what is trigonometry​

The calculated value of the dividend yield on Stock A is 2%.

The dividend yield is a ratio that indicates how much a company pays out in dividends relative to its stock price.

To calculate the dividend yield on Stock A, we need to divide the annual dividend per share by the stock price per share and then multiply by 100 to express it as a percentage.

Annual dividend per share = Quarterly dividend per share x 4

Annual dividend per share = $0.10 x 4 = $0.40

Now, we can calculate the dividend yield on Stock A:

Dividend yield = Annual dividend per share / Stock price per share x 100%

Dividend yield = $0.40 / $20 x 100%

Dividend yield = 2%

Therefore, the dividend yield on Stock A is 2%.

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The probability that all four chosen balls are red is 14/6075.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.

Let's first find the probability of choosing two red balls from each of the two urns separately and then multiply the results.

The probability of choosing two red balls from urn 1 is:

P(2 red balls from urn 1) = (7/10) * (6/9) = 7/15

Similarly, the probability of choosing two red balls from urn 2 is:

P(2 red balls from urn 2) = (2/10) * (1/9) = 1/45

And the probability of choosing two red balls from urn 3 is:

P(2 red balls from urn 3) = (5/10) * (4/9) = 2/9

Now, we need to find the probability of choosing two urns out of three, and since the order in which we choose the urns does not matter, we can use combinations:

Number of ways to choose two urns out of three = C(3, 2) = 3

Therefore, the probability of choosing two urns out of three is 3/3 = 1.

Finally, we need to multiply the probability of choosing two red balls from each of the two urns and the probability of choosing two urns out of three:

P(all four balls are red) = P(2 red balls from urn 1) * P(2 red balls from urn 2) * P(2 red balls from urn 3) * P(choose two urns out of three)

= (7/15) * (1/45) * (2/9) * 1

= 14/6075

Therefore, the probability that all four chosen balls are red is 14/6075.

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The inequality relating the figures are

25 XZ > AC

26. DF < FD

27.  38 > x > 11

28. 37/3 > x > 7/3

In the figure, the angles are related from the concept that one angle in a triangle must be greater than zero and less than 180.

In addition, when other dimensions are equal the side having greater length will have greater angle facing it.

27. since side 18 > side 12 we have that

5x - 10 > 45

5x > 45 + 10

5x > 55

x > 11

each angle must be less than 180

Also, 5x - 10 < 180

5x < 180 + 10

5x < 190

x < 38

The range of values of x is 38 > x > 11

28. since side 9 > side 6

30 > 3x - 7

30 + 7 > 3x

37 > x

x < 37/3

each angle must be greater than 0

3x - 7 < 0

3x > 7

x > 7/3

The range of values of x is 37/3 > x > 7/3

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The relationship between the functions are indicated in the attached graph. see further explanation below.

a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.

Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).

b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:

graph of f, g, and h

c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.

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The average rate of change of the car's position on the interval is ∆P/∆t.

To find the average rate of change of the car's position on the interval, follow these steps:

Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,

between times t1 and t2).

Calculate the change in position:

Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).

Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).

Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).

Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average

rate of change.

The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per

second or miles per hour) to indicate the car's rate of change in position.

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According to the given inequality,

W – 4 > –10 uses Addition Property

12 ≥ 20x not uses Addition Property

7y10 ≤ 5. 5 –3. 25 < x – 9. 75 uses Addition Property

Let's analyze each given inequality to see whether we can use the Addition Property of Inequality to solve them.

W – 4 > –10: We can use the Addition Property of Inequality to solve this inequality. To do this, we need to add 4 to both sides of the inequality, which gives us: W – 4 + 4 > –10 + 4, or W > –6.

12 ≥ 20x: We cannot use the Addition Property of Inequality to solve this inequality since we need to isolate "x" on one side of the inequality. To do this, we would need to subtract 12 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.

7y + 10 ≤ 5.5 – 3.25x: We cannot use the Addition Property of Inequality to solve this inequality either since we need to isolate "y" on one side of the inequality.

To do this, we would need to subtract 10 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.

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Answer:

c.

Step-by-step explanation:

The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.

After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.

Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:

12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy

So the answer is (C) 9y^2 + 24xy.

Answer: All the faces are rectangular.

Step-by-step explanation: A prism with three rectangular faces is called a rectangular prism. Therefore, the other faces are in the shape of rectangles.

