The data in the table describes the preferred type of exercise of 9th graders.




Find the marginal relative frequency for students who prefer swimming as their preferred type of exercise.

39%

35%

19%

16%

Answer:

the entire right column



Step-by-step explanation:

your solutions should simply to 64

Answer:2*2*2*2*2*2 and 4*16 and 8*8

Step-by-step explanation:

2*2*2*2*2*2=64

4*16=64

8*8=64

6*6*6*6*6*6=46656

2*6=12

12*12=144

The humidity should be approximately 68%.

a)

When you run the command -

> xtabs(water ~ temp+humid, snail)/4

you get the following output -

Now, we see that the humidity of 60% lies exactly in between the humidity of 45% and 75%. And also the temperature of 25oC lies exactly in between the temperature of 20oC and 30oC.

So, we can proceed by taking the average values to estimate the water content.

Create a colum for the humidity of 60% in between humidity of 45% and 75% by taking the mean of humidity of 45% and 75% as shown -

Humidity

45% 60% 75%

Temp 20 72.5 77 81.5

30 69.5 73.875 78.25

Now, similarly create a row for the temperature of 25oC by taking the average of rows for the temperature of 20oC and 30oC as shown -

Humidity

45% 60% 75%

Temp 20 72.5 77 81.5

25 71 75.4375 79.875

30 69.5 73.875 78.25

So, we can see that the estimated water content for 60% humidity and temperature of 25oC is = 75.4375.

--------------------------------------

b)

Use the following code to fit the regression model for 'water' with predictors 'temperature' and 'humidity'.

> model <- lm(water ~ temp+humid, snail)

Now, you can view the parameters using the code -

> coefficients(model)

This will give you the following output -

> coefficients (model)\n(Intercept)\nhumid\n52.6108059-0.1833333 0.4734890\ntemp\n

So, the estimated regression model is -

Water = 52.6108 - 0.1833(temp) + 0.4735(humid)

We can now use this model to predict the water content for humidity of 60% and temperature of 25oC using following code -

First define your new data using code -

> newdata = data.frame(temp = 25, humid = 60)

And now use -

> predict(model, newdata)

to get the predicted value. You will get the output as -

76.43681

-------------------------------------

c)

Again, define your new parameters as -

> newdata2 = data.frame(temp = 30, humid = 75)

And use the model to predict the water content using -

> predict(model, newdata2)

you will get the output as -

82.62248

So, the predicted water content for 75% humidity and 300C temperature is = 82.62248.

From part (a), we get that the average water content for given condition is 78.25%. The average method used in part (a) is straight forward and doesn't involve much mathematics while the linear regression method uses complex algorithm to predict the value but has much more accuracy than the simple average method because its not necessary that data is always changing with constant rate.

-------------------------------

d)

For a predicted response of 52.6%, we would have -

Water = 52.6108 - 0.1833(temp) + 0.4735(humid) = 52.6

=> 0.4735 (humid) = 0.1833(temp)

Or temp \approx 2.6 (humid)

So, any pair of values satisfying the above relation would give the predicted value same as the intercept value.

For example, humidity = 60% and temperature = 156oC

or, humidity = 45% and temperature = 117oC

But note that the regression model has been trained on values of temperature ranging between 20 to 30 while we are using the temperature of more than 100oC to get the predicted value same as intercept value.

So, this doesn't represent a reasonable prediction.

----------------------------------------------------------

e)

For, predicted value of water = 80%, and temperature of 25oC, the humidity would be -

Water = 52.6108 - 0.1833(temp) + 0.4735(humid) = 80

=> 52.6108 - 0.1833(25)+ 0.4735(humid) = 80

=> humid = 67.52%

So, humidity should be approximately 68%.

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Answer: 1.02

Step-by-step explanation:

2.67 - 1.65 =  1.02

To predict the number of situps a person who watches 13.5 hours of TV can do, we can use the given regression equation y = ax + b, where 'a' and 'b' are the coefficients and 'x' is the hours of TV watched.

Given:
a = -1.077
b = 30.98
x = 13.5

Step 1: Substitute the given values into the regression equation:
y = (-1.077)(13.5) + 30.98

Step 2: Perform the calculations:
y = (-14.5395) + 30.98

Step 3: Add the values:
y = 16.4405

Since we need the result to one decimal place, we can round it off to:
y ≈ 16.4

So, a person who watches 13.5 hours of TV per day can do approximately 16.4 situps.

