sa finished 30% of his homework in 27 minutes. How many more minutes will it take Isa to complete his homework, assuming that he works at the same pace?
A. 63 minutes
B. 67 minutes
C. 70 minutes
D. 90 minutes

A pie chart is commonly used to compare relative parts of a whole. It is a circular chart that is divided into sectors, where each sector represents a proportionate part of the whole.

The size of each sector is proportional to the value it represents, and the whole circle represents the total value. Pie charts are frequently used in business, finance, and statistics to show the relative sizes of different categories or data points. They are easy to understand and can quickly convey complex information in a simple visual format. However, it's important to note that pie charts are not always the most effective way to display data and should be used appropriately depending on the type of data being presented.

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(a) In the ring of Gaussian integers Z[i], all non-zero divisors are {1, -1, i, -i} ONLY.

(b) Among the given options, <29> and <13> are principal ideals but not prime ideals in Z. <0> is not a principal ideal, and <21> is a prime ideal but not principal.

(c) In the ring Z[i]Z, where (a+bi) is defined as a² + b², the kernel is {1, -1, i, -i}.

(d) Among the matrices A=[0], B=[%], C=[8] in M₂(R), the statement "A & C are nilpotent in M₂(R) but not B" is true.

(a) In the ring of Gaussian integers Z[i], the non-zero divisors are the elements that have multiplicative inverses. These elements are {1, -1, i, -i} ONLY, meaning that any other non-zero element is not a divisor in this context.

(b) For an ideal in the ring Z to be principal, it needs to be generated by a single element. Among the given options, <29> and <13> are principal ideals, as they can be generated by the respective elements 29 and 13. However, they are not prime ideals, meaning they do not satisfy the additional condition that if ab is in the ideal, then a or b must be in the ideal. <0> is not a principal ideal, and <21> is a prime ideal but cannot be generated by a single element.

(c) In the ring Z[i]Z, the kernel of the given function (a+bi) = a² + b² is the set of elements that map to zero under this function. The kernel is {1, -1, i, -i}, as these are the values that result in a² + b² = 0.

(d) Among the given matrices A=[0], B=[%], C=[8] in the 2x2 matrix ring M₂(R), the statement "A & C are nilpotent in M₂(R) but not B" is true. A and C are nilpotent because they can be raised to a power that results in the zero matrix, while B is not nilpotent as it cannot be raised to any power to obtain the zero matrix.

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Answer:

Slope Intercept Form: y=3x-10

Step-by-step explanation:

First, we need to solve the slope.

The formula: y2-y1/x2-x1 = m

Coordinate Points:

(2, -4) ; (4,2)

Do 2 - (-4) for the y's and 4-2 for the x's

Formula: 2-(-4)/4-2

2 - (-4) is a positive answer since the negatives cancel to a positive.

That shall be 6.

4-2 = 2

Now we have 6/2 which means 6 divided by 2 which is 3.

Our slope is 3.

Slope-Intercept Formula: y=mx+b

Our "m" is 3

y = 3x + b

Our b which is the y-intercept is undefined.

We need to plug one of the coordinates into the formula to find it.

Plug (2,-4) into the formula.

-4 = 3(2) +b

Do 3 x 2 first

-4 = 6 + b

Now subtract 6 on both sides

-6-4 = b

Our y-intercept is -10 because negative subtracted by negatives is an addition number followed by the greater number's sign.

Formula: y=3x-10

Answer:

y = 3x - 10

Step-by-step explanation:

To determine the line that passes through the points (2, -4) and (4, 2), we need to determine the slope of the line. Then, using the slope of the line and any point, we can determine the equation of the line using point slope form.

How to determine the slope of the line?

The slope of the line can be determined by using the formula (y₂ - y₁)/(x₂ - x₁), where x₂ and y₂ are the coordinates of the second point; x₁ and y₁ are the coordinates of the first point.

\(\implies\large\text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

In this case, our first point and second point are (2, -4) and (4, 2) repectively as stated in the question. Therefore,

When we substitute the following into the formula, we obtain;

\(\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 }\)

When we perform subtraction, we obtain;

\(\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 } = \dfrac{2 + 4}{2 } = \dfrac{6}{2}\)

Which when simplified, we get;

\(\implies\large\text{Slope} = \dfrac{6}{2} = 3\)

As said above, to determine the equation of the line with the slope and a point given, we can use point slope form. The chosen point must be on the line. The question states that "the line that passes through the points (2,-4) and (4, 2)". Therefore, we can tell that (2,-4) and (4, 2) are points that are on the line. Let's choose (4, 2) as our chosen point.

Now, let's substitute the slope of the line and the coordinates of the chosen point in the point slope form equation.

Finally, let's simplify the point slope equation and convert it into slope intercept form (as stated in question).

The slope intercept form states that;

We can see that the "y" variable is isolated on one side of the equation [y = (m)x + (b), Slope intercept form equation]. Thus, we need to isolate the y-variable in y - 2 = 3x - 12 to obtain our equation in slope intercept form. This can be done by adding 2 to both sides of the equation.

