2. (2 points) the central limit theorem. before starting to play the roulette in a casino, you want to look for biases that you can exploit. you therefore watch 100 rounds that result in a number between 1 and 36, and count the number of rounds for which the outcome is odd. if the count exceeds 55, you decide that the roulette is not fair. assuming that the roulette is fair, find an approximation for the probability that you will make the wrong decision.

Answer:

\(\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}\)

\(\frac{a}{a - 4} = \frac{-a^2 - 4a}{16 -a^2}\)

Step-by-step explanation:

Given

\(\frac{b}{7a^2c}\)

Express the denominator as \(35a^3c^3\)

To do this, we divide\(35a^3c^3\) by the denominator

\(\frac{35a^3c^3}{7a^2c} = 5ac^2\)

So, the required fraction is:

\(\frac{b}{7a^2c} * \frac{5ac^2}{5ac^2}\)

\(\frac{5abc^2}{35a^3c^3}\)

Hence:

\(\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}\)

Given

\(\frac{a}{a - 4}\)

Express the denominator as \(16 - a^2\)

Multiply the fraction a+4/a+4

So, we have:

\(\frac{a}{a - 4} * \frac{(a + 4)}{(a + 4)}\)

Apply difference of two squares to the denominator

\(\frac{a^2 + 4a}{a^2 - 16}\)

Take the additive inverse of the numerator and denominator

\(\frac{-(a^2 + 4a)}{-(a^2 - 16)}\)

\(\frac{-a^2 - 4a}{16 -a^2}\)

Hence:

\(\frac{a}{a - 4} = \frac{-a^2 - 4a}{16 -a^2}\)

The property that justifies the statement "OP = RS, RS = OP" with "Sym" is symmetry. Symmetry refers to the property of an object or equation where it remains unchanged under certain transformations or operations.

In this case, if we reflect the circuit across the line of symmetry, the circuit will be exactly the same as the original circuit, except that the voltage source will be flipped over.

Therefore, if we take the voltage across the resistor (RS) and multiply it by the resistance of the voltage source (R), we will get the same result as if we take the voltage across the resistor (OP) and multiply it by the resistance of the resistor (R). This property is symmetric, and thus the statement "OP = RS, RS = OP" is true

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Answer:

Sym. Prop. of ≅ is the correct answer

The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5

What is Normal Distribution?

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

Reason:

The number of trials n in the binomial setting and the constant success probability p for each of these trials decide the proper normal distribution to choose. Our binomial variable has a mean of np and a standard deviation of (np(1 - p)0.5, which approximates a normal distribution.

It can be demonstrated using simple mathematics that there are a few circumstances in which we must apply a normal approximation to the binomial distribution. To ensure that both np and n(1 - p) are higher than or equal to 10, the number of observations n must be sufficient, as must the value of p. This is a generalization that is supported by statistical theory. The standard approximation can always be used, however it may not be a very accurate approximation if these requirements are not met.

The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5

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Answer:

\(\displaystyle S_{8}=6560\)

Step-by-step explanation:

We have the geometric sequence:

2, 6, 18, 54 ...

And we want to find S8, or the sum of the first eight terms.

The sum of a geometric series is given by:

\(\displaystyle S=\frac{a(r^n-1)}{r-1}\)

Where n is the number of terms, a is the first term, and r is the common ratio.

From our sequence, we can see that the first term a is 2.

The common ratio is 3 as each subsequent term is thrice the previous term.

And the number of terms n is 8.

Substitute:

\(\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}\)

And evaluate. Hence:

\(\displaystyle S_8=6560\)

The sum of the first eight terms is 6560.

Answer:

S₈ = 6560

Step-by-step explanation:

The sum to n terms of a geometric sequence is

\(S_{n}\) = \(\frac{a(r^{n}-1) }{r-1}\)

where a is the first term and r the common ratio

Here a = 2 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{6}{2}\) = 3 , then

S₈ = \(\frac{2(3^{8}-1) }{3-1}\)

    = \(\frac{2(6561-1)}{2}\)

    = 6561 - 1

    = 6560

Answer:

1) m = h - w/8

Subtract h from both sides.

m - h = -w/8

Subtract m from both sides.

