What is
492.6 ÷ 48
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Since the statistical survey was done with 5108 randomly selected households it can be concluded that the sample is 5108 randomly selected households.

In order to draw conclusions about the population as a whole a sample of data can be chosen.
A sample is a subset of a larger population that represents the larger population that is chosen for analysis.

In this instance, the sample consists of 5108 homes that were chosen at random for the survey to determine the proportion of homes with televisions tuned to the Super Bowl.

In order to accurately represent the number of households that watched the Super Bowl, a sample size of 5108 was used.

It should be also noted that Nielsen Media Research is a market research company that specializes in measuring media audiences, including television viewership.

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Where a and b are determined by the value of D.

A parabola is a type of graph, or curve, that is represented by an equation of the form y = ax² + bx + c. The vertex of a parabola is the point where the curve reaches its maximum or minimum point, depending on the direction of the opening of the parabola. In this case, the vertex of the parabola is at (-4,-1).
To find the equation of the parabola, we need to know two more points on the graph. We are given that when the y-value is 0, the x-value is 10-D. We can use this information to find another point on the graph.
When the y-value is 0, we have:
0 = a(10-D)² + b(10-D) + c
Simplifying this equation gives:
0 = 100a - 20aD + aD² + 10b - bD + c
Since the vertex is at (-4,-1), we know that:
-1 = a(-4)² + b(-4) + c
Simplifying this equation gives:
-1 = 16a - 4b + c
We now have two equations with three unknowns (a,b,c). To solve for these variables, we need one more point on the graph. Let's use the point (0,-5) as our third point.
When x = 0, y = -5:
-5 = a(0)² + b(0) + c
Simplifying this equation gives:
-5 = c
We can now substitute this value for c into the other two equations to get:
0 = 100a - 20aD + aD² + 10b - bD - 5
-1 = 16a - 4b - 5
Simplifying these equations gives:
100a - 20aD + aD² + 10b - bD = 5
16a - 4b = 4
We now have two equations with two unknowns (a,b). We can solve for these variables by using substitution or elimination. For example, we can solve for b in the second equation and substitute it into the first equation:
16a - 4b = 4
b = 4a - 1
100a - 20aD + aD² + 10(4a-1) - D(4a-1) = 5
Simplifying this equation gives:
aD² - 20aD - 391a + 391 = 0
We can now use the quadratic formula to solve for D:

D = [20 ± sqrt(20² - 4(a)(391a-391))]/2a
D = [20 ± sqrt(400 - 1564a² + 1564a)]/2a
D = 10 ± sqrt(100 - 391a² + 391a)/a
There are two possible values for D, depending on the value of a. However, since we don't have any information about the sign of a, we cannot determine which value of D is correct. Therefore, the final equation of the parabola is:
y = ax² + bx - 5

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The completed table for the Pythagorean triples are:

\(x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (6,8,10)\\\text{ } \text{ } \text{ } 4 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)\)

  \(\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (10,24,26)\\\text{ } \text{ } \text{ } 6 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)\).

A trio of positive numbers known as a Pythagorean triple fits into the Pythagoras theorem's formula, which is written as a² + b² = c², where a, b, and c are all positive integers. Here, "a" and "b" make up the other two legs of the right-angled triangle, and "c" serves as the triangle's "hypotenuse," or longest side. In terms of the Pythagorean triples (a, b, c).

In the question, we are given that a triangle with side lengths x² - 1, 2x, x² + 1 is a right triangle, and are asked to fill in the missing table:

\(x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)\\\)

  \(\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)\).

Taking x as 3, and putting in the sides, we get:

x² + 1 = 3² + 1 = 10.

2x = 2*3 = 6.

x² - 1 = 3² - 1 = 8.

Thus, the triplet is 6,8,10.

For the triplet 8,15,17, we get the x value as:

2x = 8,

or, x = 8/2 = 4.

Thus, the x-value for the triplet (8,15,17) is 4.

Taking x as 5, and putting in the sides, we get:

x² + 1 = 5² + 1 = 26.

2x = 2*5 = 10.

x² - 1 = 5² - 1 = 24.

Thus, the triplet is 10,24,26.

For the triplet 12,35,37, we get the x value as:

2x = 12,

or, x = 12/2 = 6.

Thus, the x-value for the triplet (12,35,37) is 6.

Thus, the completed table for the Pythagorean triples are:

\(x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (6,8,10)\\\text{ } \text{ } \text{ } 4 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)\)

  \(\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (10,24,26)\\\text{ } \text{ } \text{ } 6 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)\).

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The provided question is incomplete. The complete question is:

"We know that a triangle with side lengths x² - 1,2x and x² + 1 is a right triangle. Using those side lengths, find the missing triples and x-values.

Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.