Therefore, the equation in slope intercept form is y = 3x - 10.

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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Answer:

9

Step-by-step explanation:

The distance between (2,8) and (-7,8) is 9

Answer:9

Step-by-step explanation:

Answer:

don´t

Step-by-step explanation:

in most cases of su1cide it has been proven that most who attempt (usually by hanging) regret doing that as they struggle to survive. you may not see value in your life currently, but there is always hope in the future. find someone you trust and talk to them. it never hurts to do that and could really help you :)

A decrease in the tolerable misstatement leads to an increase in the required sample size as it demands a more precise estimation and a smaller margin of error .

A decrease in the tolerable misstatement has a direct effect on the required sample size in an audit or sampling process. When the tolerable misstatement is reduced, it means that the level of error or deviation from the expected value that is acceptable is lowered. This implies that the auditor or sampler requires a more precise and accurate estimation of the population parameters. As a result, a smaller margin of error is allowed, leading to a larger sample size. Steps explaining the effect of a decrease in tolerable misstatement on the required sample size: Define tolerable misstatement: Tolerable misstatement is the maximum amount of error or deviation that the auditor or sampler considers acceptable in the financial statements or population being sampled.

Understand the relationship: The required sample size in auditing or sampling is determined by several factors, including the desired level of confidence, the acceptable margin of error, the variability of the population, and the tolerable misstatement. Impact of decreased tolerable misstatement: When the tolerable misstatement is decreased, it means that the auditor or sampler requires a more precise estimation of the population parameters. A smaller margin of error is allowed, which means that the sample needs to be more representative of the population and capable of detecting smaller deviations from the expected values. Increased sample size: To achieve a smaller margin of error and meet the reduced tolerable misstatement requirement, the required sample size needs to increase. This ensures a higher level of confidence in the estimation process and provides a more accurate assessment of the population characteristics.

In summary, a decrease in the tolerable misstatement leads to an increase in the required sample size as it demands a more precise estimation and a smaller margin of error to meet the reduced acceptable level of deviation from the expected values.

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Answer:

Step-by-step explanation:

The required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system. which is the correct answer would be an option (A).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The video game system will cost at least $450.

He earns $6 per hour babysitting and $10 per hour tutoring.

Let x be the number of hours babysitting and y be the number of hours of tutoring.

According to the given situation, we can write the inequality would be as:

⇒ 6x + 10y ≥ 450

Rearrange the terms of variables in the above inequality,

⇒ 10y ≥ 450 - 6x

Divided by 10 into both sides of the above inequality,

⇒ 10y/10 ≥ 450/10 - 6x/10

⇒ y ≥ 45 - 0.6x or

⇒ y ≥ - 0.6x + 45

Thus, the required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system.

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Answer:

Step-by-step explanation:

The distance between two points is

d^2=(y2-y1)^2+(x2-x1)^2

D) points (0,0) and (9,12)

d^2=(9-0)^2+(12-0)^2

d^2=81+144

d^2=225

d=15

E) points (1,2) and (-3,5)

d^2=(-3-1)^2+(5-2)^2

d^2=16+9

d^2=25

d=5

The linear regression equation that represents this set of data is y = 0.8x + 10.5. Also, the homework grade for a student with a test grade of 74 is equal to 73.

In this scenario, we would use an Excel worksheet to determine the regression equation. Also, the homework grade would be plotted on the x-axis of the scatter plot while test grade would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on a data point on the the scatter plot and then select "format trend line" (line of best fit) and tick the box to display a regression equation on the chart.

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that the linear regression equation for the line of best fit is given by:

y = 0.8x + 10.5

Next, we would estimate the homework grade for a student with a test grade of 74:

y = 0.8(74) + 10.5

y = 62.4 + 10.5

y = 72.9 ≈ 73.

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Answer:1 1/14

Step-by-step explanation:

The solution of the differentiation equation is Yₓ = (-1/3)t² - (1/2)t - 9/40eˣ

In this case, we will guess that the particular solution takes the form of Yₓ = At² + Bt + C, where A, B, and C are constants that we need to find.

To find these constants, we will need to differentiate the solution Yₓ twice and plug it into the differential equation. First, let's find the first derivative of Yₓ:

Yₓ' = 2At + B

Next, let's find the second derivative of Yₓ:

Yₓ'' = 2A

Now, we can plug Yₓ, Yₓ', and Yₓ'' into the differential equation:

13.5e⁻ˣ(2A) + 2(At² + Bt + C) + (At² + Bt + C) = t² + 1

Simplifying this equation gives:

(13.5e⁻ˣ)(2A) + (2A + 1)At² + (2B + 1)Bt + 2C = t² + 1

Now, we can equate the coefficients of each term on both sides of the equation to find the values of A, B, and C.

