Please order the following fractions from least to greatest: 5/6, 2/3, 5/9, 5/12, 6/5

(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:

mean = n x mean time = 50 x 5 = 250 minutes

variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9

The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:

te = n x mean time / (1 - p1 x p2)

where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:

σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:

Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.

(d) The variability class of the squared coefficients of variation can be determined as follows:

C0² (Part a): (0.6)^2 = 0.36 (low variability)

C0² (Part b): (0.6)^2 = 0.36 (low variability)

Ce² (Part c): (0.026)^2 = 0.000676 (low variability)

(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.

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Answer:

  (a)  0.413

  (b)  0.400

  (c)  1 — ... the difference should be small

Step-by-step explanation:

Given a table of experimental results from 1000 spins and a diagram of a spinner, you want the experimental and theoretical probabilities of landing on Red. You also want a statement comparing them.

The table tells you 1000 experiments resulted in 413 reds. The experimental probability of landing on red is ...

  413/1000 = 0.413

The diagram of the spinner shows 10 equal segments, of which 4 are red. The theoretical probability of landing on red is ...

  4/10 = 0.400

The presumption in statistics is that any experiment repeated a sufficient number of times should see experimental results approaching theoretical results. We expect a small difference between experimental and theoretical results for a large number of trials.

The missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.

Assume that the missing side is x.

So that side ratio in similar triangle are equal;

14/20 = 21/x

So, x = 30.

Therefore, the missing side x is 30

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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x

So, x = 30.
Therefore, the missing side x is 30

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Answer:

I am not good at this but i gess itis 11 √121 equals 11

Since means cannot be smaller than 0, the sampling distribution of the mean is always right skewed.

No matter the sample size, the form of the sampling distribution of means is always the same as the population distribution.

We require two assumptions in order to apply the sampling distribution model to sample proportions: The selected values must be independent of one another, according to the independence assumption. The Sample Size Assumption demands that the sample size, n, be sufficiently large.

While doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.

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the actual question is :

Which of the following is true about the sampling distribution of the mean?

a. It is an observed distribution of scores

b. It is a hypothetical distribution

c. It will tend to be normally distributed with a

standard deviation equal to the population

standard deviation

d. The mean will be estimated by the standard

error

e. Both (a) and (b)

Answer:

307ft^2

Step-by-step explanation:

To explain this, you are looking for the area of half a circle + the area of a triangle.

To first find the area of half a circle, we need the equation Area = pir^2/2

Plug-in radius, which is 10ft

pi(10)^2/2

= 157ft^2

Next, we find the area of the triangle. The equation to find the area of a triangle is A=1/2(b)(h)

B=base

h=height

To find the base, we simple make the base equal to the diameter of the circle, which is the radius multiplied by 2

So base = 10*2 = 20

The height is given so

height=15

Plug in base and height  = 20*15/2

= 150ft^2

Then you want to add both areas found together

157ft^2+150ft^2

= 307ft^2

Answer:

Step-by-step explanation:

The data consists of 24 rows representing gender, admission status, and department for 4,526 applicants. The admission rate for men was 45%, for women was 30%, and the table of numbers is consistent with the given rates.

The data has a tabular structure with six rows corresponding to the six departments (A-F) and four columns representing the Gender, Admission status, Department, Count

The data is different from other datasets in that it provides information for each gender and admission status for each department separately. The 24 rows in the data set represent the different combinations of gender, admission status, and department.

The admission rate for all applicants is calculated by dividing the number of admitted applicants (1,755) by the total number of applicants (4,526), which gives an overall admission rate of approximately 0.387.

The admission rate for men is calculated by dividing the number of admitted men (1,493) by the total number of male applicants (3,356), which gives a male admission rate of approximately 0.445.

The admission rate for women is calculated by dividing the number of admitted women (1,262) by the total number of female applicants (1,670), which gives a female admission rate of approximately 0.301.

