Derek is watching a thunderstorm. He hears the thunder 4.7 s after seeing a flash of lightning. How far away was the lightning?

Answer:

the third one

Step-by-step explanation:

8x + 40 ≥ 0

8x ≥ -40

x ≥ -5

Answer:

A. 10 ft

Step-by-step explanation:

Since dimensions of the wall are similar to the dimensions of the window.

Therefore, lengths and widths of wall and window would be in proportion.

So,

\( \frac{h}{2} = \frac{24.5}{4.9} \\ \\ h = \frac{24.5 \times 2}{4.9} \\ \\ h = \frac{49}{4.9} \\ \\ h = \frac{490}{49} \\ \\ h = 10 \: ft\)

R₄,₄ gives an approximation of order h⁸ when approximating ∫(a to b)f(x)dx using Romberg integration. Therefore second option is the correct answer.

When approximating the integral ∫(a to b) f(x) dx using Romberg integration, the term "R₄,₄" refers to the fourth row and fourth column of the Romberg matrix.

This specific entry represents the approximation obtained using the Romberg method with four iterations. The order of approximation is determined by the highest power of h in the error term of the approximation.

Since R₄,₄ has a subscript of 4, it indicates that the approximation is of order h⁸. This means that the error decreases at a rate of h⁸ as the step size h decreases, providing a more accurate estimation of the integral.

Therefore the correct answer is second option.

The question should be:

When approximating ∫(a to b)f(x)dx using Romberg integration, R₄,₄ gives an approximation of order:

h10  

h8

h4

h6

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In a manufacturing process, shaft diameters are normally distributed with a mean of 21.002 mm and a standard deviation of 0.005 mm. We need to calculate various probabilities and proportions related to shaft diameters.

a. To find the proportion of shafts with a diameter between 20.989 mm and 21.000 mm, we calculate the z-scores for these values using the formula: z = (x - μ) / σ, where x is the diameter, μ is the mean, and σ is the standard deviation. The z-score for 20.989 mm is z1 = (20.989 - 21.002) / 0.005, and for 21.000 mm, z2 = (21.000 - 21.002) / 0.005. We then use the z-scores to find the proportion using a standard normal distribution table or calculator. b. The probability that a shaft is acceptable corresponds to the proportion of shafts with diameters within the acceptable range of 20.989 mm to 21.011 mm. Similar to part (a), we calculate the z-scores for these values and find the proportion using the standard normal distribution.

c. To determine the diameter that will be exceeded by only 5% of the shafts, we need to find the z-score that corresponds to the cumulative probability of 0.95. Using the standard normal distribution table or calculator, we find the z-score and convert it back to the diameter using the formula: x = z * σ + μ.

d. If the standard deviation of the shaft diameters were 0.004 mm, we repeat the calculations in parts (a), (b), and (c) using the updated standard deviation value. By performing these calculations, we can obtain the requested proportions, probabilities, and diameters for the given manufacturing process.

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The type parameters act as placeholders for the types of the arguments passed to a method. The type parameter names throughout the method declaration must match those declared in the type parameter list.

Pass an array as a pointer to pass it as a parameter to a function (since it is a pointer). For instance, the following method sets array A's first n cells to 0.

In C++, an entire array cannot be provided as an argument. However, by mentioning the array's name, you can supply a pointer to an array without an index.

Only the array name is supplied as a parameter to pass a full array to a function. calculateSum(num), result But take note of how [] is used in the function specification. This tells the compiler that you are handing the function a one-dimensional array.

When we provide an array to a function as an argument, we are actually passing the address of the array in memory, which is the reference. To pass an array to a function, simply pass the array as the function's parameter (like normal variables).

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To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

How do I calculate a circle's circumference?

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

Given: theta angle (central) = 7.2°; arc length S = 800 km

This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).

By definition, "An arc's length is a portion of a circle's diameter."

Therefore, we must first establish what percentage of the circle the specified arc length represents.

360° is a complete circle.

Thus, the fraction equals 7.2°/360°, or 1/50.

As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.

Thus, the whole circumference is 800 x 50, or 40000 km.

