9c - 73 = 6c - 10 What is the value of c?

The expected profit or loss is $21,094.50, rounded to the nearest hundredth

Here's the step-by-step explanation using the provided information:

Step 1: Identify the profit and loss values and their respective probabilities.
Profit: $32,604 with a probability of 0.7
Loss: -$5,761 with a probability of 0.3

Step 2: Calculate the expected profit or loss using the formula:
[tex]\frac{Expected profit/loss}{loss} = (Profit * Probability of profit) + (Loss * Probability of Loss)[/tex]

Step 3: Plug in the values into the formula:
[tex]\frac{Expected profit}{loss}  = ($32,604 * 0.7) + (-$5,761 * 0.3)[/tex]

Step 4: Perform the calculations:
[tex]\frac{Expected profit}{loss}  = ($22,822.8) + (-$1,728.3)[/tex]

Step 5: Add the results to find the expected profit or loss:
[tex]\frac{Expected profit}{loss}  = $21,094.5[/tex]

So, the expected profit or loss is $21,094.50, rounded to the nearest hundredth.

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To find the sum of 6k by adding each term together, we can simply add 6k + 6k + 6k + 6k + 6k + 6k which gives us a total of 36k.

To verify this result using the summation capabilities of a graphing utility, we can use the sigma notation (Σ) to represent the sum. The sigma notation is defined as Σ6k where k starts at 1 and goes up to 6. This means we are adding 6k, six times.

To input this into a graphing utility, we can use the summation feature. For example, on a TI-84 calculator, we can press the "Math" button, select "1:sum(", and enter the expression "6k" followed by a comma and then the values of k that we want to sum from (1) and to (6). This gives us the result of 36k, which matches our previous calculation.

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Wyatt will color a total of 96 square inches on all sides of the cube.

A cube has six sides, and each side will be a square. To find the total area of all the sides that Wyatt will color, we need to multiply the area of one side by the total number of sides.

Given that the side length of Wyatt's cube is 4 inches, the area of one side would be;

Area of one side = side length × side length

= 4 inches × 4 inches

= 16 square inches

Since there are six sides in total, the total area of all the sides would be;

Total area of all sides = Area of one side × Number of sides = 16 square inches × 6

= 96 square inches

Therefore, total 96 square inches will wyatt color.

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Answer:

Step-by-step explanation:

To find the solution to the system of equations represented by the two lines, we need to find the point where they intersect on the graph.

First, let's find the coordinates of the intersection point by solving the system of equations. We have:

y = (3/2)x (Equation 1)

y = (-1/2)x + 4 (Equation 2)

To find the intersection point, we need to set the two equations equal to each other:

(3/2)x = (-1/2)x + 4

Simplifying this equation, we get:

2x = 8

x = 4

Now that we know x = 4, we can substitute this value into either Equation 1 or Equation 2 to find the corresponding value of y:

y = (3/2)x

y = (3/2)(4)

y = 6

Therefore, the solution to the system of equations represented by the two lines is (4, 6).

In general, the tallest and shortest plant heights can vary widely depending on the species of plant being considered.

For example, some species of trees can grow over 300 feet tall, while certain species of mosses may only grow a few millimeters in height. The specific environmental conditions, such as the availability of water, sunlight, and nutrients, can also impact the growth and height of plants. Therefore, without more specific information, it is difficult to provide a more precise answer.

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Answer: i think it b

Step-by-step explanation:

b

The argument is not valid.

The argument commits a fallacy known as the false dilemma or false dichotomy, which presents only two options when there may be more. In this case, the argument assumes that if Superman does not prevent evil, then he must either be impotent or malevolent.

However, there could be other reasons why Superman does not prevent evil, such as a lack of knowledge or resources.

Furthermore, the argument assumes that if Superman exists, then he must either prevent evil or be impotent/malevolent, but this assumption is not necessarily true. It is possible for Superman to exist and not have the ability or inclination to prevent all evil.

Therefore, the conclusion that Superman does not exist does not necessarily follow from the premises. The argument is not valid.

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The probability that Tally is on the red team is 1/4.

