A circular garden is surrounded by a fence that is 47. 1 feet long. The surface soil Of the entire garden within the fencing needs to be turned prior to planting. Calculate the square feet of soil that must be turned. Use 3. 14 as a substitute for a. Show your work

Applying the right triangle altitude theorem and the leg rule, we have:

5. x = 6; y ≈ 6.7; z ≈ 13.4       6. x = 32; y ≈ 35.8; z ≈ 17.9

The right triangle altitude theorem states that the altitude drawn on the hypotenuse of a right triangle is equal to the geometric mean of the two line segments into which the altitude divides the hypotenuse.

5. To find x, apply the right triangle altitude theorem, which is:

x = √(3*12)

x = √36

x = 6

Using the leg rule, we can find y and z. It is expressed as:

hypotenuse/leg = leg/part

Therefore, substitute and find y:

(3 + 12) / y = y / 3

Cross multiply:

y² = 15 * 3

y = √45

y ≈ 6.7

Find z using the leg rule:

15/z = z/12

z² = 180

z = √180

z ≈ 13.4

6. Use the same theorem and leg rule as done in question 5:

Find x:

16 = √(8 * x)

16² = 8x

256 = 8x

x = 256/8

x = 32

Find y using the leg rule:

(8 + 32) / y = y/32

y² = 40 * 32

y = √1,280

y ≈ 35.8

Find z:

40/z = z/8

z² = 40 * 8

z = √320

z ≈ 17.9

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the sine function that meets the given conditions is:
[tex]y(t) = 3 \times sin ((2\pi / 1200) \times t) + 2[/tex]

Function with the given characteristics.

The terms and their definitions we need to consider:
Amplitude:

The maximum displacement from the midline (in this case, 3)
Midline:

The horizontal line that passes through the center of the wave (y = 2)
Period:

The length of one complete cycle of the wave (1200)
Now, let's write the sine function:
[tex]y(t) = A \times sin (B \times t) + C[/tex]
Where:
y(t) is the sine function with respect to time (t)
A is the amplitude (3)
B is the frequency (to be determined)
C is the midline (2)
First, we need to find the frequency (B).

The period and frequency are related by the following formula:
[tex]Period = 2\pi / B[/tex]
In this case, the period is 1200:
[tex]1200 = 2\pi / B[/tex]
Now, solve for B:
[tex]B = 2\pi / 1200[/tex]
Now, we can plug in the amplitude (A), frequency (B), and midline (C) into our sine function:
[tex]y(t) = 3 \times sin((2\pi / 1200) \times t) + 2[/tex]

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The chance/

probability

is

16/33

, or roughly 0.485 that 1 and 2 are in the

same set.

Let's say we divide the range of numbers from

1 to 15

into two sets, each containing seven and eight numbers, respectively. Finding the likelihood that the numbers 1 and 2 are included in the same

set

is our goal.

We can determine the

total number

of ways to divide the numbers into the two sets of

7

and

8

in order to begin solving this issue. Calculating this yields the result 6435 using a formula.

The number of ways in which the pairs 1 and 2 can be found in the same set must then be determined. Considering that there are

seven numbers

in the set, we must select six more from the remaining thirteen to complete the set, presuming that one is among the seven .There are

1716

ways to do this. The number of methods remains the same, 1716, even if we suppose that 2 is among the set of 7 numbers.

Hence, there are

3432

different ways to combine the numbers 1 and 2 into one set. The chance is 16/33, or roughly 0.485, when we divide this number by the total number of possible

divisions

of the numbers.

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Answer:

To find the average rate of change of the function f(x) = 1.5x² over the interval [10, 11], we need to calculate the change in f(x) over the interval, and divide by the change in x.

The change in f(x) over the interval [10, 11] is:

f(11) - f(10) = (1.511^2) - (1.510^2) = 165 - 150 = 15

The change in x over the interval [10, 11] is:

11 - 10 = 1

Therefore, the average rate of change of the function over the interval [10, 11] is:

(15/1) = 15

This means that for every 1 cm increase in diameter (i.e., for every 1 unit increase in x), the number of calories in the pancake increases by an average of 15 calories per cm of diameter.

Therefore, the answer is (A) 150 calories per cm of diameter.

The probability of detecting a shift in the fraction nonconforming to 0.04 on the first day after the shift is 0.096

The expected number of nonconforming items out of the 50 items:

0.02 x 50 = 1.

