Have 5 Points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

Step-by-step explanation:

67.1< (less than) 67.09

False

1880.09< (less than) 1880.023

False

Answer:

Step-by-step explanation:

sd

Answer:Yes

Step-by-step explanation:because you are

A)  The given function does not satisfy either of these conditions, so it is neither even nor odd.

B) the Fourier series for f(t) is simply f(t)= π.

(a) To sketch the graph of the function f(t) for −3π ≤ t ≤ 3π, we can break it down into the two intervals mentioned in the definition:

For −π ≤ t < 0, f(t) = −2t − π. This is a linear function with a negative slope, passing through the points (−π, π) and (0, −π). The graph is a straight line descending from the point (−π, π) to (0, −π) in the interval −π ≤ t < 0.

For 0 ≤ t < π, f(t) = 2t − π. This is also a linear function with a positive slope, passing through the points (0, −π) and (π, π). The graph is a straight line ascending from the point (0, −π) to (π, π) in the interval 0 ≤ t < π.

Since f(t + 2π) = f(t), the function repeats every 2π interval. Therefore, the graph will continue to repeat with the same pattern for each 2π interval.

Overall, the graph of f(t) will be a series of line segments: a descending line segment from (−π, π) to (0, −π), an ascending line segment from (0, −π) to (π, π), and so on, repeating every 2π.

Regarding the symmetry, we can observe that the function is neither even nor odd. An even function would have symmetry about the y-axis, meaning f(t) = f(-t). An odd function would have symmetry about the origin, meaning f(t) = -f(-t). However, the given function does not satisfy either of these conditions, so it is neither even nor odd.

(b) To calculate the Fourier series for f(t), we need to find the Fourier coefficients for the function. The Fourier series representation of f(t) is given by:

f(t) = a0 + Σ[an cos(nt) + bn sin(nt)]

where a0 is the DC component and an, bn are the Fourier coefficients.

To calculate the Fourier coefficients, we use the following formulas:

an = (1/π) ∫[−π, π] f(t) cos(nt) dt

bn = (1/π) ∫[−π, π] f(t) sin(nt) dt

Let's calculate the coefficients for this particular function:

a0 = (1/π) ∫[−π, π] f(t) dt

= (1/π) ∫[−π, 0] (-2t - π) dt + (1/π) ∫[0, π] (2t - π) dt

= (-2/π) ∫[−π, 0] t dt + (2/π) ∫[0, π] t dt

= (-2/π) [-t^2/2] from −π to 0 + (2/π) [t^2/2] from 0 to π

= (-2/π) * (0 - (−π)^2/2) + (2/π) * ((π)^2/2 - 0)

= π

an = (1/π) ∫[−π, π] f(t) cos(nt) dt

= (1/π) ∫[−π, 0] (-2t - π) cos(nt) dt + (1/π) ∫[0, π] (2t - π) cos(nt) dt

= (-2/π) ∫[−π, 0] t cos(nt) dt - (π/π) ∫[−π, 0] cos(nt) dt

+ (2/π) ∫[0, π] t cos(nt) dt - (π/π) ∫[0, π] cos(nt) dt

= (-2/π) * [-t sin(nt)/n] from −π to 0 - (1/π) * [sin(nt)/n] from −π to 0

+ (2/π) * [t sin(nt)/n] from 0 to π - (1/π) * [sin(nt)/n] from 0 to π

= (-2/π) * (0 - (−π) sin(nπ)/n) - (1/π) * (sin(nπ)/n - sin(-nπ)/n)

+ (2/π) * (π sin(nπ)/n - 0) - (1/π) * (sin(nπ)/n - sin(-nπ)/n)

