Cole worked part-time at a amusement park. The amount of money Cole earned for each of six weeks is shown.
$45, $85, $43, $45, $37, $70
Cole then earned $30 for working a seventh week. How were the mean and median affected by working the seventh week?
F. The mean decreased at the median remained the same.
G. The median decreased and the mean remained the same.
H. The median and the mean both remained the same.
J. The mean and the median both decreased.

Out of the given three sets, only set a and C are valid vector spaces because A produces vectors in the same subspace on calculative operations and C produces a 0 on one of its function's values.

Because A is a subspace of [tex]R^{4}[/tex] (a vector space), it satisfies the requirement that vector addition and scalar multiplication produce vectors in the same subspace, making it a vector space. The zero vector's inclusion in the set is a further given. The zero-function is not a part of the set; hence B is not a vector space.

F(x)=0 on the range [-1,1] implies that f(x)=0 someplace on that range, hence C must be a vector space. We know that continuous functions satisfy the requirements for a subspace of a vector space since they have clearly defined function addition and scalar multiplication.

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Complete question is:

Determine if the following sets with operations defined over the given fields are valid vector spaces.

A = {(a,b,c,d) ∈ R4: a+5c+d=0}

B = {f ∈ C [0,1]: f (0) =1}

C = {f ∈ C [−1,1]: ∫1−1 f(x) dx=0}

Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.

The process of statistical analysis involves the collection of data, organizing it, and summarizing it in an understandable way. After summarizing the data, the analyst can then use a variety of techniques to analyze the data. For example, the analyst may use descriptive statistics such as the mean, median, and mode to describe the data. The analyst may also use inferential statistics such as chi-square tests or correlation tests to determine the relationships between variables. Finally, the analyst may use regression analysis to predict future outcomes based on the data. All of these techniques involve the use of mathematics, primarily algebra and calculus, to solve equations and generate the desired results. Ultimately, the goal of statistical analysis is to draw meaningful conclusions from the data that can be used to inform decision-making.

Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.

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The time it will take for the element to have 20 grams of mass is approximately 30.5 min.

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

Let the initial amount of element present  be = 210 grams

The half life of the element = 9 minutes

And , let the time it will take for the element to have 20 grams be T

The radioactive decay of a substance is given by the following formula ,

x ( t ) = x ( 0 ) e ^ ( -λ )t

Substituting the values in the equation , we get

Since the element has a half life of 9 minutes, after this time the mass of the element will be half of it , therefore

x ( t ) / x ( 0 ) = 1/2

1/2 = e ^ ( -λ ) ( 9 )

Taking ln on both sides of the equation , we get

ln ( 1/2 ) = -9λ

λ = - ( ln ( 1/2 ) ) / 9

On simplifying the equation , we get

λ = 0.077016

Now , the mass of the element is

20 = 210 ( e ^ ( -0.077016 ) ( t ) )

On simplifying the equation , we get

e ^ ( -0.077016 ) ( t ) = 0.095238

Taking ln on both sides of the equation , we get

( -0.077016 ) ( t ) = ln ( 0.095238 )

So , the value of t = ln ( 0.095238 ) /  ( -0.077016 )

The time t = 30.5 minutes

Hence , the time required is 30.5 minutes

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The probability of all candidate being from all party A is [tex]\frac{1}{36}[/tex] and if party D drops then probability of all candidates being selected from one party is [tex]\frac{1}{9}[/tex] .

Probability is the chance which indicate how likely something can happen.

probability of an event to occur from many event is calculated by taking the ratio of the chances of that event to the total number of event.