The table below summarizes the number of rejected and admitted applicants for each gender:

Gender Number Rejected    Number Admitted

Male          1863                 1493

Female         557                         1262

The numbers in the table are consistent with the given admission rates for men and women, as the admission rate for men is higher than that for women, and the number of male applicants is greater than the number of female applicants.

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_____The given question is incomplete, the complete question is given below:

Describe the structure of the data. Is it different than data you have examined before? Specifically, there are 24 rows in this data set, but the set provides information about 4,526 observations (the sum of the "count" column). Describe what each row represents. Each of the six departments (A-F) have four rows of data in this set corresponding to each of the following. 1st row Men who were admitted 9 . 2nd row Men who were not admitted . 3rd row Women who were admitted . 4th row Women who were not admitted . of the 4,526 applicants in this data set, 1,755 were admitted for an overall admission rate of approximately 39%. The admission rate for men was 45%, while the admission rate for women was 30%. Complete the following table. Gender Number Rejected Number Admitted 1198 Male 1493 ✓ Female 557 1278 Indicate how your numbers are consistent with these given admission rates for men and women. (Round your answers to four decimal places.)

Answer:

7.  300 miles

8. 60 miles

9. 5 miles

10. 1000 meters

Step-by-step explanation:

7.

We Take

60 x 5 = 300 miles

So, Ruth drives 300 miles in 5 hours.

8.  

5 miles = 10 minutes

1 mile = 2 minutes

2 hours = 120 minutes

We Take

120 / 2 = 60 miles

So, Carl drive 60 miles in 2 hours

9.

1 hour and 25 minutes = 85 minutes

We Take

85 / 17 = 5 miles

So, Nick travels 5 miles in an hour and 25 minutes.

10.

100 meters = 2 minutes

50 meters = 1 minute

We Take

50 x 20 = 1000 meters

So, Stan swims 1000 meters in 20 minutes.

Answer:

7. 300 miles/hours
8. 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.

10. 1000 meters in 20 minutes.

Step-by-step explanation:

7. 60 x 5= 300 miles/hours

8. 5 miles in 10 minutes so in 2 hours it will be 5 x 12 = 60 miles in 2 hours

9.  5 miles in 2 hours and 25 mins.

10. 1000 meters in 20 minutes.

Answer:

Step-by-step explanation:

We'Re looking at a normal distribution here- let's start by drawing it out to the mean me- is 315 grams standard. Deviation is 16 point. We want to know the weight corresponding to each of these events and we can use either the appendix which i assume is a z, school table or excel so the first 1. We want the highest 20 percent up here somewhere. This is what we would call the 80 percent. It separates the bottom 80 percent from the highest 20 percent. So how do we work the well? We need to start by getting the z score for it. So how do we get that, while in excel you're going to use the norm inverse function which looks like this? So it's calls norm and then in here you just put in x, where x is your percentage and that will spit out the z score and i'm using this rather than a table, because it will give me a more exact value. So we're going to do that, and so here the percent is the 80, so it's not .8 and that spits out the z score of nort .8416 to 4 decimal places. But i'm always going to this exact score, because we now have to turn it from a z score to a piece of real data. Z score is a measure of how many standard deviations away from the mean a value is so we're. Looking for the value not .84 standard deviations, above the mean or if we write it like this x, is equal to z, sigma plus mu. So here we take our exact zedscore, because we can still just use excels, multiply it by 16 and add it on to the mean and we'll get our value of 328.447328 .47 grams to 2 decimal places for part b. We want to be middle 60 percent. Now we need to cut off points and within here where, in this interval we have 60 percent of values, which means we have 40 percent of values, not in here. So we can label our 3 sections. These 2 add up to 40 percent, so they have to be 20 percent. Each are called nor .2 and not .2, and then this middle bit here is nor .6 for the total of 100 percent point. So we need these cut off points when you, the z, scores first, and because these are equal distances away from a mine they're going to have the same z score. Just 1 is going to be positive or negative, so z is going to be equal to plus and minus. Let'S look at the lower 1. This is the 20 percent here so into this excel command. We put 20 percent nor .2 and out of it we get the z score of minus, not .8416. So it's actually very similar to the top question, because the top question asked you for the 80 percent be 80 percent. Is the upper cut off point here? 20? Is below cutoff point, so we already have the up 1, let's just calculate below 1, so we've got to be minus, nor .8416 multiplied by 16, but the standard deviation and on to the mean- and we get 301.53 and the upper cut off point is from part A so that's the middle 60 percent makes more space a part c. We want to be highest 80 percent. So now what we want is the cut off between the lowest 20 and the highest 80, which we've just got from part c part b. It'S this lower 1, here, 301.53 grams. That'S an easy! 1! Now we want the lowest 15 percent, so the lowest 15 percent is the 15 percent. So we go to our exylgamant put in the 15 for percent, so that would be no .15 and it's a z score of minus 1.036 keeping the exact value put into this formula. We multiply our z by 16, as on 315, to get 298.42 grams.

