Test for any significant main effects and any interaction. Use α=0.05. Round Sum of Squares to the whole number, F value, Mean Square to two decimals, if necessary, and p-value to four decimals.

Answer:

x = ±1

Step-by-step explanation:

Step 1: Define variables

f(x) = x² + 1

f(x) = 2

Step 2: Substitute

2 = x² + 1

Step 3: Solve for x

0 = x² - 1

0 = (x - 1)(x + 1)

x - 1 = 0

x = 1

x + 1 = 0

x = -1

∴ x = ±1

The sum of first five or twelve term in the A.P given the value 60.

The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Here we have given that  A. P. 16,14,12,.

And we need to find the number of term to get the value of 60.

While we looking into the given question we have identified that the  common difference d of the A.P. is − 2

Here we also know that the terms of the A.P. are in descending order.

Now, we have to take n = 5  then then first 5 terms are 16,14,12,10,8.

Here we have identified that the sum is 60.

Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5

Here we have identified that the sum of these seven terms is 0.

Therefore, sum of first 12 terms is also 60.

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Step-by-step explanation:

Rotation would be the best answer

Answer:

A) f(2) = 120, g(2) = 4.

B) f'(x) = 5x + 20

C) R - {-2}.

Step-by-step explanation:

A) Just apply given value and resolve:

\(f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4\)

B) g(2) is 4, so just divide f(x) by 4:

\( \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20\)

C)

\( \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} \)

Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.

1. The value of F(2) = 120 and g(2) = 4.

2. The division is 5(x+4)

3. The domain is real number except -2.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours.

1. F(2)= 20(2)+ 80= 40+ 80= 120

and, g(2)= 2 + 2 = 4

2. The division is

= F(x) / g(2)

= (20x + 80)/ (2+2)

= 20 (x+4) / 4

= 5 (x+4)

3. The domain of F(x) / g(x) is all real number except -2.

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===================================================

Explanation:

2/3 of 150 = (2/3)*150 = 100 employees are male and 150-100 = 50 employees are female. This is before the resignations.

After the resignations happen, we would have:

The chances of picking a female employee at random would be 40/120 = 1/3 which is the final answer.

Notice how the chances haven't changed from earlier (male = 2/3 chance, so 1-2/3 = 1/3 are the chances of picking a woman). Why is this? Well notice the ratio of 20 men to 10 women resigning. This ratio is 2:1, meaning twice as many men resigned. Furthermore, notice how 2/3 is twice that of 1/3.

This keeps the same proportion of men to women. Therefore, the odds haven't changed.

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Answer:

15

Step-by-step explanation:

Answer:

2.3333333333333333333333333333333 sec

Answer:

  B. cylinder

Step-by-step explanation:

Any cross section of a cylinder that is parallel to the base will be a circle of the same radius as the cylinder.

__

Various cross sections of any of these figures can be made to be non-uniform. They can also be made to be uniform, if you put restrictions on how the section is done.

For example, a right pyramid will have uniform cross sections, if they are all through the point and perpendicular to the base and one edge. Similarly, a sphere will have uniform cross sections if they are all taken at the same distance from the center of the sphere.

We assume the problem intends no particular restrictions, though we would like to note that cylinder cross sections are uniform only when parallel to each other without intersecting a base.

Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

Ancient Egyptian way of computation, division was performed using a method called "repeated subtraction." (a) 26 ÷ 20 = 1 remainder 6.

(b) 55 ÷ 6 = 9 remainder 19.

(c) 71 21 ÷ = 50 remainder 29.

(d) 25 18 ÷ = 7.

(e) 52 ÷ 68 = 0 remainder 52.

(f) 13 36 ÷ = 0 remainder -23.

In the ancient Egyptian way of computation, division was performed using a method called "repeated subtraction." Here's how it would be applied to the given divisions:

(a) 26 ÷ 20:

To divide 26 by 20, we repeatedly subtract 20 from 26 until we cannot subtract anymore. The number of times we subtract is the quotient.

