The Sierpinski triangle (pictured below) is a fractal image. The original figure is an equilateral triangle. In each step, the computer splits every triangle in the design into 444 congruent equilateral triangles, and removes the center one from the design. The area remaining in a particular design after nnn steps can be shown using the following expression:
\qquad\dfrac{25\sqrt{3}}{2}\cdot\left(\dfrac{3}{4}\right)^n
2
25
3
​

​
⋅(
4
3
​
)
n
start fraction, 25, square root of, 3, end square root, divided by, 2, end fraction, dot, left parenthesis, start fraction, 3, divided by, 4, end fraction, right parenthesis, start superscript, n, end superscript
The image shows 4 triangular figures, which represent the Sierpinski triangle fractal at 0, 1, 2, and 3 iterations.
The original triangular figure is an equilateral triangle which is entirely shaded. The triangular figure labeled n = 1 is formed by subdividing the original triangle into 4 congruent triangles and removing the middle triangle. The triangular figure for n = 2 is formed by subdividing each of the congruent triangles from the figure labeled n = 1 into 4 congruent triangles and removing the middle triangles.
The triangular figure for n = 3 is formed by subdividing each of the congruent triangle from the figure labeled n = 2 into 4 congruent triangles and removing the middle triangles.
The image shows 4 triangular figures, which represent the Sierpinski triangle fractal at 0, 1, 2, and 3 iterations. The original triangular figure is an equilateral triangle which is entirely shaded. The triangular figure labeled n = 1 is formed by subdividing the original triangle into 4 congruent triangles and removing the middle triangle. The triangular figure for n = 2 is formed by subdividing each of the congruent triangles from the figure labeled n = 1 into 4 congruent triangles and removing the middle triangles.
The triangular figure for n = 3 is formed by subdividing each of the congruent triangle from the figure labeled n = 2 into 4 congruent triangles and removing the middle triangles.
What does \dfrac{25\sqrt{3}}{2}
2
25
3
​

​
start fraction, 25, square root of, 3, end square root, divided by, 2, end fraction signify in the expression?

Answer:

Step-by-step explanation:

\(f(x)=-x^3-7x^2-7x+15\\Prove:\ x_1=-5\ \ \ \ x_2=-3\ \ \ \ x_3=1\ at\ f(x)=0\\\\-x^3-7x^2-7x+15=0\)

Multiply both parts of the equation by -1:

\(x^3+7x^2+7x-15=0\\x^3+5x^2+2x^2+7x-15=0\\x^2*(x+5)+(2x^2+7x-15)=0\\x^2*(x+5)+(2x^2+10x-3x-15)=0\\x^2*(x+5)+(2x*(x+5)-3*(x+5))=0\\x^2*(x+5)+(x+5)*(2x-3)=0\\(x+5)*(x^2+2x-3)=0\\x+5=0\\x=-5\\x^2+2x-3=0\\x^2+3x-x-3=0\\x*(x+3)-(x+3)=0\\(x+3)*(x-1)=0\\x+3=0\\x=-3\\x-1=0\\x=1\)

Answer:

50 x^3 y^2

Step-by-step explanation:

25y^5 = 5*5 * y*y

5xy  = 5*x*y

2x^3y = 2*x*x*x*y

The least common multiply is  found by taking the least number of times each appears

5 appears 2 times

2 appears 1 time  

x appears 3 times

y appears 2 times

5*5*2  * x*x*x * y*y

50 x^3 y^2

Answer:

50 x^3 y^2

Step-by-step explanation:

25y^5 = 5*5 * y*y

5xy  = 5*x*y

2x^3y = 2*x*x*x*y

The least common multiply is  found by taking the least number of times each appears

5 appears 2 times

2 appears 1 time  

x appears 3 times

y appears 2 times

5*5*2  * x*x*x * y*y

50 x^3 y^2

The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.

A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).

Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.