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Answer: 401.92

Step-by-step explanation:

V=πr^2h

=π(4^2)(8)

=π(16)(8)

=π128

=401.92

Hope this helps! :)

The description of the statement is (b) inclusive.

Here, we have,

to describe the events:

The events are given as:

Drawing a red card

A card with a number

A red card can have a number and a numbered card can be a red card.

This means that

n(Red and Numbered) ≠ 0

Events that have similar features are referred to as inclusive events

Hence, the description of the statement is (b) inclusive

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The ratio of the trigonometric function of the right triangle, cos A is 3/5.

Given that,

In △ABC , ∠C is a right angle.

Then the opposite side to the right angle will be the hypotenuse.

So AB is the hypotenuse.

Sin A = BC / AB [ Since sine of an angle is opposite side / hypotenuse]

BC / AB = 4/5

BC = 4 and AB = 5

Using the Pythagoras theorem,

Third side, AC = √(5² - 4²) = 3

Cos of an angle is the ratio of adjacent side to the hypotenuse.

Cos A = 3/5

Alternatively, we can use the identity,

sin²A + cos²A = 1

to find the value of cos A.

Hence the value of cos A is 3/5.

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The correct equation representing the total number, s, of stickers is option C. s/3 = 4.

The formula or relation that can accurately indicate the total number of stickers, number of girls and number of stickers received by girl is as follows -

Total number of stickers/number of girls = number of stickers received by each girl

(We will perform division as number of stickers must be more than number of girls)

Keep the representative value of each

s/3 = 4

Solving it to know the number of stickers

s = 4 × 3

s = 12

Hence, there were 12 stickers divided four each among three girls. Thus, the correct answer is C. s/3 = 4.

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The complete question is -

Elizabeth has some stickers. She divide her stickers equally amiung herself and two friends. Each person get 4 stickers. Which equation repersents the total number,s,of stickers?

A. s + 3 = 4

B. s 3 = 4

C. s/3 = 4

D. 3s = 4

The original claim in symbolic form is μ = 68.9 bpm, and the null and alternative hypotheses are H0: μ = 68.9 bpm and Ha: μ ≠ 68.9 bpm.

Let's break it down step by step.

a. Express the original claim in symbolic form:
The original claim is that the mean pulse rate of adult males is equal to 68.9 bpm. We can represent this claim using the following symbols:
μ = 68.9 bpm

b. Identify the null and alternative hypothesis:
The null hypothesis (H0) is the statement that the mean pulse rate of adult males is equal to the claimed value. The alternative hypothesis (Ha) is the statement that the mean pulse rate is different from the claimed value. In this case, the hypotheses can be written as:

H0: μ = 68.9 bpm
Ha: μ ≠ 68.9 bpm

To summarize, the original claim in symbolic form is μ = 68.9 bpm, and the null and alternative hypotheses are H0: μ = 68.9 bpm and Ha: μ ≠ 68.9 bpm.

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The area of the circle with a circumference of 6pi m is 9π square meters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed as:

C = 2πr

Where r is radius and π is constant pi.

We are given that the circumference of the circle is 6π m, so we can set up the equation and solve for the radius.

C = 2πr

6π = 2πr

Simplifying, we get:

r = 6π/2π

r = 3

Now that we know the radius of the circle, we can use the formula for the area of a circle:

A = πr²

Substituting the value of r, we get:

A = π(3)²

Simplifying, we get:

A = 9π

Therefore, the area is 9π m.

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Answer:

Step-by-step explanation:

5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%5.3%uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

uestion

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

Answer:

8,450 minutes

Step-by-step explanation:

So the difference among smaller number is 70 and the larger number is 210.

One of the most crucial operations in algebra, which is achieved by removing two integers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two supplied numbers is the goal of determining the difference in arithmetic.  

The product of the sine of the primary angle and the cosine of the second angle less the product of the cosine of the first degree and the sine of the second angle is the sine of the difference of two angles, according to the difference formula for sines.

Let the smaller number be x. Then the larger number is 3x.

According to the problem, we have:

3x - x + 80 = 4x - 60

Simplifying and solving for x:

2x + 80 = 4x - 60

140 = 2x

x = 70

So the smaller number is 70 and the larger number is 3x = 3(70) = 210.

