Rowan is training to run in a race. He runs 15 miles in the first week, and each week following, he runs 3% more than the week before. Using a
geometric series formula, find the total number of miles Rowan runs over the first ten weeks of training, rounded to the nearest thousandth.

a) approximately 7.64% of all bags sold are underweight.

b)  the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

a) To find the fraction of all bags sold that are underweight, we need to find the area under the normal distribution curve to the left of 5 ounces. Using the standard normal distribution, we can calculate the z-score:

z = (5 - 5.1) / 0.07 = -1.43

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -1.43 is 0.0764. Therefore, approximately 7.64% of all bags sold are underweight.

b) To find the probability that none of the 5 bags in a bargain pack is underweight, we need to find the probability that each individual bag is not underweight. Using the result from part (a), the probability that one bag is underweight is approximately 0.0764. Therefore, the probability that none of the 5 bags is underweight is:

(1 - 0.0764)⁵ = 0.5595

Rounding to four decimal places, the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) To find the probability that the mean weight of the 5 bags is below the stated amount of 5 ounces, we need to use the sampling distribution of the mean. The mean of the sampling distribution is the same as the population mean, 5.1 ounces. The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size:

s = 0.07 / √(5) = 0.0313

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0313

= -3.19

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -3.19 is approximately 0.0007.

Therefore, the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) To find the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces, we need to use the sampling distribution of the mean again. The mean of the sampling distribution is still 5.1 ounces. The standard deviation of the sampling distribution is:

s = 0.07 / √(20)

= 0.0157

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0157
= -6.37

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -6.37 is essentially 0.

Therefore, the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

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Answer:

Step-by-step explanation:

Ok so we're just going to be doing a lot of supplementary work:

The angle adjacent to 85 degrees is equal to 180 - 85 = 95

We want to find the angle measures in the triangle where 95 degrees is. We can do this by using 40, finding the opposite angle, which is also 40 due to vertical angles theorem, finding the missing angle in the right-most triangle which is 180 - 105 - 40 = 35

Using vertical angles theorem again, we know the angle opposite 35 degrees is also 35. We found another angle for the middle triangle.

The missing angle for the middle triangle is 180 - 35 - 95 = 50

The angle opposite 50 is 50 because of the vertical- you already know.

Now the left triangle has angles Z, 60 and 50.

m<Z = 180 - 60 - 50

m<Z = 70

Hope this helps!

Answer:

Step-by-step explanation: First you do 5*5 and get 25. Then you do 25/8 and get 3 1/8.

When [tex]3x^{4}-x^{2}[/tex] is divided by [tex]x^{3}-x^{2}+2[/tex], the quotient is 3x and the remainder is [tex]5x^2-2x[/tex].

To see why, we perform long division as follows:    

    [tex]3x[/tex]

[tex]x^3 - x^2 + 2 | 3x^4 + 0x^3 - x^2 + 0x + 0[/tex]

                [tex]- 3x^4 + 3x^3 - 6x^2[/tex]

               -----------------------

                            [tex]3x^3 - 7x^2[/tex]

                         [tex]- 3x^3 + 3x^2 - 6x[/tex]

                          -------------------

                                    [tex]5x^2 - 2x[/tex]

The divisor is [tex]x^3 - x^2 + 2[/tex] and the dividend is [tex]3x^4 - x^2[/tex]. We start by dividing the highest degree term of the dividend by the highest degree term of the divisor, which gives 3x. We then multiply the divisor by this quotient and subtract the result from the dividend. We repeat this process with the resulting polynomial until the degree of the remainder is less than the degree of the divisor.

In this case, the remainder is [tex]5x^2-2x[/tex], which has a degree of 2 (less than the degree of the divisor). Therefore, we have found the quotient and remainder of the division.

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Answer:

x+8+2x-5. 2x+x+8-5. x=3

The correct answer is $9.50 of credit is left on the card. To find out how much credit is left on the card after Deshaun uses it for 30 minutes of calls, we need to plug in the value of x into the equation C=15.50-0.20x.

Deshaun has a card with $15.50 of credit on it. He is using it to make calls and the cost of each minute of calling is $0.20. To calculate how much credit Deshaun has left on his card after 30 minutes of calls, we need to use the equation C=15.50-0.20x, where x is the number of minutes of calls.

Since x represents the number of minutes of calls, we will plug in 30 for x:

C = 15.50 - 0.20(30)

C = 15.50 - 6

C = 9.50

Therefore, there is $9.50 of credit left on the card after Deshaun uses it for 30 minutes of calls.

