0 8. A function f(x) is said to have the jump discontinuity at a point x = a if lim a)x+a+ c) x→a+ f(x) = lim x→a+ f(x) = lim x→a¯ lim X-a f(x). b) lim x→a f(x) = lim x→a¯ _ f(x) f(x) = f(a) d) lim f(x) → +00 x→a+​

Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

Answer:

x = 2

Step-by-step explanation:

11 = 3 + 4x

8 = 4x

x = 2

Let's Check

11 = 3 + 4(2)

11 = 3 + 8

11 = 11

So, x = 2 is the correct answer.

The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10

Set operations are done on two or more sets to produce a combination of components based on the operation. There are three primary sorts of operations done on sets in a set theory, such as: Intersection of sets () Union of sets () Set difference (-).

¡) (A n B) u C:

The value of the intersection of A and B is 5, 8. As a result, (A n B) = 5, 8. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A n B) u C = 5, 8 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.

¡¡) (A-B) u C:

A-B is the set of elements in A that are not in B, which is 3, 6. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A-B) u C = 3, 6 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.

¡¡¡) (A u B):

The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10.

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¡) (A ∩ B) ∪ C  = {1,2,3,4,5,6,8}.

¡¡) (A-B) ∪ C = {1,2,3,4,5,6,8,10}.

¡¡¡) (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Recall that:

A ∩ B denotes the intersection of sets A and B, i.e., the set of elements that are in both A and B.

A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both.

A' denotes the complement of set A, i.e., the set of elements that are not in A.

Using these notations, we can solve each part of the question as follows:

¡) (A ∩ B) ∪ C

First, we need to find A ∩ B, which is the set of elements that are in both A and B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∩ B={5,8}.

Next, we take the union of (A ∩ B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:

(A ∩ B) ∪ C = {5,8} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8}

Therefore, (A ∩ B) ∪ C = {1,2,3,4,5,6,8}.

¡¡) (A-B) ∪ C

First, we need to find A-B, which is the set of elements that are in A but not in B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A-B={3,6,10}.

Next, we take the union of (A-B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:

(A-B) ∪ C = {3,6,10} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8,10}

Therefore, (A-B) ∪ C = {1,2,3,4,5,6,8,10}.

¡¡¡) (A ∪ B)'

Recall that A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both. So, (A ∪ B)' denotes the complement of A ∪ B, i.e., the set of elements that are not in A or B.

We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∪ B={1,2,3,4,5,6,8,9,10}. Therefore, (A ∪ B)' is the set of elements that are not in {1,2,3,4,5,6,8,9,10}.

The universal set U={1,2,...,10}, so (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.

Therefore, (A ∪ B)'={7}.

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Answer:

Step-by-step explanation:

Infra-red waves commonly known as heat waves and light rays are travel in a speed [tex]3*10^{8} ms^{-1}[/tex] in a vacuum.

The probability that exactly 2 students prefer salad is 0.302

From the question, we have the following parameters that can be used in our computation:

n = 10

r = 2

p = 20%

The probability is then calculated as

P(x = 2) = nCr * p^x * (1 - p)^(n - x)

substitute the known values in the above equation, so, we have the following representation

P(x = 2) = 10C2 * (20%)^2 * (1 - 20%)^8

Evaluate

P(x = 2) = 0.302

Hence, the probability is 0.302

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Answer:

16801.2cm²

Step-by-step explanation:

Cone :

SA = πrl

SA = π · 28 ·  45                     90-45 = 45

SA = 3958.406744

Cylinder :

SA = 2 · π · r · ( r+h)

SA = 2 · π · 28 ( 28 +45 )

SA = 2 · π · 28 (73)

SA = 12842.83077

12842.83077 + 3958.406744 =

16801.2cm²

So the volume of the cylindrical pool is approximately 1884.96 cubic feet.

So the volume of the soccer ball is approximately 329.59 cubic inches.

So the volume of the small container is approximately 56.55 cubic inches.

So the volume of the tank is 63 cubic feet.

In mathematics, volume is a measure of the amount of space that a three-dimensional object occupies. It is typically expressed in cubic units, such as cubic meters, cubic centimeters, cubic feet, or cubic inches. The volume of a simple shape, such as a cube, rectangular prism, cylinder, or sphere, can be calculated using a specific formula based on its dimensions.