26 - 20 = 6

6 - 20 = -14 (cannot subtract anymore)

Therefore, 26 ÷ 20 = 1 remainder 6.

(b) 55 ÷ 6:

Using the same method, we repeatedly subtract 6 from 55 until we cannot subtract anymore.

55 - 6 = 49

49 - 6 = 43

43 - 6 = 37

37 - 6 = 31

31 - 6 = 25

25 - 6 = 19 (cannot subtract anymore)

Therefore, 55 ÷ 6 = 9 remainder 19.

(c) 71 21 ÷:

To divide 71 21 by a number, we first convert it to a whole number by multiplying the fraction part by the denominator.

71 21 = 71 + (21/100) = 71 + 21/100

Now, we can perform division using repeated subtraction.

71 - 21 = 50

50 - 21 = 29 (cannot subtract anymore)

Therefore, 71 21 ÷ = 50 remainder 29.

(d) 25 18 ÷:

Similar to the previous case, we convert 25 18 to a whole number.

25 18 = 25 + (18/100) = 25 + 18/100

Performing division:

25 - 18 = 7

Therefore, 25 18 ÷ = 7.

(e) 52 ÷ 68:

Since 52 is smaller than 68, the quotient is 0.

Therefore, 52 ÷ 68 = 0 remainder 52.

(f) 13 36 ÷:

Converting to a whole number:

13 36 = 13 + (36/100) = 13 + 36/100

Performing division:

13 - 36 = -23 (cannot subtract anymore)

Therefore, 13 36 ÷ = 0 remainder -23.

Please note that the ancient Egyptian method of division is not as efficient as modern division methods and may not produce exact decimal results.

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The correct confidence interval is (5.94, 8.36)

Given:

CI = 95%

Mean = sum of given date/no. of date point

          = 186/26

          = 7.15

standard deviation = 2.996

α = (1- 0.95)/2 = 0.025

degree of freedom = sample - 1 = 26 - 25

                                 = 1

we find the t-value 2.060.

Test statics = 2.06 * (б/26) = 1.21

y - ε = 7.15 - 1.21

5.94

y + ε = 7.15 + 1.21

8.36

CI is (5.94, 8.36).

Therefore, the confidence interval for the population is (5.94, 8.36).

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Answer Step-by-step explanation:

Simplifying

y = 6x + 2

Reorder the terms:

y = 2 + 6x

Solving

y = 2 + 6x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = 2 + 6x

///////////

Simplifying

Y = 3x + 1

Reorder the terms:

Y = 1 + 3x

Solving

Y = 1 + 3x

Solving for variable 'Y'.

Move all terms containing Y to the left, all other terms to the right.

Simplifying

Y = 1 + 3x

Answer:

Of course i can help!

Step-by-step explanation:

So. 5x10.75=53.75

and because she breaks 2 more its now 2x10.75=21.50

now

53.75

21.50

+____

75.25

Ur welcome <3

The survey results suggest a potential drop in the proportion of adults watching the local TV news between 2010 and 2013, but further analysis is required to draw a definitive conclusion.

In the 2010 survey, out of 50 adults, 40 reported watching the local TV news at least once in the last month, indicating that 80% (40/50) of the adults surveyed were viewers. In the 2013 survey, out of 40 adults, 24 reported watching the local TV news at least once in the last month, suggesting that 60% (24/40) of the adults surveyed were viewers. While there is a decrease in the proportion of adults watching the nightly news based on these survey results, it is essential to consider other factors before concluding that there was a definite drop.

Firstly, the sample sizes in both surveys are relatively small, with 50 adults surveyed in 2010 and 40 in 2013. A larger sample size would provide more reliable results. Additionally, these surveys only capture the behavior of a specific group of adults within a particular geographic region, potentially limiting the generalizability of the findings to the entire adult population.

