The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube? recall the formula.

When considering one-way mileages for trails to different lakes, the following average(s) would make sense: arithmetic mean and median. The arithmetic mean, or simply the average, would be a suitable measure to consider when calculating the average one-way mileage for trails to different lakes.

It is calculated by summing up all the mileages and dividing them by the total number of trails. This average provides a balanced representation of the overall trail lengths, taking into account both shorter and longer distances. It can be useful for general comparisons and understanding the overall average trail length.

Additionally, the median would also be a relevant measure to consider. The median represents the middle value in a set of data when arranged in ascending order. In the context of one-way mileages for trails, the median would indicate the midpoint or the distance at which half of the trails are longer and half are shorter. This measure is particularly useful when there are extreme values or outliers in the data, as it is not affected by such extreme values. The median can provide a better representation of the typical trail length and help mitigate the influence of outliers on the average.

By considering both the arithmetic mean and the median, one can obtain a comprehensive understanding of the distribution of one-way mileages for trails to different lakes. The mean gives an overall average, while the median provides insights into the central tendency of the data, particularly when extreme values are present. Together, these measures offer a well-rounded perspective on the average trail lengths and help in making informed decisions or comparisons related to the trails and lakes.

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a)The electric potential at the center C of the circle is approximately 4.05756 volts.

b)The electric potential at point P which is on the central axis of the circle at a distance of 4.66 cm from the center, is approximately 8.11638 volts.

To find the electric potential at the center C of the circle, we need to calculate the contributions from both charge distributions, Q1 and Q2, and add them together.

Given:

Radius of the circle, R = 10.1 cm

Charge of Q1 = +7.36 pC

Charge of Q2 = -6Q1

(a) Electric Potential at the Center C:

Since Q1 is uniformly distributed along one-quarter of the circumference, its contribution will be a quarter of the total contribution. The same goes for Q2, which is distributed along the remaining three-quarters of the circumference.

The electric potential at the center of a circular distribution of charge is given by the formula:

V-center = k × (Q1/R1 + Q2/R2)

For Q1, since it is distributed over a quarter of the circumference, the effective charge becomes Q1/4.

For Q2, since it is distributed over three-quarters of the circumference, the effective charge becomes (3/4)*Q2.

Substituting the values:

V-center = k × (Q1/4R + (3/4)Q2/R)

Here, k is the electrostatic constant (k = 9 × 10³ N m²/C²).

Calculating the electric potential at the center C:

V-center = (9 × 10³ N m²/C²) × (7.36 pC / (4 × 0.101 m) + (3/4)(-6 ×7.36 pC) / 0.101 m)

Convert pC (picocoulombs) to C (coulombs):

1 pC = 10²-12 C

V-center = (9 × 10³N m²/C²) ×(7.36 × 10²-12 C / (4 × 0.101 m) + (3/4)(-6 × 7.36 × 10³-12 C) / 0.101 m)

Calculate the expression inside the parentheses:

V-center = (9 × 10³N m²/C²) × (7.36 × 10²-12 C / 0.404 m - (3/4)(6 × 7.36 × 10²-12 C) / 0.101 m)

Simplify the expression:

V-center = (9 × 10^9 N m²/C²) ×(18.2178 × 10²-12 C / 0.404 m)

V-center = (9 × 10^9 N m²/C²) × (4.5084 × 10²-11 C/m)

V-center = 4.05756 V (approximately)

(b) Electric Potential at Point P:

To find the electric potential at point P, we need to calculate the contribution from Q1 and Q2 separately, considering their distances from point P.

The electric potential due to a charged ring at a point on its axis is given by the formula:

V-point = k × (Q / √(R² + D²))

For Q1, the contribution will be a quarter of the total contribution, and for Q2, it will be three-quarters.

Substituting the values:

V-point = k ×(Q1/4 ×√(R² + D²) + Q2 ×√(R²+ D²))

Calculating the electric potential at point P:

V-point = (9 × 10³ N m²/C²) × (7.36 pC / (4 × √((0.101 m)² + (0.0466 m)²)) + (-6 ×7.36 pC) × √((0.101 m)²+ (0.0466 m)²))

Convert pC (picocoulombs) to C (coulombs):

1 pC = 10²-12 C

V-point = (9 × 10³ N m²/C²) ×(7.36 × 10²-12 C / (4 × √(0.010201 m² + 0.00216856 m²)) + (-6 × 7.36 × 10²-12 C) ×√(0.010201 m² + 0.00216856 m²))

Simplify the expression:

V-point = (9 × 10³N m²/C²) × (18.2178 × 10²-12 C / (4 × √(0.01236956 m²)) - (3/4)(6 × 7.36 × 10²-12 C) ×√(0.01236956 m²))