Alternately, you can calculate circumference using the formula below:

360° center angle x arc length as the circumference (theta)

Values substituted: circumference 800 = 360° 7.2°

circumference = 360°, 800°, and 7.2°, or 40000 kilometers

Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

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Answer:

489 1/2 cm

Step-by-step explanation:

So, the best first step is to break the complex shape into two smaller ones. I suggest breaking it down into 5 1/2 x 1 1/2 x 5 1/2 ( the smaller shape) and 9 1/2 x 5 1/2 x 8 1/2 (I got 8 1/2 but subtracting 5 1/2 from 14, I can elaborate if you need to). After that, just multiply and add. The first shape gives you 45 3/8. The second shape gets you 444 1/8. If you add them together, they give you 489 4/8 cm, simplified 489 1/2 cm.

(Tell me if this is incorrect)

Hope this helps!

In the given triangle, the length of AB is 3√3 units

The perimeter is 2√5 + √7 + 3√3 units

From the question, we are to determine the length of AB and then calculate the perimeter of the triangle

To determine the length of AB, we will use the Pythagorean theorem

We can write that

AB² = AC² + BC²

AB² = (2√5)² + (√7)²

AB² = 20 + 7

AB² = 27

AB = √27

AB = 3√3

The length of AB is 3√3 units

To calculate the perimeter, we will sum the length of all sides of the triangle

Perimeter of the triangle = 2√5 + √7 + 3√3 units

Hence, the perimeter is 2√5 + √7 + 3√3 units

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Answer: (I am really not sure the answer if it is wrong I am so sorry)

h=3, k=2

Horizontal: up, 2 units

Vertical: up, 3 units

Answer:

9 students play sodoku and chess.

Step-by-step explanation:

What do we have?

2/3; play sudoku

3/8; play chess

24; students total

Find a common denominator for the fractions:

2/3x8/8

3/8x3/3

Now we have:

16/24

9/24

This also makes sense because we have a total of 24 students, now we want to know how many of them play sodoku AND chess; which was originally 3/8.

It's 9 students!

There are 16 students playing chess and 6 students playing sudoku.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Given that 2/3 of the students play sudoku. of the students who play sudoku​, 3/8 also play chess.

And there are 24 students in his ​class

First, we must determine how many students play chess, which is: In this scenario, we must multiply the total number of students by fractions to reach the answer.

⇒ 2/3×24 = 16

So 16 students are playing chess, and now, 3/8 of them are playing sudoku.

⇒ 3/8×16 = 6

Hence, there are 16 students playing chess and 6 students playing sudoku.

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The limit of the function as x approaches 1 does not exist, since the function becomes infinitely large as x approaches 1 from both sides.

To evaluate the limit, we can start by analyzing the behavior of the function as x approaches 1 from both sides of the limit. We can also use a graph to visualize the function and see how it behaves near x = 1.

Here is a graph of the function f(x) = 1/(x^2 - 1):

Graph of f(x) = 1/(x^2 - 1)

As we can see from the graph, the function has vertical asymptotes at x = -1 and x = 1. This means that as x approaches 1 from both sides, the function becomes infinitely large.

To confirm this, let's evaluate the limit using algebraic manipulation:

lim x->1 1/(x^2 - 1)

= lim x->1 (1/((x-1)(x+1)))

= ∞

Therefore, the limit of the function as x approaches 1 does not exist, since the function becomes infinitely large as x approaches 1 from both sides.

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Answer:

8.5

Step-by-step explanation:

Applying pythagora's theorem,

hypotenuse^2 = opposite^2 + adjacent^2

but, hypotenuse = 9

opposite = X

adjacent = 1/2(base of triangle)= 1/2(6)

adjacent = 3

9^2 = X^2 + 3^2

X^2 = 81 - 9

X^2 = 72

X = 8.5

Two angles form a linear pair.

so, the sum of the angles are 180

the measure of the angles are z and (2.4 * z + 10)

so,

z + (2.4 * z + 10) = 180

solve for z

so,

z + 2.4 * z + 10 = 180

3.4 z = 180 - 10

3.4 * z = 170

divide both sides by 3.4

so, z = 170/3.4 = 50

so, the angles are 50 and 130

The volume of the prism would be enlarged by a factor of 8

The scale factor is given as:

k = 2

Let the initial volume be v and the final volume be V.