Here,

13. The diameter of the cylindrical pool is 20 feet, which means the radius is 10 feet (half of the diameter). The depth of the pool is 6 feet. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height or depth. Substituting the given values, we get:

V = π(10 ft)²(6 ft)

≈ 1884.96 cubic feet

14. The soccer ball has a radius of 4.3 inches. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Substituting the given value, we get:

V = (4/3)π(4.3 in)³

≈ 329.59 cubic inches

15. The conical container has a radius of 3 inches and a height of 6 inches. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Substituting the given values, we get:

V = (1/3)π(3 in)²(6 in)

≈ 56.55 cubic inches

16. The tank is in the shape of a pyramid, which means it has a rectangular base with length 3 feet and width 7 feet, and a height of 9 feet. The volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height. The base of the tank is a rectangle, so its area is given by the formula A = lw, where l is the length and w is the width. Substituting the given values, we get:

A = (3 ft)(7 ft)

= 21 square feet

V = (1/3)(21 sq ft)(9 ft)

= 63 cubic feet

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The areas of the figures are 72 square centimeter and 81 square inches

Figure 3

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Area = 9 * (12 - 4 - 4) + 12 * 3

Evaluate

Area = 72

Figure 4

The total area of the composite figure is the difference between the area of the trapezoid and the rectangle

So, we have

Area = 1/2 * (8 + 16) * 8 - 5 * 3

Evaluate

Area = 81

Hence. the area of the figure (3) is 81 square inches

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The HCF of 420 and 272 is 4.

To find the HCF of 420 and 272 using Euclid's division algorithm, we can proceed as follows:

Step 1: Divide 420 by 272

420 = 272 x 1 + 148

Step 2: Divide 272 by 148

272 = 148 x 1 + 124

Step 3: Divide 148 by 124

148 = 124 x 1 + 24

Step 4: Divide 124 by 24

124 = 24 x 5 + 4

Step 5: Divide 24 by 4

24 = 4 x 6 + 0

So, we can see that the last non-zero remainder obtained by Euclid's division algorithm is 4. Therefore, the HCF of 420 and 272 is 4.

Now, let's verify this using the Fundamental Theorem of Arithmetic.

The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be expressed as a product of prime numbers in a unique way, up to the order of the factors.

The prime factorization of 420 is:

420 = 2^2 x 3 x 5 x 7

The prime factorization of 272 is:

272 = 2^4 x 17

To find the HCF using the prime factorizations, we need to take the product of the common prime factors with the smallest exponent. In this case, the only common prime factor is 2, and it appears with an exponent of 2 in 420 and an exponent of 4 in 272. So, the HCF is:

HCF(420, 272) = 2^2 = 4

This matches the result obtained using Euclid's division algorithm. Therefore, we have verified that the HCF of 420 and 272 is indeed 4.

Answer:

Draw three overlapping circles to represent the sets A, B, and C.

Label the regions inside each circle with the name of the corresponding set (i.e., A, B, and C).

Shade the region that represents the set A - B, which includes all the elements that belong to A but not to B.

Finally, shade the region that represents the intersection of (A - B) and C, which includes all the elements that belong to both (A - B) and C.

The resulting diagram should show three overlapping circles, with the region for A shaded but with a part removed (to represent the exclusion of elements in B from A), and the region for (A - B) n C shaded within that.

Step-by-step explanation:

There are six sides...   3 pairs of equal sides

2 x ( 4x5  +  4x7   +  5x7)   = 166 cm^2

Answer:

166 cm²

Step-by-step explanation:

5x7=35

35x2=70

4x7=28

28x2=56

5x4=20

20x2=40

70+56+40= 166cm²

hope this helps!

