How many electrons does it take to reduce oxygen to water?.

Answer: A googolplexian

Step-by-step explanation: A googolplexian is a number with a googol of zeros after it.

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Answer:

[tex]\frac{1}{\sqrt{2}}[/tex]

Step-by-step explanation:

The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)

Given,

In the question:

Given that the mean of the Population = 830HP

Given that the size of the sample  'n' = 25

Given that the mean of the sample = 880HP

Given that the sample standard deviation = 55HP

To find the confidence interval for the average maximum HP for the experimental engine.

Use a significance level of α=0.01.

Now, According to the question:

Degrees of freedom = n-1 =25 - 1 = 24

t₀.₀₀₅ = 3.3554

The 99% of a confidence interval for the average maximum HP for the experimental engine.

[tex](x -\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} } , x^2 +\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} })[/tex]

(880 - 3.3554 [tex]\frac{55}{\sqrt{25} }[/tex] , 880 + 3.3554 [tex]\frac{55}{\sqrt{25} }[/tex])

(843.0906, 916.9094)

Hence, The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)

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An exponential function is a mathematical function in which the output of the function increases (or decreases) at a rate that is proportional to the current value of the output.

Exponential functions have an “asymptote”, which is a line that the graph approaches but never crosses. This asymptote is often a horizontal line, and it can be used to identify exponential functions.

To determine if a graph is an exponential function, look for a curve that rises or falls steeply and then levels off. The curve should be smooth and symmetrical, and the points should lie along a straight line when plotted on a logarithmic scale. The equation for the graph should also have an exponential form, such as y=ab^x. If these characteristics are present, then the graph is an exponential function.

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a) √2 t |1, -1>

b ) t√0 |0, 1>=0

c) 2t² |1, -1> are the eigenstates of S² with the appropriate eigen value.

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it. The associated eigenvalue, generally indicated by lambda, is the factor by which the eigenvector is scaled.

Eigenvalues and eigenvectors play an important role in the analysis of linear transformations. The prefix eigen- comes from the German word eigen, which means "property," "characteristic," or "own."

a) S- |1,0>= t√(1+0)(1-0+1) |1, 0-1>

=t√2 |1, -1>

=√2 t |1, -1>

∴S±(s, m>=t√(s±m)(s±m+1) |s, m±1>

b) S₊ |0, 0>= t√(0-0)(0+0+1) |0, +1>

=t√0 |0, 1>=0

S₋ |0, 0>=t√(0+0)(0-0+1_) |0. -1>

c) S² |1, 1>= 1(1+1)t² |1, 1>

=2t² |1, -1>

∴ S² |s, m>=s(s+1)t² |s, m>

Hence, |1, -1> and |1, -1> are eigen function of S² with eigen value 2t²s.

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The probability of a bill exceeding $300 is 0.0091.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

For normal distribution z score = (X-μ)/σ

here mean= μ = 196

std deviation  = σ = 44.0000

probability of a bill exceeding

$300  = P(X>300)

          =P(Z>(300-196)/44)  

          =P(Z>2.36)

          =0.0091

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The rate at which the distance between the runner and second base changes is 28.71 ft/s.

Given, a batter hits the ball and runs toward first base at a speed of 28 ft/s. we have to find the rate (in ft/s) at which the distance between the runner and second base change when the runner has run 20 ft.

As, distance = speed × time

d = st

On differentiating both the sides

d' = s't + s

d' = 20/28 + 28

d' = 0.71 + 28

d' = 28.71

Hence, the rate at which the distance between the runner and second base changes is 28.71 ft/s.

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The total percentage of athletes who enjoy cycling is given by:

74.5%.

A percentage is the division of an amount by a total amount, which is then multiplied by 100%.

In this problem, the percentages are already given for the entire population.

The percentage of athletes who enjoy cycling is divided into two nodes, as follows:

The percentages associated from each node are given on the text as follows:

Hence the proportion of athletes who enjoy cycling is given as follows:

0.45 x 0.80 + 0.55 x 0.70 = 0.745.

Then the percentage is of:

0.745 x 100% = 74.5%.

Which means that the last option is correct.