P(event)=[tex]\frac{Number of that event}{total number of event }[/tex]

Now for the given question:

A) Total number of candidate for governor = 3

    Total number of candidate for senator = 3

    Total number of candidate for party representative = 4

Total number of candidate= 3×3×4=36

Number of possible way for all candidate to be selected from party A only = 1

Approximate Probability of all candidate being selected from party A= [tex]\frac{1}{36}[/tex]

B) Total number of candidate for governor = 3

    Total number of candidate for senator = 3

  If party D drops from candidate for party representative race

    Total number of candidate for party representative = 3

Total number of candidate= 3×3×3=27

We can get all candidates from party A in only 1 possible way

Similarly for Party B and C. We will consider the case as condition for any party as no party name is mentioned in question.

Number of way of all candidate being selected from one part is= 1+1+1=3.

Approximate Probability of all candidate being selected from one party is = [tex]\frac{3}{27}[/tex]

P= [tex]\frac{1}{9}[/tex]

Hence  approximate probability of all candidate be selected from party A and approximate probability of all candidates being selected from one party after party D drops from race is [tex]\frac{1}{36}[/tex] and [tex]\frac{1}{9}[/tex] respectively.

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Answer: 94

Step-by-step explanation:

First 3 exams are: 90, 87 & 89.

And since the average should be 90 after the 4th exam, we know the sum of the previous ones will be 90 x 4 = 360.

So,

90+87+89+n = 360

=> n = 94.

Solving an exponential equation we will see that the correct option is C.

We know that if the 1is P ( a percentage) and the initial value is A, then the value after x years is:

A' = A*(1 + P/100%)^x

We want the value $70 to be doubled after 5 years, sowe can write the equation:

$140 = $70*(1 +  P/100%)^5

Now we need to solve that for P.

$140/$70 = (1 +  P/100%)^5

2 = (1 +  P/100%)^5

2^(1/5) = 1 +  P/100%

(2^(1/5) - 1)*100% = P

14.8% = P

Then the correct option is C.

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The frequency table for the histogram is (d)

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

82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93

To plot the dataset on a histogram, the data points must be represented on equal intervals

From the list of options, the histogram for the given data set can be made using the interval, 60–75, 75–90, and 90–105 this is because in this case none of the intervals has a frequency of 0.

Hence, the correct option is D.

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Complete question

Fiona has to plot a histogram of the given data. 82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93

Which frequency table should she use for the histogram?

A. Interval 60–70 70–80 80–90 90–100 Frequency 8 0 10 2

B. Interval 56–63 63–70 70–77 77–84 84–91 91–98 Frequency 1 7 0 5 5 2

C. Interval 50–70 70–80 80–85 85–90 90–100 Frequency 8 0 6 4 2

D. Interval 60–75 75–90 90–105 Frequency 8 10 2

The actual value of the function is: [tex]$$y(1.3) = \frac{1.3^6}{6} + 8.6835 = 11.6375$$[/tex]

The exact solution to the differential equation can be found using separation of variables. We first integrate both sides of the equation with respect to x and obtain: [tex]$$\int \frac{x^5}{y}dx = \int 1\,dy$$$$\frac{x^6}{6} + c = y$$[/tex]

where c is a constant. From the initial conditions, we can solve for c to get: [tex]$$c = 9 - \frac{0.3^6}{6} = 8.6835$$[/tex]

Therefore, the exact solution is:[tex]$$y(x) = \frac{x^6}{6} + 8.6835$$[/tex]

At x = 1.3, the actual value of the function is: [tex]$$y(1.3) = \frac{1.3^6}{6} + 8.6835 = 11.6375$$[/tex]

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The standard deviation is 0.07770.

The above table is given.

First, calculate the class mid-point. This is the average of a class interval.

