Solve the attached CLT question
Thanks!!

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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The probability that the weight of a randomly selected steer is between 1279 and 1609 lbs is 0.2288.

Given that the weights of steers in a herd are distributed normally.

The standard deviation is 300 lbs and the mean steer weight is 1100 lbs.

We are required to find the probability that the weight of a randomly selected steer is between 1279 and 1609 lbs.

Here, it is given that the mean weight of the herd is 1100 lbs and the standard deviation is 300 lbs.

We need to find the probability of the weight of a randomly selected steer between 1279 lbs and 1609 lbs.

It can be written as;

P (1279 ≤ X ≤ 1609)

We can standardize this distribution by subtracting the mean and dividing it by the standard deviation.

The standardized form is given by

Z = (X-μ)/σ

where X is the given value, μ is the mean and σ is the standard deviation.

Substituting the values we get,

for X = 1279

[tex]Z_1[/tex] = (1279 - 1100)/300 = 0.5967 and

for X = 1609

[tex]Z_2[/tex]  = (1609 - 1100)/300 = 1.6967

We are required to find the probability of Z between [tex]Z_1[/tex] and [tex]Z_2[/tex].

P([tex]Z_1[/tex] ≤ Z ≤ [tex]Z_2[/tex]) To find this probability,

we use the standard normal distribution table,

We get P(Z ≤ 1.70) = 0.9545 and P(Z ≤ 0.60) = 0.7257

Now, P ([tex]Z_1[/tex] ≤ Z ≤ [tex]Z_2[/tex]) = P(Z ≤ 1.70) - P(Z ≤ 0.60) = 0.9545 - 0.7257 = 0.2288.

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The margin of error of the 98.4% confidence interval for snapdragons  is 3.71.

The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.

The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:

`Margin of error z*(standard deviation/√n`).

The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:

`standard deviation = (range/4) * √n / 1.96`

Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`

Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`

Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`

Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`

Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`

Now that we know the sample size, we can calculate the standard error of the mean:

`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.

The margin of error is `1.96 * 1.89 = 3.71`.

The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.

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There are a total of 32 different possible footwear choices that we can make.

Given, The number of pairs of socks = 4

The number of pairs of shoes = 4

We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.

So, We can wear any pair of socks with any pair of shoes including a mismatch.

Thus, for each pair of socks, there are 4 possible pairs of shoes.

And for each pair of shoes, there are 4 possible pairs of socks.

Therefore, we can form,

Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.

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Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

The total distance encircling a two-dimensional shape's perimeter is known as its perimeter. It represents the total length of the shape's sides. The perimeter of a rectangle, for instance, can be determined by combining the lengths of its four sides: A rectangle's perimeter equals 2 x (length + width). Other shapes, such triangles, circles, and polygons, can have their perimeters determined using the appropriate formulas.

given

The formula for the perimeter of a rhombus, which is the sum of the lengths of its four sides, can be used to determine the greatest distance that can be covered in a rhombus-shaped skating rink without changing direction.

Given that the sides are each 26 metres long, the rhombus's perimeter would be:

Perimeter: (4 x 26) = 104 metres

But, we must consider that the smaller diagonal of the skating rink measures 40 metres in order to determine the most distance that may be traversed without changing directions. This means that the skater is limited to a 40-meter radius before having to change directions.

Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

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The complete question is:- 3.- What is the maximum distance that can be traveled without changing direction in a rhombus-shaped skating rink, if each side measures 26 meters and the smaller diagonal is 40 meters?

The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.

Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.

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Thus, total garden area calculated in square meters is found to be 40  sq. m.

If the degree n in the equation is equal to 1, then a linear equation only contains ONE variable. The highest exponent a single variable can have is referred to as the equation's degree. Any arbitrary variable, such as x, y, or z, may be used as long as the linear equation is homogeneous.

Given data:

Let x be the total area of land.

Area of planted flowers : 2/5 x

Remaining area = 24 sq. m.

Thus,

Total area = Area of planted flowers + Remaining area

x = 2/5 x + 24

x - 2/5 x = 24

(5 -2)/5 x = 24

3x/5 = 24

x = 24*5 / 3

x = 8*5

x = 40

Thus, total area of the garden calculated in square meters is found to be 40  sq. m.

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Answer:

true

Step-by-step explanation:

3rd quadrant sine is (-)

4th quadrant sine is (-)

Answer: The answer is 60.