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Answer:

Step-by-step explanation:

You want linear equations in standard form that describe the relations in the given tables.

A useful two-point formula for creating an equation in general form is ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

This will simplify to an equation of the form ...

  ax +by +c = 0 . . . . . . general form equation for a line

The corresponding standard form equation is ...

  ax +by = -c . . . . . . . . standard form equation for a line

The standard form has mutually prime coefficients and a positive leading coefficient. That may require removal of any common factors.

  (2 -(-2))(x -(-5) -(-1 -(-5))(y -(-2)) = 0

  4x +20 -4y -8 = 0 . . . . . . . . coefficients have a common factor of 4

  x -y +3 = 0 . . . . . . . . . general form

  x -y = -3 . . . . . . . . . standard form

  (12 -20)(x -(-2)) -(0 -(-2))(y -20) = 0

  -8x -16 -2y +40 = 0 . . . . . . coefficients have a common factor of -2

  4x +y -12 = 0 . . . . . . . . simplified to general form

  4x +y = 12 . . . . . . standard form

__

Additional comment

Another useful form of the equation of a line is "intercept form":

  x/a +y/b = 1 . . . . . . . where 'a' is the x-intercept and 'b' is the y-intercept

The table for line k shows the x-intercept is (3, 0) and the y-intercept is (0, 12). Then the line can be written as ...

  x/3 +y/12 = 1

Multiplying by 12 gives ...

  4x +y = 12 . . . . the required standard form

Answer:

When a car turns, the tire on the outside of the turn has to travel a greater distance than the tire on the inside of the turn. The difference in the distance traveled by the two tires is equal to the circumference of the circle that the car makes during the turn.

The radius of the circle is given as 16.1 ft, which means the diameter is 2 * 16.1 = 32.2 ft. The distance between the two front tires is given as 4.7 ft, which means that the radius of the circle traced by the inner tire is 16.1 - 2.35 = 13.75 ft, where 2.35 ft is half of the distance between the two front tires.

The circumference of the circle traced by the outer tire is 2 * π * 16.1 = 101.366 ft (rounded to three decimal places). The circumference of the circle traced by the inner tire is 2 * π * 13.75 = 86.415 ft (rounded to three decimal places).

The difference in the distance traveled by the two tires is:

101.366 - 86.415 = 14.951 ft (rounded to three decimal places)

Therefore, the tire on the outside of the turn travels about 14.951 ft further than the tire on the inside.

The amount we would have after 40 years will be $8183.27

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given that, an amount increasing exponentially every two years and with a rate of 15% and the amount is $500, we need to find the amount we would have after 40 years.

Since, the amount is increasing exponentially every two years, therefore,

T = 40 / 2 = 20 years

A = P(1+0.15)²⁰

A = 500(1+0.15)²⁰

A = 500(1.15)²⁰

A = 8183.27

Hence, the amount we would have after 40 years will be $8183.27

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The equation 4(x - 2) = 2(2x + 6) has no solution.

To solve the equation 4(x - 2) = 2(2x + 6), we must first use the distributive property to expand the equations. The distributive property states that a(b + c) = ab + ac.

Using the distributive property, we can expand the equation as follows:

4(x - 2) = 2(2x + 6)

4x - 8 = 4x + 12

Next, we must isolate the variable on one side of the equation. We can do this by subtracting 4x from both sides of the equation:

-8 = 12

This equation is not true, so there is no solution to the equation 4(x - 2) = 2(2x + 6).

In conclusion, the equation 4(x - 2) = 2(2x + 6) has no solution.

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Step-by-step explanation:

3 - (1/4)×(8/3 × 9)

3 - (1/4)×(8×9/3)

3 - (1/4)×(8×3)

3 - (1/4)×24

3 - 24/4

3 - 6 = -3

Answer: 7/2 + 7b

Step-by-step explanation:

When applying the distributive property, you want to start by identifying which value you are distributing. That value in this case will be 7/8.

7/8 is going to be multiplied with 4, then multiplied with 8b, and you will then find the sum of those to products:

( (7/8) * 4 ) + ( (7/8) * (8b) )

The first product simplified will be 7/2.

The second product simplified will be 7b.

The sum of those two products is: 7/2 + 7b.

Hope this helps.

The x-intercept is (-3,0) and the y-intercept is (0,9).

The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.

The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.

1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.

To find the x-intercept, set the function equal to 0 and solve for x:

0 = x^2 + 6x + 9

0 = (x+3)(x+3)

x = -3

To find the y-intercept, set x equal to 0 and solve for y:

y = 0^2 + 6(0) + 9

y = 9

Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).

