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The equation which gives infinite solutions, x-10+x = 8+2x-18.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

For the infinite solution the both side of equation must contain equal quantity.

For example,

x-10+x = 8+2x-18

now, solving for x

x-10+x = 8+2x-18

2x-10 = 2x-10

-2x = -2x

-10 = -10

As, both sides are equal  which shows the system of equation.

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The 95% confidence interval for average amount its credit card customers spent is $39.424, $61.576.

How to calculate the confidence interval?

Confidence interval is the mean or average of the estimate value minus or plus the variation in the same estimate value.

n = 15

μ = $50.50

σ = \(\sqrt{400}\) = 20

α = 1 - 95% = 0.05

df = n - 1 = 15 - 1 = 14

Since, there are only 15 samples in the question. we will use t-distribution,

Confidence interval = CI = μ ± \(t_{df,\alpha }\)\(\frac{\sigma}{\sqrt{n}}\)

= 50.50 ± \(t_{14,0.05}\)\(\frac{20}{\sqrt{15}}\)

= 50.50 ± (2.145)(5.164)

= 50.50 ± 11.076

= (39.424, 61.576)

Thus, the 95% confidence interval for average amount its credit card customers spent is $39.424, $61.576.

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Answer:

6/1 GO GO GO

Step-by-step explanation:

In the first few steps for deriving the quadratic formula left side of the equation due to the distributive property for balancing the equation.

A quadratic equation is the equation in which the highest power of the variable is two.

Here, The first few steps in deriving the quadratic formula are shown in the table.

Use the substitution property of equality to solve it further,

-c=-ax² +bx

Now factor out the term a, to solve further as,

    - c = a (x² + b/a x)

for half of the b value and square it to determine the constant of the perfect square trinomial as,

     (b/2a)² = b²/4a²

Now  the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

  -c + b²/4a² = a(x² + b/a x + b²/4a² )

Thus, the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

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Answer:

answer is 1

Step-by-step explanation:

The scale factor of triangle ABC to triangle DEF is 1. Therefore, the correct answer is option D.

In the given triangle ABC, AB=5 units, BC=5 units and AC=5 units and in triangle DEF, DE=5 units, DF=5 units and EF=5 units.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

So, the scale factor of ABC to DEF is

AB/DE = BC/EF = AC/DF = 5/5 = 1

Therefore, the correct answer is option D.

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Area is the measure of the amount of surface covered by something. Area formulas for different shapes are sometimes different, but for the most part, area is calculated by multiplying length times width. This is used when calculating area of squares and rectangles. Once you have the number answer to the problem, you need to figure out the units. When calculating area, you will take the units given in the problem (feet, yards, etc) and square them, so your unit measure would be in square feet (ft.2) (or whatever measure they gave you).

Area Example 1

Let’s try an example. Nancy has a vegetable garden that is 6 feet long and 4 feet wide. It looks like this:

Nancy wants to cover the ground with fresh dirt. How many square feet of dirt would she need?

We know that an answer in square feet would require us to calculate the area. In order to calculate the area of a rectangle, we multiply the length times the width. So, we have 6 x 4, which is 24. Therefore, the area (and amount of dirt Nancy would need) is 24 square feet.

Area Example 2

Let’s try that one more time. Zachary has a wall that he would like to paint. The wall is 10 feet wide and 16 feet long. It looks like this:

How many square feet will he be painting?

Using Area and Perimeter Together

Sometimes, you will be given either the area or the perimeter in a problem and you will be asked to calculate the value you are not given. For example, you may be given the perimeter and be asked to calculate area; or, you may be given the area and be asked to calculate the perimeter. Let’s go through a few examples of what this would look like:

Area and Perimeter Example 1

Valery has a large, square room that she wants to have carpeted. She knows that the perimeter of the room is 100 feet, but the carpet company wants to know the area. She knows that she can use the perimeter to calculate the area.

What is the area of her room?