= 0

bn = (1/π) ∫[−π, π] f(t) sin(nt) dt

= (1/π) ∫[−π, 0] (-2t - π) sin(nt) dt + (1/π) ∫[0, π] (2t - π) sin(nt) dt

= (-2/π) ∫[−π, 0] t sin(nt) dt - (π/π) ∫[−π, 0] sin(nt) dt

+ (2/π) ∫[0, π] t sin(nt) dt - (π/π) ∫[0, π] sin(nt) dt

= (-2/π) * [t (-cos(nt))/n] from −π to 0 - (1/π) * [-cos(nt)/n] from −π to 0

+ (2/π) * [t (-cos(nt))/n] from 0 to π - (1/π) * [-cos(nt)/n] from 0 to π

= (-2/π) * (0 - (−π) (-cos(nπ))/n) - (1/π) * (-cos(nπ)/n - (-cos(-nπ))/n)

+ (2/π) * (π (-cos(nπ))/n - 0) - (1/π) * (-cos(nπ)/n - (-cos(-nπ))/n)

= (4/n) * (cos(nπ) - cos(-nπ))

= (4/n) * (cos(nπ) - cos(nπ))

= 0

Since the Fourier coefficients an and bn are both 0, the Fourier series for f(t) simplifies to:

f(t) = a0

= π

Therefore, the Fourier series for f(t) is simply f(t) = π.

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The correct answer is option B which is Sn = -111974.

When there is a constant between the two successive numbers in the series then it is called a geometric series.

Here we have the following data:-

\(\sum_{n=1}^7-2.6^{n-1}\)

\(a_n = a_1r^{n-1}\ \ \ \ \ S_n = a_1(\dfrac{1-r^n}{1-r})\)

Here we need to calculate the first term second term and common ratio to calculate the sum of the series.

a₁ = -2.(6¹⁻¹) = -2

a₂ = -2.( 6²⁻¹) = -2 (6) =-12

Common ratio:-

\(a_n = a_1r^{n-1}\)

\(-12 = -2r^{2-1}\)

r = 6

Put all the values in the sum formula:-

\(S_n = -2(\dfrac{1-6^7}{1-6})\)

\(S_n = -2(\dfrac{279935}{5})=-2\times 55987\)

\(S_n\) = -111974

Therefore the correct answer is option B which is Sn = -111974.

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Answer:

90 cents

Step-by-step explanation:

7x+2(1.30)=10-1.10

7x=8.9-2.6

x=6.3/7= 0.9

Answer:

$.90 or 90 cents each

Step-by-step explanation:

10-2(1.30)-7(x)=1.10

10-2.6-7x=1.10

7.40-7x=1.10

7x=6.3

x=6.3/7

=.90

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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The angle of a body segment with respect to a fixed line of reference is known as a "relative angle."

The angle of a body segment with respect to a fixed line of reference is known as a reference angle. This angle is measured between the segment and the reference line, and is used to determine the position and orientation of the segment relative to other parts of the body or external objects. The segment itself refers to a specific part of the body, such as an arm, leg, or torso, that is bounded by two or more joints or points of attachment. By measuring the reference angle of a segment, it is possible to quantify the degree of movement or displacement of that segment, and to track changes in its position over time.
In this context, the angle represents the measurement of the difference in orientation between the body segment and the reference line, while the segment refers to a specific part of the body, such as an arm or leg. The reference line serves as a fixed point for comparison, allowing you to determine the position or orientation of the body segment in relation to it.

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Answer:

22 units.

Step-by-step explanation:

We want to find the perimeter of the polygon with vertices at: (-3, 1); (5, 1); (-3, 4); and (5, 4).

Let’s first plot the points and see what polygon we acquire. Please refer to the graph below.

As we can see, when plotting the points and connecting them, we get a rectangle.

So, we can use the perimeter formula for a rectangle, given by:

\(P=2(\ell+w)\)

Where \(\ell\) Is the length and \(w\) is width.

Remember that the perimeter is simply the distance around the figure.

So, let’s find the length. We can do so by counting or by subtracting.

By counting, we can see that the length (longer side) is 8 units.

And by subtracting, we get the same length of |5-(-3)| or 8 units.

We use absolute value because distance is always positive.