Type the correct answer in each box.

\(x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)\\\)

  \(\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)\).

The given second-order linear differential equation y" + 9y = 2x + 4 with initial conditions y(0) = 0 and y'(0) = 1 can be solved using the method of Laplace transforms.

To solve the differential equation using Laplace transforms, we first take the Laplace transform of both sides of the equation. Applying the Laplace transform to the terms individually, we have:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 2X(s) + 4,

where Y(s) and X(s) are the Laplace transforms of y(t) and x(t), respectively. Substituting the initial conditions y(0) = 0 and y'(0) = 1, we get:

s²Y(s) - s(0) - 1 + 9Y(s) = 2X(s) + 4,

s²Y(s) + 9Y(s) = 2X(s) + 5.

Next, we need to find the Laplace transform of the right-hand side terms. Using the standard Laplace transform formulas, we obtain:

L{2x + 4} = 2X(s) + 4/s,

Substituting this into the equation, we have:

s²Y(s) + 9Y(s) = 2X(s) + 4/s + 5.

Now, we can solve for Y(s) by rearranging the equation:

Y(s) = (2X(s) + 4/s + 5) / (s² + 9).

Finally, we need to take the inverse Laplace transform of Y(s) to obtain the solution y(t). Depending on the complexity of the expression, partial fraction decomposition or other techniques may be necessary to find the inverse Laplace transform.

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Answer: 55 square feet

Step-by-step explanation:

To find area:
Length * Width

11 * 5 = 55

Answer: 55 sq. feet

explanation : 5 x 11 is 55, so 55 square feet

Answer:

\( \large{ \boxed{\tt{2 {x}^{3}y + 7 {y}^{2} x - 3 {x}^{2} - 12y}}}\)

- All you gotta do is writing the polynomial in the descending order of the power of the variable.

---- HappY LearninG <3 -------

Answer:

66, 114, 114

Step-by-step explanation:

angle 3=angle 1=66

angle 2=angle 4=180- angle 3=114

1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Answer:

24.28%

Step-by-step explanation

percent saved(p)/100 (net income)(weeks needed) = (total needed)

p/100 ($123.56)(9) = $270

p/100 (1112.04) = $270

1112.04p/100 = $270

p = 24.279%

p = 24.28%

The answer is (a) (30, 50). To find the 98% confidence limits,

We can use the formula:

\(98% confidence limits = sample mean ± (Z-score for 98% confidence level) * (standard error)\)

We don't know the sample mean or the standard error, but we do know the 90% confidence limits. We can use these to estimate the standard error:

Standard error = (90% confidence limits upper bound - 90% confidence limits lower bound) / (1.645 * 2)

Standard error = (47 - 33) / (1.645 * 2) = 4.73

Now we can use this to estimate the 98% confidence limits:

98% confidence limits = sample mean ± (2.33) * (4.73)

We know that the range of the 90% confidence limits is 14 (47 - 33). The range of the 98% confidence limits will be wider than this, so we can eliminate options b), c), and e).

Now we just need to check which of the remaining options gives us a range wider than 14. We can do this by subtracting the lower limit from the upper limit:

a) (30, 50) -> range = 20
d) (38, 45) -> range = 7

Therefore, the answer is (a) (30, 50).

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\((\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{5}{4}}(x-\stackrel{x_1}{1}) \\\\\\ y-3=\cfrac{5}{4}x-\cfrac{5}{4}\implies y=\cfrac{5}{4}x-\cfrac{5}{4}+3\implies {\Large \begin{array}{llll} y=\cfrac{5}{4}x+\cfrac{7}{4} \end{array}}\)

Answer:

Step-by-step explanation: Pasoon is not only lured by the promise of money but fueled by revenge and ... and a call for nanawatai (refuge), Reshmina is conflicted!

Answer:

No, because 30 is not equal to 2.5 times 6

Step-by-step explanation:

2.5 times 6 = 15

The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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1 cup will fills double than 1/2 cup, so:

With 1 cup you will be able to fills 4/3, in other words 1 full container and 1/3 of another.

A)the density of |x| is f(|x|) = 1/(1-0) = 1. B) the density of p|x| is f(p|x|) = 1/(p-0) = 1/p. C) the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0. D) the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

(a) To find the density of |x|, we need to consider the range of values that |x| can take. Since x is uniformly distributed on the interval (-1, 1), the absolute value of x can take values between 0 and 1. The density function of |x| is given by f(|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = 1. Therefore, the density of |x| is f(|x|) = 1/(1-0) = 1.

(b) To find the density of p|x|, we need to consider the range of values that p|x| can take. Since x is uniformly distributed on the interval (-1, 1), p|x| can take values between 0 and p. The density function of p|x| is given by f(p|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = p. Therefore, the density of p|x| is f(p|x|) = 1/(p-0) = 1/p.