Step-by-step explanation:

the equation for the following graph os (-3,-5) & (1,1)

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so for this inverse, since finding the inverse of the inverse, will give us the original function :)

[tex]f^{-1}(x)=-3x+2\implies y~~ = ~~-3x+2\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~-3y+2} \\\\\\ x-2=-3y\implies \cfrac{x-2}{-3}=y\implies \cfrac{2-x}{3}=y=f(x)[/tex]

List orders the times from shortest to longest

5 1/3 seconds

5 1/2 seconds

5 5/9 seconds

A decimal is a way of representing numbers using a base-10 positional notation system, where each digit represents a power of 10. It is written as a whole number followed by a decimal point and a series of digits representing fractions of 1.

According to the given information:

To order the times from shortest to longest, we need to convert them into a common format, such as a decimal or a common denominator.

First, let's convert the times to a common denominator of 9:

5 1/3 seconds = 16/3 seconds = 48/9 seconds

5 5/9 seconds = 50/9 seconds

5 1/2 seconds = 9/2 seconds = 45/9 seconds

Now we can order the times from shortest to longest:

48/9 seconds = 5 1/3 seconds

45/9 seconds = 5 1/2 seconds

50/9 seconds = 5 5/9 seconds

Therefore, the correct list in order from shortest to longest is:

5 1/3 seconds

5 1/2 seconds

5 5/9 seconds

So Bernard's first attempt was the shortest, his third attempt was the second longest, and his second attempt was the longest.

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Answer: the equation represents a circle centered at (-6, -6) with radius 2.

Step-by-step explanation:

x^2 + 12x + 36 + y^2 + 12y + 12 - 36 = 0

Simplifying, we get:

(x + 6)^2 + y^2 - 12 = 0

For the y terms, we add (12/2)^2 = 36 to both sides to get:

x^2 + 12x + 36 + y^2 + 12y + 36 - 24 = 0

Simplifying, we get:

(x + 6)^2 + (y + 6)^2 = 4

Therefore, the equation represents a circle centered at (-6, -6) with radius 2.

Answer: 0

Step-by-step explanation:

"An integer is the number 0 or any number obtained by repeatedly adding 1 to this number" is not entirely true.

True that integers can be represented by repeatedly adding or subtracting the number 1,

The fact that integers can also be negative and can be obtained by repeatedly subtracting 1 from 0 or another negative integer.

The definition does not account for the fact that integers can be represented using other operations, such as multiplication or division. The integer 12 can be represented as 4 x 3 or as 24 ÷ 2.

A more accurate definition of an integer is a whole number that can be positive, negative, or zero.

Integers can be represented using addition, subtraction, multiplication, or division, and can be used to represent quantities such as counts, distances, temperatures, and other measurable quantities.

The original definition is a useful way to understand how integers can be represented using addition and subtraction, it is not a complete or entirely accurate definition of what integers are.

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The minimum number of coin flips required to obtain a 98% confidence interval width of at most 0.15 is 188.

Hence option d is correct.

We'll use the formula for the confidence interval of a proportion, which is given by:
CI = p-hat ± (z * sqrt(p-hat * (1-p-hat) / n))
Here, p-hat represents the sample proportion (observed proportion of heads), z is the z-score for the desired confidence level (98% in this case), and n is the number of coin flips.
We want to find the minimum number of coin flips (n) needed to obtain a confidence interval width of at most 0.15. Since we suspect that the coin is fair, we'll assume p-hat = 0.5.
For a 98% confidence interval, the z-score (rounded to three decimal places) is 2.576.

Now, we'll set up the inequality:
0.15 >[tex]= 2 * (2.576 * \sqrt{(0.5 * (1-0.5) / n))}[/tex]
Squaring both sides and solving for n, we get:
n >= [tex]((2.576 * \sqrt{(0.25))^2) / (0.15/2)^2}[/tex]
n >= 188.423
Since the number of coin flips must be a whole number, we'll round up to the nearest integer, which is 188.

Hence option d is correct.

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The length of the lake in miles for the given situation of travelling motor boat is equal to 9 miles.

Let us consider the length of the lake be d in miles.

Number of miles motor boat travelled per hour = 18 miles

When the motor boat travels at 18 miles per hour,

The time it takes to travel the length of the lake is,

t₁ = d/18

When the motor boat travels at 12 miles per hour,

The time it takes to travel the length of the lake is,

t₂ = d/12

Time it takes to travel the length of the lake at 18 miles per hour

=  one-quarter of an hour less than the time it takes at 12 miles per hour,

⇒ t₁ = t₂ - 1/4

Substituting the expressions for t₁ and t₂ from above, we get,

⇒ d/18 = d/12 - 1/4

Simplify this equation by multiplying both sides by the least common multiple of the denominators,

least common multiple = 36

⇒ 2d = 3d - 9

Solving for d, we get,

⇒ d = 9

Therefore, the length in miles of the lake is 9 miles.

