For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design. A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row. A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes. A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings. A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.

If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat. and If Sam is allowed on Signe's racing boat, then he is an expert sailor.

are both correct if-then forms of the given statement, with the first being the contrapositive of the second. The other options are not correct if-then forms.

The original statement is "Sam will be allowed on Signe's racing boat only if he is an expert sailor." This statement can be rewritten in if-then form using the formal definition of "only if," which means "if and only if" or "implies and is implied by."

One possible if-then form is "If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat." This is the contrapositive of the original statement, which means that it is logically equivalent to the original statement. It asserts that if Sam is not an expert sailor, then he cannot be on Signe's racing boat.

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The expression showing the distance between point J and point K is |-9|-|-2|

Distance between two points is the length of the line segment that connects the two given points.

Given that, two points J(6, -2) and k(6, -9), we need to find the distance between them,

The distance between two pints is given by,

D = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, the points are, (6, -2) and (6, -9)

Therefore,

|JK| = [tex]\sqrt{(0-0)^2+(-9+2)^2}[/tex]

|JK| = √7²

|JK| = 7 units

Therefore, the expression showing the distance between point J and point K is |-9|-|-2|

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Mean absolute deviation of the data is 1.

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Given, In bar chart

Number of artists n = 4

Number of albums for Lil Shane x₁ = 7

Number of albums for Ben Raises x₂ = 9

Number of albums for Nicky x₃ = 6

Number of albums for Underdog x₄ = 6

Mean of the number of albums

μ = (7 + 9 + 6 + 6)/4 = 28/4 = 7

|μ - x₁| = |7 - 7| = 0

|μ - x₂| = |7 - 9| = |-2| = 2

|μ - x₃| = |7 - 6| = 1

|μ - x₄| = |7 - 6| = 1

Mean absolute deviation = ∑|x - μ|/n

= (0 + 2 + 1 + 1)/4

= 1

Hence, 1 is the mean absolute deviation (MAD) of the data in the bar chart.

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The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.

Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

From the table, the first term of the first sequence is 4 and the first term of the second sequence is 8. If the first sequence is multiplied by 2 then we obtain the second sequence.

The common difference of the second sequence is given as,

d = 16 - 8

d = 8

Then the tenth term of the second sequence is given as,

a₁₀ = 8 + (10 - 1) x 8

a₁₀ = 8 + 72

a₁₀ = 80

The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.

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The complete question is attached below.

a) 90% confident that the true population mean μ is between 91.01 and 102.99.

b) 90% confident that the true population mean μ is between 92.26 and 101.74.

c) 80% confident that the true population mean μ is between 93.79 and 100.21.

d) Using Central Limit Theorem to approximate the population mean as normally distributed, the confidence intervals can still be computed using the same formula as before.

(a) To construct a 90% confidence interval about μ when n = 27, we use the formula:

x ± z × (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score that corresponds to the desired confidence level (in this case, z = 1.645 for a 90% confidence level). Plugging in the values given, we get:

97 ± 1.645 × (13/√27)

which simplifies to:

(91.01, 102.99)

Therefore, we are 90% confident that the true population mean μ is between 91.01 and 102.99.

(b) To construct a 90% confidence interval about μ when n = 18, we use the same formula as before, but with a different z-score (since the sample size is smaller). In this case, we use z = 1.734, and we get:

97 ± 1.734 × (13/√18)

which simplifies to:

(92.26, 101.74)

Therefore, we are 90% confident that the true population mean μ is between 92.26 and 101.74.

(c) To construct an 80% confidence interval about μ when n = 27, we use the same formula as before, but with a different z-score (since the confidence level is different). In this case, we use z = 1.282, and we get:

97 ± 1.282 × (13/√27)

which simplifies to:

(93.79, 100.21)

Therefore, we are 80% confident that the true population mean μ is between 93.79 and 100.21.

(d) The confidence intervals in parts (a)-(c) assume that the population is normally distributed. If the population is not normally distributed, we cannot rely on these intervals to accurately estimate the true population mean. However, if the sample size is sufficiently large (usually n > 30), we can use the Central Limit Theorem to approximate the population mean as normally distributed, and the confidence intervals can still be computed using the same formula as before. If the sample size is small and the population is not normally distributed, other methods may be needed to construct a confidence interval, such as bootstrapping or using a non-parametric approach.

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The solution is,

-2A = (-6, -8, 0, 8, 2, -8)

B - 2A = (2, -7, -4, 3, 4, -12)

AC is undefined.