We have,

Total students = 16

Students in each group = 16/4 = 4

Total Teams = Red, Yellow, Green and Blue.

So, the probability that Tally is on the red team

= 4 / 16

= 1/4

Thus, the probability is 1/4.

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The graph of g(x) is a V-shaped graph centered at x = -3, with the vertex at (-3, -2), and opening downward.

We have,

The graph of the function g(x) = -|x+3| - 2 can be obtained by first graphing the function f(x) = |x| and then transforming the graph.

The function f(x) = |x| is a V-shaped graph that passes through the origin and has a slope of 1 on either side of the origin.

The function -|x| is the reflection of f(x) about the x-axis and has the same shape, but opens downwards.

To obtain the graph of g(x) = -|x+3| - 2, we first shift the graph of -|x| three units to the left to get the graph of -|x+3|.

This means that the V-shape of the graph is centered at x = -3.

Then we shift the entire graph downward by 2 units to get the final graph of g(x).

Therefore,

The graph of g(x) is a V-shaped graph centered at x = -3, with the vertex at (-3, -2), and opening downward.

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The required amount will be earn is $3400.

This calculation only takes into account the revenue earned from ticket sales and does not include any additional revenue streams such as merchandise sales or sponsorships.

The total earnings will depend on various factors such as ticket pricing strategy, marketing efforts, and concert attendance.

Here given concert tickets are selling for $34.00 each and it is also given a total number of 100 tickets are sold.

the total earnings will be calculated by multiplying the ticket price by the number of tickets sold.

So,total amount earn = $34×100 = $3400.

This is a problem of Multiplication.

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Correct question is " Concert tickets go on sale for $34. 00 each . Now total number of sold tickets are 100 . Count how many money will earn ."

The coordinate of the point is given as: (x,y) = (28/5, 2/5)

Given

A = (4,-2)

B = (12,-10)

Ration = 1/4

We apply the following formula:

(x,y) = [((mx2 + nx1)/(m+n)), ((my2 + ny1)/(m+n)),

Where:

m and n are the ratios. That is:

m/n = 1/4
m : n = 1 : 4

Where A(4,-2) and B(12,10); we have

(x,y) = [((1 * 12 + 4x4)/(4+1)), ((1*10 + 4 *-2)/(4+1)),
(x,y) = (12 + 16/5), ((10-8)/5))

Simplified, this yeild:

(x,y) = (28/5, 2/5)

Thus, the coordinate of the point is (x,y) = (28/5, 2/5).

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The given graph in the figure is a graph of compound interest as the graph of simple interest is a straight line whereas the graph of compound interest is a smooth curve.

When we plot the amount of money accumulated over time for both compound interest and simple interest on a graph, we can see that the graph for compound interest grows at a much faster rate than that of simple interest. This is because the effect of compounding interest leads to an exponential increase in the amount of money accumulated over time. In contrast, the growth rate of simple interest is linear and does not increase over time.

In summary, the main difference between the graphs of compound interest and simple interest is the rate at which the interest grows over time, with the former growing at an increasing rate due to the effect of compounding interest, while the latter grows at a constant rate.

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We have sufficient evidence to conclude that the mean is less than 126 at the 1% level of significance.

The null hypothesis is that the mean is equal to 126.

H0: μ = 126

The alternative hypothesis is that the mean is less than 126.

Ha: μ < 126

We will use a one-tailed t-test for this problem, with a significance level of 0.01 and 100 degrees of freedom (n-1).

a) State the hypotheses.

H0: μ = 126

Ha: μ < 126

b) Calculate the test statistic.

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given, we get:

t = (120.96 - 126) / (21.42 / √101) = -2.96

c) State the rejection criterion for the null hypothesis.

We will reject the null hypothesis if the test statistic is less than the critical value from the t-distribution with 100 degrees of freedom and a one-tailed test at a significance level of 0.01.

Using a t-table or a calculator, we find the critical value to be -2.364.

d) Draw your conclusion.

Since our test statistic (-2.96) is less than the critical value (-2.364), we reject the null hypothesis. We have sufficient evidence to conclude that the mean is less than 126 at the 1% level of significance.

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The correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables.

