Determine which set of side measurements could be used to form a right triangle.
14, 5, 15
O 3, 4, 5
O9, 14, 16
O 5, 2,7

Answer:

[tex]x=5, y=2[/tex]

Step-by-step explanation:

[tex]4x+y=22 \implies 24x+6y=132 \\ \\ 8x-6y=28 \\ \\ 32x=160 \\ \\ x=5 \\ \\ \implies 4(5)+y=22 \implies y=2[/tex]

Answer:

Step-by-step explanation:

10 months=10/12=5/6 years.

Amount=Principal+ Interest

A=P+I

A=P+P×r×t

A=P(1+rt)

18500=P(1+4%×5/6)

18500=P(1+20/600)

18500=P(1+1/30)

18500=P(31/30)

P=18500×30/31≈17903.2258≈17903.23

Answer:

Step-by-step explanation:

If the diameter increases by 10%,

new diameter = d+⅒ = 1.1d

also new radius = 0.55r

Height also increasesby 10%,

New height = h+⅒h = 1.1h

hence diameter of larger can =

π*(0.55)²*1.1= 1.0453

hence percentage change in volume

is 4.53% which can be rounded off to

Answer:

Below

Step-by-step explanation:

1.235 <= Weight < 1.245    before rounding

As per the concept of exponential decay, the initial mass of the sample is 5,254.87 kg

What is meant by Exponential decay:

In math, the term exponential decay is a very common process especially when we are talking about radioactive materials.

The standard  formula for this type of behavior which is written below:

A = Pe^-rt

where

A refers the amount left after time t

P refers the initial amount at t=0

r refers the rate

Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago.

And we need to find if the sample has a mass of today, then the initial mass of the sample.

Now, we have to substituting the values,

Then we get the equation as,

=> A = (9575 kg)(e^-0.12*5)

When we simplify this one, then we get,

=> A = 5,254.87 kg

Therefore, the initial mass of the sample is 5,254.87 kg

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The statement that is true according to the Central Limit Theorem is B. the original PD must also be normal.

According to the central limit theorem, if you take sufficiently large samples from a population, the means of the samples will be normally distributed even if the population is not normally distributed. The central limit theorem (CLT) states that as sample size increases, the distribution of sample means approaches a normal distribution, regardless of the distribution of the population.

The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.

In conclusion, the correct option is B.

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Lk+1 is the k+1th regular language, for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.

The induction hypothesis's function The assumption made at the beginning of the induction phase is known as the induction hypothesis, and it is the situation where n = k for the proposition we are trying to prove ("P(k)"). If you don't bring this hypothesis into play at any point throughout the proof of the induction phase, something is amiss.

Given:

It is normal for two regular languages to be combined.

Give the function f(n) the name "union of n regular languages."

Question Is the language f(n) regular?

The union of a single regular language is regular

if n = 1. Base Case

The provided hypothesis tells us that f(2) is regular

if n = 2.

Assume that f(n) is regular for every n = k.

This is the inductive hypothesis.

Let n equal k+1 in the inductive step. The inductive premise tells us that f(k) is a regular language.

Consequently, f(n) = f(k+1) = Lk+1 U f(k) (k)

Lk+1 is the k+1th regular language,

for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.

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Answer:

---------------------------------------

Total length we need is the sum of the perimeter and two diagonals of the square.

Perimeter:

Diagonals:

Total length:

Number of rolls:

Answer:

12

Step-by-step explanation:

Answer:

-3

3

Step-by-step explanation:

0.1x^2-0.6x+0.9=0

(1/10)(x^2+6x+9)=0

(1/10)(x+3)^2=0

x=-3

2x^2-12x+18=0

2(x^2-6x+9)=0

2(x-3)^2=0

x=3

The solution of the equation 0.1x²-0.6x+0.9=0 is -3 and 2x²-12x+18=0 is 3.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given the system of equation as;

0.1x²-0.6x+0.9=0

2x²-12x+18=0

Solving by completing the square:

0.1x²-0.6x+0.9=0

(1/10)(x²+6x+9)=0

(1/10)(x+3)²=0

x=-3

2x²-12x+18=0

2(x²-6x+9)=0

2(x-3)²=0

x=3

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The value of the minimum sample size required to estimate the population proportion is 438.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Given:

The margin of error, ME = 0.04,

The value of p = 0.12,

The confidence level =  99%,

Calculate the minimum sample size as shown below,

ME = z √[p(1 - p) / n]

Calculate the value of z from the table attached below considering the confidence level, z = 2.576,

0.04 = 2.576 √[0.12(1 - 0.12) / n]

Squaring both sides,

0.0016 = 6.636 × 0.12 × 0.88 / n

n = 0.7 / 0.0016

n = 437.9 or 438

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To figure this out, you set up the fraction

    [tex]\dfrac{\text{number that meet the criteria}}{\text{total possible number}}[/tex]

In this case, it's [tex]\dfrac{7 \text{ A's}}{20 \text{ total students}}[/tex].