The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.

To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:

z = (x - μ) / σ

where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).

Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:

x = μ + z * σ

where z is the z-score that corresponds to the desired probability.

Event 1: The weight is less than 345 grams.

z = (345 - 360) / 9 = -1.67

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.

x = 360 + (-1.67) * 9 = 344.03 grams

Therefore, the weight that corresponds to this event is approximately 344.03 grams.

Event 2: The weight is between 355 and 365 grams.

First, we need to find the z-scores that correspond to the two boundaries:

z1 = (355 - 360) / 9 = -0.56

z2 = (365 - 360) / 9 = 0.56

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:

0.7123 - 0.2123 = 0.5

x1 = 360 + (-0.56) * 9 = 355.16 grams

x2 = 360 + (0.56) * 9 = 364.84 grams

Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.

Event 3: The weight is greater than 375 grams.

z = (375 - 360) / 9 = 1.67

Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.

x = 360 + (1.67) * 9 = 375.97 grams

Therefore, the weight that corresponds to this event is approximately 375.97 grams.

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Residual  for the 5th observation if =$500 and =$475 is  -$166.25 The consumption function C = 300 + 0.75i represents the relationship between consumption and income in a simple economy with no taxes. In this function, C is the dependent variable, while i is the independent variable.

To find the residual for the 5th observation, we need to first calculate the predicted value of consumption (C1 ) for the given value of income (i). We can do this by plugging the value of i into the consumption function and solving for C1 :

C1 = 300 + 0.75i

For the first scenario where i = $500, the predicted value of consumption is:

C 1= 300 + 0.75($500) = $675

To calculate the residual, we need to subtract the predicted value of consumption from the actual value of consumption (C):

Residual = C - C1+

For the 5th observation where C = $500, the residual would be:

Residual = $500 - $675 = -$175

This means that the actual value of consumption is $175 less than the predicted value based on the consumption function.

Similarly, for the second scenario where i = $475, the predicted value of consumption would be:

C1 = 300 + 0.75($475) = $641.25

And the residual would be:

Residual = $475 - $641.25 = -$166.25  

In both cases, the residuals are negative, indicating that actual consumption is less than predicted consumption. This could be due to factors such as unexpected changes in consumer behavior, fluctuations in the economy, or measurement errors in the data.

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The equation for a consumption function in a simple​ economy, where there are no​ taxes, is given by C​ = 300 ​+ 0.75​i,  What is the residual for the 5th observation if =$500 and =$475?c denotes consumption and i denotes income.

Answer: The correct answer is C, the X.

Answer:

Answer: C. f(x) = 2x²+x+6

The value οf the given angle x = 39.8 degree

Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.

The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.

In the figure tanx = p/h

[tex]x = tan^{-1(15/18)}[/tex]

x = 39.8

Hence the value οf the given angle x = 39.8 degree

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Answer:    

The radius of the circle is 3.

The center of the circle is (-2, 1).

