If ΔDEF is similar to ΔPRY, what is the measure of PY?




A 12 centimeters
B 21 centimeters
C 24 centimeters
D 48 centimeters

The properties of a parallelogram indicates that the variables in the segments and angles are;

A parallelogram is a four sided figure with two pairs of sides that are parallel.

Whereby the figures are parallelogram, we get;

The length of the opposite sides are the same, therefore;

1. b + 1 = 2·b

1 = 2·b - b = b

1 = b

b = 1 (symmetric property)

3·a - 4 = a + 2

3·a - a = 4 + 2

2·a = 6

a = 6/2 = 3

a = 3

2. The opposite angles of a parallelogram are congruent, therefore;

(y + 10)° = (2·y - 40)°

10 + 40 = 2·y - y = y

50 = y

y = 50

The adjacent interior angles of a parallelogram are supplementary, therefore;

(4·x)° + (2·y - 40)° = 180°

(4·x)° + (2 × 50 - 40)° = 180°

(4·x)°  = 180° - (2 × 50 - 40)° = 60°

x = 60°/4 = 15°

x = 15

3. The diagonals of a parallelogram bisect each other, therefore;

y + 3 = 12

y = 12 - 3 = 9

y = 9

x - 3 = 15

x = 15 + 3 = 18

x = 18

4. The diagonals of a parallelogram bisect each other therefore;

x + 6 = 4·x

4·x = x + 6

4·x - x = 6

3·x = 6

x = 6/3 = 2

x = 2

5·y - 8 = 3·y + 1

5·y - 3·y = 1 + 8 = 9

2·y  = 9

y = 9/2 = 4.5

y = 4.5

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Answer:

Step-by-step explanation:

(4x - 5)(4x + 5) Option 1

16x^2 + 20x - 20x - 25

Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.

To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]

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the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.

b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.

c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.

d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

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Answer: 17.888543819998

Step-by-step explanation:

Answer:

17.8885

Step-by-step explanation:

find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:

Geometric Mean = √(16 × 20)

Geometric Mean = √320

Geometric Mean ≈ 17.8885

Therefore, the geometric mean between 16 and 20 is approximately 17.8885.

The percentile rank of age 30 is 27.586%.

The percentile rank of age 30 can be calculated using the following equation:

Percentile rank = (number of scores below 30 / total number of scores) x 100

In this case, the total number of scores is 29, and there are 8 scores below 30 (18, 21, 22, 25, 26, 27, 29, and 30). Therefore, the percentile rank of age 30 is:

(8/29) x 100 = 27.586%

The percentile rank of age 30 is 27.586%.

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Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

The key features of both equations are:

Equation 1 has a vertex at (1, -16) and opens upwards. Its axis of symmetry is x = 1

Equation 2 has a vertex at (2, 2) and opens upwards. Its axis of symmetry is x = 2.

To rewrite each equation in vertex form, we need to complete the square by adding and subtracting a constant from each equation.

y = x² - 2x - 15

y = (x - 1)² - 16

The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (1, -16).

y = 2x² - 8x + 6

y = 2(x - 2)² + 2

The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (2, 2).

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The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)

The formula for the division of line segments in the ratio m:n is

P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}

We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)

Thus, if the ratio is 2:5, we have:

U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}

U(x, y) = (84/7), (42/7)

U(x, y) = (12, 6)

Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.

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Answer: a=7.6

Step-by-step explanation:

solve for angle C:

[tex]\frac{sinc}{5} =\frac{sin120}{11}[/tex]

[tex]11sinc=5sin120[/tex]

[tex]C=23.2[/tex]

solve for A:

=180-(120+23.2)

=36.8

solve for a:

Using the law of sines

[tex]\frac{sin120}{11} =\frac{sin36.8}{a}[/tex]

[tex]asin120=11sin36.8[/tex]

[tex]a=7.6[/tex]

Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ

The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:

[tex]Q = mcΔT[/tex]

Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).

Using the equation, the amount of heat produced can be calculated as follows:

Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.

There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.

The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:

Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)

Expected gain = 38/13 - 10/13 - 18/13

Expected gain = 10/13 ≈ 0.77

Therefore, the expected gain is $0.77, rounded to the nearest cent.

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The value of ∠FDE is 36°

An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.