The standard deviation of the number of nonconforming items:

√(50 x 0.02 x (1 - 0.02)) = 0.948.

The expected number of nonconforming items out of the 50 items after the shift:

0.04 x 50 = 2.

The standard deviation of the number of nonconforming items after the shift:

√(50 x 0.04 x (1 - 0.04)) = 1.1.

The Z-score:

(2 - 1) / (1.1 - 0.948) = 0.609.

The probability of detecting a shift in the fraction nonconforming to 0.04 on the first day after the shift:

The probability of detecting a shift in the fraction nonconforming to 0.04 on the first day after the shift is determined by calculating the Z-score. Z-scores measure.

The probability of detecting a shift is calculated using the Z-score and the standard normal distribution.

P(Z > 0.609) = 0.096.

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The measures of central tendency are

Mode, Median, μ

The measures of spread are;

Range, IQR

Neither of the measures are;

MAD, Outliers

Central tendency is defined as a central or typical value for a probability distribution. These measures of central tendency are often called averages.

The common measures of central tendency are the arithmetic mean, the median, and the mode.

The measures of spread simply describes how similar or varied the set of observed values are for a particular variable (data item).

Measures of spread include the range, quartiles and the interquartile range, variance and standard deviation.

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Answer:

X= 22

Step-by-step explanation:

So all the angles in a triangle will have a sum of 180°

since you already have a 90° angle you can make the equation

2x+3x-20=90

you'll add the 2x and 3x to get 5x and then you'll also add 20 on both sides

20+90=110

the equation you'll then have is 5x=110

now you'll divide five from both sides and 110/5 is 22

Checked answer: 2(22)+ 3(22)-20= 90 and then youll add that 90 ° angle from before and youll get 180°

The number of valid ways to construct the cube is [tex]4096 - 48 = 4048[/tex]

Each corner of the cube is formed by three wires coming together. Since the wires are soldered together at the ends, each corner must have either 3 silver wires or 3 copper wires coming together.

There are two choices for each wire: it can be silver or copper. Since there are 12 edges in a cube, there are 2 choices for each edge, giving a total of [tex]2^12 = 4096[/tex] possible arrangements of the edges.

However, not all of these arrangements are valid. We must eliminate the arrangements where at least one corner has two silver wires and one copper wire

There are 8 corners in a cube, and for each corner, there are 3 ways to choose which wire is different from the other two. Once we choose which wire is different, there are 2 choices for its color (silver or copper). Thus, there are [tex]8 x 3 x 2 = 48[/tex] invalid arrangements.

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Assuming a two-tailed test with 9 degrees of freedom (10 stores minus 1), the p-value for a t-value of 2.3 is approximately 0.040.

In order to calculate the p-value, we need to know the specific test being used and the significance level of the test. Let's assume that the test is a two-tailed t-test with a significance level of 0.05.

Since the test statistic is 2.3, we need to find the probability of getting a t-value of 2.3 or greater (in absolute value) under the null hypothesis. We can use a t-distribution table or a statistical software to find the corresponding p-value.

Assuming a two-tailed test with 9 degrees of freedom (10 stores minus 1), the p-value for a t-value of 2.3 is approximately 0.040. Therefore, if the significance level of the test is 0.05, we would reject the null hypothesis and conclude that there is a significant difference between the ratings given by the three reviewers.

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Answer:

7

Step-by-step explanation:

58 divided by 8 equals 7 use a calculator and you get your answer.hope it helps

The dimensions will minimize the cost of fence 3555C, armer needs a fenced-in 1 square kilometer rectangular region.

Let the length of the rectangular region be 'l' and the width be 'w'. The area of the rectangular region is given by:

A = lw = 1 sq. km = 1000 x 1000 sq. m

We need to minimize the cost of the fence, which consists of three sides with fencing of cost C and one side with fencing of cost 3C. The total cost of the fence is given by:

Cost = 3Cw + C(2l + w) = 2C(l + w) + Cw

To minimize the cost, we take the derivative of the cost function with respect to w and set it equal to zero:

dCost/dw = 2C - C[tex]w^{(-2)}[/tex]l = 0

Solving for l, we get:

l = 2w

Substituting this value of l in the area equation, we get:

w(2w) = 1000000

2w² = 1000000

w² = 500000

w = √(500000) m = 707.1 m

So, the width of the rectangular region is 707.1 m and the length is 2w = 2 x 707.1 m = 1414.2 m.