Step-by-step explanation:

   Rewrite the equation in standard form:

   We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.

x² + 4x + y²-2y = 20

(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1

(x + 2)² + (y - 1)² = 25

   Identify the center and radius:

   Now that we have the equation in standard form, we can identify the center and radius of the circle.

The center is the point (-2, 1), which we can read directly from the equation.

The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.

Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.

The required value of TV is 2 units.

A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.

We have given that;

TW = y²

WV = 2y − 1

We know that in parallelogram

TW = WV

y² = 2y − 1

y² - 2y + 1 = 0

y² - y - y + 1 =0

y(y - 1)-1(y - 1) = 0

(y - 1)(y - 1) = 0

(y - 1)² = 0

y - 1 = 0

y = 1

So;

TV = TW + WV

TV = y² + 2y − 1

TV = 1² + 2(1) - 1

TV = 1 + 2 - 1

TV = 2 units

Thus, required value of TV is 2 units.

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The statement "car:toyota" correctly describes a subclass (Toyota) of the superclass (car). Similarly, "ducks:pond" correctly describes a subclass (ducks) of the superclass (pond). So, option A) and B) are correct.

Superclasses and subclasses are used in object-oriented programming to create a hierarchical relationship between classes. In this hierarchy, a subclass is a specialized version of a superclass.

The statement "car:toyota" and  "ducks:pond" correctly describes a subclass (Toyota, ducks) of the superclass (car, pond). However, "toes:feet" and "rock:stone" do not correctly describe a subclass-superclass relationship. Rather, they describe a part-whole relationship. Toes are part of feet and rock is a type of stone.

It is important to note that a subclass can inherit traits from its superclass, but it may also have its own unique traits and restrictions. For example, a Toyota car may have some traits inherited from the car superclass, but it may also have unique features that set it apart from other car subclasses.  So, correct answer are option A) and B).

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____The given question is incomplete, the complete question is given below:

check all statements, that correctly describe traits and restrictions of superclasses and subclasses.

car:toyota

ducks:pond

toes:feet

rock:stone

Answer:

a = 9

Step-by-step explanation:

a ÷ 2 = [tex]\frac{9}{2}[/tex] ( express in fractional form )

[tex]\frac{a}{2}[/tex] = [tex]\frac{9}{2}[/tex] ( multiply both sides by 2 to clear the fractions ) , then

a = 9

Answer: For 16 dozen cookies, Rachel used 24 cups of milk.

Step-by-step explanation:

We know that for each dozen cookies, Rachel uses 1 1/2 cups of milk. To find out how much milk she used for 16 dozen cookies, we need to multiply the amount of milk used for one dozen by 16. Here are the steps:

   Calculate the amount of milk used for one dozen cookies:

   1 1/2 cups of milk = 3/2 cups of milk

   For one dozen cookies, Rachel used 3/2 cups of milk.

   Multiply the amount of milk used for one dozen by 16:

   3/2 cups of milk x 16 = 24 cups of milk

Therefore, Rachel used 24 cups of milk for 16 dozen cookies.

If each dozen cookies Rachel used  [tex]1\frac{1}{2}[/tex]  cups of milk then 24 cups of milk she uses for 16 dozen cookies

Two or more expressions with an Equal sign is called as Equation.

Given that each dozen cookies Rachel used [tex]1\frac{1}{2}[/tex] cups of milk.

We have to find the number of cups of milk required to make 16 dozen cookies

As Rachel used  [tex]1\frac{1}{2}[/tex]  cups of milk for 1 dozen cookies.

She would use  [tex]1\frac{1}{2}[/tex]  x 16 = 24 cups of milk for 16 dozen cookies.