CD = (3, 2, 12, 5)

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

here, we have,

Given the matrices:

A = (3 4 0 -4 -1 4)

B = (8 1 -4 -5 2 -4)

C = (1 -1 3 1)

D = (3 -2 4 5)

We are required to compute the following

-2A, B - 2A, AC, CD

For -2A:

-2(3 4 0 -4 -1 4)

= (-6, -8, 0, 8, 2, -8)

For B - 2A:

Because B - 2A = B + (-2A),

we have:

(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)

(2, -7, -4, 3, 4, -12)

For AC:

(3 4 0 -4 -1 4)(1 -1 3 1)

This is undefined.

For CD:

(1 -1 3 1)(3 -2 4 5)

= (3, 2, 12, 5)

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We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.

The row in the table that corresponds to the number of degrees of freedom (df) must be found before the column that corresponds to the desired level of significance or alpha value in order to use the t-table to determine a t-score that cuts off a specific percentage in the upper tail for a t-distribution with a given number of df.

Since there are 24 degrees of freedom in this situation, we need to identify the t-score that removes 2.5% of the upper tail. We will be looking at the column for the right-tail probabilities because this test has one tail (upper tail), making it a one-tailed test.

Therefore, We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.

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Answer:

D. Nonlinear

Step-by-step explanation:

y = -5x^2 - 14  is a parabola.

Linear lines are straight lines.

A parabola is not a straight line.

d.) T distribution's mean=0 and standard deviation=1 is not true. Instead, the t distribution has a mean of 0 and a standard deviation that varies based on the sample size and degrees of freedom

The t distribution is not similar to the z distribution in terms of its standard deviation. Unlike the standard normal distribution (z distribution), which has a mean of 0 and a standard deviation of 1, the t distribution has a mean of 0, but its standard deviation varies depending on the sample size. Specifically, the t distribution has heavier tails than the z distribution, which means it has more spread in the distribution and more extreme values are more likely to occur.

The t distribution's mean=0 and standard deviation=1 is not true, hence the proper response is d. The t distribution, on the other hand, has a mean of zero and a standard deviation that varies according to the sample size and degrees of freedom.

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Biography, as it provides a brief overview of the life and career of Emest Cline.

What is Biography ?

A biography is a written account of another person's life, typically written by someone else. It often includes information about the person's background, education, career, accomplishments, and other significant events and experiences throughout their life. Biographies can also provide insights into a person's personality, character, and motivations, as well as the historical or cultural context in which they lived.

Given ,

Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992

doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects.

The type of informational text that this paragraph is is A.

Therefore, Biography, as it provides a brief overview of the life and career of Emest Cline.

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To find the surface area of the composite figure, we need to break it down into simpler shapes and add up their surface areas. From the given dimensions, we can see that the composite figure consists of two rectangular prisms and a triangular prism.

The dimensions of the rectangular prism are 10 cm (length), 8 cm (width), and 24 cm (height). Therefore, its surface area is:

SA1 = 2lw + 2lh + 2wh

SA1 = 2(10 cm)(8 cm) + 2(10 cm)(24 cm) + 2(8 cm)(24 cm)

SA1 = 160 cm^2 + 480 cm^2 + 384 cm^2

SA1 = 1024 cm^2

The dimensions of the triangular prism are 5 cm (base), 12 cm (height), and 8 cm (length). Therefore, its surface area is:

SA2 = lb + 2[(1/2)bh + lh]

SA2 = (8 cm)(5 cm) + 2[(1/2)(5 cm)(12 cm) + (8 cm)(12 cm)]

SA2 = 40 cm^2 + 240 cm^2 + 96 cm^2

SA2 = 376 cm^2

The dimensions of the rectangular prism on top are 4 cm (length), 5 cm (width), and 12 cm (height). Therefore, its surface area is:

SA3 = 2lw + 2lh + 2wh

SA3 = 2(4 cm)(5 cm) + 2(4 cm)(12 cm) + 2(5 cm)(12 cm)

SA3 = 40 cm^2 + 96 cm^2 + 120 cm^2

SA3 = 256 cm^2

To find the total surface area of the composite figure, we add the surface areas of the three shapes:

Total surface area = SA1 + SA2 + SA3

Total surface area = 1024 cm^2 + 376 cm^2 + 256 cm^2

Total surface area = 1656 cm^2

Therefore, the surface area of the composite figure is 1656 cm^2.

Answer: B

Step-by-step explanation: The table represents a linear function because the graph shows a constant rate of change.

After the graph is labeled and titled, it is complete and ready to be used to represent the relationship between the two variables.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

A scatter plot is used to represent the relationship between two variables using data points. In this case, the x-axis would represent the data points, while the y-axis would be labeled in increments of 50. To construct a scatter plot, one must first gather the data points and then plot them on a graph. The data points should be connected with a line or points to form the scatter plot.

