What is the practical importance of research?.

The residuals which are associated with the given x values are as follows;

A residual is the difference between what is plotted on a scatter plot at a specific point, and what the regression equation (straight line) predicts "should be plotted" at this specific point.

Consequently, the residuals in each case are;

1). For x = 1; Residual = 1 - 1 = 0.

2). For x = 2; Residual = 3 - 2 = 1.

3). For x = 3; Residual = 2 - 3 = -1.

4). For x = 4; Residual = 4.5 - 4 = 0.5.

5). For x = 5; Residual = 5 - 5 = 0.

Ultimately, the residual values are as listed above.

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Length of the shorter diagonal of the parallelogram will be 18.46 feet

Let the Parallelogram ABCD with BD and AC as it’s diagonal

According to the question,

AB = 17 feet

AD = 11 feet

As the opposite sides of a parallelogram are parallel and equal

Therefore, AB = CD = 17 feet

                AD = BC = 11 feet

Also the longer diagonal, BD = 22 feet

In triangle BCD, using cosine formula

[tex]BD^{2}[/tex] = [tex]CD^{2}[/tex] + [tex]BC^{2}[/tex]- 2BC.CD.CosC

[tex]22^{2}[/tex] = [tex]17^{2}[/tex] + [tex]11^{2}[/tex] - 2(11)(17)Cos C

484 = 289 + 121 - 374CosC

-0.197 = Cos C

C = arc Cos(-0.197)

Therefore, C = [tex]110^{0}[/tex]

Now ∠C + ∠D = [tex]180^{0}[/tex]

101+  ∠D = 180

∠D = [tex]79^{0}[/tex]

Now, in triangle ADC

[tex]AC^{2}[/tex] = [tex]AD^{2}[/tex] + [tex]CD^{2}[/tex] - 2AD.CD.CosD

 [tex]AC^{2}[/tex] = [tex]11^{2}[/tex] + [tex]17^{2}[/tex] - 2(11)(17)Cos79

[tex]AC^{2}[/tex] = 121 + 289 - 374Cos79

[tex]AC^{2}[/tex] = 410 -364(.19)

[tex]AC^{2}[/tex] = 340.84

AC = sqrt(340.84)

AC = 18.46

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The system of inequalities to represent this scenario for Barry will be:

x + y = 12

5x + 6y ≤ 50

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let x represents the number of hens.

Let y represents the number of roosters.

The inequality will be:

5(x) + 6(y) ≤ 50

5x + 6y ≤ 50

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If function f(x) is even then so the graph of this function has a line symmetry about y-axis. So the option 3 is correct.

In the given question we have to check which statement is correct.

If f(x) is an even function, which statement about the graph of f(x) must be true.

The given statement are;

As we know that if function f(x) is even then so the graph of this function has a line symmetry about y-axis.

So the option 3 is correct.

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The solution of 1234 x 4321 using Karatsuba  multiplication is 5332114

Given,

1234 x 4321

We have to find the solution using Karatsuba  multiplication;

Karatsuba multiplication;

The first multiplication algorithm that was asymptotically quicker than the quadratic "grade school" technique was the Karatsuba algorithm. For sufficiently big n, the Schönhage-Strassen algorithm (1971) is even faster than the Toom-Cook algorithm (1963), which is a faster generalisation of Karatsuba's approach.

Here,

1234 x 4321

Lets see,

12      +      34       =      46

×                 ×                 ×

43     +      21       =       64

                                 2944 -

516    +   714      =      1230

                                 1714

Now,

516 × 100² + 714 + 1714 x 100 = 5332114

That is,

The solution of 1234 x 4321 using Karatsuba  multiplication is 5332114

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the limit will go to infinity or negative infinity (depending on the sign of the function).

How do you know if a limit is infinity or negative infinity?

The limit as x approaches zero would be negative infinity, since the graph goes down forever as you approach zero from either side: As a general rule, when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity (depending on the sign of the function).

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The series is convergent with sum 5/8

A series is said to be convergent, if it converges to a value as the terms of series tends to infinity.

A series is said to divergent, it it does not converge to a value but keeps on either increasing or decreasing as the terms of series tends to infinity.

In the question ,

[tex]\frac{1}{3} +\frac{2}{9} + \frac{1}{27} +\frac{2}{81}+..[/tex] is given series

dividing the series into two parts ,

[tex](\frac{1}{3} +\frac{1}{27} +\frac{1}{243}+..)[/tex] + [tex](\frac{2}{9} + \frac{2}{81} + \frac{2}{729}+...)[/tex]

Using infinite geometric series formula both the side ,

=> [tex]\frac{\frac{1}{3}}{1- \frac{1}{9}} + \frac{\frac{1}{2}}{1- \frac{1}{9}}[/tex]

=> [tex]\frac{1/3}{8/9}+ \frac{1/2}{8/9}[/tex]

=>  [tex]\frac{3}{8} + \frac{1}{4}[/tex]

=> [tex]\frac{5}{8}[/tex]

Hence , the series is convergent.