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Answer:

D

Step-by-step explanation:

The distance from - 2 to 10 is 12. 12/6 is 2, so 2 spaces across

Answer:40

Step-by-step explanation:

Answer:

the answer is 40 square units

Step-by-step explanation:

it basically gives you the answer and you just have to choose which one. with area it will always be square units (whatever the unit my be) or units^2

Answer:

Step-by-step explanation:

.25 mile in 2 mins

.25(5) miles in 10 min

1.25 mins in 10 mins

There is 5-2 mins in 10 mins. So times by the 5.

Answer:

Its 1.25

Step-by-step explanation:

The first four-term of the sequence is found by the given equation \(a_{n-1} = 4a_n\) is given as 144, 36, 9, and 9/4.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The given equation will be

\(\rm a_n = \dfrac{a_{n-1}}{4} \\\\a_{n-1} = 4a_n\)

And

\(a_4 = 2 \dfrac{1}{4} = \dfrac{9}{4}\)

For n = 4, we have

\(\rm a_{4-1} = 4a_4\\\\a_3 \ \ \ = 4*\dfrac{9}{4} \\\\ a_3 \ \ \ = 9\)

For n = 3, we have

\(\rm a_{3-1} = 4a_3\\\\a_2 \ \ \ = 4*9 \\\\ a_2 \ \ \ = 36\)

For n = 2, we have

\(\rm a_{2-1} = 4a_2\\\\a_1 \ \ \ = 4*36 \\\\ a_1 \ \ \ = 144\)

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Answer:

144

36

9

Step-by-step explanat

The sequence of file folders exhibits a pattern in the number of green folders at each step. Let's define G(n) as the model for the number of green folders at step n.

When observing the sequence of file folders, we can notice that the number of green folders at each step follows a specific pattern. Let's analyze this pattern and formulate a model, G(n), to represent the number of green folders at step n.

In the initial step, let's say n = 1, there are no green folders present. As we progress to the next step, n = 2, a single green folder is introduced. At step n = 3, we can observe that two green folders are added. Further examining the pattern, we find that at each subsequent step, the number of green folders is increasing by one compared to the previous step.

Based on this observation, we can formulate the model G(n) = n - 1, which represents the number of green folders at each step n. By subtracting 1 from the step number, we obtain the corresponding count of green folders. This model accurately predicts the number of green folders at each step in the sequence of file folders, providing a concise and consistent representation of the pattern.

In conclusion, the model G(n) = n - 1 serves as an effective representation of the pattern in the sequence of file folders, describing the number of green folders at each step. By applying this model, we can easily determine the count of green folders for any given step in the sequence, allowing for efficient analysis and prediction.

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The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

m = 2/3, you were correct

Step-by-step explanation:

plot the point on a graph

calculate the rise by going up alongside the y axis

the rise is 2

calcualte the run it takes to get to the second point

the run is 3

m = rise/run = 2/3

m = 2/3

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The inconsistent system of equations is System C, x + 2y = 3 and 4x + 6y = 5.

Let's analyze each system of equations to determine which one is inconsistent

A) 2x + 8y = 6

5x + 20y = 2

We can simplify the second equation by dividing both sides by 5:

x + 4y = 0.4

These equations are not contradictory or incompatible, and they can have a common solution. Therefore, System A is consistent.

B) 5x + 4y = -14

3x + 6y = 6

If we multiply the first equation by 3 and the second equation by 5, we get:

15x + 12y = -42

15x + 30y = 30

Subtracting the first equation from the second equation, we have:

(15x + 30y) - (15x + 12y) = 30 - (-42)

18y = 72

y = 4

Substituting y = 4 back into the first equation:

5x + 4(4) = -14

5x + 16 = -14

5x = -30

x = -6

The values x = -6 and y = 4 satisfy both equations in System B. Therefore, System B is consistent.

C) x + 2y = 3

4x + 6y = 5

Multiplying the first equation by 2, we have:

2x + 4y = 6

If we subtract the second equation from the modified first equation:

(2x + 4y) - (4x + 6y) = 6 - 5

-2x - 2y = 1

2x + 2y = -1

These equations are contradictory since their coefficients have opposite signs. Therefore, System C is inconsistent.

