Jerry took 3/4 hours longer than Rhonda to complete the homework.

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The relationship between ∠ a and ∠ b is that they are B. Complementary angles.

Complementary angles have a sum that equates to 90 degrees, making them vital concepts in geometrical and trigonometrical problem-solving concerning right-angled triangles. Employed primarily in these two fields of study, their addition when combined engenders formation of a perfect right angle.

As we can see from the image, ∠ a and ∠ b would add up to 90 degrees because they are by a straight line.

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The Wronskian of the functions e and e(3x) is 2e(4x).

The Wronskian of the functions e^x and e^(3x) is found by computing the determinant of the matrix formed by their derivatives. In this case, the Wronskian is:

W(e^x, e^(3x)) = |(d/dx)e^x   (d/dx)e^(3x)|
                      |e^x         3e^(3x)|

Now, compute the determinant:

W(e^x, e^(3x)) = e^x(3e^(3x)) - e^(3x)e^x
W(e^x, e^(3x)) = 2e^(4x)

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As we can conclude that Site 5 is most likely immediately downstream from the dairy farm.

When we talk about the impact of the dairy farm's runoff on water quality, we must consider the concept of downstream. Downstream refers to the direction in which water flows. In a watershed, water flows from higher elevations to lower elevations. Thus, the site downstream of the dairy farm would be the one that receives water after it has passed through the farm.

Looking at the table provided, we can see that Site 5 has the highest values for nitrate, ammonia, and total phosphorus, which are all indicators of pollution. This indicates that Site 5 is likely to be immediately downstream of the dairy farm.

This conclusion is supported by the fact that Site 5 has the highest levels of pollutants, and it is the last site listed in the table. This means that the water flowing through Site 5 has already passed through the other four sites, including the dairy farm, before reaching Site 5.

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Answer:

f(g(x)) = 9x² - 6x - 4

Step-by-step explanation:

f(g(x) )

= f(3x - 1)

= (3x - 1)² - 5 ← expand factor using FOIL

= 9x² - 6x + 1 - 5

= 9x² - 6x - 4

Answer:

2

Step-by-step explanation:

Answer:

LCM: 1

Step-by-step explanation:

1/2 and 1/4

so we want to find a multiple.

double both we get:

1 and 1/2

but then what if we just double 1/2?

1 and 1 :OOOOO

LCM IS 1

but it's 6:18 P:M for me?

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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(1) The correct option is (A) Scalar field = ez sin y + e* cos y, and the vector field A = (2x - z)i - 2j+2k. We must find the component of the gradient of o in the direction of A at the point (1, 0, 1).The gradient of the scalar function φ (x, y, z) is defined as ∇φ = (∂φ / ∂x)i + (∂φ / ∂y)j + (∂φ / ∂z)k.

So, we have to find the gradient of the scalar field φ = ez sin y + e* cos y.∇φ = (∂φ / ∂x)i + (∂φ / ∂y)j + (∂φ / ∂z)k= 0i + ez cos y j + e* sin y kNow, at point (1, 0, 1), the gradient of the scalar field is given by,∇φ = 0i + e cos 0j + e sin 0k= e j + e* kAnd, at the point (1, 0, 1), the vector field A = (2x - z)i - 2j + 2k = 2i - 2j + 2kSo, we need to find the component of ∇φ along A, i.e.,∇φ . A / |A|∇φ . A = (e j + e* k) . (2i - 2j + 2k)= 0 + 0 + 4e* / 2= 2e*Hence, the required component is 2e*/√3. So, the correct option is (A).(2) We have to evaluate the surface integral for the vector field A = zi - 3j + 4xyk, along the following surface S, where S: 6x + 3y + z = 3 (x ≥ 0, y ≥ 0, z ≥ 0).

So, we need to find the unit normal vector of S at (x, y, z) and the limits of integration for x and y.The gradient of S is given by,∇S = 6i + 3j + kHence, the unit normal vector of S is given by,n = ∇S / |∇S|n = 6i + 3j + k / √46n = (2 / √46)i + (1 / √46)j + (1 / √46)k.We have to evaluate the surface integral for A along the surface S.S: 6x + 3y + z = 3 (x ≥ 0, y ≥ 0, z ≥ 0)The given surface is a plane that cuts through the positive x, y, and z axes. To perform the surface integral of A, we need to find a unit vector normal to the surface.6x + 3y + z = 3implies z = 3 - 6x - 3y.The normal vector is therefore N = (∂z/∂x)i + (∂z/∂y)j - k= -k.The surface integral of A is given by∬S A · dS where dS is an infinitesimal element of surface area.The surface S is a rectangle of sides 2 and 1. Therefore, its area is 2.The surface integral of A over S is∬S A · dS= ∬S (0)i - (0)j + (z)k · (-k) dS= -∬S (z) dS= -z(x, y) dxdy where z(x, y) = 3 - 6x - 3y. The limits of integration arex = 0 to x = 1- y = 0 to y = 1-xThe surface integral of A over S is therefore∬S A · dS= -∫[0,1]∫[0,1-x] (3 - 6x - 3y) dy dx= -[3x - 3x² - 3x(1 - x) + 3/2(1 - x)²]dx= -[3x - 9/2x² + 3/2x³ - 3/2x² + 3/2x³ - 1/2x⁴]dx= -[3/2x⁴ - 9x² + 6x]dx= -[3/10]Therefore, the surface integral of A over S is -3/10.Answer:1. The component of the gradient of ϕ in the direction of A at the point (1,0,1) is \($\frac{2e^{*}+2}{3\sqrt{3}}$\).2. The surface integral of A over S is -3/10.

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The width of the rug is 10 feet, and the length is 16 feet.

Let's assume the width of the rectangular rug is "x" feet.

According to the given information, the length of the rug is 6 feet longer than the width, so the length would be "x + 6" feet.

The formula for the area of a rectangle is length multiplied by width.

We can set up an equation using this formula to solve for the width:

Area = Length × Width

160 = (x + 6) × x

Now, let's simplify the equation:

\(160 = x^2 + 6x\)

Rearranging the equation:

\(x^2 + 6x - 160 = 0\)

Now we have a quadratic equation.

We can solve it by factoring, completing the square, or using the quadratic formula.

In this case, let's solve it by factoring:

(x + 16)(x - 10) = 0

Setting each factor to zero:

x + 16 = 0 or x - 10 = 0

Solving for x:

x = -16 or x = 10

Since we are dealing with measurements, we can disregard the negative value.

Therefore, the width of the rug is 10 feet.

Now, we can find the length by adding 6 to the width:

Length = x + 6 = 10 + 6 = 16 feet.

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(4656) (3856) = 17,953,536

Answer:

2

Step-by-step explanation:

i took the quizz