ldentify the relationship between the angles. y : x ​

The Perimeter of the Triangle is 20.5. when the AB value is 6 m and the angles are 45°. Option B is the correct answer

Given:

AB = 6 m

∠ACB = 45°

By using Trigonometry formulas,

We can determine the AC length by using the sin 45° formula and it is given as,

sin 45° = opposite / hypothesis

sin 45° = AB /AC

1/√2 = 6/ AC

AC = 6√2

We can determine the BC length by using the tan 45° formula which is given as,

tan 45° = opposite / adjacent

tan 45° =AB/ BC

1 = 6/ BC

BC= 6

Now we can determine the perimeter of the triangle by using the perimeter of the triangle formula which is given as,

[tex]P=a+b+√a²+b²[/tex]

Where:

a = opposite side = AC

b = adjacent side = BC

Substuting the a and b values in the above equation we get,

= 6 + 6 +√ 6²+ 6²

= 6 + 6 + 6√2

= 12 +6√2

= 6(2 + √2)

= 20.48 ≅ 20.5

Therefore, The perimeter of the triangle ABC is 20.5.

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Answer:

Step-by-step explanation:

Answer:

13 years

Step-by-step explanation:

Intuition for how sons can collectively win after a certain period of time:- After a certain period of time the father's age will increase by that certain period of time (say 5 years) but for the sons (since there are 3 of them) their collective age will increase by three times that of their father (5 for each 1 one them). Therefore there exist a time after which collective increase in sons' age can cover the current gap of 13 years.

The Midpoint of AB  ((x1 + x2)/2, (y1 + y2)/2) lies on the perpendicular bisector of AB.

Assuming that chord AB is a straight line segment, the point that lies on the perpendicular bisector of AB is the midpoint of AB. This is because the perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to it.

Therefore, to find the point that lies on the perpendicular bisector of chord AB, we need to find the midpoint of AB. This can be done by finding the average of the x-coordinates and the average of the y-coordinates of points A and B, respectively.

Let (x1, y1) and (x2, y2) be the coordinates of points A and B, respectively. Then the midpoint of AB is:

((x1 + x2)/2, (y1 + y2)/2)

This point lies on the perpendicular bisector of AB.

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The length of the string needed is 65 meters

An equation is an expression that shows how numbers and variables using mathematical operators.

Pythagoras theorem shows the relationship between the sides of a right angle triangle.

To find the length of string, Mia needs. A triangle is formed with hypotenuse (l) represent the length of string. The height of the kite (h) = 33 m which is the triangle height; while the 56 m is the base of the triangle (b). Hence:

l² = b² + h²

l² = 33² + 56²

l = 65 meters

The length of the string needed is 65 meters

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Eric has completed 37.5% (or 0.375) of the project, while Victoria has completed 33.3% (or 0.333) of the project. Together, they have completed approximately 70.8% (or 0.708) of the project.

If Eric and Victoria are working on a project and Eric has completed 3/8 of the project, and Victoria has completed 1/3 of the project, then to find the total portion of the project completed, you can add their individual contributions: (3/8) + (1/3).

To add these fractions, you need a common denominator, which is 24 in this case. So, you can rewrite the fractions as (9/24) + (8/24). Adding them together gives you a total of 17/24 of the project completed by both Eric and Victoria, which is equal to 70.8% (or 0.708).

*complete question: Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project. Calculate the total work they have completed together.

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For the function,

-number of complex zeros: four

-possible # of imaginary zeros: two pairs

-possible # of positive real zeros: zero

-possible # negative real zeros: 0 or 2

-possible rational zeros:  ±1, ±3, ±5, ±9, ±15, ±45

-factors to: (x + 3i)(x - 3i)(x + √5i)(x - √5i)

-zeros: x = ±3i, x = ±√5i.

The function is: F(x) = x⁴ +14x²+45.

Number of complex zeros: By the Fundamental Theorem of Algebra, the function has at most four complex zeros.

Possible number of imaginary zeros: If the complex zeros are not real, then there are at most two pairs of imaginary zeros.