The relationship between both volumes is

V = k^3 * v

This gives

V = 2^3 * v

Evaluate

V = 8v

Hence, the volume of the prism would be enlarged by a factor of 8

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Answer:

4ft

Step-by-step explanation:

sorry for my mistake

Answer:

4 ft

Step-by-step explanation:

the ratios are as follows

X/6=50/75

50(6)=X(75)

300=75X

X=4

Solving a quadratic equation we can see that the 3 consecutive numbers are:

4, 5, and 6.

First, we can write 3 consecutive integers as:

x, (x + 1), and (x +2 )

The square of the first increased by the last is 22, then we can write:

x^2 + (x + 2) = 22

x^2 + x + 2 - 22 = 0

x^2 +x  - 20 = 0

Using the quadratic formula we will get the solutions:

\(x = \frac{-1 \pm \sqrt{1^2 - 4*1*-20} }{2} \\\\x = \frac{-1 \pm 9}{2}\)

We know that x is positive, then the solution is:

x = (-1 + 9)/2 = 4

The 3 consecutive numbers are:

4, 5, and 6.

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Answer:

(4,2)

Step-by-step explanation:

THIS IS ASSUMING you are scaling it around 0,0

S is 2,1.

(x',y') = (2,1)

You want to find the coords with a scale factor of 2.

(x',y') = 2(2,1)

x',y' = 4,2

(4,2)

Answer:

900 ml of milk

Step-by-step explanation:

the scale is 1:1 so just multiply by 3

For a two-dimensional potential flow, the potential is given by 1 r (x, y) = x (1 + arctan x² + (1+ y)², 2πT where the parameter A is a real number. Given potential function is;ϕ(x,y) = x(1 + arctan(x² + (1+y)²))/2πT

To find velocity components ux and uy, we need to take partial derivative of potential functionϕ(x,y) = x(1 + arctan(x² + (1+y)²))/2πTUsing the chain rule;    ∂ϕ/∂x = ∂ϕ/∂r * ∂r/∂x + ∂ϕ/∂θ * ∂θ/∂x                                                                                             = cosθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT           - sinθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT ∂ϕ/∂y = ∂ϕ/∂r * ∂r/∂y + ∂ϕ/∂θ * ∂θ/∂y                                                                                              = cosθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT           - sinθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πTNow, replace cosθ and sinθ with x/r and y/r respectively∂ϕ/∂x = x/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT- y/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT= [x²-y²]/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT∂ϕ/∂y = y/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT + x/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT= [2xy]/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT(2) To find stagnation point, we have to find (x,y) such that ux = uy = 0 and ϕ(x,y) is finite. Here, from (1) we get two equations;  x(1+arctan(x² + (1+y)²))/2πT= 0 and  x(1+arctan(x² + (1+y)²))/2πT + y(1+arctan(x² + (1+y)²))/2πT= 0For (1), either x=0 or arctan(x² + (1+y)²) = -1, but arctan(x² + (1+y)²) can't be negative so x=0. Thus, we get the condition y= -1  from (2)So, stagnation point is (0, -1).(3) For the far field, pressure is p, density is P. In potential flow, we have;  P = ρv²/2 + P0,  where P0 is constant pressure. Here, P0 = P and v = ∇ϕ   so, P = ρ[ (∂ϕ/∂x)² + (∂ϕ/∂y)² ]/2Using expressions of ∂ϕ/∂x and ∂ϕ/∂y obtained above, we can find pressure at (0,-2).(4) Given flow is around a cylinder. For flow around cylinder, stream function can be written as;   ψ(r,θ) = Ur sinθ (1-a²/r²)sinθTo find centre and radius of the cylinder, we find point where velocity is zero. We know that ψ is constant along any streamline. So, at the boundary of cylinder, ψ = ψ0, and at the centre of the cylinder, r=0.Using stream function, it is easy to show that ψ0= 0.So, at boundary of cylinder; U(1-a²/R²) = 0, where R is radius of cylinder, which gives R=aSimilarly, at centre; U=0To find the resulting force on the cylinder, we first have to find the lift and drag coefficients;  C_d = 2∫_0^π sin²θ dθ = π/2   and  C_l = 2∫_0^π sinθ cosθ dθ = 0We know that C_d = F_d/(1/2 ρ U²L) and C_l = F_l/(1/2 ρ U²L)where L is length of cylinder.So, F_d = π/2 (1/2 ρ U²L) and F_l= 0. Thus, the resulting force is F= (π/2) (1/2 ρ U²L) at an angle 90° to the flow direction.