D) 3x - 2y = 3

6x - 4y = 4

Multiplying the first equation by 2, we have:

6x - 4y = 6

These equations are not contradictory or incompatible, and they can have a common solution. Therefore, System D is consistent.

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--The given question is incomplete, the complete question is given below " Which system of equations is inconsistent?

A) 2x+8y=6

5x+20y=2

B) 5x+4y=-14

3x+6y=6

C) x+2y=3

4x+6y=5

D) 3x-2y=3

6x-4y=4"--

9514 1404 393

Answer:

  angles: ∠J≅∠P, ∠K≅∠M, ∠L≅∠N

  sides: JK ~ PM, KL ~ MN, LJ ~ NP

Step-by-step explanation:

The similarity statement lists corresponding parts in the same order. For example, the first letter of one triangle designator corresponds to the first letter of the other triangle designator.

It is easy to list corresponding angles. Simply list them in the same order as they show up in the similarity statement.

  angles: ∠J≅∠P, ∠K≅∠M, ∠L≅∠N

__

Likewise, corresponding segments are those between corresponding vertices. If a segment uses letter designations 2 and 3 in one triangle (KL), it will use letter designations 2 and 3 in the other triangle (MN).

  sides: JK ~ PM, KL ~ MN, LJ ~ NP

_____

Additional comment

I sometimes find it easier to list the vertices vertically. Then I can see the correspondence more directly.

  J . . P

  K . . M

  L . . N

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

angle PSR=180°-(51°+65°)

=64°

angle PST=180°-64° (linear pair angle)

=116°

The value of Angle m∠PST is 116°

Here,

In triangle PRS;

m∠SPR = 65° and m∠PRS = 51°

We have to find m∠PST.

What is exterior angles in triangle?

The angle between the extended side and the side next to it is called an exterior angle. The measure of each exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Now,

In triangle PRS;

m∠SPR = 65° and m∠PRS = 51°

Let the value of  m∠PST = x°

Then, By property of exterior angle;

The measure of each exterior angle of a triangle is equal to the sum of the two opposite interior angles.

We get,

m∠PST = m∠SPR +  m∠PRS

m∠PST =  65° + 51°

m∠PST =  116°

Hence, The value of Angle m∠PST= 116°

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The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

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The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

The probability that the IRS auditor selects none of those containing errors is approximately equal to 0.6352 (rounded to four decimal places).

Let us first calculate the probability of selecting tax returns with errors.

This will be: P(selecting tax returns with errors) = 5/41For the next part of the problem, the IRS auditor randomly selects 3 tax returns from 41 returns, but none of these should contain errors.

Thus, the probability that the auditor selects none of those containing errors is: P(selecting none of those containing errors) = \(\frac{36}{41}\) * \(\frac{35}{40}\) * \(\frac{34}{39}\)

Multiplying these fractions gives us: P(selecting none of those containing errors) = 0.6352 (rounded to four decimal places)

Therefore, the probability that the IRS auditor selects none of those containing errors is approximately equal to 0.6352 (rounded to four decimal places).

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There is a 0.5793 percent chance that the IRS auditor chooses none of the tax filings with problems.

We need to calculate the probability of selecting 3 tax returns without errors out of the total pool of returns.

The number of tax returns containing errors is 5, and the number of tax returns without errors is 41 - 5 = 36.

The total number of ways to select 3 tax returns out of 41 is given by the combination formula:

C(41, 3) = 41! / (3! * (41 - 3)!)

Now, we calculate the number of ways to select 3 tax returns without errors:

C(36, 3) = 36! / (3! * (36 - 3)!)

The probability is then given by:

Probability = (Number of ways to select 3 tax returns without errors) / (Total number of ways to select 3 tax returns)

Probability = C(36, 3) / C(41, 3)

Using a calculator to calculate this probability and rounding to four decimal places, we discover:

Probability ≈ 0.5793

Therefore, There is a 0.5793 percent chance that the IRS auditor chooses none of the tax filings with problems.

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