Therefore, the dimensions that minimize the cost of the fence are 707.1 m x 1414.2 m and the minimum cost of the fence is:

Cost = 2C(l + w) + Cw = 2C(1414.2 + 707.1) + C(707.1) = 3555C.

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The graph of the given function f(x) = -2 is as attached .

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

We are given the function as:

f(x) = -2

Thus, this means that the graph will be a straight horizontal line cutting across the point -2 on the y-axis which is indicated in the graph attached

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Answer:

The given function is k(t) = cos(2πt/3).

The general form of a cosine function is A*cos(Bx - C) + D, where:

Comparing this form to the given function, we can see that:

Therefore, the amplitude of k(t) is 1, the period of k(t) is 3, the phase shift of k(t) is 0, and the vertical shift of k(t) is 0.

Answer:

-23. In my explanation I will include in my picture how this will look in your final answer

Step-by-step explanation:

So to solve this, I first set x + 3 = 0. This means that x = -3, which we will use soon. Now, here's how you would work out this problem. It would be confusing if I explained over text, so I included a picture of my work.

You would first set up your problem like it is in the picture. Then, bring 2 down. Next, multiply 2 by -3 (for future problems, you would multiply the number you brought down by whatever number is on the side). -3 × 2 = -6, so you would put that under 3 (as shown in the picture). Now, add 3 and -6 (which = -3). Repeat this step each time.

I hope this made sense! Please let me know if you have any questions.

194 member voted against the bill whereas 241 members voted in favour of the bill.

A bill usually refers to a piece of paper money, such as a dollar bill or a euro bill.

To solve this problem, we can use algebra. Let's call the number of members who voted against the bill "x". Then, the number of members who voted in favor of the bill would be "x + 47" (since there were 47 more members voting in favor than against).

We know that the total number of members who voted (either for or against) was 435. So, we can write an equation:

x + (x + 47) = 435

Simplifying this equation, we get:

2x + 47 = 435

Subtracting 47 from both sides:

2x = 388

Dividing both sides by 2:

x = 194

So, 194 members voted against the bill, and the number of members who voted in favor would be:

x + 47 = 194 + 47 = 241

Therefore, 241 members voted in favor of the bill.

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EDA can be especially useful when dealing with complex or large datasets, as it allows for a more comprehensive and intuitive understanding of the data.

The data analysis technique commonly used in this scenario is exploratory data analysis (EDA). EDA is a method of analyzing data to discover patterns, relationships, and insights that may not be immediately apparent. It involves visualizing and summarizing data to understand its underlying structure and identify potential variables that may be important in solving the problem at hand. EDA can be especially useful when dealing with complex or large datasets, as it allows for a more comprehensive and intuitive understanding of the data.

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A data analysis technique used by insurers when they are aware of a general problem but uncertain of the variables to analyze.

The technique I will discuss is Exploratory Data Analysis (EDA).

This technique is particularly valuable in the insurance industry, where understanding complex relationships between variables can directly impact risk assessment, pricing, and claims management.

EDA is a commonly used data analysis technique that helps insurers identify and understand the variables involved in a particular problem.

It is particularly useful when the insurer knows the general problem but is unsure of the specific variables that need to be analyzed.

EDA allows insurers to summarize, visualize, and analyze data to identify patterns, trends, and relationships among variables.
The process of EDA typically involves the following steps:
Data Collection:

Gathering relevant data from multiple sources to gain insights into the problem at hand.
Data Cleaning:

Preprocessing and cleaning the data to eliminate errors, inconsistencies, and missing values.
Data Summarization:

Summarizing the data using descriptive statistics, such as mean, median, mode, and standard deviation, to provide a general understanding of the data.
Data Visualization:

Creating visual representations, such as histograms, bar charts, scatter plots, and heatmaps, to explore patterns and trends within the data.
Pattern Identification:

Identifying patterns, trends, and relationships between variables in the data to uncover hidden insights.
Hypothesis Generation:

Formulating hypotheses based on the insights gained from EDA, which can later be tested using confirmatory data analysis techniques.
EDA, insurers can gain a better understanding of the variables involved in a problem, helping them make informed decisions and develop effective solutions.

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Answer to the question is (a) longest path. The critical path is determined by identifying all the possible paths and calculating their durations, and the one with the longest duration is identified as the critical path.

The number of paths can vary depending on the specific situation or system being analyzed.

The critical path is the longest path in terms of duration or time required to complete all its activities. It is the sequence of tasks or activities that must be completed in order to complete the project within the minimum possible time.