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Using these values, we can write Bernoulli's equation as: P + 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2) = P_far

P = P_far - 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2)

(1) To determine the expression for the velocity components ux and uy, we can use the relationship between velocity and potential in potential flow:

ux = ∂Φ/∂x

uy = ∂Φ/∂y

Taking the partial derivatives of the potential function Φ(x, y) with respect to x and y:

∂Φ/∂x = (1+arctan(x^2+(1+y)^2)) - x * (1/(1+x^2+(1+y)^2)) * (2x)

∂Φ/∂y = -x * (1/(1+x^2+(1+y)^2)) * 2(1+y)

Simplifying these expressions, we have:

ux = 1 + arctan(x^2+(1+y)^2) - 2x^2 / (1+x^2+(1+y)^2)

uy = -2xy / (1+x^2+(1+y)^2)

(2) To find the value of A such that the point (x, y) = (0,0) is a stagnation point, we need to find the conditions where both velocity components ux and uy are zero at that point. By substituting (x, y) = (0,0) into the expressions for ux and uy:

ux = 1 + arctan(0^2+(1+0)^2) - 2(0)^2 / (1+0^2+(1+0)^2) = 1 + arctan(1) - 0 = 1 + π/4

uy = -2(0)(0) / (1+0^2+(1+0)^2) = 0

For the point (x, y) = (0,0) to be a stagnation point, ux and uy must both be zero. Therefore, A must be chosen such that:

1 + π/4 = 0

A = -π/4

(3) To determine the pressure at the point (0, -2), we can use Bernoulli's equation for potential flow:

P + 1/2 * ρ * (ux^2 + uy^2) = constant

At the far field, where the velocity is assumed to be zero, the pressure is constant. Let's denote this constant pressure as P_far.

At the point (0, -2), the velocity components ux and uy are:

ux = 1 + arctan(0^2+(1-2)^2) - 2(0)^2 / (1+0^2+(1-2)^2) = 1 + arctan(5) - 0 = 1 + arctan(5)

uy = -2(0)(-2) / (1+0^2+(1-2)^2) = 4 / 3

Using these values, we can write Bernoulli's equation as:

P + 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2) = P_far

Solving for P at the point (0, -2), we have:

P = P_far - 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2)

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This is because the F-statistic for omitting BDR and Age from the regression is 0.08, which is less than the critical value for the test using the F-distribution table.

To test if the coefficients on BDR and Age are statistically different from zero, we compare the F-statistic with the critical value from the F-distribution table. The F-statistic is a measure of the overall significance of the regression model when certain variables are omitted.

In this case, the F-statistic is given as 0.08. To determine if the coefficients are statistically different from zero at the 5% level, we compare this value with the critical value from the F-distribution table. The critical value represents the threshold beyond which we reject the null hypothesis.

Based on the statement provided, it states that 0.08 is "less than the critical value." Since the F-statistic is smaller than the critical value, we can conclude that the coefficients on BDR and Age are not jointly significant at the 5% level. In other words, we fail to reject the null hypothesis that the coefficients are equal to zero.

The use of the phrase "jointly significant" implies that the significance of the coefficients is considered together, rather than individually. The test assesses the overall impact of BDR and Age on the regression model, rather than their individual effects. Since the F-statistic falls below the critical value, we do not have sufficient evidence to conclude that BDR and Age have a significant impact on the model.