(c) To find the density of -ln|x|, we need to consider the range of values that -ln|x| can take. Since x is uniformly distributed on the interval (-1, 1), -ln|x| can take values between 0 and ∞. The density function of -ln|x| is given by f(-ln|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a  = 0 and b = ∞. Therefore, the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0.

(d) To find the density of sin(x), we need to consider the range of values that sin(x) can take. Since x is uniformly distributed on the interval (-1, 1), sin(x) can take values between -sin(1) and sin(1). The density function of sin(x) is given by f(sin(x)) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = -sin(1) and b = sin(1). Therefore, the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

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The estimated distance for a 20-minute trip based on the best fit line equation is 9.757 miles.

The best fit line equation is given by y = 0.467x + 0.417, where y represents the distance in miles and x represents the time for the trip in minutes.

We must find the distance for a trip that takes 20 minutes.

Substituting x = 20 into the equation, we have:

y = 0.467(20) + 0.417

y = 9.34 + 0.417

y = 9.757 miles.

Complete question :

A taxi driver records the time required to complete various trips and the distance for each trip. The best fit line is given by the equation y = 0.467 x + 0.417 where y represents the distance in miles, and x represents the time for the trip in minutes. Use the best fit line to estimate the distance for a trip that takes 20 minutes.

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Answer:

7x=(4+3x)+(2+(4+3x))

Step-by-step explanation:

Ricardo=x

Natalie=4+3x

Keisha=2+(4+3x)

7x=(4+3x)+(2+(4+3x))

By adding together Keisha and Natalie's ages, you get the sum of their ages. By setting them equal to 7 times Ricardo's age, that would make the equation 7 times Riacardo's age equals the sum of Natalie's and Keisha's ages. I think this is asking you to combine the first function to create the second one that it is asking for.

Answer:

its the last one.

Step-by-step explanation:

easy way to do inverse functions:

write out equation :

y = 2\(x^{2}\) + 2

Switch the x and y:

x = 2\(y^{2}\) + 2

Solve for y :

x = 2\(y^{2}\) + 2

subtract 2 both sides

x - 2 = 2\(y^{2}\)

Divide both sides by 2

\(\frac{x}{2}\) - \(\frac{2}{2}\) = \(y^{2}\)

reduce fraction and square root both sides

Given -

-4x + 5y = -2

To Find -

Value of x and y

Step-by-Step Explanation -

At x = 0

-4(o) + 5y = -2

y = -2/5

At y = 0

-4(x) + 5(0) = -2

-4x = -2

x = 1/2

Final Answer -

Graph:

The statement that is NOT equivalent to the others is option c. "P(0) = r."

In the context of polynomials, a factor of a polynomial is a term or expression that divides evenly into the polynomial. So, if (x - r) is a factor of P(x), it means that when P(x) is divided by (x - r), the remainder is zero. This is equivalent to saying that r is a zero or root of the polynomial P(x). In other words, if r is a zero of P(x), then P(r) = 0.

Option c, on the other hand, states that P(0) = r. This means that when x is equal to zero, the value of the polynomial P(x) is equal to r. This statement does not provide any information about whether (x - r) is a factor of P(x) or if r is a zero of P(x). It simply relates the value of the polynomial at x = 0 to the constant value r.

To summarize, options a, b, and d are equivalent because they all refer to the fact that r is a zero of the polynomial P(x), while option c does not provide the same information and is therefore not equivalent to the others.

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Answer:

1 hour and 50 minutes will take to fill up a 300 gallon swimming pool explanation just do the quation/math

At a rate of 4 gallons per min , how long will it take to fill a 300 gallon swimming pool

Time to fill = Total Gallons of the Pool / Fill Rate

Time to Fill = 300 gallons / 4 gallons per minute

Time to Fill = 75 minutes

Pierre's question is a common philosophical and scientific question about the nature of prediction and probability.

In the 18th century, there was not a comprehensive understanding of the scientific laws that govern the natural world as we have today. Therefore, the most reasonable response to Pierre's question would be that it depends on the probability model used. The probability of the sun rising tomorrow would be based on various factors such as astronomical observations, scientific knowledge of celestial mechanics, and weather patterns.

While we cannot predict the future with absolute certainty, we can use available data and knowledge to make informed predictions about the likelihood of the sun rising tomorrow.

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The probability of getting a five or higher on the first roll and getting a total of 7 on the two dice is 1/18.