Step-by-step explanation:

Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1.  ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2.  θ = 70° 

Answer:

The measure of ∠OPQ is 110°.

Step-by-step explanation:

Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).

Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.

⇒ m∠TQR = m∠SRQ = 130°

Given m∠PQR = 60° and m∠TQR = 130° then:

⇒ m∠TQP + m∠PQR = m∠TQR

⇒ m∠TQP + 60° = 130°

⇒ m∠TQP = 70°

Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).

⇒ m∠OPQ + m∠TQP = 180°

⇒ m∠OPQ + 70° = 180°

⇒ m∠OPQ = 110°

Therefore, the measure of ∠OPQ is 110°.

The dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

We know that the area of a rectangle is given by:

Area = Length x Width

Since the problem does not specify the shape of the rectangle, we cannot assume that it is a square. Therefore, we need to find two numbers whose product is 33.

The factors of 33 are 1, 3, 11, and 33. None of these factors is equal to 3, so we cannot simply multiply 3 by a factor of 33 to get the length of the rectangle. Therefore, we need to use a different approach.

One way to find two numbers whose product is 33 is to start with the square root of 33 and round up and down to the nearest integer. The two resulting integers will be close to the factors of 33 and will multiply to give 33.

The square root of 33 is approximately 5.74. Rounding up and down to the nearest integer gives:

Length = 6 ft

Width = 33 ÷ 6 = 5.5 ft (approximately)

The product of these two numbers is:

6 ft x 5.5 ft ≈ 33 sq ft

Therefore, the dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.

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Total longer distance is [tex]3\frac{2}{21} miles[/tex], that kiki run during the second week of track practice than the first week of track practice.

We have, a runner Kiki and she runs on track for practice. In first week,

Distance runs by Kiki on track practic = [tex]4 \frac{3}{7} miles[/tex]

which is a mixed fraction so, simplify it into simple fraction that is 25/7 miles. In second week,

Distance runs by Kiki on track practice = [tex]6 \frac{2}{3} miles[/tex]

After simplification, it is equals to 20/3 miles. We have to calculate the longer distance that kiki run during the second week of track practice than the first week of track practice. Let the distance run during second week be longer by 'x miles' from distance run during first week. The required distance can be calculated by difference between the distance that kiki run during the second week of track practice and the first week of track practice. So, [tex]x = \frac{20}{3} - \frac{25}{7 }[/tex].

taking least common multiple of (3,7)= 21

=> [tex] x = \frac{20× 7 - 3× 25}{21} [/tex]

[tex] =>x = \frac{ 140 - 75}{21} = \frac{65}{21 }[/tex].

Hence, required distance value is

[tex]3\frac{2}{21} [/tex].

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Answer:

11

Step-by-step explanation:

15 - (p + 1)

Let p=3

15 - (3 + 1)

Parentheses first

15 - (4)

11

Answer:

11

Step-by-step explanation:

Given that,

p = 3

So, to find the value of the expression you have to solve it by replacing p with 3.

15 - ( p + 1 )

15 - ( 3 + 1 )

15 - 4

11

Answer:

See below.

Step-by-step explanation:

to find the change in temperature from 2:00 PM to 10:00 PM, you need to subtract the final temperature from the initial temperature. In other words,

Change in temperature = Final temperature - Initial temperature

In your problem, the final temperature is -9°F and the initial temperature is 18°F. Therefore,

Change in temperature = -9°F - 18°F

Change in temperature = -27°F

So, the change in temperature from 2:00 PM to 10:00 PM is -27°F.

Number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

To find the percent of wolves that are neither female nor hunt in medium-sized packs, follow these steps:
1. Determine the total number of wolves.
2. Identify the number of female wolves and those that hunt in medium-sized packs.
3. Subtract the number of wolves that fit into either category from the total number of wolves.
4. Divide the remaining number of wolves by the total number and multiply by 100 to get the percentage.
Please provide the necessary data (total number of wolves, number of female wolves, and number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

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Answer:

3.6 miles

Step-by-step explanation:

hope this helps!

The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

What is variability?

To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.

To calculate the range, we subtract the smallest value from the largest value:

Largest value: 58

Smallest value: 10

Range = Largest value - Smallest value = 58 - 10 = 48

Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

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The least likely event from given events is Option B: A randomly selected student who is freshmen owns a skateboard.