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In triangle def, if m∠d is (2x)°, m∠e is (3x − 2)°, and m∠f is (x + 8)°, then the value of x is 29.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Triangle is DEF

if m∠d is (2x)°, m∠e is (3x − 2)°, and m∠f is (x 8)°

We need to find the value of x.

We know that the sum of three angles of triangle is 180 degrees

m∠d + m∠e + m∠f=180°

2x+3x-2+x+8= 180°

6x+6=180

Subtract 6 on both sides

6x=174

Divide by 6 on both sides.

x=174/6

x=29

Hence, the value of x is 29.

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Given the above condition, the result may translate to "Sample size and effect size."

What is Effect Size in Research?

Increasing the sample size always increases the likelihood of finding a statistically significant impact, regardless of how tiny the effect is in the actual world. In contrast, effect sizes are not affected by sample size. To compute effect sizes, just the data is utilized.

In contrast to significance tests, the effect size is not affected by sample size. Statistical significance, on the other hand, is determined by both the sample size and the effect size.

The greater the impact size, the greater the difference between the typical person in each group. A d of 0.2 or less is regarded a minor impact size, a d of roughly 0.5 is considered a medium effect size, and a d of 0.8 or above is considered a high effect size.

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The value of the original fraction is found as 4/8.

Let a be the numerator.

Let b be the denominator.

B = A + 4 has a denominator 4 times larger than a numerator.

Both the numerator as well as the denominator receive an addition of 2: (a + 4 + 2) and a + 2.

The following algebraic equation is created from the provided statement:

(a + 2)/(a + 4 + 2) = 3/5

(a + 2)/(a + 6) = 3/5

5(a + 2) = 3(a + 6)

5a - 3a = 18 - 10

a = 4

Put the value of a in the original fraction;

a/ (a + 4) = 4/(4 + 4)

= 4/8

Thus, the value of the original fraction is found as 4/8.

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The time that Ali should leave his house to get to practice on time is 7:40 am.

Fron the information given, it was stated that Ali’s soccer practice begins at 8:05 a.m and that it takes him 25 minutes to get to practice.

In this case, it should be noted that the time that he will leave the house will be the minutes subtracted from 8:05.

This will be illustrated thus:

= 8:05 a.m - 25 minutes

= 7:40am

Therefore, Ali should leave at 7:40 am.

Note that the clock wasn't given by you but the appropriate time is calculated.

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The value of c for the statement P(Z>c) = 0.1379 in the standard normal distribution is 1.09.

Φ is symbol for cumulative distribution function (CDF) for standard normal distribution with mean equal to 0 and standard deviation equal to 1.

Z follow standard normal distribution. So,

Z ∼ N(0,1)

Since,

P(Z>c) = 0.1379

1 - P(Z≤c) = 0.1379

P(Z≤c) = 1 - 0.1379

P(Z≤c) = 0.8621

or

Φ(c) = 0.8621

Next, we know Φ(Z) is equal to P(Z≤z) with z∈R is CDF for N(0,1). So,

P(Z≤z) = 0.8621

From standard normal distribution table or z table, we get z = 1.09. So,

P(Z≤1.09) =  0.8621

Φ(1.09) = 0.8621

Since, Φ(c) = 0.8621. So, c = 1.09

Thus, the value of c is 1.09 for statement P(Z>c) in standard normal distribution is equal to 0.1379.

Your question is incomplete, but most probably your full question is

Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true.

P(Z>c)=0.1379

Round your answer to two decimal places.

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The total distance the ant crawled on the number line is 16.2 centimeters

The distance the ant crawled is all added to minding if it were positive or negative.

Summation of this nature gives absolute values

Hence using addition the total distance is calculated

= 3.5 centimeters + 4.8 centimeters + 7.9 centimeters

= 16.2 centimeters

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Answer:

30 degrees

Step-by-step explanation:

(75 degrees x 2) = 150 degrees

180 degrees - 150 degrees = 30 degrees

angle 1 = 30 degrees

The given equation's solution is x = 5i or x = i.

An equation has been provided.

x⁴+6x²+5 = 0

We to settle it utilizing replacement.

If u = x2, then u2 = x4 In the above equation, we find that u2+6u+5 = 0. Now, use the factorization method.

Divide the middle term of the previous equation as follows: u2+5u+u+5 = 0; u(u+5)+1(u+5) = 0; u(u+5)(u+1) = 0 Using the zero-product property, we can determine that u+5 or u+1 equals 0; u = -5 or u = -1; x2 equals -5 or x2 equals -1; taking the square root of both sides of.