Step 1: Calculate the probability of getting a five or higher on the first roll.
There are two favorable outcomes (rolling a 5 or a 6), and there are six possible outcomes (rolling 1, 2, 3, 4, 5, or 6) on the first dice. So, the probability of getting a five or higher is:

P(5 or higher) = Favorable Outcomes / Total Outcomes = 2/6 = 1/3

Step 2: Calculate the probability of getting a total of 7 on the two dice.
There are six possible outcomes on each dice, making 6 x 6 = 36 possible outcomes in total. There are six favorable outcomes that result in a total of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of getting a total of 7 is:

P(total of 7) = Favorable Outcomes / Total Outcomes = 6/36 = 1/6

Step 3: Calculate the probability of both events occurring.
Since the two events are independent, you can multiply their probabilities to find the probability of both events occurring:

P(5 or higher on first roll and total of 7) = P(5 or higher) × P(total of 7) = (1/3) × (1/6) = 1/18

So, the probability of getting a five or higher on the first roll and getting a total of 7 on the two dice is 1/18.

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Answer:

Simplifying  the expression: \(2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)\) we get \(\mathbf{42x-100y-360}\)

Step-by-step explanation:

We need to simplify the expression: \(2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)\)

First we will solve terms inside the bracket

\(2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)\)

Converting mixed fraction \(1\frac{1}{2} y\) into improper fraction, we get: \(\frac{3}{2}y\)

Replacing the term:

\(2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-\frac{3}{2}y +3)\)

Now, taking LCM of: 5,3,4,2 we get 60

Now multiply 60 with each term inside the bracket

\(2(\frac{3}{5}x\times60+\frac{2}{3}y\times60-\frac{1}{4}x\times60-\frac{3}{2}y\times60 +3\times60)\\2(3x\times12+2y\times20-1x\times15-3x\times30-3\times60)\\2(36x+40y-15x-90y-180)\)

Now, combine like terms

\(2(36x-15x-90y+40y-180)\\2(21x-50y-180)\)

Now, multiply all terms with 2

\(42x-100y-360\)

So, Simplifying  the expression: \(2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)\) we get \(\mathbf{42x-100y-360}\)

Answer:

We can use the formula for the area of a triangle to solve for the height of the isosceles triangle, which will then allow us to find the lengths of the other two sides.

Let h be the height of the isosceles triangle, and let s be the length of each of the two equal sides. Then the area of the triangle is given by:

A = (1/2)bh = (1/2)(10m)(h) = 5h

We also know that the area of the triangle is 60 square meters, so we can set these two expressions equal to each other and solve for h:

5h = 60

h = 12

Now that we know the height of the triangle is 12 meters, we can use the Pythagorean theorem to find the length of each of the other two sides:

s^2 = h^2 + (1/2b)^2

s^2 = 12^2 + (5^2)

s^2 = 169

s = sqrt(169)

s = 13

Therefore, the lengths of the other two sides of the isosceles triangle are both 13 meters.

The composite transformations of the triangle ΔABC, with vertices A(1, -2), B(4, -1), and C(5, -3), are the points;

A''(-3, 6)

B''(6, 9)

C''(9, 3)

A composite transformation is the transformation obtained by the combination of two or more transformation on a geometric figure.

The coordinates of the vertices of the triangle are; A(1, -2), B(4, -1), and C(5, -3), therefore, we get;

1. <-2, 4>

The transformation <-2, 4> is a translation 2 units to the left and 4 units upwards

The coordinates of the image following the transformation are therefore;

A(1, -2) → <-2, 4> → (1 + -2, -2 + 4) = A'(-1, 2)

B(4, -1) → <-2, 4> → (4 + -2, -1 + 4) = B'(2, 3)

C(5, -3) → <-2, 4> → (5 + -2, -3 + 4) = C'(3, 1)

2. The dilation of a point (x, y), by a scale factor of k can b obtained using the following formula;

(x, y) → Dilation by a scale factor of k → (k·x, k·y)

Therefore, the dilation of the image of the triangle ΔABC by a scale factor of k = 3, can be obtained as follows;

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According to Chebyshev's theorem, the percentage of average low temperatures in Rochester, NY between 7.6 and 28.4 is at least 75.68%

According to Chebyshev's theorem, we have the following formula: \($$\text{Percentage of observations within }k\text{ standard deviations of the mean}\ge 1-\frac{1}{k^2}$$\)

where k is the number of standard deviations from the mean. We can rewrite the given interval [7.6,28.4] in terms of standard deviations from the mean as follows: \($$\text{Lower bound: }\frac{7.6-18}{5.2}\approx-2.02$$$$\text{Upper bound: }\frac{28.4-18}{5.2}\approx1.96$$\)

So, the interval [7.6,28.4] is approximately 2.02 to 1.96 standard deviations from the mean. The minimum percentage of observations within this range is given by:\($$1-\frac{1}{(2.02)^2}=1-\frac{1}{4.0804}=0.7568$$\). Therefore, the answer is 75.68%.

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