Possible number of positive real zeros: The function has no positive real zeros since F(x) is always positive for x>0.

Possible number of negative real zeros: By Descartes' Rule of Signs, the function has either 0 or 2 negative real zeros.

Possible rational zeros: The rational zeros can be found using the Rational Root Theorem. They are of the form ±(a factor of 45) / (a factor of 1), which gives the following possible rational zeros: ±1, ±3, ±5, ±9, ±15, ±45.

To factor the polynomial:

F(x) = x⁴ +14x²+45

= (x² + 9)(x² + 5)

So the factors to linear factors are: (x + 3i)(x - 3i)(x + √5i)(x - √5i), where i is the imaginary unit.

Therefore, the zeros are: x = ±3i, x = ±√5i.

Note that all zeros are complex since there are no real roots.

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In this case, it's important for the librarian to make sure that the sample of patrons who were randomly selected is representative of the larger population of patrons in the children's section, and that any assumptions made in the statistical inference process are valid.

To infer the ages of all patrons in the children's section of the library, the librarian should use statistical inference techniques such as estimation or hypothesis testing.

If the librarian wants to estimate the average age of all patrons in the children's section, they can use a point estimate or an interval estimate. A point estimate would involve calculating the sample mean age of the patrons who were randomly selected and using that as an estimate for the population means age. An interval estimate would involve calculating a confidence interval around the sample mean, which would give a range of likely values for the population means.

Alternatively, if the librarian wants to test a hypothesis about the ages of patrons in the children's section, they can use a hypothesis test. For example, they could test whether the average age of patrons in the children's section is significantly different from a certain value (such as the national average age of children), or whether there is a significant difference in age between male and female patrons.

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Let's use "a" to represent the length of the equal sides of the isosceles triangle, and let's use "b" to represent the length of the third side. We're told that one of the equal sides is 2x + 1ft long, so we can set up an equation:

2a + b = 55

We're also told that the other two sides are both 3x - 14ft long, so we can set up another equation:

a = 3x - 14

Now, we can substitute the second equation into the first equation and solve for "b":

2a + b = 55

2(3x-14) + b = 55

6x - 28 + b = 55

b = 83 - 6x

Now, we can substitute both equations into the equation a = 3x - 14 and solve for "x":

3x - 14 = 2x + 1 + 3x - 14

6x - 27 = 0

x = 4.5

Finally, we can substitute "x" into our equations to find the lengths of the sides:

a = 3x - 14 = 3(4.5) - 14 = 0.5

b = 83 - 6x = 83 - 6(4.5) = 55

So the length of the equal sides is 0.5ft, and the length of the third side is 55ft. Therefore, the lengths of the sides of the isosceles triangle are 0.5ft, 0.5ft, and 55ft.

Answer:

Step-by-step explanation:

201.87 + 3(9.82) + 15.79 + 32.80(o) < 480

247.12 + 32.80(o) < 480

32.80(o) < 480 - 247.12

32.80(o) < 232.88

o < 232.88/32.8

o < 7.1

He can purchase 7 outfits and stay within the $480 budget

Mrs. Carter used 954 square inches of frosting.

To find the surface area of the rectangular prism cake, we need to find the area of all six sides and then subtract the bottom since frosting was not applied to it.

The area of the top and bottom sides is 24 x 15 = 360 square inches each.

The area of the two side faces is 24 x 3 = 72 square inches each.

The area of the two end faces is 15 x 3 = 45 square inches each.

So, the total surface area of the cake is:

2(360) + 2(72) + 2(45) = 720 + 144 + 90 = 954 square inches.

Since frosting was applied to all sides, including the top, we use this surface area to find the amount of frosting used.

Therefore, Mrs. Carter used 954 square inches of frosting.

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Applying the arc length formula, the radius of the circle is calculated as: r = 9 units.

In a circle, the measure of an angle in radians is related to the length of the intercepted arc and the radius by the formula:

arc length = radius * angle measure

In this case, we are given that the angle measure is π radians and the arc length is 9π. Substituting these values into the formula, we get:

9π = r * π

where r is the radius of the circle.