To begin, the data points must be collected and organized. This can be done by organizing the data points in a table, using two columns to represent the x-axis and y-axis values. Once the data is organized, the x-axis and y-axis values can then be plotted on a graph. The y-axis should then be labeled in increments of 50. Once the data points are plotted, a line or points should be used to connect the data points, forming the scatter plot.

Finally, the scatter plot should be labeled and given a title, if applicable. The x-axis should be labeled with the data points, while the y-axis should be labeled in increments of 50. The title should provide a brief description of what the scatter plot is depicting. After the graph is labeled and titled, it is complete and ready to be used to represent the relationship between the two variables.

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hola i can help... all you have to do is grab a calculator and add 100 to each number, them sbract them by 302

Answer: A. 32 fish and 12 birds

Step-by-step explanation:

Since their greatest common factor is [tex]4[/tex], [tex]32\div 4= 8[/tex] and [tex]12\div 4 =3[/tex]. This satisfies the ration [tex]8:3[/tex].

The best definition of the term mirror line is "A mirror line is the line over which an object in the coordinate plane is reflected". So option A is correct.

A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.

Given options,

A. A mirror line is the line over which an object in the coordinate plane is reflected.

Yes this statement is according to definition of mirror line.

B. A mirror line is a line in the plane that is units away from the y-axis.

no its is not like that so it is incorrect option.

C. A mirror line is another name for the line of translation. no translation is a different concept so it also incorrect.

D. A mirror line is always a diagonal line in the plane that divides it into eight sections. it is also not correct.

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The missing variables of the line transversal using similarity ratio are;

x = 10

MT = 14

UP = 23

When two parallel lines crossed by a transversal, they formed same-side interior angles and their sum is equal to 180 degrees. As the sum of the same side interior angles is 180 degrees therefore the angles are supplementary.

Now, from the diagram, using the concept of similarity ratio, we can say that;

2/3 = (x + 2)/(x + 8)

Cross multiply to get;

2(x + 8) = 3(x + 2)

2x + 16 = 3x + 6

x = 10

Thus;

MT = (10 + 2) + 2

MT = 14

UP = (12 + 8) + 3

UP = 23

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The volume of the solid is equal to one third of the area of the base times the height. Therefore, the volume of the tetrahedron is equal to [tex](1/3)*(a^2)*h[/tex].

The volume of a pyramid (or tetrahedron) is equal to one third of the area of the base times the height. Therefore, if we were given a pyramid with a base that is an equilateral triangle with side a and a height of h, then the volume of the solid can be calculated by using the formula [tex](1/3)*(a^2)*h[/tex]. This is because an equilateral triangle has sides of equal length and all of its angles are equal to 60°. Since the area of an equilateral triangle is equal to [tex](a^2)*√3/4[/tex], then the volume of the solid can be calculated by multiplying the area of the base by one third and then multiplying it by the height of the pyramid, which is [tex](1/3)*(a^2)*√3/4*h[/tex]. The final result is the volume of the solid, which is [tex](1/3)*(a^2)*h[/tex].

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Answer:

Step-by-step explanation:

Let's call the weight of each container "w". We can set up two equations based on the information given:

Equation 1: 3w = 70.8 (the weight of 3 containers holding 9 gallons)

Equation 2: 5w = 118.0 (the weight of 5 containers holding 15 gallons)

To solve for "w", we can first solve Equation 1 for "w":

3w = 70.8

w = 70.8/3

w = 23.6

Now we can substitute this value of "w" into Equation 2 and solve for the total weight of 5 containers:

5w = 118.0

5(23.6) = 118.0

So each container weighs 23.6 pounds.

When the interpreting the covariance between X and Y , a positive value of covariance indicates that , on average ,if x below its mean then y tends to be below its mean.

Covariance is a statistical measure that indicates how two variables are related to each other. Specifically, covariance measures the degree to which the values of two variables vary together. If two variables have a positive covariance, it means that they tend to increase or decrease together. Conversely, if two variables have a negative covariance, it means that they tend to move in opposite directions.

Mathematically, covariance is calculated as the average of the products of the deviations of each value from their respective means, for two variables. A positive covariance indicates that the two variables tend to be above or below their respective means together, while a negative covariance indicates that one variable tends to be above its mean when the other is below its mean, and vice versa.