We know that all four sides of a square are equal. Therefore, in order to find the length of each side, we would divide the perimeter by 4. We would do this because we know a square has four sides, and they are each the same length and we want the division to be equal. So, we do our division—100 divided by 4—and get 25 as our answer. 25 is the length of each side of the room. Now, we just have to figure out the area. We know that the area of a square is length times width, and since all sides of a square are the same, we would multiply 25 x 25, which is 625. Thus, she would be carpeting 625 square feet.

Area and Perimeter Example 2

Now let’s see how we would work with area to figure out perimeter. Let’s say that John has a square sandbox with an area of 100 square feet. He wants to put a short fence around his sandbox, but in order to figure out how much fence material he should buy, he needs to know the perimeter. He knows that he can figure out the perimeter by using the area.

What is the perimeter of his sandbox?

We know that the area of a square is length times width. In the case of squares, these two numbers are the same. Therefore, we need to think, what number times itself gives us 100? We know that 10 x 10 = 100, so we know that 10 is the length of one side of the sandbox. Now, we just need to find the perimeter. We know that perimeter is calculated by adding together the lengths of all the sides. Therefore, we have 10 + 10 + 10 + 10 = 40 (or, 10 x 4 = 40), so we know that our perimeter is 40 ft. John would need to buy 40 feet of fencing material to make it all the way around his garden.

Calculating Area and Perimeter Using Algebraic Equations

So far, we have been calculating area and perimeter after having been given the length and the width of a square or rectangle. Sometimes, however, you will be given the total perimeter, and a ratio of one side to the other, and be expected to set up an algebraic equation (using variables) in order to solve the problem. We’ll show you how to set this up so that you can be successful in solving these types of problems.

Eleanor has a room that is not square. The length of the room is five feet more than the width of the room. The total perimeter of the room is 50 ft. Eleanor wants to tile the floor of the room. How many square feet (ft 2) will she be tiling?

a) The utility depends on both health (H) and consumption of other goods (X).

b) The coefficient is negative, indicating a negative relationship between two variables.

c) Health (H) is greater than zero, suggesting a positive value for health.

d) Health (H) is a function of a variable denoted as 'm'.

e) The variable 'm' is greater than zero and the coefficient is negative.

f) The product of two variables, 'm' and 'm', is negative.

a) The expression in (a) is reasonable as it acknowledges that utility is influenced by both health and consumption of other goods. It recognizes that happiness or satisfaction is derived not only from health but also from other aspects of life.

b) The expression in (b) suggests a negative coefficient and a negative relationship between the variables. This could imply that an increase in one variable leads to a decrease in the other. The reasonableness of this relationship would depend on the specific variables involved and the context of the theoretical framework.

c) The expression in (c) states that health (H) is greater than zero, which is reasonable as health is generally considered a positive attribute that contributes to well-being.

d) The expression in (d) indicates that health (H) is a function of a variable denoted as 'm'. The specific nature of the function or the relationship between 'm' and health is not provided, making it difficult to assess its reasonableness without further information.

e) The expression in (e) states that the variable 'm' is greater than zero and the coefficient is negative. This implies that an increase in 'm' leads to a decrease in some other variable. The reasonableness of this relationship depends on the specific variables involved and the theoretical context.

f) The expression in (f) suggests that the product of two variables, 'm' and 'm', is negative. This implies that either 'm' or 'm' (or both) are negative. The reasonableness of this expression would depend on the meaning and interpretation of the variables involved in the theoretical framework.

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Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

Answer:

C. 500

Step-by-step explanation:

\(a {(1.1}^{3} ) = 665.5\)

\(1.331a = 665.5\)

\(a = 500\)

The probability of getting 2 or more heads in 5 successive coin tosses is 13/16 or approximately 0.8125.

To calculate the probability of getting 2 or more heads in 5 successive tosses of a fair coin, we need to consider all the possible outcomes that satisfy this condition.

The total number of possible outcomes when tossing a coin 5 times is 2^5 = 32, as each toss has 2 possible outcomes (heads or tails).

To find the probability of getting 2 or more heads, we need to calculate the probability of the complementary event, which is getting 0 or 1 head and subtract it from 1.

The probability of getting 0 heads (all tails) is (1/2)^5 = 1/32.