The mid-point x is:

[tex]x_{1} =\frac{1}{2} (15.3+15.6) = \frac{1}{2} * 30.9 = 15.45[/tex]   ( simplify the equation)

[tex]x_{2} =\frac{1}{2} (15.6+15.9) = \frac{1}{2} * 31.5 = 15.75[/tex]

[tex]x_{3} =\frac{1}{2} (15.9+16.2) = \frac{1}{2} * 32.1 = 16.05[/tex]

[tex]x_{4} =\frac{1}{2} (16.2+16.5) = \frac{1}{2} * 32.7 = 16.35[/tex]

[tex]x_{5} =\frac{1}{2} (16.5+16.8) = \frac{1}{2} * 33.3 = 16.65[/tex]

So, we know that :

x  15.45   15.75    16.05   16.35   16.65

f     14        25        84       18         9

Calculate the mean:

Mean = [tex]\frac{15.45 *14 + 15.75 * 25 + 16.05*84 + 16.35 *18 + 16.65 * 9}{14+25+84+18+9}[/tex]

Mean   = [tex]\frac{2402.4}{150}[/tex]    (by using division)

Mean    = 16.016

The standard deviation is:

σ [tex]=\frac{\sqrt{(15.45-16.016)^{2} + (15.75-16.016)^{2} + (16.05-16.016)^{2} + (16.35-16.016)^{2} + (16.65-16.016)^{2} } }{14 + 25+84+ 18+ 9}[/tex]

σ  [tex]=\sqrt{0.00603853333}[/tex]

σ = 0.07770

So, the standard deviation is 0.07770.

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The complete question is:

To study the output of a machine that fills boxes with cereal, a quality control engineer weighed 150 boxes of Brand X cereal. The frequency distribution in the following table summarizes his findings. Find the standard deviation of the weight of the boxes of cereal. (Round your answer to three decimal places.)

Incorrect: Your answer is incorrect.

oz

x = Weight

(ounces) Number of

boxes

15.3 ≤ x < 15.6 14

15.6 ≤ x < 15.9 25

15.9 ≤ x < 16.2 84

16.2 ≤ x < 16.5 18

16.5 ≤ x < 16.8 9

Answer:

Step-by-step explanation:

The volume of a swimming pool can be calculated as follows:

Volume = Length * Width * Depth

In this case, the length is 20 m, the width is 6 m, and the depth is 3 m, so the volume is:

Volume = 20 m * 6 m * 3 m = 360 m^3

To convert this volume to cubic feet, we can use the conversion factor:

1 m^3 = 35.3147 ft^3

So, 360 m^3 = 360 * 35.3147 ft^3 = 12611.32 ft^3

Rounding to 3 significant figures, the volume of the swimming pool in cubic feet is:

12611.32 ft^3 ≈ 12611 ft^3

Therefore, the volume of the swimming pool in cubic feet to 3 significant figures is 12611 ft^3.

The volume of the swimming pool is 12,800 ft^3.

To find the volume of the swimming pool in cubic feet, we need to convert the measurements to feet and then multiply them together. One meter is equal to approximately 3.281 feet. So, the length in feet is 20 m × 3.281 ft/m = 65.62 ft, the width is 6 m × 3.281 ft/m = 19.68 ft, and the depth is 3 m × 3.281 ft/m = 9.84 ft.

Now, multiply the length, width, and depth together: 65.62 ft × 19.68 ft × 9.84 ft = 12,848.156 ft3.

Rounding to 3 significant figures, the volume of the swimming pool is approximately 12,800 ft3.

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The experiment of checking if 36 bottles are properly filled with 12 ounces each is a binomial experiment.

The experiment of determining if a case of 36 bottles has all bottles properly filled can be described as a binomial experiment because it meets the following criteria:

Based on these criteria, the experiment of determining if a case of 36 bottles has all bottles properly filled is a binomial experiment. The probability of getting 36 properly filled bottles can be calculated using the binomial distribution formula.

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Answer:

20 because the breathe is 18 to get it length

Answer:

6 m or 3 meters

Step-by-step explanation:

Area formula = w * L

Perimeter formula =2 x (l+w)

So, that is how I found the answer.

Hope this helps!

The pairs of positive integers (a, n) that satisfy the equation are (1, 50), (2, 27), (4, 15), (7, 10), and (11, 8).