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Correct Question:

The difference of two numbers plus 80 units is equal to four times the smaller number minus 60 units. Find the two numbers if the larger is three times the smaller.

True. The orthogonal projection of vector x onto the line determined by non-zero vector y is indeed a vector. The projection creates a new vector that lies on the line determined by y and is orthogonal (perpendicular) to y.

2. If the orthogonal projection of x onto the line determined by non-zero y is the vector, then x - is orthogonal to y: True

If the orthogonal projection of x onto the line determined by non-zero y is the vector, then the difference between x and the projection (x - projection) will be orthogonal to y. This is because the projection is the closest point on the line determined by y to x, and thus the difference vector will be perpendicular to the line.

3. For unit vector y ∈ R, the projection matrix for orthogonal projection onto the line determined by y is yy^T: True

For a unit vector y, the projection matrix P for the orthogonal projection onto the line determined by y is given by P = yy^T, where y^T is the transpose of the vector y. This matrix is used to calculate the orthogonal projection of a vector onto the line determined by y.

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The probability of rolling 1 and 2 is 1/36 of an experiment consists of rolling two fair number cubes.

Hence, the correct option is A

In the sample space diagram of rolling two number cubes, there are 36 equally likely outcomes since there are 6 possible outcomes for the first cube and 6 possible outcomes for the second cube. The outcome of rolling a 1 and 2 is shown in the sample space diagram and there is only one such outcome.

Therefore, the probability of rolling a 1 and 2 is

P(1 and 2) = (number of favorable outcomes) / (total number of outcomes) = 1/36

So the probability of rolling a 1 and 2 is 1/36.

Hence, the correct option is A

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Answer: x = 4.

Step-by-step explanation:

Taking the logarithm of both sides with base 3, we get:

x = log3(81)

x = log3(3^4)  [Since 81 is equal to 3 raised to 4th power]

x = 4

Therefore, the solution is x = 4.

Answer:

Step-by-step explanatiON

X=81/3

X=4

The average speed of the train is both greater than or equal to 2.3928 km/minute and less than or equal to 3.3567 km/minute.

To find the average speed of the train, we divide the distance traveled by the time taken:

Average speed = distance / time

= 503 km / 180 minutes

= 2.7944... km/minute

Since the distance is measured correct to the nearest kilometer, the actual distance could be as low as 502.5 km or as high as 503.5 km. Similarly, since the time is measured correct to the nearest minute, the actual time taken could be as low as 2.5 hours or as high as 3.5 hours.

To find the maximum average speed, we assume that the distance traveled is 503.5 km and the time taken is 2.5 hours.

Maximum average speed = 503.5 km / 150 minutes = 3.3567... km/minute

To find the minimum average speed, we assume that the distance traveled is 502.5 km and the time taken is 3.5 hours.

Minimum average speed = 502.5 km / 210 minutes = 2.3928... km/minute

Therefore, the average speed of the train is both greater than or equal to 2.3928 km/minute and less than or equal to 3.3567 km/minute.

Rounding to two decimal places, the average speed of the train is 2.79 km/minute.

Reason: Both 2.79 km/minute and the minimum and maximum average speeds are correct to the nearest hundredth of a kilometer per minute and take into account the maximum possible error in the measurements.

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A one-tailed t-test is used when the researcher has a specific directional hypothesis.

If you are comparing the difference between two separate populations, such as children who attend two different Elementary schools, you should use an independent-measures design. In an independent-measures design, two separate groups of participants are sampled, and each participant is only tested once. The purpose of this design is to compare the means of two independent populations to determine if there is a statistically significant difference between them. In contrast, a within-groups design would involve testing the same group of participants twice under different conditions, while a repeated-measures design would involve testing the same group of participants under all conditions. A one-tailed t-test is a specific type of statistical test that can be used in either an independent-measures or within-groups design to test a directional hypothesis.

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Answer:

  x = 3√3

Step-by-step explanation:

You want the middle-length side of a 30°-60°-90° triangle whose short side is 3.

There are two "special" triangles in trigonometry. The ratios of their side lengths are used in many algebra, trig, and geometry problems.

  30°-60°-90° triangle has sides in the ratios 1 : √3 : 2

  45°-45°-90° isosceles right triangle has sides in the ratios 1 : 1 :√2

The triangle shown in this problem is a 30°-60°-90° right triangle with a short side of length 3. You want the middle-length side (x), which the above tells us is √3 times the length of the short side.

  x = 3√3

__

Additional comment

You can use the trig relation ...