The event whose occurence is minimum is least likely event.

Suppose there are finite elementary events in sample space of considered experiment and all are equally likely.

Then, we want to find the probability of an event E.

Then, its probability is given as

P(E) = Number of favourable cases/ Number of total cases = n(E)/n(S)

where favorable cases are the elementary events who belong to E, and total cases are size of sample space.

For two events A and B, by chain rule, we have:

P(A∩B) = P(B)P(A|B) = P(A)P(A|B)

How to find the conditional probability:

Suppose that there are two events A and B. Then suppose the conditional probability are:

P(A|B) = probability of occurrence of A given B has already occurred.

P(B|A) = probability of occurrence of B given A has already occurred.

We can then use the chain rule to find them, or Bayes theorem also helps in finding these probabilities.

We are given the table of joint relative frequency:

We take events as A, A' and B and B'

Important probabilities which will be used are evaluated as:

P(A) = n(A)/n(S) = 150/1200 = 1/8

P(B) = n(B)/n(S) = 250/1200 = 5/24

P(A') = 1 - P(A) = 7/8

P(B') = 1 - P(B) = 1 - 5/24 = 19/24

P(A∩B) = n(A∩B) / n(S) = 40/1200 = 1/30

P(A'∩B') = n(A'∩B') / n(S) = 840/1200 = 7/10

P(A'∩B) = n(A'∩B) / n(S) = 210/1200 = 7/40

Evaluating probabilities of choices given, we get:

Case 1: E = A random selected student who owns skateboard is freshmen

P(E) = ?

P(E) = P(B|A) = P(A∩B) / P(A) = 1/30 ÷ 1/8 = 4/15

Case 2: E = A random selected student who is freshmen owns skateboard:

P(E) = P(A|B) = P(A∩B) / P(B) = 1/30 ÷ 5/24 = 4/25

Case 3: E = A random selected student who doesn't owns skateboard is freshmen

P(E) = P(B|A') = P(A'∩B) / P(A') = 7/40 ÷ 19/24 = 21/95

Case 4: E = A randomly selected student who doesn't owns skateboard is not freshmen

P(E) = P(B'|A') = P(A'∩B') / P(A') = 7/10 ÷ 19/24 = 84/95

So, the least probability is for second case.

Question - Seth is analyzing number of students in class and high school who own skateboards. He puts the data in table shown. Given information in table, which event is least likely?

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Born: 582 BCE

Died: 497 BCE

582-497= 85

Answer: 85 years old

The price of 1 liter of petrol at the cheaper petrol station is £0.68.

What is the conversion rate?

Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. Your conversion rate would be 5%, for instance, if you had 50 conversions out of 1,000 interactions, as 50 divided by 1,000 equals 5%.

Here, we have

Given: The prices of petrol in a British and an American petrol station are shown below. The conversion rate is $1 = £0.80.

We have to find the price of 1 liter of petrol in the cheaper petrol station.

$1 = £0.80

= £13.20×($1/£0.80)

= $16.5

For British petrol station

12 liter of petrol = $16.5

1 liter = $16.5/12

1 liter = $1.375

For American petrol station

20 liters of petrol = $17

1 liter = $17/20

1 liter = $0.85

The price of cheaper petrol from American petrol stations = $0.85× (£0.80/$1)

= £0.68

Hence, the price of 1 liter of petrol at the cheaper petrol station is £0.68.

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After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the cost of each blouse and skirt:

x be the price of one blouse and y is the price of one skirt.

For a total of $215, Carol purchased 3 skirts and 5 blouses.

5x + 3y = 215

For a total of $135, Ellen purchased 2 skirts and 3 blouses.

3x + 2y = 135

By resolving the equations in the system:

5x + 3y = 215

3x + 2y = 135

We will obtain:
x = $25

y = $30

Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.

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Correct question:

Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?

Answer:r=25

Step-by-step explanation: he spends 96$ on 12 pairs of gloves and 25 dollars per 1 rake.  thus r equals 25

Answer:

See below answer of each.

Step-by-step explanation:

Let's assume the cost of one small popcorn to be 'x'.

Each friend bought one ticket and one small popcorn, so the cost of one ticket and one small popcorn is $7.50 + x.

The total amount spent by 8 friends is $83.60.