Simplifying this equation, we can divide both sides by π:

9 = r

Therefore, the radius of the circle is 9.

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Hudson Marine experiences the largest seasonal effect in quarter 4.

a. The four-quarter moving average values can be calculated as follows:

Quarter 1: (7 + 9 + 13 + 18) / 4 = 11.75

Quarter 2: (17 + 19 + 28 + 27) / 4 = 22.75

Quarter 3: (9 + 17 + 23 + 23) / 4 = 18

Quarter 4: (2 + 8 + 12 + 17) / 4 = 9.75

Quarter 5: (17 + 8 + 12 + 20) / 4 = 14.25

Quarter 6: (53 + 23 + 17 + 19) / 4 = 28

Quarter 7: (76 + 85 + 105 + 111) / 4 = 94.25

The centered moving average values can be calculated by averaging the adjacent four-quarter moving averages:

Quarter 3: (11.75 + 22.75 + 18 + 9.75) / 4 = 15.06

Quarter 4: (22.75 + 18 + 9.75 + 14.25) / 4 = 16.19

Quarter 5: (18 + 9.75 + 14.25 + 28) / 4 = 17.75

Quarter 6: (9.75 + 14.25 + 28 + 94.25) / 4 = 36.31

Quarter 7: (14.25 + 28 + 94.25 + 28) / 4 = 41.38

Therefore, the centered moving average values are:

Quarter 3: 15.06

Quarter 4: 16.19

Quarter 5: 17.75

Quarter 6: 36.31

Quarter 7: 41.38

b. The seasonal indexes for the four quarters can be calculated by dividing the centered moving average values by the average of all the centered moving average values and then multiplying by 100:

Quarter 1: (15.06 / 20.31) x 100 = 74.18

Quarter 2: (16.19 / 20.31) x 100 = 79.79

Quarter 3: (17.75 / 20.31) x 100 = 87.40

Quarter 4: (36.31 / 20.31) x 100 = 178.63

Therefore, the seasonal indexes for the four quarters are:

Quarter 1: 74.18

Quarter 2: 79.79

Quarter 3: 87.40

Quarter 4: 178.63

c. Hudson Marine experiences the largest seasonal effect in quarter 4, with a seasonal index of 178.63. This means that the sales in quarter 4 are, on average, 178.63% higher than the average sales for all quarters.

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The possible coordinates of point A are (-9, -7) and (-9, 11).

Coordinates refers to a set of numbers that are used to identify the position of a point in a space, usually defined by an x-axis, y-axis, and in sometimes a z-axis.

Let the y-coordinate of point A be y. Then the coordinates of point A are (-9, y).

Using the distance formula, we have:

√[(3 - (-9))² + (2 - y)²] = 15

Simplify the equation:

√[(12)² + (2 - y)² = 15

Square both sides of the equation, we get:

(12)² + (2 - y)² = 15²

144 + (2 - y)² = 225

(2 - y)² = 225 - 144

(2 - y)² = 81

We now take the square root of both sides:

2 - y = ±9

Solve for y in each case, we get:

y = 2 - 9 = -7 or y = 2 + 9 = 11

Therefore, the possible coordinates of point A are (-9, -7) and (-9, 11).

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The probability of rolling a number greater than three and an R on the first roll of both objects is 5/48. The answer is C.

What's P(rolling >3 and R on the first roll of both objects)?

The probability of rolling a number greater than three on the eight-faced object is 5/8 because there are five numbers greater than three (4, 5, 6, 7, and 8) out of eight possible outcomes. The probability of rolling an R on the six-faced object is 1/6 because there is only one R out of six possible outcomes.

To find the probability of both events occurring simultaneously, we multiply the probabilities together:

P(rolling a number > 3 and rolling an R) = P(rolling a number > 3) x P(rolling an R)

= (5/8) x (1/6)

= 5/48

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A net for the pyramid is drawn and labeled. The surface area of the pyramid is found using the formula and the given measurements is 96 square units. The number of boxes of papers Nico can pack into the back of his truck is 135 boxes.