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The resulting disjoint sets after the operation union({7, 4}) would be: {5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

The union of two sets A and B is denoted by A ∪ B and is defined as the set of all elements that are either in A or in B or in both. Therefore, the resulting disjoint sets after the operation union({7, 4}) would be:

{5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

To calculate the union, we can use the following formula:

A ∪ B = {x : x ∈ A or x ∈ B}

Therefore, the union of {7, 4} can be calculated as:

{7, 4} ∪ {7, 4} = {x : x ∈ {7, 4} or x ∈ {7, 4}}

= {7, 4}

Therefore, the resulting disjoint sets after the operation union({7, 4}) would be: {5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

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Answer:

Cost of one pack = h+8

Step-by-step explanation:

Given that:

Amount Azil have = RM (h²-64)

Packs of flour Azil wants to buy = h-8

To find the price of a pack of flour, we will divide the total amount by packs of flour.

Unit rate = \(\frac{h^2-64}{h-8}\)

Unit rate = \(\frac{h^2-8h+8h-64}{h-8} = \frac{h(h-8)+8(h-8)}{h-8}\)

Unit rate = \(\frac{(h-8)(h+8)}{(h-8)}\)

Unit rate = h+8

Hence,

Cost of one pack = h+8

The system 2x+3y=12 and 2x+3y=18 does not have any solution

The given system of equations is:

2x + 3y = 12 ...(1)

2x + 3y = 18 ...(2)

We can rewrite the equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, as follows:

Equation (1): 3y = -2x + 12 => y = (-2/3)x + 4

Equation (2): 3y = -2x + 18 => y = (-2/3)x + 6

From the equations in slope-intercept form, we can see that the two lines have the same slope of -2/3, which means they are parallel.

Parallel lines never intersect, which means there are no solutions to the given system of equations.

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Answer:

volume of prism is b×h=5×12= 60cm( cube)

surface is p×l+b×h=13×28+60=424cm( square)

Answer:

t= -105

Step-by-step explanation:

To solve the equation, we want to find out what t is. In order to do this, we have to get t by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

-1/15t=7

t is being multiplied by -1/15. The opposite of multiplication is division. Divide both sides by -1/15.

-1/15t/-1/15=7/ -1/15

t=7/ -1/15

Instead of dividing a number by a fraction, you can multiply the number by the reciprocal of the fraction.

To find the reciprocal, flip the numerator (top number) and denominator (bottom number).

-1/15--flip--> -15/1=-15

Substitute -15 in for -1/15, and switch the division sign to a multiplication sign.

t= 7* -15

t=-105

Let's check out solution. Plug -105 back in for t in the original equation.

-1/15t=7

-1/15*-105=7

7=7

Both sides are the same, so we know that t=-105.

Answer:

t=-105

Step-by-step explanation:

\(-\frac{1}{15} t =7\)

What we need to do here is to isolate t.

Let's multiply both sides by -15.

\(-\frac{1}{15}t * -15 = 1t\)

7*-15= -105

t=-105

Answer:

B

Step-by-step explanation:

none of the domain is repeting

(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

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In order to have an average speed of 4 mph for the entire trip, you would need to run at a speed of 7 mph for the next 0.5 hours after walking for 1.5 hours at 3 mph.

Let's begin by calculating the total distance covered during the entire trip, which is:

distance = (time walked) x (walking speed) + (time ran) x (running speed)

We know that the time walked is 1.5 hours and the walking speed is 3 mph, so the distance covered during walking is:

distance walked = (time walked) x (walking speed) = 1.5 x 3 = 4.5 miles

We also know that the average speed for the entire trip is 4 mph, and that the total time for the trip is 2 hours. Therefore, the distance covered during the entire trip is:

distance = (average speed) x (total time) = 4 x 2 = 8 miles

So the distance covered during running is:

distance ran = distance - distance walked = 8 - 4.5 = 3.5 miles

Now we can use the formula for average speed:

average speed = total distance / total time

To find the running speed, we need to solve for the running time, which is:

time ran = distance ran / running speed

Substituting this expression into the average speed formula, we get:

4 = (distance walked + distance ran) / (1.5 + time ran)

4 = (4.5 + 3.5) / (1.5 + distance ran / running speed)

Simplifying this expression, we get:

1.5 + distance ran / running speed = 2

distance ran / running speed = 0.5

Substituting the values we calculated, we get:

3.5 / running speed = 0.5

Solving for the running speed, we get:

running speed = 3.5 / 0.5 = 7 mph

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the series is divergent.