The critical path determines the total duration of the project, and any delay in the critical path activities will cause a delay in the project's completion time.

Therefore, the answer to the question is (a) longest path. The critical path is determined by identifying all the possible paths and calculating their durations, and the one with the longest duration is identified as the critical path.

The critical path method (CPM) is a popular technique used in project management to identify and manage the critical path.

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Triangle PQR's perimeter is **60 inches**.

The lengths of a triangle's sides added together form its perimeter.

The Pythagorean theorem asserts that in a right-angled triangle, the square of the hypotenuse's length (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides 1. A Pythagorean triplet is a group of three positive integers that satisfies this condition.

Triangle PQR has sides PQ = 15 inches, QR = 20 inches, and PR = 25 inches.

A triangle's perimeter is equal to the sum of its sides. Triangle PQR's perimeter is 15 + 20 + 25= **60 inches**.  as a result.

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Answer:

1- $5.54

2- $6.03

3- $17.94

4- $1.20

5- $8.14

Step-by-step explanation:

1. 3.58 a pound a cheese

3.58/2 =1.79 half a pound

1.25x3 =3.75

3.75+1/79= $5.54

total cost was then $5.54

2. 2.69-0.50coupon= 2.19 toothpaste

2.19+0.49+1.29= $3.97

10-3.97= $6.03

He has a total of $6.03 left

3. 4.39x3= 13.17

49+13.17+19.89= 82.06

100-82.06= 17.94

She put $17.94 in her savings

4. 2.89x5= 14.45

14.45+3.25+3.50= 21.2

21.2-20= 1.20

He needed $1.20 more

5. 3.75/3= 1.25

1.25+2.50+4.39= 8.14

The total was $8.14

1. $5.50 in total

2. $6.03 money left

3. $17.94 money put in her savings

4. $1.20 dollars needed

5. $8.14 total cost

1. $3.58 ÷ 2 = $1.75 of the cheese

$1.25 × 3 = $3.75 of energy bars

$1.75 + $3.75 = $5.50 in total

2. $2.69 - $0.50 = $2.19

$2.19 + $1.29 + $0.49 = $3.97

$10 - 3.97 = $6.03 money left

3. $4.39 × 3 = $13.17

$49.00 + $13.17 + $19.89 = $82.06

$100 - $82.06 = $17.94 money put in her savings

4. $2.89 × 5 = $14.45

$14.45 + $3.25 + $3.50 = $21.20

$21.2 - $20 = $1.20 dollars needed

5. $3.75 ÷ 3 = $1.25

$1.25 + $2.50 + $4.39 = $8.14 total cost

Hope this helps! ^-^

The sum of the first 10 terms of the sequence is 20.

The sequence is made up of alternating blocks of 's and 's, with the 's occurring in the blocks.

In other words, the sequence might look something like this:
[tex]s, sss, s, sss, s, sss, s, sss, ...[/tex]
Assuming that this is indeed the case, we can try to find the sum of the first terms of the sequence using a couple of different methods.
One way to approach the problem is to simply add up the first n terms of the sequence by hand.

The sum of the first 10 terms, we could write out the sequence like this:
[tex]s + sss + s + sss + s + sss + s + sss + s + sss[/tex]
and then add up the individual terms:
[tex]1 + 3 + 1 + 3 + 1 + 3 + 1 + 3 + 1 + 3 = 17[/tex]
So, the sum of the first 10 terms of the sequence is 17.
The problem is to look for a pattern in the sequence and use that pattern to find the sum of the first n terms more quickly.

In this case, we can see that each block of 's contributes 3 to the sum (since there are three 's in each block), while each individual s contributes 1.

So we can break the sum down into two parts:

the sum of the blocks of 's, and the sum of the individual s's.
The sum of the blocks of 's can be found by dividing n (the number of terms we want to sum) by 2 and rounding up to the nearest integer (since there are two terms per block).

The sum of the first 10 terms, we have 5 blocks of 's, so the sum of the blocks is:
[tex]5 * 3 = 15[/tex]
The sum of the individual s's is simply n minus the number of blocks, since each block contains three terms.