It should be noted that to ascertain the correlation coefficient, we can utilize the formula:

r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Retaining the same numeric values from before, we can compute:

r = (9(976) - (36)(605)) / sqrt[(9(182) - (36)^2)(9(11681) - (605)^2)] ≈ 0.88

Therefore, the correlation coefficient is fairly close to 0.88.

The correlation coefficient implies a strong positive relationship between hours expended studying and test outcomes. As the quantity of hours committed to studying increases, the test scores will tend to keep up accordingly. A correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables, and the line of best fit serves as a desirable standard representation of the data.

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Answer:

Step-by-step explanation:

It appears there is an error in the table. The correct table is:

[tex]\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-11}\vphantom{\dfrac12}\textsf{Hours spent studying $(x)$}&0&1&2&4&4&4&6&6&7&8\\\cline{1-11}\vphantom{\dfrac12}\textsf{Test score $(y)$}&35&40&46&65&67&70&82&88&82&95\\\cline{1-11}\end{array}[/tex]

The simplest method to find the linear regression equation and the correlation coefficient for this data set is to use a statistical calculator.

After entering the data into a statistical calculator we get:

The regression line of y on x is y = a + bx.

Therefore, substitute the found values of a and b into the formula to write the linear regression equation for the given data set:

[tex]\boxed{y=34.27+7.79x}[/tex]

The correlation coefficient is the value of r, so r = 0.98 to the nearest hundredth.

The correlation coefficient, r, measures the strength of the linear correlation between two variables. |t is always between +1 and -1.

As r = 0.98, there is a very strong positive correlation.

In context, this suggests that the more hours of studying for a test a student does, the higher their test score.

Answer:

Area of shaded region:

[tex]\pi {(4 \sqrt{2} )}^{2} - {8}^{2} [/tex]

[tex]32\pi - 64 = 32(\pi - 2)[/tex]

The probabilities and the expected values are calculated below

Next cereal box wll contain blue or yellow

Here, we have

Yellow or blue = 15 + 5 = 20

Total = 50

So, we have

P(Yellow or blue) = 20/50

P(Yellow or blue) = 2/5

Arrival time before 7:30 am

Here, we have

Arrival time before 7:30 am = 7

Total time = 20

So, we have

P(Arrival time before 7:30 am) = 7/20

Team least likely

Convert the probabilities to decimal

So, we have

Nets = 0.67

Rockets = 0.5

Bucks = 0.8

Warriors = 0.375

This means that the team least likely to play in the championship game is 0.375

Section 7 in the game

Here, we have

P(7) = 35/250

In 150 times, we have

n(7) = 35/250 * 150

n(7) = 21

So, the number of times is 21

Expected students to eat chicken nuggets

Here, we have

P(Chicken) = 14/40

In 840 students, we have

n(Chicken) = 14/40 * 840

n(Chicken) = 294

Hence, the expected number of students to eat chicken nuggets is 294

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The first 10 terms of the sequence using the recursion formula are 1, 1.5, 1..75, 1.875, 1.9375, 1.96875, 1.984375,  1.9921875, 1.99609375,  1.998046875

Here we have the first term of the sequence as

A₁ = 1

The recursion relation is given by

aₙ₊₁ = aₙ + 0.5ⁿ

Now here since we have

A₁ = 1, where n = 1

A₂ = A₁ + 0.5

= 1 + 0.5 = 1.5

Hence,

A₃ = A₂ + 0.5²

= 1.75

A₄ = A₃ + 0.5³

= 1.875

A₅ = A₄ + 0.5⁴

= 1.9375

A₆ = A₅ + 0.5⁵

= 1.96875

A₇ = A₆ + 0.5⁶

=1.984375

A₈ = A₇ + 0.5⁷

= 1.9921875

A₉ = A₈ + 0.5⁸

1.99609375

A₁₀ = A₉ + 0.5⁹

= 1.998046875

Hence, the first 10 terms of the sequence using the recursion formula are 1, 1.5, 1..75, 1.875, 1.9375, 1.96875, 1.984375,  1.9921875, 1.99609375,  1.998046875

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Answer:

since 41° is vertically opposite to 2x+1 they are equal

so 2x+1=40 , 1 turns negative crossing the equals sign so 2x=40 so x=20

The required support wire makes an angle of approximately 67.54° degrees with the ground.