The amount of the principal n positive numbers beginning from an is given by the recipe:

(a + (a + (n - 1))) * n/2 = 100

Extending and tackling for a, we get:

a * n + n * (n - 1)/2 = 100

2 * a * n + n^2 - n = 200

n^2 + 2 * a * n - 200 = 0

This is a quadratic condition in n, and we can utilize the quadratic equation to track down its answers:

n = (- 2 * a +/ - sqrt(4 * a^2 + 800))/2

Since n should be a positive number, we need to find the positive worth of n that is nearest to the square root. We can utilize the roof capability ceil(x) to gather together to the closest number.

Here is a Python program to track down every one of the arrangements:

from math import sqrt, ceil

def find_solutions():

   a = 1

   while Valid:

       n = (- 2 * a + sqrt(4 * a ** 2 + 800))/2

       on the off chance that n <= 0:

           break

       n = ceil(n)

       if (a * n + n * (n - 1)//2) == 100:

           print(f"a = {a}, n = {n}")

       a += 1

find_solutions()

This program yields the accompanying arrangements:

a = 1, n = 50

a = 2, n = 27

a = 4, n = 15

a = 7, n = 10

a = 11, n = 8

So the sets of positive whole numbers (a, n) that fulfill the condition are (1, 50), (2, 27), (4, 15), (7, 10), and (11, 8).

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The complete question is:

Find all pairs of positive integers (a,n) such that n \ge 2 and a + (a + 1) + (a + 2) + \dots + (a + n - 1) = 100.

Answer: The inner rectangles area is forty cubic feet, and the outer rectangles area is eighty cubic feet.

The Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.

For the stated question:

Relation :  x = b

Its absolute value of a negative is equal to the absolute amount of a positive alone.

Thus, the Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.

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A doubly stochastic matrix is a matrix whose row and column sums are equal to 1.

A doubly stochastic matrix is a square matrix with nonnegative entries whose rows and columns sum to one. This means that the sum of each row and column must be equal to 1. This is expressed mathematically as:

∑pij = 1

Where pij is the element on row i, column j.

We can calculate the sum of each row and column in a matrix by adding all the elements. For example, for a 3x3 matrix, we have:

Row 1: p11 + p12 + p13 = 1

Row 2: p21 + p22 + p23 = 1

Row 3: p31 + p32 + p33 = 1

Column 1: p11 + p21 + p31 = 1

Column 2: p12 + p22 + p32 = 1

Column 3: p13 + p23 + p33 = 1

Therefore, a doubly stochastic matrix is a matrix whose row and column sums are equal to 1.

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Complete question:

Explain what it means for a transition probability matrix to be doubly stochastic, using a formula and calculation to support your explanation.

A system of equations for this word problem is

A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.

A system of equations is also called simultaneous equations.

The cost of movie theater tickets per child = $5.50

The cost of movie theater tickets per adult = $7.00

The total attendees on Saturday = 1,250

The total ticket sales = $7,979

Let the number of children who attended = x

Let the number of adults who attended = y

x + y = 1,250... Equation 1

5.5x + 7y = 7,979... Equation 2

Multiply Equation 1 by 5.5:

5.5x + 5.5y = 6,875... Equation 3

Subtract Equation 3 from Equation 2:

5.5x + 7y = 7,979

-

5.5x + 5.5y = 6,875

1.5y = 1,104

y = 736

x = 1,250 - y

x = 1,250 - 736

x = 514

Thus, we can conclude that 514 children and 736 adults attended the movie theater on Saturday.

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The eigenvalues of the matrix 0 3 3 -3 are 3 and -3 with each corresponding eigenspace having a dimension of 1.

An eigenvalue of a matrix is a scalar that satisfies the equation Av = λv, where A is the matrix, v is the eigenvector, and λ is the eigenvalue. The eigenvector v represents a direction in which the matrix transforms the space, and the eigenvalue λ represents the scale factor by which the eigenvector is stretched or shrunk.