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Answer:

  A (top)

Step-by-step explanation:

You want to know which box plot represents the data in the given list.

The difference between the box plots is the location of the median.

When the data is sorted into order, it is ...

  {2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500}

There are an even number of elements in this list, so the median is the average of the middle two:

  median = (4247 +4753)/2 = 9000/2 = 4500

The median is represented by the line inside the box of the box plot. The plot with its median at 4500 is the top one (shown in the attachment).

The top box plot represents the data.

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1. The area of the semi circle is 56.52ft²

2. The area of the rectangle is 228ft²

3. The total area is 284.52ft²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of a semi circle is expressed as;

A = 1/2 πr²

r = d/2 = 12/2 = 6ft

A = 1/2×3.14 × 6²

A = 56.52ft²

therefore the area of the semicircle is 56.52ft²

The area of a rectangle is expressed as;

A = l×w

= 19×12

= 228ft²

therefore the area of the rectangle is 228ft²

The total area = (228+56.52)ft²

= 284.52ft²

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A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.

To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:

n = [Z*(σ/ME)]^2

where:

n = the sample size needed

Z = the Z-score for the desired confidence level (98% or 2.33)

σ = the standard deviation of apartments for rent in the area ($200)

ME = the margin of error ($50)

Plugging in the given values, we get:

n = [2.33*(200/50)]^2

n = [9.32]^2

n ≈ 86.7

Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.

Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.

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After 5 and a half minutes, the temperature of the water will be 77°F.

In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.

To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.

After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.

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The correct graph is: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44

Since the data is categorical and discrete, a bar graph is appropriate to display the data. The bars should be labeled with the sports, and their heights should correspond to the number of students who chose each sport.

A histogram is not appropriate because the data is not continuous. Also, the order of the bars does not matter in this case since the data is not ordinal.

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Answer: Yes

Step-by-step explanation: SSS criteria

Answer: 12 inches is one foot

Step-by-step explanation: hope that this is what you were asking ;)

As per the data mentioned in the table, Jade's mom is 0.7 ft or 1 ft taller than jade.

Mixed numbers represent whole numbers and proper fractions together. Usually represents a number between any two integers. Hybrid numbers are made by combining three parts:

An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number.

Height of jade's mom = 5⁵/₈ ft

Jade's height = 4⁵/₆

The difference in their heights is:

= (45/8) - (29/6)

= (270 - 232)/48

= 38/48

= 0.7 ft

0.7 ft ≈ 1 ft

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-2: | -2 |

-9: | -9 |

The probability of detecting this shift on the first sample following the shift would be 68.3%.

The probability of detecting can be calculated by taking the difference between the sample mean and the new process mean (92-100 = -8) and dividing it by the process standard deviation (6).

The result is -1.33, which is then used to calculate the probability of a sample mean falling within the three-sigma control limits.

The difference between the sample mean and the new process mean (92-100 = -8).

The difference by the process standard deviation (6).

The result is -1.33.

The number to calculate the probability of a sample mean falling within the three-sigma control limits.

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The theoretical and experimental probability of rolling a 5 are 1/6 and 4/15 respectively.

We will calculate the theoretical probability by substituting 30 for the number of favorable outcomes as the die is rolled 30 times with one option each for 30 rolls and 180 for total number of outcomes in theoretical probability formula.

P(Theoretical probability of rolling a 5) = 30/180

P(Theoretical probability of rolling a 5) = 1/6.

The experimental probability is calculated by substituting 8 for the number of time the event occurs and 30 for the total number of trials.

P(Experimental probability of rolling a 5)= 8/30

P(Experimental probability of rolling a 5) =4/15

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Hence, it is expected that 14 flights will arrive on time out of the 100 trials of this experiment.

The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, between 0% and 100% it is expressed as a number between 0 and 1, or . The higher the likelihood, the more likely it is that the event will take place.

 when we refer to an experiment or trial, we mean a random experiment. When difference  between a trial and an experiment, think of the experiment as a larger entity created by the fusion of several trials.

Unless otherwise stated,A trial is any specific outcome of a random experiment. In other words, a trial of the experiment is what we call when we conduct an experiment.

according to question, the number of on-time flights in 100 trials as a binomial random variable with parameters n = 100 (the number of trials) and p (the chance of success, i.e., a flight being on time), presuming that the probability of a flight being on time is the same in all trials.

The expected number of on-time flights in 100 trials is E(X) = np if the same of a flight being on time is p. Given that E(X) = 15, we determine p ,

E(X) = n p = 15 n = 100

p = [tex]\frac{E(X)}{n} = \frac{15}{100}[/tex] = 0.15

Therefore, it is probability that 0.15 %of flights will arrive on time.