So in this case:
[tex]10 - 5 = 5[/tex]
Putting it all together, we get:
[tex]15 + 5 = 20[/tex]

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The approximated area Jamie needs to cover is 462.05 ft

From the question, we have the following parameters that can be used in our computation:

The area Jamie needs to cover in the figure is calculated as

Area = Pentagon + Trapezoid + Parallelogram

Using the given dimensions, we have

Area = 1/4 * √[5 * (5 + 2√5)] * 10² + 1/2 * (18 + 20) * 10 + 10 * 10

Evaluate

Area = 462.05

Hence, the area Jamie needs to cover is 462.05 ft

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Step-by-step explanation:

vf = vo + at      vo = 0 in this case  ( you dropped it from 'at rest')

4 f/s = 32 t

t = 1/8 s

df = do + vot + 1/2 at^2                  df = final position = 0 ft (on the ground)

0 = do  + 0   + 1/2 (-32)(1/8)^2

   solve for do = 1/4 foot

Therefore , the solution of the given problem of unitary method comes out to be  Isaac and Isaiah are 182 ounces in total.

Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.

Here,

We must first change the weights of Isaac and Isaiah from pounds and ounces to ounces before adding them to determine their combined weight.

Weight of Isaac: six pounds 2 ounces = 6 * 16 + 2

= 96 + 2

= 98 ounces

Isaiah is 5 pounds in weight.

= 5 * 16 + 4

= 80 + 4

= 84 ounces

Together, Isaac and Isaiah weighed

98 ounces + 84 ounces = 182 ounces

As a result, Isaac and Isaiah are 182 ounces in total.

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The probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%

Assuming that each prize is drawn independently of the others and that any person can win any of the prizes, we can find the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, by using the multiplication principle of probability.

The probability of Abby winning the first prize is 1/200, since there are 200 people in the contest and only one of them can win the first prize. Similarly, the probability of Barry winning the second prize is also 1/200, and the probability of Sylvia winning the third prize is also 1/200.

Since winning more than one prize is allowed, the probability of all three of these events occurring simultaneously is simply the product of their individual probabilities:

P(Abby wins 1st prize AND Barry wins 2nd prize AND Sylvia wins 3rd prize) = (1/200) * (1/200) * (1/200) = 1/8,000,000

Therefore, the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%

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False. All values in a dataset with a normal distribution can be converted to a z-score.

False. All values in a dataset with a normal distribution can be converted to a z-score. The z-score standardizes the data, allowing for comparisons across different distributions by representing the number of standard deviations a data point is away from the mean.

A continuous random variable that tends to cluster around a centre or average value with a particular degree of spread or variation is described by the normal distribution, commonly referred to as the Gaussian distribution. The maximum frequency is near the mean and decreases in frequency as one moves farther away from the mean in both directions. It is a symmetrical bell-shaped curve.

The standard normal distribution, in which the mean and standard deviation are both 0, is a particular instance of the normal distribution. The standard score, also referred to as the z-score, is a measurement of how many standard deviations a data point deviates from the distribution's mean. The difference between the observation's value and the mean is used to calculate it.

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False. All values in a dataset with a normal distribution can be converted to a z-score.

The z-score transformation is used precisely to transform values from a normal distribution to a standard normal distribution, which has a mean of 0 and a standard deviation of 1.

All values in a dataset with a normal distribution can be converted to a z-score.

The statement "not all values in a dataset with a normal distribution can be converted to a z-score" is false.

A z-score represents the number of standard deviations a data point is away from the mean of a distribution and can be calculated for any value within a normal distribution.

In fact, the conversion of values to z-scores is a common method of standardizing data for statistical analysis.
To calculate a z-score, you subtract the mean of the distribution from the individual value and then divide the result by the standard deviation of the distribution.

This transformation allows for easier comparison between data points and across different datasets.

Z-scores can also be used to calculate probabilities and determine the likelihood of certain events occurring within a distribution.
While it is true that some datasets may not follow a normal distribution, this does not mean that z-scores cannot be calculated for all values within the dataset.

The distribution is not normal, other statistical techniques such as transformation or non-parametric tests may be necessary.

A normally distributed dataset, every value can be converted to a z-score, allowing for standardized comparisons and analysis.