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The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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The regression analysis evaluates the amount of relationship that exists

between the variables in the analysis.

Reasons:

First part;

The given data is presented as follows;

\(\begin{tabular}{|cc|c|}Lemon Imports (x) &&Crash Fatality Rate\\232&&16\\268&&15.7\\361&&15.4\\472&&15.5\\535&&15\end{array}\right]\)

The least squares regression equation is; \(\overline y = b \cdot \overline x + c\)

Where;

\(b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}\)

\(\overline y\) = The mean crash fatality = 15.52

\(\overline x\) = The mean lemon import = 373.6

Therefore;

\(b = \dfrac{-171.36 }{67093.2 } = -0.00255\)

c = \(\overline y\) - b·\(\overline x\) = 15.52 - (-0.00255)×373.6 = 16.47268

Therefore;

Second part;

When the imports is 425 metric tons of lemon, we have;

\(\overline y\) = -0.00255 × 425 + 16.47268 = 15.38893 ≈ 15.4

Therefore;

When the import is 425 metric tons, the Crash Fatality Rate ≈ 15.4

Given that the predicted value is between the values for 268 and 535, we

have that the prediction is approximately correct or worthwhile

The prediction is worthwhile

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In the given triangle, the length of g, to the nearest 10th of a centimeter is  134.3 cm

From the question, we are to determine the length of side g in the given triangle.

From the given information,

We have triangle FGH

From the law of sines, we can write that

g/sinG = h/sinH

From the given information,

h = 40 cm

∠H = 17°

and ∠F = 84°

Therefore,

∠H + ∠G + ∠F = 180° (Sum of angles in a triangle)

17° + ∠G + 84° = 180°

∠G + 101° = 180°

∠G = 180° - 101°

∠G = 79°

Thus,

g/sinG = h/sinH

g/sin79° = 40/sin17°

g = (40×sin79°)/sin17°

g = 134.3 cm

Hence, the length is 134.3 cm

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A quadrilateral is a polygon with four sides. It is a two-dimensional shape formed by connecting four non-collinear points. The perimeter of the quadrilateral is 20 units.

The angles of a quadrilateral can vary, and it can have sides of different lengths. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Quadrilaterals have certain properties and characteristics. Some common properties include:

Interior angles: The sum of the interior angles of a quadrilateral is always equal to 360 degrees.

Diagonals: A quadrilateral has two diagonals, which are line segments connecting opposite vertices. The diagonals of some quadrilaterals are perpendicular, while in others they intersect at a point inside the shape.

To find the perimeter of a quadrilateral with vertices at c (-2, 1), d (2, 4), e (5, 0), and f (1, -3), you can use the distance formula. The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)² )

So, let's calculate the distances between the vertices:

Distance between c and d:
d_cd = √((2 - (-2))² + (4 - 1)² )

Distance between d and e:
d_de = √((5 - 2)²  + (0 - 4)² )

Distance between e and f:
d_ef = √((1 - 5)² + (-3 - 0)² )

Distance between f and c:
d_cf = √((-2 - 1)²  + (1 - (-3))² )

Now, we sum the lengths of all four sides to find the perimeter:

Perimeter = CD + DE + EF + FC = 5 + 5 + 5 + 5 = 20

Therefore, the perimeter of the quadrilateral is 20 units.

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Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Answer:

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35 and 90 are the minimum and maximum values of the data set.

It means all observations are between those two numbers.

Hence the answer is 100%

Approximately 100% of the observations are between 35 and 90 in the given data set.

What is a median?

In statistics, the median is a measure of central tendency that represents the middle value of a set of data when arranged in ascending or descending order. It divides the data into two equal halves, with 50% of the values falling below the median and 50% falling above it.

To find the median, the data set is first arranged in order from smallest to largest (or vice versa). If the data set has an odd number of observations, the median is the middle value. For example, in a set of {1, 3, 5, 7, 9}, the median is 5.

The five-number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. In this case, the minimum value is 35, and the maximum value is 90. Since these values define the range of the data set, all the observations are between these two values.

Therefore, approximately 100% of the observations are between 35 and 90.

To know more about median, refer here:
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