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Answer:

1/6

Step-by-step explanation:

1/2 *1/3=1/6

The area of the shaded portion of the inscribed hexagon is; 3.395 ft²

We are given;

Diameter of circle = 5 ft

Thus;

radius; r = 5/2 = 2.5 ft

Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;

a = d/2

where d is the length of the long diagonal

Formula for area of hexagon is;

A = (3/2) * √3 * a²

Thus;

A =  (3/2) * √3 * 2.5²

A = 16.24 ft²

Area of circle is gotten from the formula;

A = πr²

A = π * 2.5²

A = 19.635 ft²

Thus;

Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²

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The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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Answer: -15

Step-by-step explanation:

do 17-32= -15

The average speed of a car is 93.34 km/h

Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time.

Average speed formula is the average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as: Total distance travelled / total speed

According to the equation,

A car covers the road from city A to city B, 40 km, in 30 minutes, and the road from city B to C, 30 km, in 15 minutes

Total distance a car covers is 40 + 30

= 70km

Total time a car takes is 30 + 15

= 45minutes = 0.75 hours

Average speed = total distance / total time

Average speed = 70 / 0.75

= 93.34 km/h

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The inverse of the 4 × 4 matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] found using an online matrix tool  is presented as follows;

[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\begin{bmatrix}\dfrac{1}{a} & 0& 0 &0 \\\\ 0& \dfrac{1}{b} & 0 & 0\\\\0 &0 &\dfrac{1}{c} & \\\\0 &0 &0 &\dfrac{1}{d} \\\end{bmatrix}[/tex]

The inverse, A⁻¹ of a matrix, A, can be found using the formula;

[tex]A^{-1}=\dfrac{adj \, A}{det\, A}[/tex]

The adjugate of the specified matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] is found using an online tool as follows;

[tex]adj\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}=\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}[/tex]

The value of the determinant of the matrix found using an online calculator is presented as follows;

[tex]det\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix} = a\cdot b \cdot c\cdot d[/tex]

The inverse of the matrix in the question is therefore;

[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\dfrac{\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}}{a\cdot b\cdot c \cdot d} = \begin{bmatrix}\dfrac{1}{a} &0 &0 &0 \\ \\0& \dfrac{1}{b} & 0& 0 \\ \\0&0 &\dfrac{1}{c} &0 \\\\ 0& 0& 0& \dfrac{1}{b} \\\end{bmatrix}[/tex]

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The energy that an object has as a result of being in a gravitational field is known as gravitational potential energy. It may be expressed as,

U = mgh

Where, m is the object's mass, g is its gravitational field, and h is its height.

The body has a weight of 2 kg and a height of 60 cm. the gravitational potential energy is as follows:

U₁ = 60× 2×g

U₁ = 120kg

The body has a weight of 1 kg and a height of 60 cm. the gravitational potential energy is as follows:

U₂ = 60× 1×g

U₂ = 60g

A body that weighs 4 kg and measures 30 cm in height. the gravitational potential energy is as follows,

U₃ = 4 ×30× g

U₃ = 120g

A body that weighs 3 kg and measures 45 cm in height. the gravitational potential energy is as follows,

U₄ = 3×45×g

U₄ = 135g

The body  has a weight of 2 kg and a height of 30 cm. the gravitational potential energy is as follows,

U₅= 2×30× g

U₅ = 60g

A body that weighs 8 kg and measures 15 cm in height. the gravitational potential energy is as follows,

U₆ = 8 ×15×g

U₆ = 120g

Consequently, the initial gravitational potential energy of the specified pendulum has the following rank:

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24 hours takes all five machines to fill the same production order.

Given,

Four machines take 30 hours to fill a certain production order.

[tex]Rate = \frac{Work}{Time}[/tex]

Let, Total work = 1 unit

The rate of 4 machines = [tex]\frac{1}{30}[/tex]

We can let the rate of 5 machines be n and create the equation:

[tex]\frac{4}{\frac{1}{30} }=\frac{5}{n}[/tex]

[tex]120=\frac{5}{n}[/tex]

[tex]120n = 5[/tex]

[tex]n=\frac{5}{120}[/tex]

[tex]n=\frac{1}{24}[/tex]

Time taken by five machines = [tex]\frac{1}{\frac{1}{24} }[/tex]

Time is taken by five machines = 24 hours

Hence, 24 hours takes all five machines to fill the same production order.