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Answer:

Starting with the given equation:

Ob₁ = 2h/A - 2b₂

We want to solve for b₁. First, we can simplify the equation by multiplying both sides by 2:

2Ob₁ = 4h/A - 4b₂

Next, we can add 4b₂ to both sides to isolate the term involving b₁:

2Ob₁ + 4b₂ = 4h/A

Then, we can multiply both sides by A/4h to solve for b₁:

b₁ = (2Ob₁ + 4b₂) * A/4h

Simplifying this expression, we get:

b₁ = (O/h + 2b₂) * A/2

Therefore, the solution for b₁ is:

b₁ = (O/h + 2b₂) * A/2

or

b₁ = (A O + 2b₂h)/2h

In the equation A=bh, b can be solved as b=A/h. For the equation h(b₁ + b₂)=2, b₁ can be solved as b₁=2/h-b₂

To solve the equation A = bh for b, we can isolate b by dividing both sides of the equation by h. Thus, b = A/h. For the equation h(b₁ + b₂) = 2, we isolate b₁ by first dividing both sides by h to get (b₁ + b₂) = 2/h. Then, we can subtract b₂ from both sides to solve for b₁, yielding b₁ = 2/h - b₂.

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Using the centers we know that the equation of the circle is (x+2)²+(y−3)² =40.

A circle is a two-dimensional, symmetrical figure in mathematics.

The circle's center is a place inside the circle from which all points on the circle's edge are equally far.

A circle's general equation is (x - h)² + (y - k)² = r², where (h, k) denotes the circle's center's location and r denotes the radius.

So, the equation of the circle form:

(x−h)² +(y−k)² =r²

The centers we have: (-2, 3)

(x+2)²+(y−3)²=r²

It passes through points (4, 5). Now:

(4+2)² +(5−3)²=r²

6²+2²=r²

r² =36+4

r² =40

Then, equation: (x+2)²+(y−3)² =40

Therefore, using the centers we know that the equation of the circle is (x+2)²+(y−3)² =40.

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Correct question:

Find the Equation of the circle whose center is (−2,3) which passes through the point (4,5).

(a) The probability that this genetic disease can be present is that at least someone in the town is 2.8% of the total population.

To compute the possibility that at least one person in town has the sickness, we may first calculate the probability that no one in town has the disease and then deduct that from 1. The probability that no one in the town has the disease is calculated by binomial distribution formula.

P(X ≥ 1) = 1 - P(X = 0)

where X is the number of people in the town with the disease.

P(X = 0) is the probability that nobody in the town has the disease. When we calculate P(X = 0) as:

P(X = 0) = (15000 chooses 0) * (1/5000)⁰ * (4999/5000)¹⁵⁰⁰⁰

P(0) ≈0.972

The probability that at least one person in the town has the disease is:

P(X ≥ 1) = 1 - P(X = 0)

≈ 1 - 0.972

P(X ≥ 1)  ≈ 0.028

As a result, there is a 2.8% probability that at least one person in town has the condition.

(b) The probability that this genetic disease can be present is that at most 2 people in the town is 99.9% of the total population.

To compute the probability that no more than two persons in the town have the sickness, we must sum the probabilities of none, one, and two people having the condition. The binomial distribution gives the chance that precisely x persons have the disease:

P(x) = (n choose x) * pˣ * (1-p)ⁿ⁻ˣ

where n is the sample size (15,000)

p is the illness probability (1/5000)

(n pick x) is the binomial coefficient, which is the number of ways to select x items from a collection of n items.

We can calculate using this formula:

P(0) = (15000 choose 0) * (1/5000)⁰ * (4999/5000)¹⁵⁰⁰⁰

P(0) ≈ 0.972

P(1) = (15000 choose 1) * (1/5000)¹ * (4999/5000)¹⁴⁹⁹⁹

P(1) ≈ 0.027

P(2) = (15000 choose 2) * (1/5000)² * (4999/5000)¹⁴⁹⁹⁸

P(2) ≈ 0.001

So the probability of at most 2 people in the town having the disease is:

P(0) + P(1) + P(2) ≈ 0.999

As a result, there is a 99.9%  probability that at most 2 people in the town have the disease.

(c) The expected number of people in the town who have the disease is 3 among the 15000 people.

The mean of the binomial distribution gives the expected amount of persons in the town who have the disease.

E(X) = n*p

where X is the random variable representing the number of people in the town with the disease.

Substituting n = 15,000 and p = 1/5000, we get:

E(X) = 15,000 * (1/5000) = 3

E(X) = 3

So we would expect about 3 people in the town to have the disease among the total population.

(d) The variance for the number of people in the town with the disease is 2.998 among the total population.

The binomial distribution's variance is given by:

Var(X) = n*p*(1-p)

considering n = 15,000 and p = 1/5000, we get:

Var(X) = 15,000 * (1/5000) * (4999/5000)

Var(X)  ≈ 2.998

So the variation in the number of persons in the town infected with the illness is around 2.998.

Learn more about Binomial Distribution:

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