To determine whether the series ∑(5n ln(n)), n = 2, is convergent or divergent, we can use the Integral Test.

The Integral Test states that if f(x) is a positive, continuous, and decreasing function on the interval [a, ∞), and if the series ∑f(n) is represented by the integral ∫[a, ∞] f(x) dx, then the series and integral either both converge or both diverge.

In this case, let's consider the function f(x) = 5x ln(x).

1. Positivity: The function f(x) = 5x ln(x) is positive for x > 0 since ln(x) is positive for x > 1.

2. Continuity: The function f(x) = 5x ln(x) is continuous on the interval [2, ∞) since ln(x) is continuous on (1, ∞).

3. Decreasing: To check if f(x) = 5x ln(x) is decreasing on the interval [2, ∞), we can take the derivative:

f'(x) = 5 ln(x) + 5

To determine the sign of f'(x), we can set it equal to zero and solve for x:

5 ln(x) + 5 = 0

ln(x) = -1

x = e^(-1) ≈ 0.3679

Since f'(x) = 5 ln(x) + 5 is positive for x < e^(-1) and negative for x > e^(-1), we can conclude that f(x) = 5x ln(x) is decreasing on the interval [2, ∞).

Now, let's apply the Integral Test:

∫[2, ∞] 5x ln(x) dx = [5/2 x^2 ln(x) - (5/4) x^2] evaluated from 2 to ∞

By taking the limit as the upper bound approaches infinity:

lim(x→∞) [(5/2 x^2 ln(x) - (5/4) x^2)] - [(5/2)(2^2 ln(2) - (5/4)(2^2)]

lim(x→∞) [(5/2 x^2 ln(x) - (5/4) x^2)] - 10 ln(2)

If the above limit is finite, then the series converges. If the limit is infinite or does not exist, then the series diverges.

By evaluating the limit, we find:

lim(x→∞) [(\(5/2 x^2 ln(x) - (5/4) x^2)\)] - 10 ln(2) = ∞

Since the limit is infinite, we can conclude that the series ∑(5n ln(n)) diverges.

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Answer:

Step-by-step explanation:

Answer:

z = 5

Step-by-step explanation:

-0.25z = -1.25

-1.25 ÷ -0.25 = 5

z = 5

Answer:

D 5.4

Step-by-step explanation:

The pythagoras theorem states that a² + b² = c²

2² + 5² = ?²

4 + 25 = ?²

29=?²

? =

\( \sqrt{29} \)

? = 5.4 rounded 2 sig fig one decimal place

Answer:

xy*(2x^2 + 7x^2 - y^2)

Step-by-step explanation:

You can get xy out of the expression since all have xy

Answer:

1. 4/5, 3/5, 4/3 || 2. x = 13.78

Step-by-step explanation:

1)

Sin = Opposite/Hypotenuse = 16/20 = 4/5

Cos = Adjacent/Hypotenuse = 12/20 = 3/5

Tan = Opposite/Adjacent = 16/12 = 4/3

So the answer is 4/5, 3/5, 4/3

2) The unknown side is the opposite, and 21 is the hypotenuse. Opposite/Hypotenuse is the sine function.

Sin(41) ≈ 0.656

0.656 = x/21

x = 13.776

The closest answer to this is 13.78

Answer:

Step-by-step explanation:

The answer is -2.81

Plz mark me brainliest.