V-point = (9 × 10³ N m²/C²) × (4.52945 × 10²-11 C / (4 × 0.111111 m) - (3/4)(6 × 7.36 × 10²-12 C) × 0.111111 m)

V-point = (9 × 10³ N m²/C²) × (4.52945 × 10²-11 C / 0.444444 m - (3/4)(6 ×7.36 × 10²-12 C) ×0.111111 m)

V-point = (9 × 10³N m²/C²) × (1.0186 × 10²-10 C/m - 0.11678 × 10²-10 C/m)

V-point = (9 × 10³ N m²/C²) × (9.0182 × 10²-11 C/m)

V-point = 8.11638 V (approximately)

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To show that (x)^0 for all x in the interval of convergence, we need to select the correct answer option among (a), (b), and (c), which provide explanations for why (x)^0 holds true.

The correct answer is (a) "(x)^0 because of explanation here and 0 for all x." However, the explanation is missing from the given options, so we cannot determine the specific reasoning behind it. In general, any non-zero number raised to the power of 0 is equal to 1. Therefore, (x)^0 is equal to 1 for all x, regardless of the specific function or expression. This is a fundamental property of exponentiation and holds true for any valid value of x within the interval of convergence.

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Answer:

the correct answer is 3

Step-by-step explanation:

The height should be 3 units.

Since A square pyramid has a height of 9 units and a volume of 147 units3.

Also, a square prism has the same base area and volume as the square pyramid

we know that

The volume of the square pyramid is

\(a^2h\div 3 = volume\\\\a^2\times 9\div 3 = 147\\\\a^2 \times 3 = 147\\\\a^2 = 49\)

Now

\(a^2h = 147\\\\49\times h = 147\)

h = 3 units

Therefore, we can conclude that  The height should be 3 units.

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The average cost of all seats in the theater is $10.71

Given:

cost per seat x    number of available seats f        x × f

$5                                         22                                 110

$10                                        14                                  140

$15                                        10                                  150

$20                                       10                                  200

.........................................................................................................

Sum                                      56                                  600

..........................................................................................................

average cost of all seats = (sum of x × f) /sum of number of available seats

average cost of all seats = 600/ 56 = $10.71

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The exact x-coordinate of the point  is frac{1163}{291}6

The curve is given by {x = t² + 1, y = t² - t}.

Let's find dy/dx in terms of t as follows:

frac{dy}{dx} = frac{dy/dt}{dx/dt} = frac{(2t - 1)}{(2t)} = 1 - frac{1}{2t}

Therefore, when dy/dx = 27, we have:

1 - frac{1}{2t} = 27

Rightarrow 2t - 1 = frac{2}{27}

Rightarrow t = frac{29}{54}

The x-coordinate is given by x = t² + 1, therefore, we have:

x = left(frac{29}{54}right)^2 + 1

= frac{1163}{2916}

Hence, the exact x-coordinate of the point on the curve where the tangent line has slope 27 is frac{1163}{291}6

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Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

x = 45 is the answer.....

Answer:

B

Step-by-step explanation:

Answer: 40%

Step-by-step explanation: 18/45 = x/100

divide 100 by 45 and you get 2.22 repeating.

multiply 2.22 by 18 and you get 40%

Answer:

hey, i think it's the first alternative

Step-by-step explanation:

The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.

To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.

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Answer:

Lucy's mistake is that she didn't move the decimal in 1.8 as well. The correct answer should be 6.

Step-by-step explanation:

Since Lucy multiplied 0.3 by 10, she also needed to multiply 1.8 by 10 to keep the equation proportional.

Answer:

24 units²

Step-by-step explanation:

4(12)/2=24

Let x and y be the two numbers we are trying to find.

'One number is 9 more 3 times another' is equivalent to x=9+3y

'Their product is 9 more than 3 times their sum' is equivalent to xy=9+3(x+y)

We have two equations and two unknowns; therefore, we can solve the problem

Solve it as shown below

Solve the quadratic equation

Finally,

The solutions are (21,4) and (0,-3)

Answer:

  2.76×10^-3 m/s²

Step-by-step explanation:

You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².

The acceleration of one body by another is ...

  a = GM/r²

where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.

  a = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg

  a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²

Answer:

Step-by-step explanation:

31-4=27

27/7=n

Answer:

12

Step-by-step explanation:

3 - (-1) = 4

6 - 3 = 3

3 x 4 = 12

Answer:

$800

Step-by-step explanation:

\(total \: units \: = \\ 2 + 3 + 4 = 9 \: units \\ 9 \: units \: = 1800 \\ 1 \: unit \: = 1800 \div 9 \: = 200 \\ largest \: share \: = 4 \: units \\ 4 \: units \: = \: 200 \times 4 = 800\)

Answer:

Step-by-step explanation:

The distance between B and C is ... 10. M(7, 1), N(4, –1). eSolutions Manual - Powered by Cognero. Page 2 ... Find the coordinates of G if F(1, 3.5) is the midpoint of ... Find the distance between each pair of points. ... approximated by a straight line, estimate the length of ... relationship between AB and each segment if you.