Using the same process, we find the width to be 3 units.

Using subtract, we can see that this is indeed true as |1-4|=3.

So, we can now substitute the values into our formula:

\(P=2(8+3)\)

Evaluate:

\(P=2(8+3)=2(11)=22\text{ units}\)

So, the perimeter of the polygon is 22 units.

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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9514 1404 393

Answer:

  2.41×10^14 miles

Step-by-step explanation:

The distance usually associated with a light-year is about 6 trillion miles. More precisely, it is about 5.879×10^12 miles. Then 41 light-years is 41 times that distance, or ...

  41 light-years = 41(5.879×10^12 miles) ≈ 2.41×10^14 miles

_____

You can figure the length of a light-year from the speed of light and the length of a year. The speed of light is about 186,282.4 miles per second. The number of seconds in a day is 86,400, and the number of days in a year averages 365.2425. Multiplying these values gets you to 5.878664e12 miles per year. The number used above is reasonable for most purposes. At astronomical distances, it is difficult to measure precisely.

The constants that we have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Here we can cancel both x term and y terms, lets choose x terms  and apply the elimination method

The coefficient of x in first equation is 5 and 12 in second equation

We have to make it same

Prime factorization

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Here we have eliminated x term

Hence, the constants that we have to multiply to eliminate one variable from the system are 12 and 5.

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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Answer:

25p^2 + 4 + 20p

Step-by-step explanation:

(5p + 2)^2 = (5p)^2 + (2)^2 + 2 × 5p × 2

= 25p^2 + 4 + 20p

The first 4 terms are 4 ,16,36 and 64 of the sequence (bn)n>=1 of partial sums of the sequence.

To find the first 4 terms of the sequence (bn)n≥1, we will calculate the partial sums as follows:

1. b1 = 4 (the first term)
2. b2 = b1 + 12 = 4 + 12 = 16 (sum of the first two terms)
3. b3 = b2 + 20 = 16 + 20 = 36 (sum of the first three terms)
4. b4 = b3 + 28 = 36 + 28 = 64 (sum of the first four terms)

So, the first 4 terms of the sequence (bn)n≥1 are 4, 16, 36, 64.

Now let's determine a recursive definition for bn. Notice that the difference between each term in the original sequence is 8 (12 - 4, 20 - 12, and 28 - 20). So, we can write the recursive definition as:

bn = bn-1 + 8n, for n > 1, and b1 = 4 (the first term).

This recursive definition can be used to find any term in the sequence (bn)n≥1 of partial sums.

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The measure of the other two angles of the triangle in the ratio 3:11 are 15° and 55° respectively.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

We recall that the sum of interior angles of a triangle is 180° and given one angle 110° and the ratio of the other two as 3: 11, then by comparison using the variable x;

110° + 3x + 11x = 180°

110° + 14x = 180°

14x = 180° - 110° {collect like terms}

14x = 70°

x = 70/14 {divide through by 14}

x = 5

so the two angles will be:

3(5) = 15°

11(5) = 55°

Therefore, the measure of the other two angles of the triangle in the ratio 3:11 are 15° and 55° respectively.

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The Correlation coefficient is 0.9754.

First step is to calculate the coefficient of determination R² using this formula

R²=13555.42/14248.90

R²=0.9513

Second step is to calculate the correlation coefficient using this formula

Correlation coefficient=√R²

Let plug in the formula

Correlation coefficient=√0.9513

Correlation coefficient=0.9754

Therefore the Correlation coefficient is 0.9754.

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Answer:

1633.52 cm^3

Step-by-step explanation:

first I find that the length of the side nearest to the 45 degree mark, it being  approximately 8 square roots of 2

next  i find that the diameter is equal to this height, when i put it through my calculations, so this is the radius of the cone.

the final answer is approximately 1633.52 cm^3

Answer:

\( \frac{1}{3} \pi {( \frac{8}{ \sqrt{2} } )}^{2} ( \frac{16}{ \sqrt{2} } ) = \frac{1}{3} \pi(32)(8 \sqrt{2} ) = 379.13\)

\( \frac{1}{3} (3.14)(32)(8 \sqrt{2} ) = 378.93\)

Since we need to use 3.14 for π, the volume of this cone is about 378.93 cm^3.