You then divide 7/20 = 0.35 and convert that decimal into a percent: 35%

Answer:

[tex]x^2 - 6x + 10[/tex] or in general: [tex]a(x^2 - 6x + 10)[/tex] where "a" is any constant real number except zero.  

Step-by-step explanation:

If we're given a complex root of a polynomial to be: [tex](a+bi)\text{ or }(a-bi)[/tex], then we know that its conjugate is also a root of the polynomial: [tex](a-bi)\text{ or }(a+bi)[/tex].

So since we're given the root: [tex](3+i)[/tex], then we know that its conjugate: [tex](3-i)[/tex] is also a root. Thus we have two roots so far.

The Fundamental Theorem of Algebra simply states that any polynomial, with degree "n", will have "n" roots, which can consist of both real and imaginary solutions.

So let's say I have a polynomial: [tex]x^6+3x+2=0[/tex], this has 6 roots, according to the Fundamental Theorem of Algebra, since the degree of the polynomial is 6 (remember the degree is simply the variable with the highest degree)

Since we already have two roots, and a quadratic function has a degree of two, we know that these are all the roots the quadratic has, since the Fundamental Theorem of Algebra states that a quadratic will only have 2 roots.

We can generally express any polynomial in factored form, that is: [tex]a(x-b)(x-c)(x-d)...=y[/tex]

where "b", "c", and "d", and so on... are zeros of the function. This aligns with the behavior of zeros, since if we plug any of them into the function, then one of the factors will become zero, and since zero times anything is zero, well the entire thing is zero.

For example if I plug in "b", which is zero we get: [tex]a(b-b)(b-c)(b-d)...=y\implies a(0)(b-c)(b-d)=y\implies 0=y[/tex]

this is since plugging in zero, makes the factor: [tex]x-b[/tex] equal to zero, making the entire thing zero.

One last thing to mention is the "a" value in front which just generally determines the stretch/compression of the polynomial.

So with this information, we can write a polynomial:

[tex]a(x-(3+i))(x-(3-i))[/tex]

From here let's distribute the negative sign:

[tex]a(x-3-i)(x-3+i)[/tex]

Now this may look a bit tough to distribute, but you may notice a pattern here, we have a difference of squares. It may not be obvious, but if we make one substitution, let's say: [tex]u=x-3[/tex], then we get the equation

[tex]a(u-i)(u+i)[/tex]

The difference of squares is expressed as: [tex]a^2 - b^2 = (a-b)(a+b)[/tex], so our expression will expand out into:

[tex]a(u^2 - i^2)[/tex]

The substitution was just to make things a bit more clear, but let's just substitute x-3 back into the equation.

[tex]a((x-3)^2 - i^2)[/tex]

From here, we know that i^2 is simply -1, since: [tex]\sqrt{-1} = i, \text{ so }i^2 = -1[/tex]

We can also easily expand out the polynomial using FOIL

[tex]a((x^2 - 6x + 9) -(-1))\\a(x^2 - 6x + 9 + 1)\\a(x^2 - 6x + 10)[/tex]

You may notice the "a value, and that's just a constant, which determines the stretch/compression of the polynomial, and can be any real number, except for zero since that will make the entire thing zero regardless of what x is. For the sake of simplicity, let's just write this to be 1.

The standard equation of a circle is [tex](x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}[/tex]. The equation of the circle in general form is (x-1)² + (x-1)² = 3.

Standard form of circle equation is (x – a)² + (y – b)² = r²

General form of Equation of a Circle.

x² + y² + 2gx + 2fy + c = 0, for all values of g, f and c.

The equation of a circle is

(x-h)²+ (y-k)² = r²

So, it's given that radius,

r = √3

h=1 and k=-5

So, by substituting all values to the standard equation of a circle is :

[tex](x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}[/tex]

The equation of the circle in the general form is written as :

(x-1)² + (x-1)² = 3

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Null Hypothesis: There is no association between handedness and career for Accountants. And Alternative Hypothesis: There is an association between handedness and career for Accountants.