To determine the expected  number of trials from a total of 100

Using the probability mass function of the binomial distribution, we can get the expected probability of trials out of 100 that result in precisely 15 flights departing on time:

[tex]P(X = 15)=(100 choose 15) * 0.15^{15} * 0.85^{85}[/tex]

We can calculate this 0.144 get  using a calculator.

therefore it is expected that 14 flights will arrive on time out of the 100 trials of this experiment. It should be noted that while this is an expected value, random fluctuation may cause the actual number of on-time flights in each trial to deviate somewhat from this figure.

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Answer: it is 3/2x x + 0

Step-by-step explanation:

you do rise over run which is 3 up and 2 over in this case. and the 0 is the y intercept but its at the center also known as the origin so its 0

Answer:

Step-by-step explanation:

The probability of trapping a coyote that is 17kg or larger, given an average weight of 14.5kg and a standard deviation of 4kg is approximately 0.2743 or 27.43%.

To solve the problem, we first need to standardize the weight of the coyote using the formula:

z = (x - μ) / σ

Where:

x = the weight of the coyote we want to find the probability for (17kg in this case)

μ = the population mean (14.5kg in this case)

σ = the population standard deviation (4kg in this case)

z = the standardized score

Substituting the given values in the formula, we get:

z = (17 - 14.5) / 4

z = 0.625

Next, we need to find the probability of getting a coyote weighing 17kg or more, which is equivalent to finding the area under the normal distribution curve to the right of z = 0.625. We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the area under the curve to the left of a specified z-score. Since we want the area to the right of z = 0.625, we can subtract the CDF from 1 to get the area to the right.

Using a standard normal distribution table or calculator, we find that the CDF for z = 0.625 is approximately 0.734. Therefore, the area to the right of z = 0.625 is 1 - 0.734 = 0.266 or 26.6%.

Thus, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

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Using a standard normal distribution table or a calculator, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

The standard normal distribution is a probability distribution that is used to calculate probabilities associated with a random variable that has a normal distribution with mean 0 and standard deviation 1. Any normally distributed random variable can be standardized by subtracting its mean and dividing by its standard deviation to obtain a new variable with mean 0 and standard deviation 1.

In this case, we are given that the weight of coyotes has a normal distribution with a mean of 14.5kg and a standard deviation of 4kg. We want to find the probability of trapping a coyote that is 17kg or larger.

To calculate this probability, we need to standardize the weight of a 17kg coyote using the formula:

z = (× - μ) / σ

where:

x is the value we want to standardize (in this case, 17kg),

μ is the mean of the distribution (14.5kg),

σ is the standard deviation of the distribution (4kg).

Substituting the values we have:

[tex]z =\frac{(17 - 14.5)}{4} = 0.625[/tex]

This value of 0.625 is the z-score for a coyote weighing 17kg. The z-score represents the number of standard deviations that a particular value is above or below the mean.

Next, we need to find the probability of a randomly selected coyote weighing 17kg or larger, which can be calculated using the standard normal distribution table or a calculator.

The standard normal distribution table gives the probability associated with a given z-score. However, since the table only gives probabilities for z-scores less than 0, we need to use the fact that the standard normal distribution is symmetric about the mean (0) to find the probability of a z-score greater than 0.625.

Specifically, we can use the property that:

P(Z > z) = 1 - P(Z < z)

where Z is a standard normal random variable and z is a z-score. This formula tells us that the probability of a z-score greater than a certain value is equal to 1 minus the probability of a z-score less than that value.

Using this formula, we can calculate:

P(Z > 0.625) = 1 - P(Z < 0.625)

We can look up the value of P(Z < 0.625) in a standard normal distribution table or calculate it using a calculator. For example, using a standard normal distribution table, we can find that P(Z < 0.625) = 0.734.

Substituting this value into the formula, we get:

P(Z > 0.625) = 1 - 0.734 = 0.266

Therefore, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

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The area of the circle for given problem will be approx. 254 [tex]cm^2[/tex].

The formula for finding the area of a circle is given by:

Area =[tex]\pi* r^2[/tex]

where "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle.

Given,

Find the radius (r) of the circle. The radius is half of the diameter, so divide the diameter by 2:

Radius (r) = Diameter / 2 = 18 cm / 2 = 9 cm

Area = [tex]\pi * r^2[/tex] = [tex]3.14*(9 \;cm)^2[/tex] = [tex]254.34 \;cm^2[/tex] (rounded to two decimal places)

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Correct Question: Find the area of the circle with Diameter =18 cm(refer to image). Use 3.14 for π.( Round to the nearest unit).