Hence, if each dozen cookies Rachel used  [tex]1\frac{1}{2}[/tex]  cups of milk then 24 cups of milk she uses for 16 dozen cookies

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Answer:

angle 4 and angle 1 are vertical angles

Step-by-step explanation:

vertical angles are opposite each other

Answer:

60 degrees

Step-by-step explanation:

cos(x)=1/2

cos(x)=0.5

(x)=[tex]cos^-1[/tex] (0.5)

(x)=60

Step-by-step explanation:

the volume of container B is Travers from A to B.

so, the volume of the empty space in A is exactly the volume of container B.

the volume of a cylinder is

base area × height = pi×r² × height.

the reside is as always half of the diameter.

r = 8/2 = 4 ft

the volume of the empty space in A = the volume of container B =

= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈

≈ 1,005.3 ft³

The relative maximum of the function is (0, 4), and the relative minimum is (6, -152).

To find the relative extrema of the function f(x) = x^4 - 8x^3 + 4, we first take the derivative of the function:

f'(x) = 4x^3 - 24x^2

Then we set f'(x) = 0 to find the critical points:

4x^3 - 24x^2 = 0

4x^2(x - 6) = 0

This gives us two critical points: x = 0 and x = 6.

Next, we find the second derivative of f(x):

f''(x) = 12x^2 - 48x

We can use the Second-Derivative Test to determine the nature of the critical points.

For x = 0, we have:

f''(0) = 0 - 0 = 0

This tells us that the Second-Derivative Test is inconclusive at x = 0.

For x = 6, we have:

f''(6) = 12(6)^2 - 48(6) = 0

Since the second derivative is zero at x = 6, we cannot use the Second-Derivative Test to determine the nature of the critical point at x = 6.

To determine whether the critical points are relative maxima or minima, we can use the first derivative test or examine the behavior of the function around the critical points.

For x < 0, f'(x) < 0, so the function is decreasing.

For 0 < x < 6, f'(x) > 0, so the function is increasing.

For x > 6, f'(x) < 0, so the function is decreasing.

Therefore, we can conclude that the critical point at x = 0 is a relative maximum and the critical point at x = 6 is a relative minimum.

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The scale of the map = 682.5.

We kept a safe distance and followed them. She perceives a separation between her and her brother that wasn't there before. Although they were previously close friends, there was now a great deal of gap between them.

We must calculate the ratio of the distance shown on the map to the real distance between the cities in order to ascertain the scale of the map.

We are aware that there are 210 miles separating the two cities. Let x represent the precise location of this distance on the map. From that, we may establish the ratio:

Actual distance / Map Distance = 210 / x

The distance on the map is indicated as 3 1/4 inches, which is also known as 13/4 inches. When we enter this into the percentage, we obtain:

Actual distance divided by (13/4) = 210 / x

We can cross-multiply and simplify to find x's value:

Actual distance: 682.5 = x * 210 x = 3.25 when 210 * (13/4) Equals x.

Consequently, 3.25 inches on the map represent the actual distance between the cities. We can write: To determine the map's scale:

Actual distance divided by 1 inch on the chart equals 210 miles.

When we replace the values we discovered earlier, we obtain:

1 / 210 = 3.25 / scale

If we solve for the scale, we obtain:

scale = 682.5.

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The Sunday game brought in $2232.50, while the Thursday game brought in $1832.00.

A company's income, costs, and profit are compiled in a profit and loss (P&L) statement, a financial report. It provides information to investors and other interested parties about a company's operations and financial viability.

The issue informs us that the combined revenue from the two games was $4064.50.

S + (S - 400.50) = 4064.50

Simplifying the left side, we get:

2S - 400.50 = 4064.50

Adding 400.50 to both sides, we get:

2S = 4465

Dividing both sides by 2, we get:

S = 2232.50

So the Sunday game generated $2232.50, and the Thursday game generated $2232.50 - $400.50 = $1832.00.

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To find the area of the triangle with vertices (9,-1), (6,1), and (6,3), we can use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices.

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 9(1-3) + 6(3-(-1)) + 6((-1)-1) \right|$[/tex]

[tex]$A = \frac{1}{2} \left| -6 + 24 - 12 \right| = \frac{1}{2} \cdot 6 = 3$[/tex]

Therefore, the area of the triangle is 3 square units.