A ) ⅔ x + 6 = 16

→ ⅔ × 15 + 6 = 16

→ 10 + 6 = 16

→ 16 = 16

Proved

B ) ⅓ x + 4 = 22

→ ⅓ × 15 + 4 = 22

→ 20 = 2

Not Proved

C) 3x + 15 = 30

→ 3×15+15 = 30

→ 3× 30 =30

→ 90= 30

Not Proved

D) x + 25 = 50

→ 15 + 25 = 50

→ 40 = 50

Not Proved

10r -24 = 7r + 12

→ 10r - 7r = 12+24

→ 3r = 36

→ r = 12

3r -2r-8 = -8r + 10

→ 3r - 2r + 8r = 10+8

→ r + 8r = 18

→ 9r = 18

→ r = 2

m/3-18 = m + 6

→ 54- m/ 3 = m + 6

→ 54- m = m + 6×3

→ 54- m = m + 18

→ 18 - 54

→ -36

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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Answer:

The answer is -3

Step-by-step explanation:

log(1/1000)=x

log 10(1/1000)=x

10^x=(1/1000)

10^x=10⁰/10³

10^x=10^-3

x= -3

Answer:

-3

Step-by-step explanation:

I did the test

Hope this helps :)

(PLS MARK BRAINLIEST)

Answer:

The answer is d.

Step-by-step explanation:

Let m = a number

Let n = a different number

[tex]log(m^n)=nlog(m)[/tex]

[tex]log(10^3)=3*log(10)[/tex]

[tex]log(10)=1[/tex]

[tex]log(10^3)=3[/tex]

Answer: 3 and 14

Step-by-step explanation: x ft = 3ft and x + 4 x = 10 (as you stated) x would be 10 so (10 + 4)ft= 14ft

Answer:

apples per pound: 0.25

pears per pound: 0.33

Apples give him the best value per pound

Step-by-step explanation:

to find apple per pound: 4/16= 0.25

to find pears per pound: 7/21= 0.33

The true statement regarding the line of best fit is that C. the equipment starts producing items after about 20 minutes of warming up

The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points.

The equipment starts producing items after about 25 minutes of warning up. This is false because machine takes 20 minutes to produce the items.

The equipment starts producing items after about 20 minutes of warming up. This is True.

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Answer:

  y = (1/3)(e^(-9(x+2)/(x+1)) -1)

Step-by-step explanation:

You want the particular solution to the differential equation ...

  y' = 3(1+3y)/(1+x)^2   with  y(-2) = 0

The differential equation can be rewritten as ...

  [tex]\dfrac{dy}{3(1+3y)}=\dfrac{dx}{(1+x)^2}[/tex]

We can define u = 1+3y, then du = 3 and the left side becomes ...

  dy/(3(1+3y)) = (1/9)du/u

and its integral is ...

  ∫(1/9)du/u = (1/9)ln(u) = (1/9)ln(1 +3y)

The integral of the right side is ...

  [tex]\int{(1+x)^{-2}}\,dx=-(1+x)^{-1}+C[/tex]

Then the result of integrating both sides of this rewritten differential equation is ...

  [tex]\dfrac{1}{9}\ln{(1+3y)}=-\dfrac{1}{1+x}+C[/tex]

The boundary condition can be used to find C:

  [tex]\dfrac{\ln(1+3\cdot0)}{9}=-\dfrac{1}{1-2}+C\\\\0=1+C\\\\C=-1[/tex]

Solving this equation for y, we get ...

  [tex]\ln(1+3y)=-9\left(\dfrac{1}{1+x}+1\right)\\\\\\1+3y=e^{\left(-\dfrac{9(x+2)}{x+1}\right)}\\\\\\\boxed{y=\dfrac{e^{\left(-\dfrac{9(x+2)}{x+1}\right)}-1}{3}}[/tex]

Answer:

a) (2x+9) + (3x-4) + 36 = 180

b) x = 27.8

c) 79.4°

Step-by-step explanation:

a) (2x+9) + (3x-4) + 36 = 180

This is because all 3 angles of a triangle equal to 180 degrees.

b) Firstly add like terms

5x + 41 = 180

Subtract 41 from both sides.