Therefore, we can set up the following equation:

8(7.50 + x) = 83.60

Simplifying the equation, we get:

60 + 8x = 83.60

8x = 23.60

x = 2.95

Therefore, the cost of one small popcorn is $2.95.

The equation to represent the situation is:

Total cost = Initial cost + (Cost per mile x Number of miles)

$24.25 = $3.00 + ($2.50 x m)

where m represents the number of miles to Jeremiah's house.

Let's start by setting up the equation for the total cost of the gloves:

12 pairs of gloves x $8 per pair = $96

We know that the gardener spent a total of $300 on both rakes and gloves, so we can set up an equation:

12r + $96 = $300

Now we can solve for r:

12r = $204

r = $17

Therefore, the cost of 1 rake is $17.

The equation that models the situation is:

12($17) + $96 = $300

The approximate probability that the actual proportion requiring aid will exceed 0.08 is 0.5 (or 50%) rounded to four decimal places.

Given: The number of members in town = 400

The number of members requiring aid = 32

The proportion of members requiring aid = (number of members requiring aid) / (total number of members) = 32 / 400 = 0.08

To find the approximate probability that the actual proportion requiring aid will exceed this value, we need to assume a distribution for the proportion of members requiring aid. Assuming a normal distribution, we can use the Central Limit Theorem to approximate the sampling distribution of the sample proportion.

The standard error of the sample proportion is given by:

SE = √[p(1-p)/n]

where p is the population proportion and n is the sample size.

Substituting the values, we get:

SE = sqrt [(0.08 × 0.92) / 32] = 0.043

To find the probability that the actual proportion requiring aid will exceed 0.08, we can standardize the distribution using the z-score formula:

z = (x - p) / SE

where x is the value of the proportion we are interested in, p is the population proportion, and SE is the standard error of the sample proportion.

Substituting the values, we get:

z = (0.08 - 0.08) / 0.043 = 0

The probability that the actual proportion requiring aid will exceed 0.08 is equal to the probability of observing a z-score greater than 0, which is 0.5 (or 50%).

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The question is -

The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town? .08 What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)

The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.

In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.

The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.

Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565

The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.

Therefore, the expected value of a ticket is:$5565 / 833 = $6.68

Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.

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Answer:

There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

Step-by-step explanation:

the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two  without neighbors regard to whether they are right or left neighbors is:5!6⋅2=10.6⋅25! = 10

There are $(6-1)! = 5! = 120$ ways to seat six people around a circular table if the seatings are considered distinct. However, we must divide this number by $6$ to account for the fact that rotations of the same seating arrangement are considered the same. We also must divide by $2$ to account for the fact that reflections (i.e., reversing the order of people) of the same seating arrangement are also considered the same.

Therefore, the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors is:

5!6⋅2=10.6⋅25! = 10

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The relative frequency for the event "spin a 2" is 1/5.

Relative frequency measures how often a value appears relative to the sum of the total values.

In order to determine the relative frequency of spinning a 2, divide the frequency of spinning a two by the total number of trials.

Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign that is used to represent division is ÷.

Relative frequency = number of times a two was spun / total number of trials

= 10 / 50 = 1/5

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Answer:

40 and 45

Step-by-step explanation:

let the 2 numbers be x and y with y the larger of the two, then

x + y = 85 → (1)

x = y + 5 → (2)

substitute x = y + 5 into (1)

y + 5 + y = 85

2y + 5 = 85 ( subtract 5 from both sides )

2y = 80 ( divide both sides by 2 )

y = 40

substitute y = 40 into (2)

x = 40 + 5 = 45

the two numbers are 40 and 45

Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50. The problem can be solved using a system of equations.

Let's use a system of equations to solve this problem:

Let x be the number of shirts that Siona bought, and y be the number of pairs of shorts that she bought. Then we have:

Equation 1: x + y = 10 (Siona bought 10 outfits in total)

Equation 2: 3.50x + 4.00y = 36.50 (The total cost of the outfits is $36.50)

To solve for x and y, we can use substitution or elimination. Let's use substitution:

From Equation 1, we can solve for x in terms of y:

x = 10 - y

Substitute this expression for x into Equation 2:

3.50(10 - y) + 4.00y = 36.50

Simplify and solve for y:

35 - 3.50y + 4.00y = 36.50

0.50y = 1.50

y = 3

Now we can substitute y = 3 back into Equation 1 to solve for x:

x + 3 = 10

x = 7

Therefore, Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50.

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