Profession 1: Lawyer

Null Hypothesis: There is no association between handedness and career for Lawyers.

Alternative Hypothesis: There is an association between handedness and career for Lawyers.

Profession 2: Pilot

Null Hypothesis: There is no association between handedness and career for Pilots.

Alternative Hypothesis: There is an association between handedness and career for Pilots.

Profession 3: Accountant

Null Hypothesis: There is no association between handedness and career for Accountants.

Alternative Hypothesis: There is an association between handedness and career for Accountants.

Profession 4: Nurse

Null Hypothesis: There is no association between handedness and career for Nurses.

Alternative Hypothesis: There is an association between handedness and career for Nurses.

Profession 5: Teacher

Null Hypothesis: There is no association between handedness and career for Teachers.

Alternative Hypothesis: There is an association between handedness and career for Teachers.

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5.25 option c is the test statistics for the given data.

Given,

The observed values;-

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

 To verify the following claim, a chi square test must be performed:

H0: The proportions for the final grades are the same.

H1: The final grade proportions varies from one another.

The level of significance assumed for this case is α = 0.01  

The statistic to check the hypothesis is given by:  

X² = ∑ⁿi = 1 (Oi - Ei)²/Ei

Now all that remains is to use the following formula to determine the predicted values, Ei = % × total

And the calculations are given by:  

EA = 0.25 × 160 = 40

EB = 0.25 × 160 = 40

EC = 0.4 × 160 = 64

ED = 0.05 × 160 = 8

EF = 0.05 × 160 = 8

Here, the statistics;-

X² = (36 - 40)²/40 + (42 - 40)²/40 + (60 - 64)²/64 + (14 - 8)²/8 + (8 -8)²/8

= 16/40 + 4/40 + 16/64 + 36/8 + 0/8

= 5.25

 Therefore,

The test statistics for the given data is option c 5.25

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A

5-1=4

34+5=39

5-1=4

5+5=10

Answer:

[tex]A)g-1=4\\g=4+1\\g=5[/tex]

Step-by-step explanation:

[tex]A)g-1=4\\g=4+1\\g=5\\\\B)34+g=50\\g=50-34\\g=16\\\\C)g-1=15\\g=15+1\\g=16\\\\\\D)g+5=15\\g=15-5\\g=10\\So the only Option remaining is A) which the correct answer[/tex]

Answer:

Step-by-step explanation:

To find the y-intercept of the equation y - 6 = -2(x + 5), we can set x equal to 0, since the y-intercept is the point where the graph of the equation crosses the y-axis.

Substituting 0 for x, we get:

y - 6 = -2(0 + 5)

y - 6 = -2(5)

y - 6 = -10

y = -4

Therefore, the y-intercept of the equation y - 6 = -2(x + 5) is (0, -4). This means that the graph of the equation crosses the y-axis at the point (0, -4).

By using the property of angle, it can be calculated that [tex]\angle EBA \cong \angle ECD[/tex]

What are angles?

Angles are a way of measuring the amount of turn between two lines or three or more planes. An angle is formed when two lines intersect or when two planes meet. It is measured in degrees, with a full circle being 360 degrees. The angle is measured in terms of the amount of turn between the two lines or planes. Angles are typically used to describe the orientation of objects in space, such as the corners of a triangle, the angle of a flight path, or the angle of the sun’s rays. Angles are also used to measure the size of an angle and the distance between two points. Angles are important in mathematics because they help to analyze the size and shape of objects, and also to help solve problems.

Here,

It is given that

[tex]\angle EBC \cong \angle ECB[/tex]

Now,

[tex]180-\angle EBC \cong 180-\angle ECB[/tex] [Angle on a straight line]

[tex]\angle EBA \cong \angle ECD[/tex]

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Answer: 2

Step-by-step explanation: hope it helps

1000 times were added to the n=30 sample. Even with n=30, the sample variance distribution is still very biased.

Probability refers to possibility.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

According to our question-

The sample variance's variance (SD) is still very large. The range is from 20 to 30%.

Because we are utilizing estimated population variance rather than the genuine population variance, which has some degree of uncertainty, the e t distribution has a longer tail when degrees of freedom are limited. Given that the estimated population variance is nearer to the actual population variance when sample size = 30, the t distribution will be closer to the z distribution.

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On a scatter diagram, you can see outliers if there is a regression line. The point or points that are furthest distant from the regression line are considered outliers in a scatter diagram.