5x = 139

Divide 5 on both sides.

x = 27.8

c) <GTN = 3x-4

Plug in x = 27.8

3(27.8)-4 = 79.4

<GTN is 79.4 degrees

Answer:

The average velocity for a time period is given by the change in position divided by the change in time. For the time period beginning when t=3 and lasting 0.01 seconds, we have:

The change in position is y2 - y1 = -0.603 feet, and the change in time is t2 - t1 = 0.01 seconds. Therefore, the average velocity for this time period is:

average velocity = change in position / change in time = (-0.603 feet) / (0.01 seconds) ≈ -60.3 feet/second

Similarly, for the time periods beginning when t=3 and lasting 0.005 seconds, 0.002 seconds, and 0.001 seconds, we have:

To estimate the instantaneous velocity when t=3, we can calculate the derivative of the position function with respect to time:

y = 33t - 20t²

dy/dt = 33 - 40t

At t=3, we have:

dy/dt = 33 - 40(3) = -87

Therefore, the estimated instantaneous velocity when t=3 is -87 feet/second.

Answer:

To find the maximum height of the ball, we need to determine the vertex of the parabolic function f(t) = -16t^2 + 5t + 11. The vertex of a parabola is the point where the function reaches its maximum or minimum value.

The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, a = -16 and b = 5, so the x-coordinate of the vertex is:

t = -b/2a = -5/(2*(-16)) = 0.15625

To find the y-coordinate of the vertex, we can substitute t = 0.15625 into the function f(t):

f(0.15625) = -16(0.15625)^2 + 5(0.15625) + 11 ≈ 11.36

Therefore, the maximum height of the ball is approximately 11.4 (rounded to 1/10th).

The true statements are:

p(factor of 24) = 6/8: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the numbers 1, 2, 3, 4, 6, and 8 are on the 8-sided die. So, there are 6 favorable outcomes out of 8 possible outcomes. This statement is true.

p(odd number) = 1/2: There are 4 odd numbers (1, 3, 5, 7) on the 8-sided die, so the probability of rolling an odd number is 4/8 = 1/2. This statement is true.

p(number less than 8) = 1: All numbers on the 8-sided die are less than or equal to 8, but not all are less than 8. There are 7 numbers less than 8 (1, 2, 3, 4, 5, 6, 7), so the probability is 7/8, not 1. This statement is false.

p(multiple of 3) = 1/4: There are 2 multiples of 3 on the 8-sided die (3 and 6), so the probability of rolling a multiple of 3 is 2/8 = 1/4. This statement is true.

p(even number) = 1/8: There are 4 even numbers (2, 4, 6, 8) on the 8-sided die, so the probability of rolling an even number is 4/8 = 1/2, not 1/8. This statement is false.

P(the number 9) = 0: The 8-sided die only has numbers 1 through 8, so it is impossible to roll a 9. The probability of rolling a 9 is indeed 0. This statement is true.

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By finding the ratio of total volume to lemmon juice, we can see that In 600ml of juice we have 150ml of lemmon juice.

We know that 1000 ml of lemonade contains 250 ml of lemon juice. Then the ratio to total volume to lemon juice is:

R = 250/1000 = 0.25

Then in 600ml of juice, we will have 0.25 times that of lemmon juice, it gives:

0.25*600ml = 150 ml

In 600ml of juice we have 150ml of lemmon juice.

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Answer:

Step-by-step explanation:

We are given four graphs, and we want to determine which one is a function.

When given graphs, we can use the vertical line test to determine if a graph is a function or not. If the vertical line hits only one point on the graph, it means that it is a function.

If the vertical line hits more than one point, it means it is not a function.

This is because a function must have one unique output for every input. In other words, if we substitute 3 into a function, it cannot equal both 2 AND 4.

We can draw a vertical line down each graph. Feel free to use an online annotating tool to do this, or simply use your finger to draw a vertical line down each graph.

On the first one, we can see that if we draw a vertical line down it, the vertical line hits only one point on the graph. This means that the graph shows a function.

On the second graph, if we draw a vertical line through it, we can see it hits more than one point on the graph. This means the graph is not a function.

On the third graph, if we draw a vertical line through it, we can see it also hits more than one point on the graph, so it is not a function.

The final graph is a vertical line itself. If we draw a vertical line through it, all of the points will be shared; the line hits all of the points in the graph, so it is not a function.

This means that the first graph is a function.

See below for annotations.

An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.

The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:

N(m) = 45,000(1.073)^m

Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.

For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)^5 = 60,731. Thus, the warehouse will contain 60,731 trees at the end of 5 months.