The probability of getting 1 head and 4 tails is (5 choose 1) * (1/2)^5 = 5/32.

Therefore, the probability of getting 2 or more heads is 1 - (1/32 + 5/32) = 26/32 = 13/16.

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To find the value of p(b), we can use the formula for conditional probability:

p(a|b) = p(a ∩ b) / p(b)

Since a and b are independent events, p(a ∩ b) = p(a) * p(b). Substituting this into the formula, we have:

0.60 = (0.60 * p(b)) / p(b)

Simplifying, we can cancel out p(b) on both sides of the equation:

0.60 = 0.60

This equation is true for any value of p(b), as long as p(b) is not equal to zero. Therefore, we can conclude that p(b) can be any non-zero value.

In summary, the value of p(b) is not uniquely determined by the given information and can take any non-zero value.

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If you agree to be a part of your friend's partnership business, you will receive $5,000 at the end of each of the next 6 years.

To calculate the equivalent amount needed in one large payment at the end of year 6, we need to consider the time value of money. The discount rate represents the rate of return required for an investment to be considered worthwhile. In this case, the partnership generates a 3% annual return.

Using the concept of present value, we can calculate the equivalent amount needed. We need to find the present value of receiving $5,000 at the end of each year for 6 years, discounted at a rate of 3% per year.

The formula to calculate the present value of an annuity is:

PV = PMT * \([(1 - (1 + r)^(-n)) / r]\)

Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

Substituting the given values, we have:

PV = $5,000 *\([(1 - (1 + 0.03)^(-6)) / 0.03]\)

Solving this equation will give us the equivalent amount needed in one large payment at the end of year 6.

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Answer:

-1/4

Step-by-step explanation:

in y=mx+b, m represents the slope. Let's try to get your equation to look like that. We can see that on the left side, the y is not yet alone so we must try to accomplish that. to do that we divide by -8 from the -8y, but we must also do that to the other side. you would get y=-2/8x-5/8. then we would simplify the -2/8x into -1/4x. Now it is y=-1/4x-5/8 and that resembles y=mx+b. m is slope and -1/4 is m.

Answer:

7.1ºF

Step-by-step explanation:

I took the k12 test

hope this helps! ^^

the gamma distribution becomes approximately normal due to the Central Limit Theorem when n is large.X ︽.Norm(a/λ, a/λ²) since it is an approximately normal distribution with mean a/λ and variance a/λ².

(a) Gamma random variables are sums of random variables, and as n gets large, the Central Limit Theorem applies. When n is large, the gamma random variable with parameters (n, λ) approaches a normal distribution, as the sum of independent and identically distributed Exponential(λ) random variables is distributed roughly as a normal distribution with mean n/λ and variance n/λ². In other words, the gamma distribution becomes approximately normal due to the Central Limit Theorem when n is large.

(b) The problem asks to show that:lim (1 + x/n)-n = e⁻x.The expression (1 + x/n)⁻ⁿ can be written as [(1 + x/n)¹/n]ⁿ. Now letting n → ∞ in this equation and replacing x with aλ yields the desired result from part (a):lim (1 + x/n)ⁿ

= lim [(1 + aλ/n)¹/n]ⁿ

= e⁻aλ(d)

The central limit theorem with continuity correction can be expressed as:P(Z ≤ z) ≈ Φ(z + 0.5/n)if X ~ B(n,p), where Φ is the standard normal distribution and Z is the standard normal variable.

This continuity correction adjusts for the error made by approximating a discrete distribution with a continuous one.(e) The exact probability that the walk is within 500 steps from the origin can be calculated by using the normal distribution. Specifically, we have that:

P(|X - a/λ| < 500)

= P(-500 < X - a/λ < 500)

= P(-500 + a/λ < X < 500 + a/λ)

= Φ((500 + a/λ - μ)/(σ/√n)) - Φ((-500 + a/λ - μ)/(σ/√n)),

where X ~ N(μ, σ²), and in this case, μ = a/λ and σ² = a/λ².

Therefore, X ︽.Norm(a/λ, a/λ²) since it is an approximately normal distribution with mean a/λ and variance a/λ².