In a scatter plot, dots are used to show the values of two separate numerical variables. To see how different variables relate to one another, utilize scatter plots. The link between an independent and dependent variable is shown as a straight line in a linear regression.

If a linear model is adequate, the residuals scatterplot should display random scatter and the histogram should appear about normal. The linear model is inappropriate if we see a curved connection in the residual plot. The residuals are displayed against the explanatory variable in a different form of residual plot.

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The sampling distribution of statistics is the allocation of all matters of the statistic when all viable examples of the exact size n are taken from the exact people.

What is sampling distribution mean?

The group of averages drawn from all feasible random samples of a certain size (n) drawn from a particular population is referred to as the distribution of sample means.

A statistical probability distribution that results from selecting random samples from a specific population is referred to as a sampling distribution.

It depicts the distribution of frequencies on how dispersed various outcomes will be for a particular population and is also referred to as a finite-sample distribution.

To determine the sample distribution, you must know the population's standard deviation.

Divide the total number of observations in the sample by the sum of all the observations.

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We use Z-Distribution for large sample sizes, The reduced sample size is 200.

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

confidence interval = 0.06

Sample size= 400

new interval of confidence = 0.03

new sample size = 400/0.06 * 0.03

=200

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given a triangle with side of  lengths of 5 and 8 then c^2 =89 inequality describes all possible lengths of the third side

In the right triangle of sides a, b, and c

a^2 + b^2 = c^2

Since a = 5 and c = 8

Substitute them in the given rule

we get

25+64= c^2

89= c^2

Take a square root for both sides

c= sqrt 89

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We need to use the concept of Relative Abundance. Relative Abundance of A,B and C are 14.28,57.14 and 28.57% respectively.

The percentage of an organism of a specific sort in relation to the overall number of organisms in the area is known as relative abundance. Relative species abundances frequently follow particular patterns, some of the most well-known and extensively researched patterns in macroecology. Over a large variety of biological ecosystems, relative species abundances exhibit relatively similar patterns. Most species are rare (represented by a single individual in a community sample), while only a small number of species are prolific, according to a histogram of the number of species represented by 1, 2, 3,..., n individuals.

(M1)(x) + (M2)(1-x) = M(E) is the formula for Relative Abundance.

A weighs 12g, B weighs 16g and C weighs 24g.

A customer buys 1 apple A, 3 apples B and 1 apple

So assume A,B and C as different isotopes of apples.

Relative Abundance of A=12/84 ×100⇒14.28%

Relative Abundance of B=48/84 ×100⇒57.14%

Relative Abundance of C=24/84 ×100⇒28.57%

We need to use the concept of Relative Abundance. Relative Abundance of A,B and C are 14.28,57.14 and 28.57% respectively.

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Dependent variable: A dependent variable is a variable that changes or is impacted by other factors. independent variable: An independent variable is a variable that does not change or are impacted by other factors.

Regression is a method for figuring out the relationship between two or more variables. In other words, it is determined by how the predictor variable changes and how the dependent variable changes. Additionally, when more than one independent variable is included in a regression analysis, the change in the dependent is examined while maintaining the same values for the other independent variables.

The best fit for the data is linear regression if the data set is bivariate. The data with two variables are best represented by the straight line known as the least squares regression line.

When the explanatory variable has a value of zero, the response variable's projected value is shown by the regression line's y-intercept (though be wary of extrapolation in interpreting the intercept or other values outside the original data range).

The best fit for the data is linear regression if the data set is bivariate. The data with two variables are best represented by the straight line known as the least squares regression line. The line's equation is provided by,

y = a+bx

where,

a—Intercept

b—Regression coefficient

y—Predicted value of the dependent variable

x —Independent or predictor variable

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Answer: In Shay's wind farm their can be 4 arrays

Search up the meaning of a Array if you are confused

Step-by-step explanation:

24 has 4 pairs of factors.

The difference between the two population means is estimated at -1.05.

Null Hypothesis: The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

The information presented here represents the golfers' first and final round scores.

a. α= 0.10 is the significance level.

The following hypothesis test can be created:

Hypothesis of nullity H₀ μₐ= 0

This suggests that the population means of the first round and final round are identical.

Alternative formulation: Hₐ μₐ≠0

This suggests that the population means of the first round and final round are different.

The test statistic is now:

t=(d-meanₐ)[tex]\sqrt{n}[/tex]/sₐ

Excel can be used to determine the test statistic.

This will result in: 0.10<P<0.20.

b. The 90% confidence level is the primary margin of error. This indicates that there is no discernible difference, and the result is -1.05.

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