Answer:

%41.8 or 0.418

Step-by-step explanation:

I didn't know how you wanted the answer so there.

To get the answer you divide 627 by 1500 to get 0.418 then multiply that by 100 to get your percent.

hope this helps. . .

have a good day. UwU

Answer:

41.8%

Step-by-step explanation:

(627/1500) * 100 = 41.8

While calculating percentage for such questions, the total always is the denominator, while 'to be found percentage number' is the numerator.

Hope it helps!

An ellipsoid is a three-dimensional geometric shape that resembles a stretched or flattened sphere. It is defined by two axes of different lengths and a third axis that is perpendicular to the other two. The equation for the flattening factor is given by \(\(f = \frac{a - b}{a}\),\)where \(a\) represents the length of the major axis and \(b\) represents the length of the minor axis.

An ellipsoid is a geometric shape that is obtained by rotating an ellipse around one of its axes. It is characterized by three axes: two semi-major axes of different lengths and a semi-minor axis perpendicular to the other two. The ellipsoid can be thought of as a generalized version of a sphere that has been stretched or flattened in certain directions. It is used to model the shape of celestial bodies, such as the Earth, which is approximated as an oblate ellipsoid.

An ellipse, on the other hand, is a two-dimensional geometric shape that is obtained by intersecting a plane with a cone. It is defined by two foci and a set of points for which the sum of the distances to the foci is constant. An ellipse differs from a sphere in that it is a flat, two-dimensional shape, while a sphere is a three-dimensional object that is perfectly symmetrical.

The flattening factor (\(f\)) of an ellipsoid represents the degree of flattening compared to a perfect sphere. It is calculated using the equation\(\(f = \frac{a - b}{a}\),\\\) where \(a\) is the length of the major axis (semi-major axis) and \(b\) is the length of the minor axis (semi-minor axis). The flattening factor provides a quantitative measure of how much the ellipsoid deviates from a spherical shape.

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Answer:

x = 15

Step-by-step explanation:

Step 1: Set up the equation.

Step 2: Simplify both sides of the equation.

Step 3: Subtract 45 from both sides.

Step 4: Divide both sides by 9.

If your train travels at 65 miles per hour for 3.5 hours, it go 227.5 miles.

What is Speed ?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

Given:

Speed S = 65 miles per hour

Time T = 3.5 hours

We know that,

S= D/T  Where D is the distance traveled.

Therefore,

65 miles per hour = D/ 3.5 hours

D = 65 x 3.5 miles

=227.5 miles

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Answer: Let x be the number of shirts that David buys.

The cost of the shirts can be represented by the equation: $15x.

The total amount of money that David has spent can be represented by the equation: $32.25 + $15x.

Since David has a total of $65 to spend, we can write the inequality:

$32.25 + $15x ≤ $65

Solving for x, we get:

$15x ≤ $65 - $32.25 = $32.75

$15x ≤ $32.75

$x ≤ $32.75 / $15 = 2.183333

Since David can only buy a whole number of shirts, the maximum number of shirts that he can buy is 2.

So, the maximum number of shirts David can buy is 2.

Step-by-step explanation:

The length, in units, of the rectangle is 7 units

The formula for calculating the area of a rectangle is expressed with the equation

A = lw

Given that the parameters are given as;

Now, we have that;

Length = l

width = 3 - l

Area = 28

Substitute the values, we get;

28 = l(3-l)

expand the bracket

28 = l² - 3l

Solve the quadratic equation

l² - 7l + 4l - 28 = 0

l - 7 = 0

l = 7 or l = -4

Hence, the value is 7 units

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4.