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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When evaluating the quality of a good or service, there are several dimensions that are commonly considered. These dimensions provide a framework for assessing the overall quality and performance of a product or service. Here are six key dimensions of quality:

1. Performance: Performance refers to how well a product or service meets or exceeds the customer's expectations and requirements. It focuses on the primary function or purpose of the product or service and its ability to deliver the desired outcomes effectively.

2. Reliability: Reliability relates to the consistency and dependability of a product or service to perform as intended over a specified period of time. It involves the absence of failures, defects, or breakdowns, and the ability to maintain consistent performance over the product's or service's lifespan.

3. Durability: Durability is the measure of a product's expected lifespan or the ability of a service to withstand repeated use or wear without significant deterioration. It indicates the product's ability to withstand normal operating conditions and the expected frequency and intensity of use.

4. Features: Features refer to the additional characteristics or functionalities provided by a product or service beyond its basic performance. These may include extra capabilities, options, customization, or innovative elements that enhance the value and utility of the offering.

5. Aesthetics: Aesthetics encompasses the visual appeal, design, and sensory aspects of a product or service. It considers factors such as appearance, style, packaging, colors, and overall sensory experience, which can influence the customer's perception of quality.

6. Serviceability: Serviceability is the ease with which a product can be repaired, maintained, or supported. It includes aspects such as accessibility of spare parts, the availability of technical support, the speed and efficiency of repairs, and the overall customer service experience.

These six dimensions of quality provide a comprehensive framework for evaluating the quality of both goods and services, taking into account various aspects that contribute to customer satisfaction and value.

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The number of strings of length 10 over the alphabet {a, b, c, A, B} that have at least one uppercase letter is 9,706,576. This is calculated by subtracting the number of strings with only lowercase letters (3^10) from the total number of possible strings (5^10).

To calculate the number of strings of length 10 over the given alphabet that have at least one uppercase letter, we need to subtract the number of strings with only lowercase letters from the total number of possible strings.

The total number of possible strings of length 10 over the given alphabet is 5^10 since each position in the string can be filled with any of the five characters {a, b, c, A, B}. Therefore, there are 9,765,625 total strings.

Now, let's calculate the number of strings with only lowercase letters. Since there are three lowercase letters {a, b, c}, each position in the string can be filled with any of these three characters. Hence, the number of strings with only lowercase letters is 3^10, which equals 59,049.

To find the number of strings that have at least one uppercase letter, we subtract the number of strings with only lowercase letters from the total number of possible strings:

9,765,625 - 59,049 = 9,706,576.

Therefore, there are 9,706,576 strings of length 10 over the alphabet {a, b, c, A, B} that have at least one uppercase letter.

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Answer: (-3,5) would be the orgin but if you rotated it more it would be (3,-5)

Step-by-step explanation: you can use a peace of gragh paper to do that it makes it a lot easer.

Answer:

D

Step-by-step explanation:

Answer: D 3<x<infinity

Step-by-step explanation:

The set of functions Pn(x) = {cos(n arccos(x))} on the interval [-1, 1] is orthogonal, and the norm of each function is 1.

We have,

To verify the orthogonality of the set of functions

Pn(x) = {cos(n arccos(x))} on the interval [-1, 1], we need to show that the inner product of any two distinct functions in the set is equal to zero.

Let's consider two different functions, Pn(x) and Pm(x), where n and m are positive integers.

The inner product of Pn(x) and Pm(x) can be defined as:

⟨Pn, Pm⟩ = ∫[-1, 1] Pn(x) Pm(x) p(x) dx

where p(x) = √2 is the weight function.

Substituting the expressions for Pn(x) and Pm(x), we have:

⟨Pn, Pm⟩ = ∫[-1, 1] cos(n arccos(x)) cos(m arccos(x))√2 dx

Using the trigonometric identity

cos(a) cos(b) = (1/2) [cos(a + b) + cos(a - b)],

we can rewrite the integrand as:

cos(n arccos(x)) cos(m arccos(x))

= (1/2) [cos((n + m) arccos(x)) + cos((n - m) arccos(x))]

Now, integrating this expression over the interval [-1, 1], we can evaluate the integral:

⟨Pn, Pm⟩ = (1/2) [∫[-1, 1] cos((n + m) arccos(x)) √2 dx + ∫[-1, 1] cos((n - m) arccos(x)) √2 dx]

To evaluate these integrals, we can use the properties of the trigonometric functions.