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

For this triangle, this means ...

  x = 3/tan(30°)

  x = 3/(1/√3) = 3√3

A suitable calculator can show this in the desired format.

The area of the circles are calculated below.

The area of a circle is given by the formula:

A = πr²

Where r is the radius of the circle

No. 1

r = 0.7 in

A = π * 0.7² = 0.49π in²

No. 2

r = 1.0/2 = 0.5 in

A = π * 0.5² = 0.25π in²

No. 3

r = 1.6/2 = 0.8 in

A = π * 0.8² = 0.64π in²

No. 4

r = 0.4/2 = 0.2 in

A = π * 0.2² = 0.04π in²

No. 5

r = 0.3 yd

A = π * 0.3² = 0.09π yd²

No. 6

r = 0.9 ft

A = π * 0.9² = 0.81π ft²

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Answer: :)

The correct answer is C. A scalene triangle is a triangle with no sides that are the same length. This means that all three sides of a scalene triangle have different lengths. In addition, a scalene triangle does not have any angles that are congruent. This is in contrast to an isosceles triangle, which has two sides of equal length, and an equilateral triangle, which has all three sides of equal length.

Step-by-step explanation:

The correct answer is c. Learning curves are important for estimating performance improvement as workers become experienced.

Learning curves are often used in project management to estimating the time, effort, and resources required to complete a task or project. They help to estimate how long it will take for a worker or team to become proficient at a task or process, based on the amount of time and effort that they have put into it.

This can be helpful in estimating performance improvement as workers become more experienced and efficient in their work. The concept of a learning curve is a curved line that represents the rate of improvement over time, which is why the term "curve" is relevant. While learning curves do involve some math, they are not primarily focused on helping new PMs understand required math, nor are they used for visualization of curved mechanical parts or estimating cost improvement as parts become "broken in."
Learning curves are important for:
c. estimating performance improvement as workers become experienced.
Learning curves represent the progress made in a skill or job over time, whereas a curve illustrates the relationship between experience and efficiency. As workers become more experienced, their performance typically improves, which can be estimated using a learning curve in various industries and tasks.

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

0.2

Step-by-step explanation:

a) The light flashes as the circuit leaves the field at a speed of 16 ms.

b) The current flow as the loop exits the field in the clockwise direction.

c) The power dissipated in the bulb during the flash is 0.04 W. 

To reply to these questions, we will utilize Faraday's Law, which states that a changing attractive field actuates an electromotive drive (EMF) in a circuit, and the initiated EMF is rise to the rate of alter of attractive flux through the circuit.

a) The attractive flux through the circle is given by the item of the attractive field, region of the circle, and cosine of the point between the attractive field and the ordinary to the plane of the circle.

As the circle is pulled out of the attractive field, the magnetic flux through the circle diminishes, and thus, an EMF is actuated within the circle. This initiated EMF drives a current through the light bulb, causing it to light up.

The time term of the streak of light can be decided from the time taken by the circle to move out of the attractive field.

The removal voyage by the circle is 40 cm, and the speed is 25 m/s, so the time taken is:

t = d/v = 0.4 m / 25 m/s = 0.016 s = 16 ms

Subsequently, the streak of light endures for 16 ms.

b) Concurring to Lenz's Law, the course of the initiated current is such that it contradicts the alter within the attractive flux that produces it. As the circle is pulled out of the attractive field, the attractive flux through the circle diminishes.

Hence, the actuated current flows in a course that makes a magnetic field that restricts the initial attractive field. This could be accomplished by the induced current streaming clockwise as seen from above. Hence, the reply is clockwise.

c) The control scattered within the light bulb can be calculated utilizing the equation P = V²/R, where V is the voltage over the bulb and R is its resistance.

The voltage over the bulb is break even with to the initiated EMF, which can be calculated from Faraday's Law. The attractive flux through the circle changes at a rate of (40 cm) x (25 m/s) = 1 T.m²/s.

