The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool? w ≤ 10 â€" l 2l 2w ≥ 62 w ≤ 10 â€" l 2l 2w > 62 w ≤ l â€" 10 2l 2w ≥ 62 w ≤ l â€" 10 2l 2w > 62.

The mean absolute percent error (MAPE) is 25%.

The mean absolute percent error (MAPE) is a measure of forecasting accuracy that quantifies the average deviation between predicted and actual values as a percentage of the actual values. In this case, the mean absolute deviation (MAD) is given as 25 units for the past 10 periods, and the total demand is 1,000 units.

To calculate the MAPE, we need to divide the MAD by the total demand and multiply by 100 to express it as a percentage. In this scenario, the MAPE is calculated as follows:

MAPE = (MAD / Total Demand) * 100

     = (25 / 1,000) * 100

     = 2.5%

Therefore, the MAPE is 2.5%, which means that, on average, the forecasts have a 2.5% deviation from the actual demand.

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Answer:

\(A = 212.1 \text{ cm}^2\)

Step-by-step explanation:

We can identify the bases of the trapezoid as:

9cm and 21.3 cm

(notice how they are parallel)

We know the height is 14 cm.

Using these values, we can solve for the trapezoid's area.

\(A = \dfrac{1}{2}(b_1 + b_2) \cdot h\)

↓ plugging in the values

\(A = \dfrac{1}{2}(9 + 21.3) \cdot 14\)

↓ simplifying the parentheses

\(A = \dfrac{1}{2}(30.3) \cdot 14\)

↓ multiplying 14 and (1/2)

\(A = 7 \cdot 30.3\)

↓ multiplying

\(A = 212.1 \text{ cm}^2\)

The amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.

The amount of water an Olympic-sized pool can hold is, 660,000 gallons.

The pool is 63% full at the moment

The of water in the pool now is:66% of  660,000 gallons

If the pool is 90% full then the amount of water in the pool is:

90% of 660,000 = 594,000 gallons

The amount of water added by the pool maintenance is:

Amount of water added = 90% of 660,000 - 63% of 660,000

594,000 - 415,800

= 178200                                  

Thus, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.

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Answer: √

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x

2

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2

Substitute the actual values of the points into the distance formula.

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Step-by-step explanati i hope you under stand

The answer as a fraction, decimal, and percent is 3/10, 0.3, and 30%, respectively.

The table on air travel outside of the airport is not provided in the question. However, to answer the question, we can assume that the table contains information about flight arrivals and departure times.In order to determine if a flight arrived on time, we need to know the scheduled arrival time and the actual arrival time. If the actual arrival time is later than the scheduled arrival time, then the flight is considered delayed. If the actual arrival time is earlier than the scheduled arrival time, then the flight is considered early. If the actual arrival time is the same as the scheduled arrival time, then the flight is considered on time.To find the percentage of flights that arrive on time, we need to divide the number of on-time flights by the total number of flights and then multiply by 100. For example, if there are 200 flights and 140 of them arrived on time, then the percentage of flights that arrived on time would be:

(140/200) x 100 = 70%

To find the percentage of flights that did not arrive on time, we need to subtract the percentage of on-time flights from 100. For example, if the percentage of on-time flights is 70%, then the percentage of flights that did not arrive on time would be:

100 - 70 = 30%

Therefore, the answer as a fraction, decimal, and percent is 3/10, 0.3, and 30%, respectively.

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Answer:

-10y+11.2

Step-by-step explanation:

A quadrilateral with two pairs of opposite sides always parallel is a  parallelogram. A parallelogram is a quadrilateral with two pairs of opposite sides that are always parallel.

It is a special type of quadrilateral because its properties allow it to be manipulated in unique ways. For example, if one angle of a parallelogram is a right angle, it becomes a rectangle. If all four sides are congruent, it becomes a rhombus. If both pairs of opposite sides are congruent, it becomes a square.

If only one pair of opposite sides is congruent, it becomes a kite. And if it has two parallel sides that are not congruent, it becomes an isosceles trapezoid. A trapezoid also has two pairs of opposite sides, but they are not always parallel. Therefore, it cannot be the answer to this question. Overall, the parallelogram is a versatile shape with unique properties that make it an important concept in geometry.

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Answer:

If the shipping is for all books then the total cost is 164.95

the 95% confidence interval for the difference in the true mean tooth damage for the two types of cereal eaters is (-1.167, 3.587).

Margin of error (MOE) is a statistical term that refers to the amount of random sampling error that is expected to be present in a survey or experiment. It is the range of values above and below the point estimate of a population parameter that is likely to contain the true value of the parameter with a certain level of confidence.

Based on the summary data provided,

we can use a two-sample t-test to construct an approximate 95% confidence interval for the difference in the true mean tooth damage for the two types of cereal eaters.