The integral of cos(nx) over the interval [-1, 1] is zero for any positive integer n, except when n = 0.

In that case, the integral is equal to 2.

Since we have (n + m) and (n - m) in the integrand, these values will be positive integers.

Therefore, both integrals will be equal to zero.

This shows that the inner product ⟨Pn, Pm⟩ is zero for any two distinct functions Pn(x) and Pm(x) in the set.

Hence, the functions Pn(x) = cos(n arccos(x)) are orthogonal on the interval [-1, 1].

To find the norm of the functions ||Pn||, we can calculate:

||Pn|| = √⟨Pn, Pn⟩ = √∫[-1, 1] (cos(n arccos(x)))²√2 dx

Simplifying the integral and evaluating it, we get:

||Pn|| = √(∫[-1, 1] (1/2)  [1 + cos(2n arccos(x))] dx)

= √[(1/2) [x + (1/2n)  sin(2n arccos(x))] |[-1, 1]]

= √[(1/2) (1 + 1)]

= √1

= 1

Therefore,

The norm of the functions ||Pn|| is equal to 1.

Thus,

The set of functions Pn(x) = {cos(n arccos(x))} on the interval [-1, 1] is orthogonal, and the norm of each function is 1.

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The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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On a scatter plot, the line that runs through the center of the dots is called a "trendline" or "line of best fit."

Scatter Plot: A scatter plot is a graphical representation of data points in a Cartesian coordinate system, where each point represents the values of two variables.

Data Points: Each data point on the scatter plot represents the values of the two variables being plotted. The position of each point is determined by the respective values of the variables.

Trendline: A trendline is a line that attempts to represent the general pattern or trend in the data. It is often drawn through the center of the dots to provide a visual indication of the relationship between the variables.

Line of Best Fit: The trendline is also known as the "line of best fit" because it is the line that minimizes the overall distance between the line and the data points. It represents the best approximation of the overall trend in the data.

Therefore, the trendline or line of best fit on a scatter plot is the line that runs through the center of the dots and represents the general pattern or trend in the data.

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The distance Jason and Caleb walked is 1523 m. The correct option is the fourth option 1523 meters

From the question, we are to determine how far Jason and Caleb walk

Let the distance covered be x

We will determine the value of the horizontal and vertical components of their journey

From the diagram,

Horizontal distance covered = 3 units

Vertical distance covered = 7 units

Using the Pythagorean theorem

x² = 3² + 7²

x² = 9 + 49

x² = 58

x = √58

x = 7.6158 units

From the diagram,

1 unit = 200 m

∴ x = 7.6158 × 200

x = 1523.16 m

x ≈ 1523 m

Hence, the distance Jason and Caleb walked is 1523 m. The correct option is the fourth option 1523 meters

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The expected payout for one draw is $0.19327.

To calculate how much Mark should pay for one draw, we need to determine the probability of drawing each type of card and the corresponding payouts, and then take a weighted average.

There are 13 clubs in the deck, so the probability of drawing a club is 13/52 = 1/4. The payout for a club is $0.50.

There are 4 aces in the deck, so the probability of drawing an ace is 4/52 = 1/13. The payout for an ace is $0.65.

There is only one ace of clubs in the deck, so the probability of drawing the ace of clubs is 1/52. The payout for the ace of clubs is $0.95.

To calculate the weighted average payout, we can multiply the probability of each outcome by its corresponding payout, and then add up the products:

(1/4) x $0.50 + (1/13) x $0.65 + (1/52) x $0.95 = $0.125 + $0.05 + $0.01827

So the expected payout for one draw is $0.19327.

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Answer:

32768

Step-by-step explanation:

8^6 is 262144

then divide 262144 by 8

so 262144 / 8 = 32768

Hope This Helped