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Answer:

16

Step-by-step explanation:

(a) The mean is 32, and the standard error is 0.068 (b) The expected shape will be approximately normal (c) The probability of scoring less than 60% is 0.278

As the number of questions (n) is 50 and the probability of getting the correct answer (p) is 0.64, the mean can be calculated as follows;

E(x) = np

E(x) = 50 × 0.64

E(x) = 32

The standard error is calculated as follows;

SE = √p×(1-p) ÷ n

SE = √0.64 × (1-0.64) ÷ 50

SE = √0.004608

SE = 0.068

Therefore, the mean is calculated to be 32, and the standard error is 0.068

As the sample size is large therefore the expected shape will be approximately normal

To calculate the probability of scoring less than 60%, we first calculate the z-score using:

z = (x – μ) / σ

z = (0.60 - 0.64) / 0.068

z = -0.588

So we have;

P (x < 60%) = P (z < -0.588)

P (x < 60%) = 0.278

Therefore the probability of scoring less than 60% is 0.278

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The minimum sample size needed is 93.

Given:

A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.

here

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

[tex]n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }[/tex]

On submitting and solving using calculator

n = 93

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The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is  4x+y-6=0.

The line's equation is expressed in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

The slope intercept form is used to calculate the y-intercept and slope of a straight line.

We know that the equation of the line is, y= mx +b

4x+y-1=0 is the same as y= -4x+1

For this equation, b=1, but for a line with slope -4 passing through the point (1,2), the y-intercept changes.

y= -4x+b

The above line is passing through the point (1, 2)

2=-4(1)+b

Now, we have to solve for b value we get b=6.

The equation that we get is,

y= -4x+6 or 4x+y-6=0.

The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is  4x+y-6=0.

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If your data contradict your hypothesis, it is by no means a failure.

Data that can be measured or gathered using some benchmark objectives, according to your experimental needs. According to the needs of your experiment, the data produced using this method should either be qualitative or quantitative.

Information not obtained through the random selection of study participants or as part of a controlled experiment. In social science research, non-experimental data are frequently employed, especially when collecting experimental data would be prohibitively expensive or immoral. Non-experimental data require more analysis and interpretation than experimental data since the researcher cannot control which people are placed in the treatment and control groups. Nonexperimental data examples include administrative files, test results, and survey data. As well, they are referred to as observational data.

If your data contradict your hypothesis, it is by no means a failure; in fact, it could be more intriguing since you might discover a fresh way to view the facts. In science, it's usual for theories to be wrong, and new investigations frequently begin as a result.

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We apply permutation formula to the number of participants considering that there are no ties and find out that there are 60 different outcomes possible if there are no ties.

It is given to us that -

There are 5 participants - Abe, Bobby, Charles, Devin, and Edwin

We have to find out the number of different 1st - 2nd - 3rd place outcomes that are possible if there are no ties.

Considering that there should be no ties,

If we select one person, say Abe, then there are 4 different ways remaining for the second place in the race.

Similarly, assuming that Abe ranked 1st in the race and Bobby ranked 2nd in the race, there are 3 different ways remaining for the third place in the race.

Continuing like this, the 5 different participants can be ranked accordingly such that there are no ties.

For this situation, we have to find the permutation where -

Total number of objects (in this case, participants) = n = 5

and, total number of objects selected = r = 3

We know that the formula for permutation is -

[tex]P = \frac{n!}{(n-r)!}\\[/tex]

Substituting the values of 'n' and 'r' in the above equation, we have

[tex]P = \frac{n!}{(n-r)!}\\= > P = \frac{5!}{(5-3)!}\\= > P = 60[/tex]

Thus, by applying permutation formula, we find out that there are 60 different outcomes possible if there are no ties.

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The quadrants that give the solution of the inequality y ≤ ²/₃x - 4 is; I, III, and IV

We are given the inequality as;

y ≤ ²/₃x - 4

Let us draft some coordinates before plotting the graph;

When x = 0;

y ≤ ²/₃(0) - 4

y ≤ -4

When x = 1;

y ≤ ²/₃(1) - 4

y ≤ -3¹/₃

When x = 2;

y ≤ ²/₃(2) - 4

y ≤ -2 ²/₃

when x = -1;

y ≤ ²/₃(-1) - 4

y ≤ -4²/₃

From the attached graph Inequality, it is clear that the shaded area which represents the quadrants that possess the solution to the inequality that;

Quadrants I, III, and IV

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The dollar interval would be ± 6.70 to present in order to obtain a probability of 0.500.

