Prove the following two properties of the Huffman encoding scheme. (a) If some character occurs with frequency more than 2=5, then there is guaranteed to be a codeword of length 1. (b) If all characters occur with frequency less than 1=3, then there is guaranteed to be no codeword of length 1

The resultant moment about a both forces is zero. The statement is true.

A man B exerts a force on the rope, P = 30 lb

To find:

The magnitude of force, F

Consider a statement:

"The resultant moment about A of both forces is Zero."

Diagram attached at the end of the  solution

\($ \theta=\tan ^{-1}\left(\frac{3}{4}\right) \\\)

\(& \theta=36.87^0\)

To prevent the pole from rotating, so that the resultant moment is about A = 0

We will apply the equilibrium Equation \($\sum \mathrm{M}_{\mathbf{A}}=0$\)

Here force \($P \times \sin (45)$\) and \($F \times \sin (\theta)$\) will not produce the moment at A.

Taking clockwise moment as a negative and anticlockwise moment as a positive.

\(& \mathrm{P} \times \cos (45) \times(18)-\mathrm{F} \times \cos (\theta) \times 12=0 \\\)

\(& 30 \times \cos (45) \times(18)=\mathrm{F} \times \cos (\theta) \times 12 \\\)

\($ \mathrm{~F}=\frac{30 \times \cos (45) \times(18)}{\cos (36.87) \times 12} \\\)

F = 39.77 lb

Based on the given parameters,

The magnitude of force, F = 39.77 lb

So there exists the force by considering the resultant moment about an of both forces as zero.

The statement is true.

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Answer:

n

Step-by-step explanation:

Answer: y≥2

Step-by-step explanation:

Step-by-step explanation:

\(2y \geqslant 4\)

\(y \geqslant \frac{4}{2} \)

\(y \geqslant 2\)

Therefore, the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin is (0, -28).

In mathematics, a scale factor is a numerical value that describes how much an object has been scaled or resized. It is the ratio of the size of the image to the size of the original object. Scale factors can be applied to two-dimensional or three-dimensional objects, and can be used to describe enlargements (scaling up) or reductions (scaling down) of the object.

Here,

To find the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) is the original point, (x', y') is the image of the point after dilation, k is the scale factor, and the dilation is centered at the origin.

In this case, the original point is (0, -7), the scale factor is 4, and the origin is (0, 0). Plugging these values into the formula, we get:

(x', y') = (4 * 0, 4 * (-7))

Simplifying, we get:

(x', y') = (0, -28)

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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27-y:25 points

Explanation

Step 1

Let y represents the points she scored in the second half

total = 27 points

we also know that

total poitns= points first half+points sencond half

replace

therefore, the expression is

Step 2

now, if she scored 2 poitns in the second half

let

y=2

now, replace

she scored 25 points in the first half

therefore, the answer is

27-y:25 points

I hope this helps you

Answer:

b=-3

Step-by-step explanation:

4b+3=−9

-3 -3

4b=-12

4b/4 =-12/4

b=-3

Answer:

D

Step-by-step explanation:

I Looked at te graph and counted each space

Answer:

Step-by-step explanation:

The Anwser is B

Answer:

The answer is -10/9

Step-by-step explanation:

10*x=(-1.111...*10 .) second equation

10x=-11.111....

subtruct second equation from the first equation

10x=10*-11.111.

-

x=-1.1111.

9x=10

x=10/9

Normal probability distribution is applied to a continuous random variable. The correct option is D.

The normal probability distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is often used to model the behavior of a wide range of variables, such as physical measurements like height, weight, and temperature.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). It is a bell-shaped curve that is symmetrical around the mean, with the highest point of the curve being located at the mean. The standard deviation determines the width of the curve, and 68% of the data falls within one standard deviation of the mean, while 95% falls within two standard deviations.

The normal distribution is widely used in statistical inference and hypothesis testing, as many test statistics are approximately normally distributed under certain conditions. It is also used in modeling various phenomena, including financial markets, population growth, and natural phenomena like earthquakes and weather patterns.

Overall, the normal probability distribution is a powerful tool for modeling and analyzing a wide range of continuous random variables in a variety of fields.

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Answer:

2 miles per hour

Step-by-step explanation:

To find her walking pace in 'miles per hour' we need to divide the distance (in miles) by the time (in hours).