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Answer:

3) The commercial costs $900 to produce and $110 each times it is aired.

Step-by-step explanation:

We can determine how expensive it is to produce a commercial by looking at the function C(n)'s output when n = 0 (when the commercial hasn't been aired yet).

C(0) = 110(0) + 900

C(0) = $900

So, the cost of producing a commercial is $900.

We can see that $110 is added to the cost each time n is incremented by 1. Therefore, it costs $110 each time the commercial is aired.

We can put these two statements together to deduce that answer option 3 is correct:

The commercial costs $900 to produce and $110 each times it is aired.

Answer:

Option 3

Step-by-step explanation:

900 is a constant number that never changes. However, the value of "110n" changes every time it is aired, because 110 is multiplied by a different number. This means that $110 represents the cost of airing it each time, because if it was hypothetically aired three times, you would multiply 110 by 3, proving that it is the cost to air it, and $900 is the production cost. It also makes no sense to produce the same commercial over and over again, so the cost that is multiplied has to be the amount of times that it is aired.

The expression [tex]log(x^4)[/tex] can be expanded as a constant multiple of log(x).

What is the logarithms?

A logarithm is a mathematical function that measures the number of times a given value (called the base) must be multiplied by itself to produce a specified value.

We can use the following properties of logarithms to expand the expression:

The expression [tex]log(x^4[/tex]) can be expanded using the following property of logarithms:

[tex]log(a^n) = n * log(a)[/tex]

Using this property, we can write:

[tex]log(x^4) = 4 * log(x)[/tex]

Hence, the expression [tex]log(x^4)[/tex] can be expanded as a constant multiple of log(x).

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Given trigonometric equation is equal to 2 so the it has been proved.

what is trigonometric identity?

A trigonometric identity is a mathematical equation that expresses a relationship between trigonometric functions of an angle. These identities are true for all values of the angle, and they allow us to simplify expressions involving trigonometric functions, manipulate them algebraically, or evaluate them more easily.

Trigonometric identities include basic relationships such as [tex]sin^2(x) + cos^2(x) = 1,[/tex] as well as more complex identities involving multiple functions such as the Pythagorean identity.

According to the question:
Let us begin by applying the trigonometric identity[tex]cos^2(x) + sin^2(x) = 1,[/tex]which is true for any angle x. Solving for[tex]cos^2(x)[/tex], we get [tex]cos^2(x) = 1 - sin^2(x).[/tex]

Using this identity, we can rewrite the given equation as

[tex]1 - sin^2((1/8)^2) + 1 - sin^2(3n/8) + 1 - sin^2(5n/8) + 1 - sin^2(7n/8) = 2[/tex]

Simplifying, we get:

[tex]4 - (sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8)) = 2[/tex]

Rearranging, we get:

[tex]sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8) = 2[/tex]
Now, let us apply the trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex], which is true for any angle x. Solving for [tex]sin^2(x),[/tex] we get [tex]sin^2(x) = 1 - cos^2(x)[/tex].
2=2
Therefore, the equation is true

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The value $\frac{6}{\sqrt{2}}$

a) The method of moments estimator for ϕ is given by:

$\hat{\phi} = \frac{\sum_{i=1}^{n}X_i}{n} = \frac{1.20}{60} = 0.02$

b) The likelihood and log-likelihood functions for ϕ are given by:

Likelihood: $L(\phi) = \prod_{i=1}^{n}\frac{1}{\sqrt{2\pi e \phi}} \exp \bigg( \frac{-X_i^2}{2\phi}\bigg)$

Log-Likelihood: $lnL(\phi) = -\frac{n}{2}ln(2\pi e \phi) - \frac{1}{2\phi}\sum_{i=1}^{n}X_i^2$

c) The score and observed Fisher information functions for ϕ are given by:

Score: $S(\phi) = \frac{1}{\phi}\sum_{i=1}^{n}X_i^2 - \frac{n}{\phi}$

Observed Fisher Information: $I(\phi) = \frac{n}{\phi^2}$

d) The maximum likelihood estimator for ϕ is given by:

$\hat{\phi}_{ML} = \frac{\sum_{i=1}^{n}X_i^2}{n} = \frac{1.20^2}{60} = 0.0096$

e) To use a Normal distribution to approximate the distribution of the maximum likelihood estimator for ϕ, it is necessary to show that $E[I(\phi)] = 2$. This can be done by computing $E[I(\phi)]$ directly:

$E[I(\phi)] = \frac{1}{\phi^2}E[\sum_{i=1}^{n}X_i^2] = \frac{n}{\phi^2}E[X_i^2] = \frac{n}{\phi^2}(2\phi + \phi^2) = \frac{2n + n\phi}{\phi^2}$

Setting this equal to 2 and solving for ϕ gives $\phi = \frac{\sqrt{n}}{\sqrt{2}} = \frac{6}{\sqrt{2}}$

f) To investigate the properties of the maximum likelihood estimator for ϕ, 1000 values of ÔMle can be simulated. This can be done by first simulating 60 random values of X and then calculating the MLE for each set. After this, the 1000 samples of ÔMle can be compared to the approximate density obtained in part (e). The histogram should match the approximate density, with the distribution centered around the value $\frac{6}{\sqrt{2}}$.

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2 1/8 pints

2.125 pints

The completed table showing the radius, angle at the center, arc length, and area of the sector of the circle are as follows;

[tex]{}[/tex]       Radius             Angle at center            Arc Length           Area

(a)    4 cm      [tex]{}[/tex]         1.25 rad                          5 cm                   22.5 cm²

(b) [tex]{}[/tex]  6 cm                1.5 rad                            9 cm                   22.5 cm²

(c) [tex]{}[/tex]  12 cm               0.8 rad                           9.6 m                  57.6 m²

(d)  [tex]{}[/tex] 10 m                 1.2 rad                            12 m                   60 m²

(e) [tex]{}[/tex]  8 mm               2 rad                               16 mm               64 mm²

(f)  [tex]{}[/tex]  9 mm              (2/3) rad                          6 mm                 27 mm²

A sector of a circle is a part of a circle that is pie shaped, with parts including, two radii of the circle and part of the circumference of the circle.

4(a) The specified dimensions of the sectors of the circles are;

Radius = 4 cm

Angle at the center = 1.25 radians

The arc length is therefore;

The area of the sector is therefore;

(b) Radius = 6 cm

Arc length = 9 cm

The angle at the center, θ, is therefore;

Arc length = 2×π×6 × θ/(2·π) = 9

6 × θ = 9

θ = 9/6 = 1.5

(c) Angle at center = 0.8 rad

Arc length = 9.6 m

Arc length = 2×π× Radius × 0.8 rad/(2·π rad) = 9.6

Radius = 9.6 m/0.8 = 12 m

(d) Angle at the center = 1.2 radians

Area = 60 m²

The area = π × (Radius)² × 1.2/(2·π) = 60 m²

(Radius)² × 0.6 = 60 m²

(Radius)² = 60 m²/(0.6) = 100 m²

The arc length = 2 × π × 10 mm × 1.2/(2·π) = 12 mm

(e) The radius of the circle = 8 mm

The area of the sector = 64 mm²

The angle at the center, θ, can therefore, be found as follows;

Area = π × (8 mm)² × θ/(2·π) = 64 mm²

θ = 2 × 64 mm²/((8 mm)²) rad = 2 rad

(f) Arc length = 6 mm

Area = 27 mm²

The radius and angle at the are found as follows

Let r represent the radius, we get;

Arc length = 2 × π × r × θ/(2·π) = 6

Therefore; θ = 6/r

Area of the sector = π × r² × θ/(2·π) = 27 mm²

Therefore; π × r² × (1 mm²) × (6/(r × 1 mm))/(2·π) = 27 mm²

r × (1 mm) × 3 = 27 mm²

r = 27 mm²/(3 × 1 mm) = 9 mm

Please find the completed table for the sectors of a circle above

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The expression to represent the length of the rectangular space is 2x - 3.

The product of the length and breadth makes up the area of a rectangular space. Area is defined mathematically as Length x Width. So, using the equation Length = Area / Width, we can determine the length of a rectangular space if we know its area and breadth. Instead, using the formula Width = Area / Length, we may determine the width of a rectangular region if we know its area and length.

Given that the width of the rectangle is 4x.

The Area of the rectangle is given as:

A = lw

Substituting the values we have:

8x² - 12x = 4x (Length)

l = 2x - 3

Hence, the expression to represent the length of the rectangular space is 2x - 3.

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Answer:

Two quantities are in direct proportion if an increase in one quantity leads to a proportional increase in the other quantity. In this case, the number of melons and the cost of melons are in direct proportion if an increase in the number of melons leads to a proportional increase in the cost of melons.

To check if the given statement is true, we can use the concept of unit rate. Unit rate is the rate for one unit of a given quantity. In this case, the unit rate for melons would be the cost of one melon.