The volume of a cube equals its side cubed. Since the side of the cube is 12ft long, then its volume is given by:

Then, the volume of the cube, is:

5.

The volume of the prism equals the product of each of its dimensions. Then:

Then, the volume of the rectangular prism, is:

Answer:

Step-by-step explanation:

−4−(−7)=

The opposite of −7 is 7.

−4+7

Add −4 and 7 to get 3.

3

Answer:

3

Step-by-step explanation:

Think of -4-(-7) as -4+7

just remove the negative and add instead

your answer is 3

A parallelogram that must be a square can be described by the statement: "A parallelogram in which all angles are right angles (90 degrees) is a square."

In a parallelogram, opposite sides are parallel and congruent, and opposite angles are also congruent. However, for a parallelogram to be a square, it must have additional properties:

All angles are right angles: In a square, all four angles are equal and measure 90 degrees. This distinguishes a square from a general parallelogram where the angles can be acute or obtuse.

All sides are congruent: In a square, all four sides are equal in length. This equality of side lengths sets a square apart from a rectangular parallelogram, where only opposite sides are congruent.

Diagonals are congruent and bisect each other at right angles: The diagonals of a square are equal in length and intersect at right angles, dividing the square into four congruent right triangles.

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Complete question:

Which statement describes a parallelogram that must be a square? A parallelogram with opposite sides that are congruent and diagonals that bisect the angles. A parallelogram with a right angle and diagonals that bisect the angles. A parallelogram with a right angle and opposites sides that are congruent. A parallelogram with all sides congruent.

The number of ways can the selection be made is 84.

Given:

an executive hires 3 office workers from 8 applicants.

a ) .

Number of ways = C ( 8 , 3 )

C ( n , r ) = n! / ( n - r ) ! r!

C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!

= 8! / 5! * 3 !

= 8 * 7 * 6 * 5! / 5! * 3!

= 56 * 6 / 3!

= 56 * 6 / 3 * 2 * 1

= 56 * 3 / 2 * 1

= 28 * 3 / 1

= 28 * 3

= 84 ways

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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My age is 2 years from the given condition.

Given that, if you square my age and subtract 28 times my age, the result is 60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be my age.

Now, square my age is x²

28 times my age =28x

The square of my age and subtract 28 times my age, the result is 60.

x²-28x=60

⇒ x²-28x-60=0

⇒ x²+30-2x-60=0

⇒ x(x+30)-2(x+30)=0

⇒ (x+30)(x-2)=0

⇒ x=2

Hence, my age is 2 years from the given condition.

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To compute the values for X* and X**, we need to use the standard normal distribution and the cumulative distribution function (CDF).

Since X follows a normal distribution with mean 100 and standard deviation 20, we can standardize the values using the formula:

Z = (X - μ) / σ

where Z is the standardized value, X is the given value, μ is the mean, and σ is the standard deviation.

a. P(X < X*) = 80%

To find the value X* for which P(X < X*) = 80%, we need to find the z-score corresponding to this probability. Using Excel, we can use the NORM.INV function.

Excel Command: NORM.INV(0.8, 100, 20)

This command calculates the inverse of the cumulative distribution function (CDF) for the standard normal distribution with a probability of 0.8. The mean is set to 100, and the standard deviation is set to 20. The result will give us the value of X*.

b. P(X > X**) = 60%

To find the value X** for which P(X > X**) = 60%, we need to find the z-score corresponding to this probability and then use the formula to calculate X. Since we want the probability of X being greater than X**, we can use the complementary probability (1 - 0.6 = 0.4) to find the z-score.

Excel Command: NORM.INV (0.4, 100, 20)

This command calculates the inverse of the cumulative distribution function (CDF) for the standard normal distribution with a probability of 0.4. The mean is set to 100, and the standard deviation is set to 20. The result will give us the value of X**.

Using these Excel commands, you can input the formulas into Excel and obtain the values for X* and X**.

Learn more about cumulative distribution function (CDF) here,

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