The region of the circle is (40 cm) x (10 cm) = 0.04 m². The cosine of the point between the attractive field and the ordinary plane of the circle is 1 (since the circle is opposite to the field). Subsequently, the induced EMF is:

EMF = -d(phi)/dt = -NA(dB/dt)

= -(1)(0.04 m²)(1 T.m²/s)/0.016 s

= -1 V

The negative sign indicates that the actuated EMF is within the inverse course of the current stream. Subsequently, the voltage over the light bulb is:

V = -EMF = 1 V

The power dissipated within the bulb is:

P = V²/R = (1 V)²/25 ohm = 0.04 W

Subsequently, the control scattered within the bulb during the streak is 0.04 W. 

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We can conclude that if X is normally distributed with a mean of 11 and a standard deviation of 3, then the value of x that solves P(X > x) = 0.8 is x = 13.52.

We need to find the value of x such that P(X > x) = 0.8, where X is a normally distributed random variable with mean μ = 11 and standard deviation σ = 3.

From the properties of the standard normal distribution, we know that if Z is a standard normal random variable, then P(Z > z) = 0.8 corresponds to z = 0.84 (found using a standard normal table or calculator).

We can standardize X to a standard normal random variable Z using the formula:

Z = (X - μ) / σ

Substituting the values μ = 11 and σ = 3, we get:

Z = (X - 11) / 3

Now, we want to find the value of x such that P(X > x) = 0.8. We can rewrite this as:

P(Z > (x - 11) / 3) = 0.8

Using the standard normal table or calculator, we find that P(Z > 0.84) = 0.2005.

Therefore, we can write:

0.2005 = P(Z > 0.84) = P((X - 11) / 3 > 0.84) = P(X > 11 + 3(0.84)) = P(X > 13.52)

So the value of x that solves P(X > x) = 0.8 is x = 13.52.

Therefore, we can conclude that if X is normally distributed with a mean of 11 and a standard deviation of 3, then the value of x that solves P(X > x) = 0.8 is x = 13.52.

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The value of x in the triangle is 21, option B is correct.

The given triangle is right triangle

We know that the sine function is the ratio of opposite side and hypotenuse

Opposite side =19

Hypotenuse =x

We have to find the value of x

Sin 65 = 19/x

0.91 =19/x

x=19/0.91

x=20.8

x=21

Hence, the value of x in the triangle is 21, option B is correct.

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The polynomial long division of 6x³+x²+7x+9 by 2x+1 gives a quotient of 3x² - x + 4

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

6x³+x²+7x+9 by 2x+1

Using the polynomial long division setup, we have

2x + 1   |  6x³ + x² + 7x + 9

Evaluating the division, we have

              3x² - x + 4

2x + 1   |  6x³ + x² + 7x + 9

              6x³ + 3x²

             ---------------------------------------

                     -2x² + 7x + 9

                     -2x² - x

             ---------------------------------------

                           8x + 9

                           8x + 4

                        ---------------------------------------

                                  5

Hence, the quotient is 3x² - x + 4

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Answer:

mean = 52

Step-by-step explanation:

In mathematics, the mean is a measure of central tendency that represents the average of a set of numbers. It is also commonly known as the arithmetic mean.

To calculate the mean, you add up all the numbers in a set and then divide by the total number of values in the set.

So in tho case we would add all the values then divide by the amount of values there are.

1) rewrite values:

42  45  58  63

2) add:

42 + 45 + 58 + 63
= 208

3) divide:

Since there arev4 values we will divide by 4.

208 / 4 = 52

Therefore, the mean is 52

Answer:

[tex]\huge\boxed{\sf Mean = 52}[/tex]

Step-by-step explanation:

42, 45, 58, 63

[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data} \\\\Mean = \frac{42+45+58+63}{4} \\\\Mean = \frac{208}{4} \\\\Mean = 52\\\\\rule[225]{225}{2}[/tex]

The required, equation to determine the number of people is T + (T + 5,500) + 2T + (2T + 300) = 36,700 and there were 10,300 people at the fair on Saturday.

Let's call the number of people who attended the fair on Thursday "T". Then we can use the information in the problem to set up an equation:

Friday's attendance = T + 5,500

Saturday's attendance = 2T

Sunday's attendance = 2T + 300

Total attendance = T + (T + 5,500) + 2T + (2T + 300) = 36,700

Simplifying the equation, we get:

6T + 5,800 = 36,700

6T = 30,900

T = 5,150

Therefore, the attendance on Thursday was 5,150 people. We can use this information to find the attendance on Saturday:

Saturday's attendance = 2T = 2(5,150) = 10,300

Thus, there were 10,300 people at the fair on Saturday.

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