Answer:

Answer Option C

Step-by-step explanation:

They make a big plus sign, PLUS=PERPENDICULAR

Answer:

Look at the big picture. Make sure you understand what the end product is supposed to look like.

Examine the parts of the task. Figure out step-by-step what you need to do because it’s not going to happen through magic.

Think about the logical order of completing the pieces. What should you do first, second, third, etc.?

Step-by-step explanation:

Ya basically that!

please mark brainliest i need 2 more :(

Answer:

6 cm

Step-by-step explanation:

Given that:

A line that contains the points R, S and T.

Distance between R and S = \(2x\)

Distance between S and T = \(3x\)

To find:

The distance between S and T = ?

Solution:

The given situation and dimensions can be represented in the form of a diagram as shown in the attached diagram.

As per given statement and in the diagram, we can deduce that the sum of distance between R and S, S and T is equal to distance between R and T.

i.e. RS + ST = RT

\(2x + 3x = 10\\\Rightarrow 5x=10\\\Rightarrow x = 2\)

ST = 3\(x\) = 3 \(\times\) 2 = 6 cm

Therefore, the answer is:

Distance between S and T is 6 cm.

If the space between R and S is 2x, the space between S and T is 3x, and RT is 10 centimeters long, then ST is 6 centimeters

Point S lies between points R and T on Line segment RT

RT   =  RS   +  ST

The space between R and S is 2x

That is, RS  =  2x

The space between S and T is 3x

That is, ST  =  3x

RT is 10 centimeters long

RT  =  10cm

Substitute RT = 10, ST = 3x and RS = 2x into the equation RT = RS + ST

10  =  2x  +  3x

10   =  5x

x  =  10/5

x   =  2

If x = 2, then

ST  =  3x

ST = 3(2)

ST =  6 centimeters

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The correct answer is option (D) "The graph shifts 7 units right and 8 units down".Explanation:To solve the given question, we need to use the rules for vertical and horizontal shifts, which are as follows:

Vertical Shift: y=f(x)+a moves the graph of f(x) upward if a > 0 and downward if a < 0.Horizontal Shift: y=f(x+a) moves the graph of f(x) left if a > 0 and right if a < 0.Now, let's transform the function f(x) into function g(x) and determine the shift required.The transformation of f(x) to g(x) is: g(x) = f(x - a) + bwhere a = horizontal shift and b = vertical shiftThe equation of the given functions is:f(x) = 1/(x − 2) and g(x) = 1/(x^(5/9))Let's set the equation of function f(x) in the standard form:y = 1/(x - 2)and the equation of function g(x) in the standard form:y = 1/(x^(5/9))

Now, we can observe that:To transform the graph of f(x) onto the graph of g(x), we need to shift the graph of f(x) right by 7 units and down by 8 units, which is given in option (D).Hence, the correct option is (D) "The graph shifts 7 units right and 8 units down".

The graph shifts 7 units right and 8 units down is the statement that describes the transformation of the graph of function f onto the graph of function g.Conclusion:Thus, we have determined the correct answer with an explanation and concluded that the correct option is (D) "The graph shifts 7 units right and 8 units down".

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Answer:

I could but can you please put down the problem.

Step-by-step explanation:

The first mathematician who came close to calculating pi was Archimedes of Syracuse.

In 250 BCE, he found the value of pi to be between 3.1408 and 3.1429 by inscribing and circumscribing a circle with polygons.

Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Pi has an infinite number of decimal places and is commonly represented by the Greek letter π. It is approximately equal to 3.14159 but is an irrational number, meaning it cannot be expressed as a fraction of two integers.

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer who lived from 287-212 BCE. Archimedes is considered one of the greatest mathematicians in history and made significant contributions to mathematics, physics, engineering, and astronomy. He was also known for his inventions, including the Archimedes screw and the compound pulley system.

Archimedes of Syracuse was the first mathematician who was close to the value of pi.