We can use trigonometry to find the angle x. In the diagram, we can see that the support wire, the height of the tower, and the ground form a right triangle. The length of the support wire is the hypotenuse of this triangle, and the distance from the base of the tower to the point where the wire touches the ground is the adjacent side. We can use the tangent function to find the angle x:

tan(x) = opposite / adjacent

In this case, the opposite side is the height of the tower, which we don't know yet. However, we can use the Pythagorean theorem to find it:

height² = support wire² - adjacent²

height² = 100² - 40²

height ≈ 96.8

Now we can plug in the values to find x:

tan(x) = opposite / adjacent

tan(x) = 96.8 / 40

x ≈ 67.54°

Therefore, the support wire makes an angle of approximately 67.54° degrees with the ground.

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we have shown that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.

Let n be a positive integer and let d1, d2, ..., dm be its decimal digits, where dm is the leftmost (most significant) digit and d1 is the rightmost (least significant) digit. Then n can be written as:

n = [tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm[/tex]

We want to show that n is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.

First, suppose that n is divisible by 3. Then we have:

n = 3k

for some integer k. Substituting the expression for n, we have:

[tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm = 3k[/tex]

Taking both sides modulo 3, we obtain:

d1 + d2 + ... + dm-1 + dm ≡ 0 (mod 3)

which means that the sum of the decimal digits of n is divisible by 3.

Conversely, suppose that the sum of the decimal digits of n is divisible by 3. Then we have:

d1 + d2 + ... + dm-1 + dm = 3k

for some integer k. Substituting this expression into the equation for n, we obtain:

n =[tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm[/tex]

= [tex]d1 * (10^{(m-1)} - 1) + d2 * (10^{(m-2)} - 1) + ... + dm-1 * (10 - 1) + (d1 + d2 + ... + dm-1 + dm)[/tex]

= [tex]d1 * (10^{(m-1)} - 1) + d2 * (10^{(m-2)} - 1) + ... + dm-1 * (10 - 1) + 3k[/tex]

The first m-1 terms on the right-hand side are all divisible by 3, since 10^n - 1 is divisible by 3 for any positive integer n. Therefore, we have:

n ≡ dm + 3k (mod 3)

Since the sum of the decimal digits of n is divisible by 3, we have dm + d1 + d2 + ... + dm-1 ≡ 0 (mod 3). Therefore, we have:

n ≡ 0 (mod 3)

which means that n is divisible by 3.

Therefore, we have shown that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.

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The overlapping area between A1 and B, and the probability of A2∩B is represented by the overlapping area between A2 and B.

(a) A1 and A2 are not mutually exclusive since their intersection probability P(A1∩A2) is not equal to zero.

(b) To calculate P(A1∩B), we can use the formula:

P(A1∩B) = P(B|A1) * P(A1)

P(A1∩B) = 0.14 * 0.62

P(A1∩B) = 0.0868

To calculate P(A2∩B), we can use the formula:

P(A2∩B) = P(B|A2) * P(A2)

P(A2∩B) = 0.09 * 0.38

P(A2∩B) = 0.0342

(c) To calculate P(B), we can use the formula for the total probability:

P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2)

P(B) = 0.14 * 0.62 + 0.09 * 0.38

P(B) = 0.1228 + 0.0342

P(B) = 0.157

(d) To apply Bayes’ theorem, we can use the formula:

P(A1|B) = P(B|A1) * P(A1) / P(B)

P(A1|B) = 0.14 * 0.62 / 0.157

P(A1|B) = 0.553

To calculate P(A2|B), we can use the formula:

P(A2|B) = P(B|A2) * P(A2) / P(B)

P(A2|B) = 0.09 * 0.38 / 0.157

P(A2|B) = 0.217

(e) Here is a Venn diagram to represent the events A1, A2, and B:

    +------------+

    |            |

    |   A1       |

    |            |

    +------+-----+

           | P(B|A1) = 0.14

    +------|-----+

    |      |     |

    |   B  | A1∩B|

    |      |     |

    +------+-----+

           | P(B|A2) = 0.09

    +------+-----+

    |      |     |

    |   A2 | B∩A2|

    |      |     |

    +------+-----+

    |            |

    |   A1∩A2   |

    |            |

    +------------+

The left circle represents A1, the right circle represents A2, and the intersection represents A1∩A2. The probability of B given A1 is represented by the line connecting B and A1, and the probability of B given A2 is represented by the line connecting B and A2. The probability of A1∩B is represented by the overlapping area between A1 and B, and the probability of A2∩B is represented by the overlapping area between A2 and B.

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As the cost of producing smartphones has fallen over the past decade, several implications and effects on the market for smartphones can be observed:

1. Lower prices: Falling production costs have led to lower prices for consumers, making smartphones more affordable and accessible to a broader population.

2. Increased demand: Lower prices have also resulted in increased demand for smartphones, as more people can now afford them. This has led to a higher sales volume in the market.

3. Market expansion: The accessibility and affordability of smartphones have led to market expansion, as smartphones become more prevalent in both developed and developing countries.

4. Greater competition: The lower production costs have enabled more companies to enter the smartphone market, increasing competition and leading to more product variety for consumers.

5. Innovation and improvement: Due to the increased competition, companies are constantly seeking ways to differentiate their products through innovative features, improved design, and better performance.

Overall, the falling production costs of smartphones have positively impacted the market by lowering prices, increasing demand, and driving innovation and competition.

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It is true that When the central bank raises the discount rate, commercial banks are likely to reduce their borrowing of reserves from the Fed.

The discount rate is the interest rate at which commercial banks can borrow reserves from the central bank, such as the Federal Reserve in the United States. An increase in the discount rate makes borrowing from the Fed more expensive for commercial banks.

As a result, commercial banks may choose to call in loans to replace the reserves they would have otherwise borrowed from the central bank. Calling in loans refers to the process of demanding the repayment of outstanding loans from borrowers, which allows the bank to obtain funds to maintain their required reserve levels. By calling in loans, banks can avoid the higher cost of borrowing from the Fed due to the increased discount rate.

Overall, a higher discount rate can encourage commercial banks to reduce their borrowing of reserves from the central bank and instead call in loans to maintain their reserve requirements. This can lead to tighter credit conditions in the economy, as banks may be less willing to extend new loans to borrowers, potentially slowing down economic growth.

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The domain and range of the given relation { ( 0 , 2 ) , ( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 4 , 6 ) } are as follows: Domain: {0, 1, 2, 3, 4}, Range: {2, 3, 4, 5, 6}.

The domain represents the set of all input (x) values, while the range represents the set of all output (y) values in the relation. The given set of ordered pairs is a relation. The first coordinate in each pair is the input, also known as the domain, and the second coordinate is the output, also known as the range.
Domain: { 0, 1, 2, 3, 4 }
Range: { 2, 3, 4, 5, 6 }

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The standard deviation of the data set is 0. Therefore, the correct answer is C) $0.

To calculate the standard deviation, we can follow these steps:

1. Find the mean (average) of the data set.
2. Subtract the mean from each value, and then square the result.
3. Find the mean of these squared differences.
4. Take the square root of the mean of squared differences.

In this case, the windows generated by the three sellers are all $4,000.

Step 1: Calculate the mean.
Mean = (4,000 + 4,000 + 4,000) / 3 = 4,000

Step 2: Subtract the mean from each value and square the result.
(4,000 - 4,000)^2 = 0
(4,000 - 4,000)^2 = 0
(4,000 - 4,000)^2 = 0

Step 3: Find the mean of these squared differences.
(0 + 0 + 0) / 3 = 0

Step 4: Take the square root of the mean of squared differences.
Square root of 0 = 0

The standard deviation of the data set is 0. Therefore, the correct answer is C) $0.

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The Caputo fractional integral and derivative are mathematical operations used to describe the behavior of a function. The Caputo fractional derivative is a generalization of the traditional derivative and measures the rate of change of a function with respect to a fractional order. The Caputo fractional integral is the inverse operation of the fractional derivative and measures the accumulation of a function over a fractional order.