Speed = Distance/ Time

The time is given in minutes , but 50 minutes = 50/60 hours

=5/6 hours

1 2/3 ÷ 5/6

=5/3 × 6/5 miles per hour

Now cut it

= 2 miles per hour

Answer:

6

Step-by-step explanation:

well 5 divided by 3/4 is 6.66666666667 which you can say is 6

Answer:

1.2

Step-by-step explanation:

8.8 - 2.2 x 4 + 1.2

8.8 - 8.8 + 1.2

1.2

Ms. Sanders bought 6 packages of cheese sticks and 3 packages of waffles.

Let c = cheese sticks and w = waffles.

We have

c + w = 9

4c + 7w = 45

Solving using substitution,

w = 9 - c

4c + 7(9 - c) = 45

4c + 63 - 7c = 45

-3c = -18

c = 6

6 + w = 9

w = 3

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Answer:

y = x + 6

Step-by-step explanation:

m = gradient

m = rise / run = 4/4 = 1

m = 1

c = y intercept at x = 0

c = 6

now sub into y = mx+c

y = x + 6

you dont need to write the 1 in front of the x becuase 1 x X is the same as just X

The probability of getting a B in three or fewer rolls is :

19/27

To find the probability of getting a B in three or fewer rolls, we can calculate the probability of not getting a B in three rolls and then subtract that from 1.

In a single roll, the probability of not getting a B is 4/6 (3 faces A and 1 face C), since there are 2 faces with B.

The probability of not getting a B in three rolls is (4/6) * (4/6) * (4/6) = (2/3)^3 = 8/27.

Now, to find the probability of getting a B in three or fewer rolls, we subtract the probability of not getting a B in three rolls from 1:

1 - 8/27 = 19/27.

So, the probability of getting a B in three or fewer rolls is 19/27.

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Answer: x=3, y-3

Step-by-step explanation:

I would use elimination

Multiply second equation by 2

2x + 2y = 12

2x + 3y = 15

Subtract both

-1y = -3, y = 3

Plug in 3 for y in any equation

x + 3 = 6, x = 3

Final answer: x = 3, y = 3

Enjoy!!

a)The total energy needed during pregnancy is a quantitative variable because it represents a measurable quantity rather than a non-numerical characteristic.

b) The probability that a randomly selected pregnant woman has an energy need of more than 2625 is approximately 0.3085, or 30.85%.

c) The sample mean daily energy requirement for a random sample of 20 pregnant women, will be approximately normally distributed.

d) the probability corresponding to a z-score of 2.23 is approximately 0.9864.

(a) The total energy needed during pregnancy is a quantitative variable because it represents a measurable quantity (i.e., the amount of energy needed) rather than a non-numerical characteristic.

(b) To calculate the probability that a randomly selected pregnant woman has an energy need of more than 2625, we need to determine the z-score and consult the standard normal distribution table. With the following formula, we determine the z-score:

z = (x - μ) / σ

z = (2625 - 2600) / 50

z = 25 / 50

z = 0.5

Looking up the z-score of 0.5 in the standard normal distribution table, we find that the corresponding probability is approximately 0.6915. However, since we are interested in the probability of a value greater than 2625, we need to subtract this probability from 1:

Probability = 1 - 0.6915

Probability = 0.3085

Interpretation: Approximately 0.3085, or 30.85%, of randomly selected pregnant women have energy needs greater than 2625. This means that there is about a 30.85% chance of selecting a pregnant woman with an energy need greater than 2625.

(c) The sample mean daily energy demand for a randomly selected sample of 20 pregnant women, X, will have a roughly normal distribution. The population mean (2600) will be used as the sampling distribution's mean, and the standard deviation will be calculated as the population standard deviation divided by the sample size's square root. (50 / √20 ≈ 11.18).

(d) We follow the same procedure as in (a) to determine the likelihood that a randomly selected sample of 20 pregnant women has a mean energy need greater than 2625. Now we determine the z-score:

z = (2625 - 2600) / (50 / √20)

z = 25 / (50 / √20)

z = 25 / (50 / 4.47)

z = 2.23

Consulting the standard normal distribution table, we find that the probability corresponding to a z-score of 2.23 is approximately 0.9864.

Interpretation: About 0.9864, or 98.64%, of 20 pregnant women in a random sample would have a mean energy requirement greater than 2625. This means that if we repeatedly take random samples of 20 pregnant women and calculate their mean energy needs, about 98.64% of the time, the sample mean will be greater than 2625.

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Answer:

B

Step-by-step explanation:

there is a hole at -1, so -1 is less than x and x is greater than or equal to 4

The compound inequality shown on the graph is x < -1 and x≥4.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the graph for the inequality.