Here given a right angle ∠CDE = 90°

So, we can say that,

∠CDF + ∠FDE = ∠CDE

(2x)° + (x+9)° = 90°

(3x + 9)° = 90°

Simplify it, x = 27°

So, the value of ∠FDE = (x+9)° = (27+9)° = 36°

Therefore, the value of ∠FDE is 36°

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The angle FDE is 36°. The required answer for the given question is option (A). 36°.

Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.

An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.

From the given figure,

∠CDF + ∠FDE = 90

Thus,

(2x)+(x+9) = 90

3x + 9 = 90

3x = 81

x = 27

Then we will have that the angle FDE is:

∠FDE = (27) + 9

∠FDE = 36

The angle of FDE is 36°

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The central limit theorem is a statistical theory that specifies the probability distribution of a sum or average of several random variables whose distribution is not known.

It is an important theorem since it is utilized to help forecast or estimate the behavior of a specific set of data.

This theorem holds that when you take repeated samples of the same size from a population with a finite standard deviation, the means of those samples will be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Further more, the theorem indicates that the larger the sample size, the more closely the sample mean distribution will approximate a normal distribution.

This is why it is vital in the development and use of statistical quality control techniques, since they rely on correct assumptions about the population’s normality.

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Implementing multiple types of technology and thereby precluding that the failure of one system will compromise the security of information is referred to as redundancy.

Explanation:

Redundancy is the term used to describe the use of multiple components in a system to ensure that the failure of one component does not lead to system failure. Redundancy is a method of protecting computer systems against damage and disruption caused by component failure.The use of redundancy in computer systems is usually targeted at increasing system availability and lowering the likelihood of data loss.

                                       Multiple types of technology may be employed to achieve redundancy in a computer system, such as mirroring data across multiple disks, deploying standby servers, using a hot backup server, and so on. Redundancy can be implemented in numerous ways to provide reliable service and protect against system failure.

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Answer:

x=7

Step-by-step explanation:

28/4 = 7

Answer:x=7

Step-by-step explanation:

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

__________________

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Answer:

Step-by-step explanation:

The total revenue from ticket sales is:

300 x £5 = £1500

The profit is the revenue minus the cost of the prize:

Profit = £1500 - £400 = £1100

Charity A receives 55% of the profit:

55% of £1100 = £605

Charity B receives 45% of the profit:

45% of £1100 = £495

Therefore, Charity A receives £605 and Charity B receives £495.

The four uppercase letters of the alphabet in block style with rotational symmetry are H, I, O, and X. Rotational symmetry refers to the property of a figure or object that appears identical after being rotated around a central point by a certain angle.

In block style writing, letters are written with straight lines and sharp corners, creating a uniform and geometric appearance. H, I, O, and X are the only uppercase letters that have rotational symmetry and can be written in block style.

H has a rotational symmetry of 180 degrees, meaning it looks the same when rotated 180 degrees around its center point.

I has a rotational symmetry of 180 degrees as well, with the dot above the letter acting as its center point.

O has a rotational symmetry of 360 degrees, meaning it looks the same when rotated any number of degrees around its center point.

Lastly, X has a rotational symmetry of 180 degrees, with the intersection of the two lines acting as its center point.

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Julie hourly rate of pay from the given different rates of the day with total earning of $612 is equal to $12per hour.

Total number of hours Julie works in a week is equal to,

On Sunday = 10 hours

On Monday = 10 hours

On Tuesday = 7 hours

On Wednesday = 10 hours

On Thursday = 7 hours

On Friday = 7 hours

On Saturday = 0 hours

Total hours worked in whole week is

= 10 + 10 + 7 + 10 + 7 + 7 + 0

= 51 hours

Total money earned by Julie in whole week = $612

Hourly rate of pay = Weekly earnings / Total hours worked

Substitute the value we have,

⇒ Hourly rate of pay = $612 / 51 hours

⇒ Hourly rate of pay = $12 per hour

Therefore, Julie's hourly rate of pay is $12 per hour.

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The above question is incomplete , the complete question is:

Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. What is Julie's hourly rate of pay, in dollars?

Answer:

1-

a. 19

b. -8

2-

a. -31

b. 0

c. -10.7

d. -3/7

e. 4

3-

a. -5

b. -60

c. 0

d. -1/4

4. -13/2

5. -85/18

6.  -5/12

7. -11

8. 16/11

9. -20/27

10.  26/11

11. -55/9

Step-by-step explanation:

why did i do this