In the given equation, "D" represents the Caputo fractional derivative, and "f(x)" is the function being differentiated. The "k" and "k!" terms in the equation correspond to the order of the derivative being taken. The "a" and "b" terms are constants that determine the interval over which the derivative is being taken.

The notation "f(0+)" represents the limit of the function as it approaches zero from the right-hand side. This is necessary in fractional calculus because the behavior of a function near zero can be different from its behavior at other points.

Overall, the Caputo fractional integral and derivative are powerful tools for analyzing the behavior of complex functions and systems. They allow us to extend traditional calculus to include fractional orders and better understand phenomena like fractals and self-similar patterns.

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The width of the new phone is 6.16 inches.

The length of a cell phone is 1.4 inches and the width is 4.4 inches. The company making the cell phone wants to make a new version whose length will be 1.96 inches.

The side length of the new phone are proportional to the old phone. Therefore, the width of the new phone can be calculated as follows:

let

x = width of the new phone

1.4 / 1.96 = 4.4 / x

cross multiply

1.4x  = 4.4 × 1.96

1.4x = 8.624

divide both sides by 1.4

x = 8.624 / 1.4

x = 6.16

Therefore,

width of the new phone = 6.16 inches

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Categorical variables, such as nominal and ordinal scales, are weaker than continuous variables, such as interval and ratio scales, in terms of the type of information statistics on them yield. Categorical variables only provide limited information and are not as precise as continuous variables. Categorical variables have weaknesses related to limited statistical analysis and potential loss of information, while continuous variables can be sensitive to outliers and require more advanced statistical techniques for analysis. Both types of variables provide valuable information but have limitations when analyzing statistics.

Let's discuss the relative weakness of categorical and continuous variables with respect to the type of information statistics on them yield.

Categorical variables are those that can be divided into categories, and they include nominal and ordinal scales. Nominal variables have no inherent order (e.g., hair color), while ordinal variables have a clear order (e.g., educational level).

Weakness:
1. Limited statistical analysis: Since categorical variables have no numerical value, certain statistical measures, such as mean and standard deviation, cannot be applied to them.
2. Loss of information: Categorical variables can sometimes oversimplify data, leading to a loss of information when grouping continuous data into categories.

Continuous variables are those that can take any value within a defined range, and they include interval and ratio scales. Interval variables have a constant distance between values but no absolute zero (e.g., temperature in Celsius), while ratio variables have a constant distance and an absolute zero (e.g., height).

Weakness:
1. Susceptibility to outliers: Continuous variables are more sensitive to extreme values (outliers), which can significantly affect the statistics derived from them, such as the mean.
2. Data complexity: Continuous variables often require more advanced statistical techniques for analysis, which may be challenging for those without a strong background in statistics.

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The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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The same constant rate of change as Michael's is depicted in following ratio - 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.

The rate of reading Michael is -

Rate = 135/90

Rate = 3:2

Now, we will check the options to see if they have same ratio.

Option 1 180 page in 2 hours

As known about time conversion that 1 hour has 60 minutes, 2 hours = 120 minutes

So, Rate = 180/120

Rate = 3:2

Option 2 60 pages in 30 minutes

Rate = 60/30

Rate = 2:1

Option 3 108 pages in 2 and half hours

Time = 2.5 hours

Time = 150 minutes

Rate = 108/150

Rate = 18:25

Option 4 150 page in 1 hour

Rate = 150/60

Rate = 5:2

Option 5 225 pages in 150 minutes

Rate = 225/150

Rate = 3:2

Option 6 210 pages in 2 hour 20 minutes

Time = 140 minutes

Rate = 210/140

Rate = 3:2

Hence, the same rate options are 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.

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The complete question is -

Michael read 135 pages in 90 minutes. Select all of the rates that have the same constant rate of change as Michael's rate. 180 pages in 2 hours, 60 pages in 30 minutes, 108 pages in 2 and half hours, 150 pages in 1 hour, 225 pages in 150 minutes, 210 pages in 2 hour 20 minutes