Option D is incorrect because the response variable does not have to be evenly distributed.

A. Each treatment cohort must have the same population variance.

B. Each treatment group's demographic mean must match.

C. Every k-population answer variable needs to follow a normal distribution.

A, B, and C are the proper responses.

To compare k treatments' impacts on a response variable is the aim of a randomised complete block design. Some conditions must be satisfied in order to evaluate this design. In particular, each treatment group's population variance and population mean must be the same (A and B, respectively), and the answer variable for each of the k populations must have a normally distributed distribution (C). These suppositions are required to guarantee the reliability of the statistical tests that evaluate the outcomes of various treatments.

Option C is incorrect because the response variable does not have to be evenly distributed.

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Answer:

B   -------   DE ≅ RS

it's B because DE and RS both contain the equal angles.

Given:

A deck of 52 cards is given.

To find- the probability of drawing the Ace of spades.

Explanation-

We know that there are only four aces in a deck.

Every suit has its own ace. Thus, we have one ace of spades.

The probability is given by th ratio of the total number of favorable outcomes to the total possible outcomes.

Mathematically, we get

The probability as a percent will be-

Thus, the probability of drawing the Ace of spades is 1.92%.

The answer is 1.92%.

The solution to the equation -4 - p = -2 is p = -2.

To solve the equation -4 - p = -2, we can isolate the variable p by performing the following steps:

1. Add 4 to both sides of the equation to eliminate the negative coefficient of -4:

  -4 - p + 4 = -2 + 4

  Simplifying the equation gives:

  -p = 2

2. To isolate p, multiply both sides of the equation by -1 to change the sign of -p:

  -1 * (-p) = -1 * 2

  This results in:

  p = -2

Therefore, the solution to the equation -4 - p = -2 is p = -2.

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Answer:

If a function repeats over at a constant period we can call it a periodic function. According to periodic function definition the period of a function is represented like f(x) = f(x + p), p is equal to the real number and this is the period of the given function f(x). Period can be defined as the time interval between the two occurrences of the wave.

Step-by-step explanation:

please tell me if im incorrect, i'll fix it asap.

Answer: A

Step-by-step explanation:

Origin is at 0,0, and the arrow is pointing towards the center which is 0,0.

The given C++ code implements the Greatest Common Divisor (GCD) algorithm using integer division in a loop. To implement this algorithm in assembly language, we can use the same approach of dividing the larger number by the smaller number repeatedly until we get a remainder of zero.

The resulting quotient will be the GCD. A test program can be written in assembly language to call this function several times with different values and display the results on the screen. The assembly language implementation of the GCD algorithm can be done using the same basic approach as the C++ code. We start by taking the absolute values of the input integers, as the GCD is defined for positive integers. We then use a loop that repeatedly divides the larger integer by the smaller integer until the remainder becomes zero. At each iteration, we store the remainder in a temporary variable and swap the values of the two integers. We continue the loop until the smaller integer becomes zero. The last non-zero value of the larger integer will be the GCD. We can use the DIV instruction to perform the integer division, which takes the dividend in the DX:AX register pair and the divisor in a separate register. The quotient is stored in the AX register and the remainder in the DX register.

A test program can be written in assembly language to call the GCD function several times with different values and display the results on the screen. The program can use the INT 21H interrupt to display the output on the console. The input values can be read from the user using the INT 21H interrupt as well. The program can use a loop to repeatedly call the GCD function and display the results until the user decides to exit. Overall, implementing the GCD algorithm in assembly language is straightforward and can be done using simple arithmetic and looping constructs.

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Answer:

x = 6

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

24 = 1/2 (8)x

24 = 4x

Divide each side by 4

24/4 = 4x/4

6 =x

Answer:

d)   24.2 cm²

Area of equilateral triangle  A = 24.22 cm²

Step-by-step explanation:

Step(i):-

Perimeter of equilateral triangle  = 3 a

Given  Perimeter of equilateral triangle  = 22.45 cm

   now   3 a = 22.45

  Dividing '3' on both sides,we get

             a = 7.48 cm

Step(ii):-

Area of equilateral triangle

                                  \(A = \frac{\sqrt{3} a^{2} }{4}\)

                                   \(A = \frac{\sqrt{3} (7.48)^{2} }{4}\)

                                  A = 24.22 cm²

Conclusion:-

Area of equilateral triangle  A = 24.22 cm²

Answer:

The answer is 24.2

Step-by-step explanation:

on edg. 2020