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The fundamental niche is the entire niche that an organism is capable of occupying if there was no competition. whereas, the realized niche is the niche occupied by the organism in the presence of competitors.

What is a niche?

This refers to the role an organism plays in an ecosystem/community.

Types of  niches

.The fundamental niche: This refers to the organism that is capable of occupying if there were no competitors.

. The realized niche:  This refers to organisms that exist in the presence of competitors. They are perceived to be less effective due to the presence of competitors.

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The velocity v(t), speed s(t), and acceleration a(t), of the object are explained below.

A vector is an amount or peculiarity that has two free properties: greatness and bearing. The term likewise means the numerical or mathematical portrayal of such an amount. Instances of vectors in nature are speed, energy, force, electromagnetic fields, and weight.

We have given,

r(t) = ti+t^2j+t^2k/2 at t = 4

For velocity = dr(t)/dt=d( ti+t^2j+t^2k/2)/dt

v(t) = i+2tj+tk

put t = 4

velocity= i+8j+4k

And speed =[tex]\sqrt{(1)^2+(8)^2+(4)^2}[/tex]= [tex]\sqrt{81}[/tex]= 9 unit/second

acceleration =dv(t)/dt=d( i+2tj+tk)/dt = 2j+k

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Answer:

$1,296

Step-by-step explanation:

kelly earns $288 during her first 8 hour shift. how much would kelly earn on a full paycheck of 36 hours? interpret your answer.

288/8 = $36 per hour

If she worked 36 hours at $36 per hour:

36* $36 = $1,296

Therefore, the intensity pattern due to each single slit only extends over a finite region, and the double slit interference pattern can only be observed within this region.

In mathematics, interference is a phenomena that happens when two or more waves interact with one another. Depending on the waves' respective frequency  to reinforce or cancel. Interference can be constructive, where the waves combine to generate a bigger wave, or destructive, where the waves cancel each other out. This phenomena is widely observed in light waves, sound waves, and water waves. The superposition principle, which asserts that the total wave at any place in space equals the sum of all the individual waves existing at that point, is a mathematical concept that describes interference. In disciplines including physics, engineering, and signal processing, this idea is frequently applied.

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The average rate of change of function is 10.2 inches per day

The equation to show the height of the flower is

g(n) = 10(1.02)n

Where g(n) is the height of the flower

n is the number of days

The value of n is from n = 1 to n = 5

The average rate of change of the function = f(5) - f(1) / 5 -1

Then,

f(5) = 10(1.02)(5)

= 51 inches

f(1) = 10(1.02)(1)

= 10.2 inches

Substitute the values in the equation

The average rate of change of function = 51 - 10.2 / 5 - 1

= 40.8 / 4

= 10.2 inches per day

Hence, the average rate of change of function is 10.2 inches per day

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When you see a right triangle and need to solve for one side, use the Pythagorean Theorem. This states that the square of the hypotenuse is equal to the sum of the squares of the adjacent sides. In algebraic terms:

[tex]a^2+b^2=c^2[/tex]

In triangle 1, we are given c and b, we need to find a.

[tex]a^2+8.7^2=9.4^2\\a^2+75.69=88.36\\a^2+75.69-75.69=88.36-75.69\\a^2=12.67\\\sqrt{a^2}=\sqrt{12.67}\\a=3.56[/tex]

In triangle 2, we have a and c, we need to find b.

[tex]6^2+b^2=14^2\\36+b^2=196\\36-36+b^2=196-36\\b^2=160\\\sqrt{b^2} = \sqrt{160}\\b=4\sqrt{10}[/tex]

The slope of the line of best fit to the raw-score scatter plot is 0.98

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

The slope (b) of the line is calculated as

b = r * Sy/Sx

Substitute the known values in the above equation, so, we have the following representation

b = 0.75 * 2.45/1.88

Evaluate

b = 0.98

A linear equation is represented as

y = bx + c

Where

Slope = b

y-intercept = c

In (a), we have

b = 0.98

So, we have

y = 0.98x + c

Recall that the point (13, 9) is on the line of best fit.

So, we have

9 = 0.98 * 13 + c

This gives

9 = 12.74 + c

Evaluate

c = -3.74

So, we have

y = 0.98x - 3.74

Here, we have

x = 12

So, we have

y = 0.98 x 12 - 3.74

Evaluate

y = 8.02

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we are 99% confident that the population proportion lies between the confidence interval.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced from a statistical model with a 95% confidence interval of 9.50 - 10.50.

margin of error =E

=0.03p

=101/300

=0.337

For 95% CI, alpha is 5% and z=1.96

Sample size n=(z/E)² × (p(1-p)

=(1.96/0.03)² × (0.337(1-0.337))

=953.7

=954(approximately)

confidence interval is interpreted as that we are 99% confident that the population proportion lies between the confidence interval.