What is probability?

Probability is a branch of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of error in research by using probability.

z value for the probability of 0.5  is 0.67

standard error = sd/√n = 80/√64 =10

dollar interval = z*se

                      = 0.67*10

                       =6.70

Hence, the dollar interval would be ±6.70.

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The true Statements are : π is the area of the circle of radius 1 and π is the circumference of diameter 1.

What is Area of a Circle ?

The area of a circle is pi times the radius squared (A = π r²)

Putting r =1 ,we get

A = π×(1)² = π

What is Circumference of a Circle ?

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

C = π×D

putting D =1 , we get

C = π

Hence,  π is the area of the circle of radius 1 and π is the circumference of diameter 1.

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The number of degrees of freedom we should use is 14 for makin95% confidence interval.

Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate. It’s not quite the same as the number of items in the sample. In order to get the df for the estimate, you have to subtract 1 from the number of items.

Degree of freedom of sample size of n : n -1

When we don't have any idea about population standard deviation,

and also, the sample size is less than 30 .

We use t-distribution to calculated the statistics.

According to the question,

We are making a 95% confidence interval

The sample is 15 (<30) . So , we have to adjust and use a t-value instead of a Z score in order to account for the smaller sample size and using the sample SD.  

Note that the t-value depends on the degrees of freedom (df) as a reflection of sample size. When using the t-distribution to compute a confidence interval, df = n-1.

So , making 95% confidence interval for population mean from sample size 15 , we need degree of freedom of 14

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The sum of and diffrence identities to find the exact values of sine cosine and tangent are calculated below :

Given that,

1. 75º = 30° + 45 2. 15º = 45° - 30° 3. 105° = 60° + 450 4. 165º = 135° + 30° 5. 195º = 225º – 30° 6. 255 – 300

To find them we need to know the respective formulas:

In relation to the illustration above, the key sin,cos,tan formulas are:

sin A = Opposite side/Hypotenuse = BC/AB

cos A = Adjacent side/Hypotenuse = AC/AB

tan A = Opposite side of triangle /Adjacent side of triangle = BC/AC

1) 75°

sin(75°)= 0.966

cos(75°)=0.259

tan(75°)=3.732

2) 105°

sin(105°)=0.966

cos(105°)= -0.259

tan(105°)= -3.732

3) 175°

sin(175°)=-0.259

cos(175°)= -0.966

tan(175 )=0.268

4) 11π/12

sin(11π/12)=0.050

cos(11π/12)=0.999

tan(11π/12)=0.050

5) 17π/12

sin(17π/12)=0.078

cos(17π/12)=0.997

tan(17π/12)=0.078

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The compound inequality describes the possible lengths for the third side, x is -4< c< 14.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.

A triangle with A, B, and C vertices is symbolized by ΔABC

The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:

(a - b) < c < (a + b)

As a result, let a = 5 and b = 9

(5-9) <c (5+9)

-4< c< 14

As a result, the third side of the triangle must follow the inequality, which is -4< c <14

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Example of  linear inequalities; y ≤ x – 1 and y < –2x + 1

A combination of linear inequality equations with the same variables is referred to as a system of linear inequalities.

There are five inequality symbols used to represent equations of inequality.

These are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.

Example of  linear inequalities;

Graph the following system of linear inequalities:

y ≤ x – 1 and y < –2x + 1

Graph the first inequality y ≤ x − 1.

We will draw a solid border and shade below the line due to the "less than or equal to" mark.

On the same x-y axis, graph the second inequality, y -2x + 1.

In this instance, the less-than symbol will cause our boundaries to be dashed or dotted. Under the border, cast a shade.

As a result, the darker-colored zone extending indefinitely downward is the solution to this inequality problem, as seen below.

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Hence, the property is based on addition property,

OG=NQ and GE=UY,

so OG +GE=NQ +UY.

When the same amount is added to both sides of an equation, the equation does not change, according to the addition property of equality. A = B remains valid even if a number x is added to both sides of the equation. It can be mathematically stated as A + x = B + x.

As demonstrated below

OG=NQ and GE=UY,

so OG +GE=NQ +UY

So this property leads to addition property.

So the correct option regarding this,

Addition property.

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