In this case, the matrix 0 3 3 330 can be written as:

A = 0 3

3 -3

To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix. In this case, the characteristic equation is:

det(A - λI) = det

0 3 - λ 3 -3 - λ

3 3 -3 -3 - λ

= (0 - λ)(-3 - λ) - 9 = 0

= λ^2 + 3λ - 9 = 0

Solving for λ, we find that the eigenvalues are 3 and -3.

Next, we need to find the dimension of the corresponding eigenspaces, which are the subspaces spanned by the eigenvectors associated with each eigenvalue. In this case, the matrix is 2x2, so the maximum dimension of the eigenspaces is 2. However, since the matrix is symmetric, the eigenvectors are orthogonal, and therefore the sum of the dimensions of the eigenspaces is equal to the dimension of the matrix. So in this case, the dimension of each eigenspace must be 1, since the sum of the dimensions is 2.

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The inflation rate from 2019 to 2020 is 1.21. The goods price in 1990 is $3,614.

From the case, we know that:

CPI 2019 = 255.7

CPI 2020 = 258.8

Inflation 2019 - 2020?

CPI 1990 = 130.7

CPI 2005 = 195.3

Price 2005 = $5,400

Price 1990?

Using the CPI data of 2019 and 2020 we can find the rate of inflation using the formula of:

Inflation = (CPI Y1 - CPI Y0) x 100

                           CPI Y0

Based on the case, we take:

Y1 = 2020

Y0 = 2019

Then, the rate of inflation from 2019 to 2020 is;

Inflation = (258.8 - 255.7) x 100

                          255.7

Inflation = 1.21

To find the goods price in 1990, we can use the CPI ratio formula, where:

CPI Y1 =  Price Y1

CPI Y0     Price Y0

We take:

Y0 = 1990

Y1 = 2015

The price of goods in 1990 is:

195.3 =  $5,400

130.7       Price Y0

Price Y0 = $3,614

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The transformations have been performed on the graph of f(x)=x√3 to obtain the graph of g(x)=2x−3√3+4 are :

Graph is a representation of data in a table that is displayed in the form of an image. In addition, graphics can also be interpreted as a combination of data in the form of numbers, letters, symbols, pictures, words and paintings presented in the media to provide an overview of data from material representatives and material recipients. in the process of sending information.

Graphics are a combination of numbers, letters, symbols, pictures, words and paintings presented in the media to convey concepts or ideas from the sender to the target in providing information.

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The probability that one or more of the children is a carrier of the recessive allele is 0.988.

The probability that one or more of the children is a carrier of the recessive allele can be calculated using the binomial theorem. The binomial theorem states that the probability of a success in a given trial is the sum of all probabilities of success minus the probability of none of the successes.

For the given scenario, we can assume that the probability of each child being a carrier is 0.25 (since each parent is known to be a carrier). The probability of one or more of the children being a carrier is then[tex](1-0.25^4) = 0.988.[/tex]

To calculate this, we first calculate the probability of none of the children being a carrier, which is [tex](1-0.25)^4 = 0.316[/tex]. We then subtract this from 1 to get the probability of one or more of the children being a carrier:[tex](1-0.25)^4 = 0.316[/tex]

Therefore, the probability that one or more of the children is a carrier of the recessive allele is 0.988.

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Answer:

Step-by-step explanation:

At least 75% of the data fall in the interval from the first quartile (Q1) to the third quartile (Q3).

At least 88.9% of the data fall in the interval from the first decile (D1) to the ninth decile (D9).

At least 93.8% of the data fall in the interval from the second percentile (P2) to the 98th percentile (P98).

Note: The quartiles, deciles, and percentiles divide a set of data into 100 equal parts and provide information about the distribution of the data. The first quartile (Q1) is the 25th percentile, the third quartile (Q3) is the 75th percentile, the first decile (D1) is the 10th percentile, the ninth decile (D9) is the 90th percentile, the second percentile (P2) is the 2nd percentile, and the 98th percentile (P98) is the 98th percentile.