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a)The 95% confidence interval are

0-44,44-88

b))Yes, we can claim significant reduction in the rate of intrusion attempts

We have firewall change of 14 people.

We need to compute total sum before firewall change which can be done by

(56+47+49+37+38+60+50+43+59+50+56+54+58)/14

=657/14

=46.92

Now, similarly, after firewall change total sum is

(53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20

=756/20

=37.8

Now the difference between average number of intrusion attempts before and after firewall change is

(46.92-37.8)

=9.12

Now, we need to make confidence interval to only 95% of this difference=

(95×9.12)/100

=44.196=44(approx)

It means our interval range varies from 0-44,44-88 with a difference of 44.

b)Yes, we can easily claim that rate of intrusion attempts decreases.

Before firewall change, we can see average number of intrusion attempt is =46.92

After firewall change, we can see average number of intrusion attempt is

37.8

So, we can see rate of intrusion decreases on increasing the number of blocked intrusions.

For computing z-value, we just need to take square root of the difference of average number of intrusions attempst

=>Z-value= √9.12=3.01

Using the z-table, we get that for the above z-value, corresponding p-value is 0.067

Hence, the interval range is 0-44,44-88 and b)Yes we can claim, p-value is 0.067.No, this assumption does not make a difference.

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According to the given information for the normal distribution, we can expect that the corresponding z-score may be negative.

It is given to us that -

The normal distribution has mean 11

The normal distribution has data value of 9

We have to find out if the corresponding z-score is to be positive or negative.

The z-score calculates the number of standard deviations higher or lower the mean, the data point is present.

The formula for z-score is given by -

[tex]z=\frac{data point - mean}{standard deviation}[/tex]

Although we do not have the value of standard deviation in the question, we can see that the value of

data point - mean = 9-11 = -2

So, we can see that the numerator of the z-value formula is already negative.

Thus, we can expect that the corresponding z-score may be negative according to the information provided for the normal distribution.

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There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds

Given:

In the question;

Suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.

Now, According to the question:

Since we have to test that whether the mean weight is greater than 14 pounds, so test is right tailed and if ta is the value of test static then p-value is P(t> t_a ) . Where t_a={16-14\over 6/\sqrt {40}} .

Now p-value is 0.021.

So, the correct conclusion is:

There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds

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F(x) = sin x, F(x) = x2 + 3, F(x) = 1/x, F(x) = 2x + 3, etc. are a few further instances of functions.

Polynomial functions include functions like the identity function, linear function, quadratic function, and cubic function. Therefore, it is useful to define the type of function using the function equation y = f(x).

Algebraic, exponential, logarithmic, and trigonometric functions are available depending on the domain. Modulus, rational, signum, even and odd, periodic, biggest integer, smallest integer, inverse, and composite functions are the functions based on the range.

For instance: It is declared that the polynomial function with degree zero is a constant function. One-degree polynomial functions are referred to as linear functions. Quadratic function is the name given to the degree two polynomial function.

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The intervals in the solution set are those that make the inequalities 5(x – 2)(x + 4) > 0 true is (-∞, -4) U (2,∞).

Given that,

The inequality is 5(x – 2)(x + 4) > 0

We need to address the inequality and find a solution.

We know that,

Take the inequality

5(x – 2)(x + 4) = 0

Divide the equation both sides by 5

(x – 2)(x + 4) = 0

Now, we take each factor equal to 0

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we get

First interval (-∞,-4)

Second interval (-4,2)

Third interval (2,∞)

Now,

We take each interval with our inequality

First interval (-∞,-4), pick a number in this interval and check with our inequality.

Lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

Second interval (-4,2), pick a number in this interval and check with our inequality.

Lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval (2,∞), pick a number in this interval and check with our inequality.

Lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

The intervals in the solution set are those that make the inequalities true is (-∞, -4) U (2,∞).

Therefore, The intervals in the solution set are those that make the inequalities 5(x – 2)(x + 4) > 0 true is (-∞, -4) U (2,∞).

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(4x² - 9)(4x² + 9) = 0 equation is equivalent to the given equation.

What is factorization?

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.

Here, we have

Given equation,

f(x) = 16x⁴ – 81 = 0

The difference of squares is used to solve this equation. There are three perfect squares: 16, x⁴, and 81. ( which means that it is a number multiplied by itself, 16 is 4 x4 for example).

We solve this equation by formula: (a² - b²) = (a - b)(a + b)

= 16x⁴ – 81 = 0

Now, we determine the square root of 16 which is 4, and of x⁴ which is x², and 81 which is 9.

Now we write the equation in the (a - b)(a + b) form :

⇒ (4x² - 9)(4x² + 9) = 0

Hence, the (4x² - 9)(4x² + 9) = 0 equation is equivalent to the given equation.

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