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The signficant changes that are happening as per the information provided in the question will be as follows:

1. The p-value for Factor A is 0.4194 option e. greater than 0.10.

2. The conclusion with respect to Factor A will be option b. Factor A is not significant.

3. The conclusion with respect to Factor B will be option b. Factor B is not significant.

4. The p-value for the interaction of factors A and B is 0.1621 option e. greater than .10

5. There is no effect of decreasing the waiting time and changing the loading and unloading methods  between the rides.

Here, we are going to perform two-way ANOVA Observation

A       B               C                

41, 43, 49 52, 44, 46 50, 46, 48

49, 50, 48 50, 46, 48 48, 44, 46          

Sums of row and column

A      B        C          Row total (xa)

133     142   144                    419

147     144   138                    429

Col total (xb)

280   286 282                    848

For A,

∑x²=412+432+492+...+482+442+462=40088

∑x²b/ra =1/3⋅2(280²+286²+282²)

=1/6(78400+81796+79524)

=1/6(239720)

For B,

=39953.3333

∑x²a/rb=1/3⋅3(419²+429²)

=1/9(175561+184041)

=1/9(359602)

For C,

=39955.7778

∑∑x²ab/r=  1/3(133²+142²+144²+147²+144²+138²)

=1/3(17689+20164+20736+21609+20736+19044)

=1/3(119978)

=39992.6667

For D,

(∑x)²/rab

=(848)²/3⋅2⋅3

=719104/18

=39950.2222

Sum of squares total

SST=∑x²-(∑x)²/n

Now we subtract A and D

=(A)-(D)

=40088-39950.2222

=137.7778

Sum of squares between rows will be,

SSA=∑x²a/rb-(∑x)²/n

Now, we subtract C and D

=(C)-(D)

=39955.7778-39950.2222

=5.5556

Sum of squares between columns

SSB=∑x²b/ra- (∑x)²/n

Now, we subtract B and D

=(B)-(D)

=39953.3333-39950.2222

=3.1111

Sum of squares between columns

SSAB=∑∑x²ab/r-(∑x)²/n-SSA-SSB

Now we subtract B, D and Sum of squares between columns

=(B)-(D)-SSA-SSB

=39992.6667-39950.2222-5.5556-3.1111

=33.7778

The residual value of sum of squares Error,

SSE=SST-SSA-SSB-SSAB

=137.7778-5.5556-3.1111-33.7778

=95.3333

ANOVA table

Source. Sums    Degrees Mean Squares Square

of squares of freedom variation freedom

                       SS              DF          MS              F        

A         SSA=5.5556     a-1=1 MSR=5.5556    0.6993   0.4194 (p-value)

B            SSB=3.1111      b-1=2 MSC=1.5556    0.1958

0.8247 (p-value)

AB       SSAB=33.7778   2   MSAB=16.8889   2.1259 0..1621 (p-value)

Error (residual) SSE=95.33      12         MSE= 7.9444            

Total of SST=137.7778      will be    17  

In conclusion,

1. F for between columns, the critical value F(1,2) at 0.05 level of significance will be 4.7472. As computed that FR=0.6993<4.7472

H0 has been accepted, thus, there is no significant difference between rows.

P value is 0.4194 > 0.05. Hence, we fail to reject H0

2. F for between columns, the critical value F(2,2) at 0.05 level of significance will be 3.8853. As computed, FC=0.1958<3.8853. Thus, H0 is accepted and there is no significant difference between columns. P value is 0.8247 > 0.05. Hence, we fail to reject H0

3. The interaction between the Factors AB, there is no sufficient evidence to support the claim of interaction between the factors. Thus, P value is 0.1621 > 0.05. Hence, we fail to reject H0.

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Note that the full question is:

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches.Type of Ride

Roller Coaster Screaming Demon Log Flume

Method 1 41 52 50

43 44 46

49 46 48

Method 2

49 50 48

51 46 44

47 48 46

1. The p-value for Factor A is:__________.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

e. greater than .10Item 18

2. What is your conclusion with respect to Factor A?

a. Factor A is significant

b. Factor A is not significant

3. The p-value for Factor B is:_______.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

e. greater than .10

3. What is your conclusion with respect to Factor B?

a. Factor B is significant

b. Factor B is not significant

4. The p-value for the interaction of factors A and B is:_______.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

5. What is your recommendation to the amusement park?

The graph of the function is attached

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

f(x) = square root 4x

This can be expressed as

f(x) = √(4x)

Take the square root of 4

So, we have the following representation

f(x) = 2√x

This means that the graph f(x) = √(4x) and f(x) = √(4x) are the same

Next, we plot the graph

See attachment for the graph of f(x)

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The square root of zero is a counterexample of the statement, so it is false.

Here we have the following statement about square roots:

"the square root of a number will always have two outcomes One is positive and the other is negative."