The sample mean tooth damage for sweetened-cereal lovers = 6.41 with a sample size of 15, and the sample mean tooth damage for unsweetened-cereal lovers is 5.20 with a sample size of 10. The pooled sample standard deviation is calculated as follows:

sₐ = √(((n1-1)×s₁² + (n2-1)×s₂²) / (n₁+ n₂ - 2))

= √(((15-1)×3.59² + (10-1)×1.81²) / (15 + 10 - 2))

= 2.715

Using the formula for the standard error of the difference between two means, we can calculate the margin of error for a 95% confidence interval as:

ME = t (d f ) × sₐ × √(1/n₁ + 1/n₂)

= 2.262× 2.715 ×√(1/15 + 1/10)

= 2.377

Therefore, the approximate 95% confidence interval for the difference in the true mean tooth damage for the two types of cereal eaters is:

(6.41 - 5.20) ± ME

= 1.21 ± 2.377

= (-1.167, 3.587)

So, the answer is (6.41-5.20) ± 2.377, or (-1.167, 3.587), which is the third option.

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The measure of angle 3 based on the information is 142°.

We are given that L and M are parallel. Use all the condition or properties of parallel lines.

Here use vertically opposite angle. Also, coointerior angles sum is 180°.

Now, angle 6= 38° { Vertically opposite angle}.

angle 6 + angle 5 = 180° { as sum of coointerior angles are equal to 180°}

38°+angle 5 = 180°

or, angle 5 = 180°-38°

Therefore, angle 5 = 142°

Now, angle 3 = angle 5 { Vertically opposite angle}

Therefore, the measure of angle 3 is 142°.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Anil Kumar should pay a compound amount of Rs. 23,397.12 at the end of 2 years.

Compound interest is a method of calculating interest where the interest earned is added to the principal amount, and the resulting sum becomes the new principal for the next period's interest calculation. This process is repeated until the end of the investment period.

The formula to calculate the compound interest is:

\(A = P(1 + r/n)^(^n^t^)\)

Where,

A = Amount after the given time

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time duration for which the interest is calculated (in years)

In this case, Anil Kumar took a loan of Rs. 20,000 from a bank at the rate of 8% per annum, compounded half-yearly, for 2 years. Therefore, we can plug in the values as follows:

P = Rs. 20,000

r = 8% per annum = 0.08 (as a decimal)

n = 2 (since the interest is compounded half-yearly)

t = 2 years

Now, we can calculate the compound amount using the above formula:

\(A = P(1 + r/n)^(^n^t^)\)

\(A = 20,000(1 + 0.08/2)^(^4^)\)

\(A = 20,000(1 + 0.04)^4\)

\(A = 20,000(1.04)^4\)

\(A = 23397.1712\)

Therefore, Anil Kumar should pay a compound amount of Rs. 23,397.123 at the end of 2 years.

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To verify that the vector xp is a particular solution of the given nonhomogeneous linear system, we need to substitute xp into the system and check if it satisfies the equation.

The given nonhomogeneous linear system can be written in the form x' = Ax + f, where A is the coefficient matrix (2 1 1 -1) and f is the constant vector (-5 2). The vector xp = (1 3) is a particular solution if it satisfies the equation x' = Ax + f.

Substituting xp into the equation, we get:

x' = (2 1 1 -1) (1 3) + (-5 2)
  = (1 -1 2 -8)

Therefore, the left-hand side of the equation is:

x' = (1 -1 2 -8)

And the right-hand side is:

Ax + f = (2 1 1 -1) (1 3) + (-5 2)
       = (1 -1 2 -8)

Since the left-hand side is equal to the right-hand side, we can conclude that the vector xp = (1 3) is indeed a particular solution of the given nonhomogeneous linear system.

We have verified that the vector xp = (1 3) is a particular solution of the given nonhomogeneous linear system by substituting it into the equation and checking if it satisfies the equation.

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K-Means uses Euclidean distance. The output includes average and maximum distances, separation, and convergence after iterations related to the number of starting seeds.

In the output of a K-Means cluster analysis, "Ave Distance" refers to the average distance between the data points and their assigned cluster centroids.

"Max Distance" represents the maximum distance between any data point and its assigned centroid. "Separation" indicates the distance between the centroids of different clusters, reflecting how well-separated the clusters are.

Convergence in K-Means clustering refers to the point when the algorithm reaches stability and the cluster assignments no longer change significantly.

When the video mentions convergence after 4 iterations, it means that after four rounds of updating cluster assignments and re-computing centroids, the algorithm has achieved a stable result.

The "Number of starting seeds" option determines how many initial random seeds are used for the algorithm, and it can affect the number of iterations needed for convergence. Increasing the number of starting seeds may result in faster convergence as it explores different initial configurations.

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The inequality solved for y is:

y ≥ 21/25

To solve an inequality for one variable, we need to isolate that variable.

Here we have:

(8/7)y -1 ≥ (3/7)y - 2/5

Move the terms with y to the left side and the others to the right side.

(8/7)y - (3/7)y ≥ -2/5 + 1

(5/7)y ≥ (3/5)

Now multiply both sides by 7/5, we will get:

y  ≥ (3/5)*(7/5)

y ≥ 21/25

That is the solution simplfied.

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4a ^2, 5a

Constants- -3, 7, 5

Coefficients- 4, -5, -3, 11

Terms- 7(3x+5), 11y