The labeled pyramid is shown in image.

To find the surface area of the pyramid, we need to find the area of each face and add them together. The area of the base is a square with side length 6, so its area is

6² = 36 square units.

The area of each triangular face can be found by using the formula for the area of a triangle, which is 1/2 times base times height.

The height of each face is the slant height of the pyramid, which we can find using the Pythagorean Theorem.

The base of each face is one of the sides of the base of the pyramid, which has length 6.

The slant height of the pyramid can be found by drawing the height from the apex to the center of the base and then using the Pythagorean Theorem to find the length of the hypotenuse of the right triangle formed by the height, half the base (3), and the slant height. We get

slant height = √(4² + 3²) = 5

So the area of each triangular face is 1/2 times base times height = 1/2 times 6 times 5 = 15 square units. Since there are four triangular faces, the total surface area of the pyramid is

4(15) + 36 = 96 square units.

Therefore, the surface area of the pyramid is 96 square units.

The volume of one box of papers is 1.5 x 1.5 x 1.5 = 3.375 cubic feet. The volume of the truck is 9.5 x 6 x 8 = 456 cubic feet. The number of boxes Nico can pack into the truck is therefore

456 / 3.375 = 135.11

Since Nico cannot pack a fraction of a box, he can fit a maximum of 135 boxes of papers in his truck.

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Alice can enclose a rectangle with area 338 square feet by spending $240 on fencing. The minimum cost to enclose 300 square feet is $476.64.

Let's suppose that the rectangle is x feet wide, so its length is 2x. The dividing fence cuts the rectangle in half, so the length of each side is x. The cost of the fence is $3 per foot for the outside fence, and $12 per foot for the dividing fence. Alice has $240 to spend, so

$3(2x) + $12(x) = $240

Solving for x, we get

6x + 12x = 240

18x = 240

x = 13.33

Since x has to be a whole number, we can use 13 as the width. The length is 2x, or 26 feet. The area of the rectangle is

13 x 26 = 338 square feet

If Alice wants to enclose 300 square feet, we know that the area of the rectangle is

Area = width x length

Since the rectangle is divided in half by the dividing fence, the length of each side is half the total length, or x. So

Area = x²

We can rearrange this to solve for x

x² = 300

x = √(300) = 17.32 (rounded to two decimal places)

Since the width of the rectangle is half the length, the width is:

Width = 17.32 / 2 = 8.66 (rounded to two decimal places)

The total length is twice the width, or 17.32. The perimeter of the rectangle is

2(8.66 + 17.32) = 52.96 feet

The cost of the outside fence is $3 per foot, so the cost of the outside fence is

$3(52.96) = $158.88

The dividing fence is in the middle of the rectangle, so the length is half the perimeter, or 26.48 feet. The cost of the dividing fence is $12 per foot, so the cost is

$12(26.48) = $317.76

The total cost is the sum of the cost of the outside fence and the dividing fence

$158.88 + $317.76 = $476.64.

Therefore, the minimum cost to enclose 300 square feet is $476.64.

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Saleem scored 50 on the next test, and his average dropped to 58.

To find Saleem's grade on the next test, we can use the concept of weighted averages.

Since Saleem has an average of 60 in 4 subjects, we can calculate the total marks he has obtained so far. Let's denote the total marks in the 4 subjects as "T."

Average = Total marks / Number of subjects

60 = T / 4

To find T, multiply both sides by 4:

T = 60 * 4

T = 240

Now, Saleem's total marks after attempting the next test would be (240 + X), where X is the score he gets on the next test.

The new average after attempting the next test is 58.

Average = Total marks / (Number of subjects + 1)

58 = (240 + X) / 5

To find X, first multiply both sides by 5:

58 * 5 = 240 + X

290 = 240 + X

Now, isolate X:

X = 290 - 240

X = 50

So, Saleem scored 50 on the next test.

To summarize, Saleem scored 50 on the next test, and his average dropped to 58.