Starting with the coefficient of t² on both sides, we get:

(13.5e⁻ˣ)(2A) + (2A + 1)A = 1

Simplifying this equation gives:

A = -1/3

Next, we can look at the coefficient of t on both sides:

(2B + 1)B = 0

This equation tells us that either B = 0 or B = -1/2. However, if we set B = 0, then the coefficient of t² on the left side of the equation will be 0, which is not equal to the coefficient of t² on the right side of the equation. Therefore, we must choose B = -1/2.

Finally, we can look at the constant term on both sides:

(13.5e⁻ˣ)(2A) + (2A + 1)C + 2C = 1

Substituting the values of A and B that we found earlier, we get:

(13.5e⁻ˣ)(-2/3) - 1/3C = 0

Simplifying this equation gives:

C = -9/40eˣ

Therefore, our particular solution Yₓ is:

Yₓ = (-1/3)t² - (1/2)t - 9/40eˣ

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Answer:

37.68cm (i used 3.14 for pi)

Answer:

16h^2-4h-42

Step-by-step explanation:

4h times 4h is 16h^2

4h times -7 is -28h

4h times 6 is 24h

6 times -7 is -42

Combine like terms to get 16h^2-4h-42

The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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Answer:

Step-by-step explanation:

Hello, please consider the following.

\(6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)\)

And the we know that if the discriminant is

***** \(\Delta\) < 0, meaning 8-3k<0, meaning

\(\boxed{k>\dfrac{8}{3}}\)

then, there is no real solution.

***** \(\Delta = 0\), meaning

\(\boxed{k=\dfrac{8}{3}}\)

There is 1 solution.

***** \(\Delta\) > 0, meaning

\(\boxed{k<\dfrac{8}{3}}\)

There are 2 solutions.

Thank you

PS: To give more details...

\(8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}\)

If a person has a slow reaction time that puts them in the top 10% of responses, it means that their reaction time is slower than 90% of the population.

The value that separates the top 10% of responses from the bottom 90% is determined by the distribution of reaction times in the population.

Assuming a normal distribution of reaction times, the value that separates the top 10% of responses from the bottom 90% is the 90th percentile. This means that 90% of the population has a reaction time below this value, while the top 10% have a reaction time equal to or above it.

The specific value that separates the top 10% from the bottom 90% can vary depending on the population being studied and the task being performed. However, in general, a value around 1.5 standard deviations above the mean reaction time would be a reasonable estimate for the 90th percentile.

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Answer:

-2/3

Step-by-step explanation:

the triangle on the line is 2 by 3 and the slope formula is:

rise over run aka length over height!

Since the line is going downhill it would be negative!

Hope this helped!

Answer:

-2/3

Step-by-step explanation:

Start with looking at the y-axis, and count down the line until you get to a definite point. So we can see there is a definite point at (0,4) and (3,2). To get from (0,4) to (3,2), we have to go down 2 (-y) and to the right by 3 (positive x).

Slope formula is y/x, so our slope would be -2/3!

Answer:

10^24

Step-by-step explanation:

Answer:

\(\frac{-5y+6x^7+7x^5}{x^2y^1}\)

Step-by-step explanation:

Step 1: Write out expression

-5x⁻²y + 6x⁷y⁻¹ + 7x⁵

Step 2: Move negative exponents to denominator

*x⁻² and y⁻¹ have to be moved. Everything else stays.*

\(\frac{-5y+6x^7+7x^5}{x^2y^1}\)

3/4+6/7 = (21 + 24)/28 = 45/28

The answer is C. 45/28

The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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Answer:

600

Step-by-step explanation:

6x10^2 = 600

Answer:

600

Step-by-step explanation:

The constant of proportionality is 28.2.

It should be noted that the miles driven and the number of gallons used has been given.

Therefore, the constant of proportionality will be:

= Miles driven / Gallons used

= 930.6 / 33

= 28.2

Therefore, the constant of proportionality is 28.2.

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x = 0°, 180°

cos²(x) + 2cos(x) = 5cos(x) + 4

let cos x = y

y² + 2y = 5y + 4

collect like terms:

y² + 2y - 5y - 4 = 0

y² - 3y - 4 = 0

Using factorisation method to solve the above equation:

The factors of -4 that we can sum up to get -3 are: -4 and +1

y² - 4y + y - 4 = 0

y(y +4) + 1(y - 4) = 0

(y + 1) (y - 4) = 0

y + 1 = 0 or y - 4 = 0

y = -1 or y = 4

Recall cosx = y

This means:

cos x = -1 or cos x = 4

We were given an interval of [0, 2π). This means the interval is from 0° ≤ x < 360°

Greater than 0° but less than 360°

cosx = -1

x = arc cos (-1)

x = 180 degrees

cos x = 4

x = arc cos (4)

x = 0 degrees

x = 0°, 180°

1. The average of the set of data is 88.325

2. The average absolute deviation for the set of data is 0.575

The following data were obtained from the question:

The average of the given set of data can be obtained as follow:

Average = Summation of data / number of data

Average = 353.3 / 4

Average = 88.325

The average absolute deviation for the data can be obtained as follow:

Average absolute deviation = absolute deviation / number of data

Average absolute deviation = 2.3 / 4

Average absolute deviation = 0.575

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