If 7 melons cost £5, then the cost of one melon can be calculated by dividing the total cost by the number of melons:

Cost of one melon = Total cost / Number of melons

= £5 / 7

= £0.714 (rounded to 3 decimal places)

Now, let's calculate the cost of different numbers of melons and see if they are in direct proportion:

For 1 melon, the cost would be £0.714

For 2 melons, the cost would be £1.429

For 3 melons, the cost would be £2.143

For 4 melons, the cost would be £2.857

For 5 melons, the cost would be £3.571

For 6 melons, the cost would be £4.286

For 7 melons, the cost would be £5.000

As we can see, the cost of melons increases proportionally with the number of melons. Therefore, we can conclude that the number of melons and the cost of melons are in direct proportion

The polynomial that 3x^(2)-22x+26 is divided by is x - 6.

To find the polynomial that 3x^(2)-22x+26 is divided by, we can use the formula:

Dividend = Quotient * Divisor + Remainder

In this case, the dividend is 3x^(2)-22x+26, the quotient is 3x-4, and the remainder is 2. We can plug these values into the formula and solve for the divisor:

3x^(2)-22x+26 = (3x-4) * Divisor + 2

Next, we can rearrange the equation to isolate the divisor:

Divisor = (3x^(2)-22x+26 - 2) / (3x-4)

Divisor = (3x^(2)-22x+24) / (3x-4)

Now, we can use polynomial long division to find the divisor:

```
3x - 4 | 3x^2 - 22x + 24
      - (3x^2 - 4x)
      -------------
           -18x + 24
          - (-18x + 24)
          -------------
                0
```

Therefore, the divisor is x - 6.

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Answer:$18

Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount

Answer:

18$

Step-by-step explanation:

go to Safari and look it up is how I got the answer

The formula for the polynomial P(x) with degree 3, real coefficients, zeros at x=3-3i and x=1, and y-intercept at (0,-36) is P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

To find the formula for the polynomial, we first need to find the conjugate of the complex zero, which is 3+3i. This is because a polynomial with real coefficients must have complex zeros in conjugate pairs.

Next, we can use the factored form of a polynomial, P(x) = a(x-r1)(x-r2)(x-r3), where r1, r2, and r3 are the zeros of the polynomial and a is a constant. In this case, r1 = 1, r2 = 3-3i, and r3 = 3+3i.

Finally, we can use the y-intercept to find the value of a. When x = 0, P(x) = -36, so we can plug in the values and solve for a:
-36 = a(0-1)(0-(3-3i))(0-(3+3i))
-36 = a(-1)(-3+3i)(-3-3i)
-36 = a(9+9i-9i-9)
-36 = a(-36)
a = 4

So the formula for the polynomial is P(x) = 4(x-1)(x-(3-3i))(x-(3+3i)). However, since we want the y-intercept to be negative, we can multiply the entire polynomial by -1 to get P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

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Answer: $139.00

Step-by-step explanation: 5x11 = 55
12x7 = 84

55+84=139

The following formula is used to determine how long it will take the car to cover the same distance at 50 miles per hour:

Distance (in miles) divided by Speed (in miles per hour) = Time (in hours). In this case, it is:

Distance / Speed = Time

Distance / 50 = Time

Time = Distance / 50

Time (in minutes) = (Distance / 50) * 60

Therefore, the time it will take the vehicle to travel the same distance at 50 miles perhour is (Distance / 50) * 60 minutes.

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The value of kˣ for the exponential function is [tex]27^{(1/x)}.[/tex]

We can use the properties of exponents to solve this problem and determine the value of kˣ.

To find the value of h(3x), we can use the property that [tex](a^b)^c = a^{bc}[/tex] for any real numbers a, b, and c. This is shown in the solution below.

h(3x) = 3³ˣ    (since h(x) = 3ˣ)

= (3³)ˣ

= 27ˣ

Therefore, we have:

kˣ = 27ˣ

To find the value of kˣ, we can take the x-th root of both sides:

[tex]k = 27^{(1/x)}[/tex]

So, the value of kˣ is [tex]27^{(1/x)}[/tex].

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The whole number that is a solution for the inequality x ≥ 4 but is not a solution for the inequality x > 4 is 4.

Option B is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

here,

We have,

x ≥ 4 and x > 4

Now,

x ≥ 4 means that x can be 4 and greater than 4.

x > 4 mean x is greater than 4.

So,

4 is a solution to x ≥ 4 but not a solution to x > 4.

Thus,

4 is the whole number.

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