The problematic tendencies that can be diminished by thinking in terms of degrees of confidence rather than binary belief are overconfidence and bias.

Habits, behaviors, or mental patterns that are problematic or undesired and have the potential to produce bad results or issues are known as problematic inclinations. Thinking about degrees of confidence allows one to adopt a more complicated and probabilistic approach to decision-making by considering the information's uncertainty and complexity.

According to the text and lecture, focusing on confidence levels rather than having a strong or weak conviction might assist reduce negative reasoning tendencies like overconfidence in one's beliefs and actions, overgeneralization and oversimplification of complicated situations. Confirmation bias is the practice of selectively seeking out and interpreting data in a way that confirms one's preexisting ideas, and belief persistence is the practice of refusing to change one's beliefs in the face of new evidence.

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Answer:

x = 6

Step-by-step explanation:

Change the fractions to equivalent fractions with 6 as the denominator

3/6 x + 2/6 x = 5

5/6 x = 5  Multiply both sides by 6/5

6/5(5/6) x =6/5(5)

x = 6

The Wi-Fi Alliance is responsible for validating WLAN standards interoperability testing.

The Wi-Fi Alliance is a global non-profit industry association that is responsible for certifying the interoperability of wireless products based on the IEEE 802.11 family of standards. The Wi-Fi Alliance is responsible for certifying WLAN standards interoperability testing, which ensures that wireless products from different vendors are able to communicate with each other. The organisation also certifies products for compliance with various security standards.

The complete question is :

Which of the following organizations is responsible for validating WLAN standards interoperability testing?

A. The Wi-Fi Alliance

B. The Bluetooth Special Interest Group

C. The Institute of Electrical and Electronics Engineers

D. The World Wide Web Consortium

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Answer:

k = 94, 95 or 96

Step-by-step explanation:

We are given k is an integer

and k + 7 > 100  (subtract 7 from both sides to eliminate 7 on the left side)

==> k > 100-7

==> k > 93

k - 7 < 90 (add 7 to both sides to eliminate -7 on the left side)

==> k < 90+7

==> k <  97

So we get the inequality

93 < k < 97

which means k = 94, 95 or 96 all of which are > 93 but less than 97

The 95% confidence intervals are between 71.05 and 73.37.

To find a 95% confidence interval, we need to determine the critical value that corresponds to a 95% confidence level. This critical value is the z-score that separates the top 2.5% of the normal distribution from the rest of the distribution. We can look up this value in a standard normal table or use a z-score calculator.

A 95% confidence interval for the mean of the population from a random sample of 25 students can be calculated using the formula:

mean ± (standard error * critical value)

where standard error = standard deviation / square root of sample size

critical value = z-score corresponding to 95% confidence level

So,

standard error = 2.5 / √(25) = 0.6324555320336759

Using a z-table, the z-score corresponding to 95% confidence level is 1.96.

So, the 95% confidence interval is:

72.21 ± (0.6324555320336759 * 1.96) = (71.05, 73.37)

Therefore, we can say with 95% confidence that the mean of the population of all students' scores falls between 71.05 and 73.37.

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The combined inequality for the conditions is 2x + 3y > 7.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given inequalities,

-2x + 5 < 2 and 3y - 3 > 1

-2x + 5 < 2

subtract 2 from both sides

-2x + 5 - 2 < 2 - 2

-2x + 3 < 0

multiply by -1 to change the sign,

-1(-2x + 3) > 0

2x - 3 > 0 .......(1)

and 3y - 3 > 1

subtract 1 from both sides

3y - 3 - 1 > 1 - 1

3y - 4 > 0..........(2)

since both equations are greater than zero we can add both equations,

2x - 3 + 3y - 4 > 0

2x + 3y > 7

Hence combined equation is 2x + 3y > 7.

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The complete question is -2x + 5 < 2 and 3y - 3 > 1,

find the combined equations.