To find the area of the triangle with vertices (0,-8), (0,-10), and (7,-10), we can again use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 0((-10)-(-10)) + 0((7)-0) + 7((-8)-(-10)) \right|$[/tex]

$A = \frac{1}{2} \cdot 14 = 7$

Therefore, the area of the triangle is 7 square units.

To find the area of the triangle with vertices (6,-7), (3,-1), and (-1,4), we can again use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 6((-1)-4) + 3(4-(-7)) + (-1)((-7)-(-1)) \right|$[/tex][tex]$A = \frac{1}{2} \cdot 55 = \frac{55}{2}$[/tex]

Therefore, the area of the triangle is $\frac{55}{2}$ square units.

To find the area of the quadrilateral with vertices (-6,1), (-9,1), (-6,-4), and (-9,-4), we can divide it into two triangles and find the area of each triangle using the determinant method. The area of the quadrilateral is the sum of the areas of the two triangles.

First, we find the coordinates of the diagonals:

$D_1=(-6,1)$ and $D_2=(-9,-4)$

The area of the quadrilateral can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} -6 & 1 \ -9 & -4 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -9 & -4 \ -6 & -4 \end{array}\right|\

&=\frac{1}{2}\cdot 21 + \frac{1}{2}\cdot 9\

&=\frac{15}{2}\

\end{align*}

Therefore, the area of the quadrilateral is $\frac{15}{2}$ square units.

To find the area of the pentagon with vertices (0,3), (-3,3), (-5,1), (-3,-3), and (-1,-2), we can divide it into three triangles and find the area of each triangle using the determinant method. The area of the pentagon is the sum of the areas of the three triangles.

First, we find the coordinates of the diagonals:

$D_1=(0,3)$ and $D_2=(-1,-2)$

The area of the pentagon can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_3 & y_3 \ x_4 & y_4 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} 0 & 3 \ -3 & 3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -3 & 3 \ -5 & 1 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -5 & 1 \ -3 & -3 \end{array}\right|\

&=\frac{1}{2}\cdot 9 + \frac{1}{2}\cdot (-6) + \frac{1}{2}\cdot (-8)\

&=\frac{5}{2}\

\end{align*}

Therefore, the area of the pentagon is $\frac{5}{2}$ square units.

Area of triangle whose vertices are (6,1), (9,-1) and (6,-3) is 6 square units and the area of triangle whose vertices are (0,-8), (7,-10) and (0,-10) is 7 square units.

A polygon having 3 edges and 3 vertices is called a triangle. It is one of the fundamental geometric forms.

Lets find the area of triangle ( Pink Colour) whose vertices are (6,1), (9,-1) and (6,-3), [tex]Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ][/tex]

Area = 1/2 [ 6 ( -1 - (-3) ) + 9( -3 -1 ) + 6( 1 - ( -1 ) ) ]

Area = 1/2 [6 * 2 + 9 * (-4) + 6 * 2]

Area = 1/2 [12-36+12] = 1/2 (-12) = -6

Therefore , Area of Triangle is 6 square units.

Now, Lets find the area of triangle ( Brown Colour ) whose vertices are (0,-8), (7,-10) and (0,-10),

[tex]Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ][/tex]

Area = 1/2 [  0( -10 - ( -10 )) + 7 ( -10 - ( -8 ) ) + 0 ( -8 - ( -1- ) ) ]

Area = 1/2 [ 0 + 7 * (-2) + 0]

Area = 1/2 ( -14 ) = -7

Therefore, Area of Triangle is 7 square units.

Now. Lets find the area of Rectangle( Blue Colour ) whose length is 5 unit and Breadth is 3 unit.

So, Area of Rectangle = Length * Breadth

= 5 * 3 square units

= 15 square units.

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Answer:

x=6

Step-by-step explanation:

Because the angles will be equal we set the equations to be equal to each other

4x+19=6x+7

12=2x

x=6