In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

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An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

What is function?

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.

The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:

[tex]N(m) = 45,000(1.073)^m[/tex]

Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.

For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)⁵ =60,731.

Thus, the warehouse will contain 60,731 trees at the end of 5 months.

In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.

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We have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

What is the Leibniz's theorem?

Leibniz's theorem, also known as the product rule for derivatives, is a rule for finding the nth derivative of a product of two functions. It states that if u(x) and v(x) are functions of x, then the nth derivative of their product

To apply Leibniz's theorem, we need to express the function in terms of a product of two functions: u and v.

Let u = xⁿ and v = ln(x)

Then, du/dx = n*xⁿ⁻¹ and dv/dx = 1/x

Using the formula,

d/dx(xⁿ ln(x)) = u(dv/dx) + v(du/dx)

= xⁿ * (1/x) + ln(x) * n * xⁿ⁻¹

= xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

To find the nth derivative, we differentiate n times using the product rule.

First, we need to find the first few derivatives:

f(x) = xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

[tex]f'(x) = nx^{(n-2)} + (n-1)*x^{(n-2)} ln(x)[/tex]

[tex]f''(x) = n(n-2)x^{(n-3)} + 2(n-1)x^{(n-3)} ln(x) - (n-1)x^{(n-3)}/(x^2)[/tex]

[tex]f'''(x) = n(n-2)(n-3)x^{(n-4)} + 3(n-1)(n-2)x^{(n-4)} ln(x) - 3(n-1)x^{(n-4)}/(x^2) - 2(n-1)x^{(n-4)} ln(x)/(x^2)[/tex]

and so on...

The pattern becomes apparent and the nth derivative can be expressed as:

[tex]f^{(n)}(x) = n!/(x^{(n+1)})[/tex]

So,

dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = [tex]f^{(n)}(x) = n!/(x^{(n+1)})[/tex]

Hence, we have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

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Answer:

180,000 (OR 90,000 if the figure is a triangle)

Step-by-step explanation:

3 x 3 x 5 x 5 x 4 x 8 x 5 x 5 = 180,000

Area = 180,000

IF THE FIGURE IS A TRIANGLE THEN DIVIDE 180,000 BY 2 AND YOU WILL GET 90,000 AS THE AREA

Por lo tanto, el área del vidrio de la lupa es de aproximadamente 50.24 centímetros cuadrados.

What is el área?

"El área" is a Spanish phrase that translates to "the area" in English. "The area" is a mathematical term that refers to the measure of the size of a two-dimensional region, usually measured in square units such as square centimeters (cm²) or square meters (m²). The area of a figure can be calculated using various mathematical formulas, depending on the shape of the figure.

El área del vidrio de una lupa circular se puede calcular usando la fórmula del área del círculo, que es A = πr², donde "A" es el área, "π" es una constante aproximadamente igual a 3.14 y "r" es el radio de la lupa.

En este caso, el radio de la lupa es de 4 centímetros. Sustituyendo este valor en la fórmula, obtenemos:

A = πr²

A = 3.14 x 4²

A = 3.14 x 16

A = 50.24

Por lo tanto, el área del vidrio de la lupa es de aproximadamente 50.24 centímetros cuadrados.

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The mode, mean, and median are relatively close together (mode=33, mean=32.125, median=32), we can conclude that this data set is symmetric and does not have any significant outliers.

The area of mathematics known as statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.

The mean, median, and mode are all measures of central tendency that describe the center of a data set in different ways.

The mean is calculated by dividing the total number of values in a data collection by their sum.

The median is the median of the data set when the values ​​are ordered.  It is not affected by outliers.

The value that appears most frequently in a data collection is the mode.

It may not be unique or exist in a data set.

For the given data set, the mode is likely to be the best measure of center as it is the value that occurs most frequently. In this case, the mode is 33, which occurs three times, whereas all other values occur only once or twice. Therefore, the mode is the most representative value for this data set.

Alternatively, we can also calculate the mean and median to see how they compare with the mode:

The mean is (33+33+33+31+31+34+32+31)/8 = 32.125

The median is the middle value when the values are arranged in order, which is 32.

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