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To determine the number of terms we need to add in order to find the sum of the series with an error less than or equal to 0.002, we can use the concept of the Alternating Series Estimation Theorem.

The Alternating Series Estimation Theorem states that for an alternating series with terms decreasing in absolute value, the error in approximating the sum of the series by the sum of a finite number of terms is less than or equal to the absolute value of the next term.

In the given series, ∑n=1[infinity](−1)n−1n^2, the terms are decreasing in absolute value as n increases, so we can apply the Alternating Series Estimation Theorem.

The next term in the series, which determines the error, is given by (-1)^n * (n+1)^2. To ensure the error is less than or equal to 0.002, we need to find the smallest value of n such that:

|(-1)^n * (n+1)^2| ≤ 0.002

We can solve this inequality by testing values of n until we find the smallest value that satisfies it. Starting with n = 1:

|(-1)^1 * (1+1)^2| = 4 > 0.002

The inequality is not satisfied for n = 1.

Let's continue testing values of n:

|(-1)^2 * (2+1)^2| = 9 > 0.002

|(-1)^3 * (3+1)^2| = 16 > 0.002

|(-1)^4 * (4+1)^2| = 25 > 0.002

|(-1)^5 * (5+1)^2| = 36 > 0.002

|(-1)^6 * (6+1)^2| = 49 > 0.002

...

After testing a few values, we can see that the smallest value of n that satisfies the inequality is n = 9:

|(-1)^9 * (9+1)^2| = 100 > 0.002

Therefore, we need to add at least 9 terms in order to find the sum of the series with an error less than or equal to 0.002.

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The probability of out of any two students chosen at random, one student will be absent while the other is present is 29/450 or approximately 0.064.

Let's denote the event that a student is absent as A and the event that a student is present as P.

The probability of a student being absent is P(A) = 1/30, which means the probability of a student being present is P(P) = 29/30.

We want to find the probability that out of any two students chosen at random, one student will be absent while the other is present.

There are two possible cases for this event:

The first student is absent and the second student is present

The first student is present and the second student is absent

Let's calculate the probability of each case separately:

Case 1: The probability of the first student being absent is P(A) = 1/30. The probability of the second student being present is P(P) = 29/30. Therefore, the probability of the first student being absent and the second student being present is:

P(A and P) = P(A) × P(P) = (1/30) × (29/30) = 29/900

Case 2: The probability of the first student being present is P(P) = 29/30. The probability of the second student being absent is P(A) = 1/30. Therefore, the probability of the first student being present and the second student being absent is:

P(P and A) = P(P) × P(A) = (29/30) × (1/30) = 29/900

The total probability of one student being absent and the other being present is the sum of the probabilities of the two cases:

P = P(A and P) + P(P and A) = (29/900) + (29/900) = 58/900

Simplifying the fraction by dividing both the numerator and denominator by 2, we get:

P = 29/450

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a) The regional automobile dealership sent out flyers to prospective customers, and we need to determine how many flyers were sent out.

b) Based on the number of flyers sent out (as determined in part a) and the probabilities listed on the flyer, we can calculate the expected value of the prize won by a prospective customer.

c) Using the number of flyers sent out and the probabilities listed on the flyer, we can calculate the standard deviation of the value of the prize won by a prospective customer.

a) To determine the number of flyers sent out, we need more information or assumptions. The problem does not provide any specific information about the number of flyers sent out.

b) The expected value of the prize won by a prospective customer can be calculated by multiplying the value of each prize by its respective probability of winning, and then summing up these values. For example, if we assume 10,000 flyers were sent out, the expected value would be (1/31,107) * $28,000 + (1/31,107) * $575 + (31,105/31,107) * $5.

c) The standard deviation of the value of the prize won can be calculated using the probabilities and the expected value. It involves calculating the squared difference between each prize value and the expected value, multiplying it by the probability, and then summing up these values. The square root of this sum gives the standard deviation.

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