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The values of the variables x and y area 42 and 12 respectively

We can see that the quadrilateral that is inscribed in the circle is a parallelogram.

The properties of a parallelogram includes;

Then, from the information given, we have that;

x + 35 = 77

Now. collect the like terms, we get;

x = 77 - 35

subtract the values, we have;

x = 42

Also,

4y + 46 = 94

collect the like terms

4y = 94 - 46

4y = 48

Divide by the coefficient of y, we have;

y = 12

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a. There is insufficient evidence to conclude that the average age of all lottery players in the county is different from 50 years at the 5% significance level.

b. Referring to the conclusion in part (a), the type of error that may have been made is a type II error, where we fail to reject a false null hypothesis.

(a) To test if the present-day average age of all lottery players in the county is different from 50 years, we can use a one-sample t-test with the null hypothesis:

H0: μ = 50

And the alternative hypothesis:

Ha: μ ≠ 50

Where μ is the population mean age of lottery players.

We have a sample size of n = 81, sample mean x = 48.7, and sample standard deviation s = 8.5. We can calculate the t-statistic as:

t = (x - μ) / (s / √n) = (48.7 - 50) / (8.5 / √81) = -1.29

Using a t-distribution table with 80 degrees of freedom (df = n - 1), we find the critical values to be ±1.990 at a significance level of α = 0.05 (two-tailed test).

Since the calculated t-statistic (-1.29) does not fall outside the critical values, we fail to reject the null hypothesis. There is insufficient evidence to conclude that the average age of all lottery players in the county is different from 50 years at the 5% significance level.

(b) Referring to the conclusion in part (a), the type of error that may have been made is a type II error, where we fail to reject a false null hypothesis. In other words, there may not be enough evidence to conclude that the population mean age is different from 50 years, even if it truly is.

The error in this context means that the lottery official may have missed an opportunity to update their estimate of the average age of all lottery players in the county.

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Answer:

       To change a mixed number to an improper fraction quickly we can multiply the whole number by the denominator, add the numerator and then write that over the original denominator.

Answer:

The third graph from the top could be the graph of f(x) = (2/5)^x. As x approaches infinity, f(x) approaches 0.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 5.1\%\to \frac{5.1}{100}\dotfill &0.051\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 25000[1+(0.051)(4)] \implies A=25000(1.204)\implies A = 30100[/tex]

Answer:

Carlos=1.5041

Mykala=2.6991

William=4.1350

Emily=4.1773

The speed of the van traveling south is 46 miles per hour.

Let the speed of the van traveling south be x miles per hour. Then, the speed of the van traveling north is (x + 10) miles per hour.

Since both vans are moving apart, we add their speeds: x + (x + 10) = 2x + 10 miles per hour.

In 2.5 hours, they are 255 miles apart. So, (2x + 10) * 2.5 = 255.

Now, we solve for x:

5x + 25 = 255
5x = 230
x = 46

The speed of the van traveling south is 46 miles per hour.

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The 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542).,

The formula for the confidence interval of a proportion:

CI = p ± z* (√(p*(1-p)/n))

where:

p is the sample proportion (40/90 = 0.4444)

z* is the critical value of the standard normal distribution at the 95% confidence level (1.96)

n is the sample size (90)

Substituting the  values, we have

CI = 0.4444 ± 1.96 * (√(0.4444*(1-0.4444)/90))

CI = 0.4444 ± 1.96 * (√(0.00245))

CI = 0.4444 ± 1.96 * 0.0495

CI = 0.4444 ± 0.097

Hence, the 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542) when rounded to three decimal places.

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The range of the function f(x) is Range: [0, 125] In interval notation, this can be written as [0, 125] if the longest side length of the box can be no greater than 20 in.

The function f(x) = 1.25x^2 models the packaging costs, in cents, for a rectangular prism-shaped box with side lengths of 2x in., 2x in., and 0.5x in.

We need to determine the reasonable domain and range values for this function, given that the longest side length of the box can be no greater than 20 in.