This seems to be true because:

-2*-2 = 2*2 = 4

So √4 = 2 and -2

But, particularly the square root of zero is:

√0 = 0

So here we have only one outcome that is neither positive nor negative, then the statement is false.

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To eliminate the x-variable using addition in this system of equations we must multiply 3(2x + 3y = 25) and 2(- 3x + 4y = 22).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of equations 2x + 3y = 25 and - 3x + 4y = 22.

Now, To eliminate the x-variable using addition we have to multiply equation (i) by 3 and equation (ii) by 2 which results in,

6x + 9y = 75 and - 6x + 8y = 44,        (6x + (-6x) would cancel out).

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The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.370

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

"Information available from the question"

The parameters are:

Sample size, n = 25

Probability of success, p = 0.65

Number of success, x ≤ 15

The probability is represented using the following binomial formula:
[tex]P(x) =n_C_x*p^x*(1-p)^n^-^x[/tex]

Using the above formula, we have:

P(x ≤ 15) = 0.370

Hence, the probability is 0.370

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Graph 2

It is the graph with the line on the positive Y-Axis as the equation is ended with +3

The amount to be paid by Bo is 0.82B

A percent of a number is the 100th part of it.

Given that, the board game costs B dollars. Price is reduced by 18%.  we need to calculate the final bill.

Cost of game = B dollars

Discount = 18% = 0.18

Discount amount = 0.18B

Final cost = B-0.18B

Amount to pay = 0.82B

Hence, the amount to be paid by Bo is 0.82B

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The complete question is:-

Bo is buying a board game which usually costs B dollars. The game is on sale, and the price has been reduced by 18% There are different ways of thinking about how to calculate Bo's final bill. Match the expressions to their meanings.

Sarah spend $161.24 before two weeks.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

Sarah spends an average of $64.11 per week.

She spent $53.22 last week, and $64.11 this week.

As, 1 month = 4.34524 weeks

So, before two weeks she spends

64.11 = (64.11 + 53.22 +x )/ 4.34524

278.5733364 = 117.33 + x

x= 161.24

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(a) Ratio of the volume of a right circular cone to the volume of a cylinder with same height and base radius= 1/3

(b)Ratio of the volume of a paraboloid to the volume of a cylinder= 1/2

(c)Ratio of the volume of a sphere and cylinder= 4/6

(a)Let r be the radius and h be the height of the right circular cylinder and right circular cone.

Volume of the right circular cylinder= πr²h

Volume of the right circular cone= 1/3 πr²h

Ratio of volume of a cone to the volume of a cylinder

= 1/3

Therefore, Ratio of the volume of a right circular cone to the volume of a cylinder with same height and base radius= 1/3

(b) Volume of the paraboloid = π/2r²h

Ratio of volume of a paraboloid to the ratio of volume of a cylinder

=1/2 πr²h/ πr²h

= 1/2

Therefore, Ratio of the volume of a paraboloid to the volume of a cylinder= 1/2

(c)Volume of a sphere= 4/3πr³

Given: Height of a cylinder h=2r (the diameter of the sphere)

Volume of a cylinder = 2πr³

Ratio of volume of a sphere to the volume of a cylinder

= 4/3πr³/ 2πr³

= 4/6

Therefore, Ratio of the volume of a sphere and cylinder= 4/6

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Complete question:

(a) Determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius:

First you will need to determine the equation of the line which rotates to generate the cone.)

b) Determine the ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius:

(c) Archimedes was particularly pleased when he determined the ratio of the volumes of a sphere and cylinder. Determine the ratio of the volume of a sphere to the volume of a cylinder having the same radius, and having height the same as the diameter of the sphere:

The value of h such that the matrix is the augmented matrix of a consistent linear system is 2

For the given matrix to be the augmented matrix of a consistent linear system, we need to check whether the matrix is in row echelon form or not. If the matrix is in row echelon form and the last row is not all zeros, then the linear system is consistent.

We can use elementary row operations to transform the matrix into row echelon form.

[tex]\left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right][/tex]

R2 <- R2 - 3R1

[tex]\left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right][/tex]

The matrix is in row echelon form. Now, we need to check whether the last row is all zeros or not.

If 6-3h = 0, then the last row will be all zeros, which implies that the linear system is inconsistent.

If 6-3h ≠ 0, then the last row will not be all zeros, which implies that the linear system is consistent.

Therefore, we need to solve the equation 6-3h = 0 to determine the value of h that makes the linear system consistent.

6-3h = 0

3h = 6

h = 2

So, the value of h that makes the matrix the augmented matrix of a consistent linear system is h = 2.

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