The first part of the inequality is

x < -1

and, the second part of inequality x≥4

So, the compound inequality is x < -1 and x≥4.

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Answer:$1.10

Step-by-step explanation:n/A

Answer: $1.10

Step-by-step explanation:

took the test

The cοffee shοp that typically sells the mοst amοunt οf cοffee per hοur is Perks A Lοt, with a mean value οf 5.75 gallοns. Sο cοrrect οptiοn is C.

The median is a measure οf central tendency in statistics that represents the middle value οf a dataset when the data is arranged in οrder frοm least tο greatest.

Tο find the median οf a dataset, yοu first arrange the values in οrder. If the dataset has an οdd number οf values, the median is the middle value. Fοr example, in the dataset {2, 3, 5, 6, 8}, the median is 5 because it is the middle value.

If the dataset has an even number οf values, the median is the average οf the twο middle values. Fοr example, in the dataset {2, 3, 5, 6, 8, 10}, the median is (5+6)/2 = 5.5 because it is the average οf the twο middle values.

Tο determine which cοffee shοp typically sells the mοst amοunt οf cοffee per hοur, we need tο cοmpare the central tendency οf the data fοr bοth shοps.

The measure οf center that we can use here is either the mean οr the median. The mean is the average value οf the data, while the median is the middle value οf the data when it is arranged in οrder.

Tο calculate the mean, we can add up all the values and divide by the number οf values. Tο calculate the median, we can arrange the values in οrder and find the middle value.

Fοr Perks A Lοt:

Mean = (10 + 3.5 + 3 + 5 + 2.5 + 7 + 8 + 5.5 + 9.5 + 6 + 9 + 4.5) / 12 = 5.75 gallοns

Median = (3 + 3.5 + 5 + 5.5 + 6 + 7 + 8 + 9 + 9.5) / 9 = 5.75 gallοns

Fοr Wide Awake:

Mean = (2.5 + 10 + 4 + 18 + 4 + 3 + 6.5 + 15 + 6 + 5 + 2.5) / 11 = 6.36 gallοns

Median = (3 + 4 + 4 + 5 + 6.5 + 6 + 10 + 15 + 18) / 9 = 4.5 gallοns

Cοmparing the mean and median values, we can see that Perks A Lοt has bοth a mean and median value οf 5.75 gallοns, while Wide Awake has a mean value οf 6.36 gallοns and a median value οf 4.5 gallοns.

Therefοre, the cοrrect measure οf center tο determine which shοp typically sells the mοst amοunt οf cοffee per hοur is the mean, and the cοffee shοp that typically sells the mοst amοunt οf cοffee per hοur is Perks A Lοt, with a mean value οf 5.75 gallοns.

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Therefore, the expression's 48th component is the cost per scarf.

A mathematical expression is a sentence that has at least two variables or integers and one mathematical action. In mathematics, it is possible to multiply, divide, add, or remove. An expression's structure is (Mathematical Operator, Number or Variable, Expression).

Here,

In the following expression, 483 denotes the total number of scarves, and 48 is the cost per scarf. For each scarf order, customers are charged a $4.75 delivery fee:

The 48 denotes the price per scarf, as can be seen from the supplied.

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Answer:

149

Step-by-step explanation:

12× 24 = 288

228 - 139 = 149

Answer:

B. 149

Step-by-step explanation:

If the students have already filled 139 balloons with air and are going to use all the bags. They would need to fill 149 more balloons.

The first step would be to find the total number of ballons by calculating 12x24 which will give you 288.

From here you would need to subtract the number of ballons that are already filled with air from the balloons that remain which would be 288-139. This would give you a total of 149 balloons that still need to be inflated.

Step-by-step explanation:

x²+3x-10 =

(x+5)(x-2)

______

Answer:

$61.80

Step-by-step explanation:

you first want to find out how much one pint costs so you do 8.24/4 which is 2.06 then you multiply it by 30 to get 61.80

Answer: I believe it would cost $61.8

Step-by-step explanation:

\(\frac{4}{8.24} x \frac{30}{x}\)

8. 24 x 30 = 247.2

247.2 / 4 = 61.8

Answer:

b or c

Step-by-step explanation:

Answer:

A. Angles 4 and 5 are Alternate Interior Angles.

your answer would be 33.

step 1

2(+14)−1(2−5)

2+28−1(2−5)

step 2 distribute

2+28−1(2−5)

2+28−2+5

step 3 then add the numbers

2+28−2+5

2+33−2

combine

2+33−2

ANSWER IS

33