Since the longest side length is 20 in., we know that:

2x ≤ 20

x ≤ 10

Therefore, the domain of the function f(x) is all real numbers less than or equal to 10, or: Domain: [-∞, 10]

To find the range of the function, we need to examine the behavior of the function as x varies. Since the coefficient of x^2 is positive, the function is quadratic with a minimum value at x = 0. Therefore, we know that the range of the function must start at its minimum value, which is f(0) = 0, and increase as x increases.

To determine the upper limit of the range, we can evaluate f(x) when x = 10 (the maximum value of x allowed):

f(10) = 1.25(10)^2 = 125

Therefore, the range of the function f(x) is:

Range: [0, 125]

In interval notation, this can be written as [0, 125].

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At a significance level of 0.05, the critical value is 2.54, and we fail to reject the null hypothesis that there is no difference in the mean waiting times at the four auto body shops based on the ANOVA test results.

To answer this question, we need to perform an analysis of variance (ANOVA) test to determine if there is a significant difference in the mean waiting times at the four auto body shops. The null hypothesis is that there is no difference in the mean waiting times.

Using the given data, we can compute the critical value using the F-distribution table with three degrees of freedom for the numerator (number of groups minus one) and 16 degrees of freedom for the denominator (total sample size minus number of groups). At a significance level of 0.05, the critical value is 2.54.

Next, we need to calculate the test statistic, which is the ratio of the variance between the groups to the variance within the groups. The output from the statistical software package provides the necessary information to compute the test statistic:

Source | SS   | df | MS     | F    |
------------------------------------
Between| 2.98 | 3  | 0.99   | 1.15 |
Within | 48.28| 16 | 3.02   |      |
Total  | 51.26| 19 |        |      |

The test statistic is F = 1.15, which is less than the critical value of 2.54. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the mean waiting times at the four auto body shops.

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Answer:

y = (x+5)/3

Step-by-step explanation:

Isolate y

x = 3y - 5

x + 5 = 3y

(x+5)/3 = y

The mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.

The mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.

The median for City A is 5.5 inches, and for City B, it is 6 inches.

(a) To find the mean monthly rainfall amount for each city, we sum up the rainfall amounts for each city and divide by the number of months.

For City A:

Mean = (5 + 2.5 + 6 + 2008.5 + 5 + 3) / 6 = 2030 / 6 ≈ 338.3 inches per month

For City B:

Mean = (7 + 6 + 5.5 + 6.5 + 5 + 6) / 6 = 36 / 6 = 6 inches per month

So, the mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.

(b) The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean. To calculate the MAD, we first find the absolute difference between each data point and the mean, sum them up, and then divide by the number of data points.

For City A:

Absolute differences from the mean: |5 - 338.3|, |2.5 - 338.3|, |6 - 338.3|, |2008.5 - 338.3|, |5 - 338.3|, |3 - 338.3|

MAD = (333.3 + 335.8 + 332.3 + 1670.2 + 333.3 + 335.3) / 6 ≈ 557.0 / 6 ≈ 92.8

For City B:

Absolute differences from the mean: |7 - 6|, |6 - 6|, |5.5 - 6|, |6.5 - 6|, |5 - 6|, |6 - 6|

MAD = (1 + 0 + 0.5 + 0.5 + 1 + 0) / 6 ≈ 3 / 6 = 0.5

So, the mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.

(c) To find the median, we arrange the rainfall amounts in ascending order and find the middle value. If there are an even number of data points, we take the average of the two middle values.

For City A: {2.5, 3, 5, 5, 6, 2008.5}

Median = (5 + 6) / 2 = 11 / 2 = 5.5 inches

For City B: {5, 5.5, 6, 6, 6.5, 7}

Median = 6 inches

So, the median for City A is 5.5 inches, and for City B, it is 6 inches.

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Infectious diseases, chronic conditions, mental health, healthcare access, health disparities. Vaccination campaigns, disease prevention, healthcare access, mental health support, social determinants. Increased disease burden, higher costs, reduced quality of life, higher mortality, strained healthcare systems, hindered socio-economic development.

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