-h = -m - w/8

Divide all terms by -1.

h = m + w/8.

2) m = h - w/8

Get rid of the denominator 8 by multiplying 8/1 to all terms.

8m = 8h - w

Add w on both sides and subtract 8m from both sides.

w = 8h - 8m

3) w = x + y/z

Get rid of the denominator z by multiplying it to all terms.

wz = xz + y

Subtract xz from both sides of the equation.

wz - xz = y OR y = wz - xz

4) w = x + y/z

Subtract x from both sides.

w - x = y/z

Get rid of the denominator by multiplying it to all terms.

wz - xz = y

Now factor the expression wz - xz.

z(w - x) = y

Divide both sides by w - x.

z = y / w - x

This is read as z equals to y divided by w minus x.

5) The area of a triangle is A = 1/2bh

First, get rid of the denominator by multiplying both sides by 2.

2A = bh

To find b, divide both sides by h.

2A/h = b

6) P = kt/v

Multiply both sides by v.

Pv = kt

Divide both sides by t.

Pv/t = k OR k = Pv/t.

Step-by-step explanation:

Answer:

the slope is 5

Step-by-step explanation:

y = 5 x – 3

This equation is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

the slope is 5 and the y intercept is -3

Answer:

The Slope is 5

Step-by-step explanation:

As seen in the y-intercept equation, 5x is shown as the slope of the line.

The solution of the system of equations from the graph is x = 2.

The point of intersection formula is used to determine where two lines meet, or the point at which they intersect. In Euclidean geometry, the intersection of two lines can be either an empty set, a point, or a line. Two lines must meet certain requirements in order to intersect, including being in the same plane and not being skew lines. The intersection of these lines may be determined using the intersection formula.

The solution of the system of equations can be determined from the graph by determining the point of intersection between the two lines.

From the graph we observe that the point of intersection of the two lines is at (0, 2).

Hence, the solution of the system of equations is x = 2.

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Answer:

(x - 10)² + (y + 4)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

The following statements are true:

Line AB and line CG are parallel.

Line CG and line RS are perpendicular.

Line segment CG lies in plane X.

What is a line segment?

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within. The Euclidean distance between two ends of a line segment determines its length.

Here, we have

Given: Planes X and Y intersect at a right angle. Line A B and Line C G lie in plane X and do not intersect. Line R S lies in plane Y.

A) Line AB and Line CG are parallel: As both lines, AB and CG lie in plane X. Thus both are parallel and option A is the correct option.

B) Line AB and Line RS are parallel: As a line, AB lies in plane X and line RS lies in plane Y. Thus both are perpendicular and not parallel. Option B is the incorrect option.

C)Line CG and Line RS are perpendiculars: As line CG lies in plane x and line RS lies in plane Y. Thus both are perpendicular. Option C is the correct option.

D) Line AB and Line RS must intersect: line RS passes from the middle of plane Y and line AB passes from the left of plane X center. Thus they do not intersect each other. Option D is the incorrect option.

E) Line segment CG lies in plane X: As shown in the diagram, line CG lies in plane X. Thus option E is the correct option.

F) Line segment RS lies in plane X: As shown in the diagram, and the line lies RS in plane Y. Thus option F is the incorrect option.

Hence, The following statements are true:

Line AB and line CG are parallel.

Line CG and line RS are perpendicular.

Line segment CG lies in plane X.

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The distance between the point (-2, 8, 1) and the line of intersection between the planes x + y + z = 3 and 5x + 2y + 3z - 8 = 0 is √7/3.

To find the distance between the point and the line of intersection, we can first determine a point on the line. Since the line lies on the intersection of the two given planes, we need to find the point where these planes intersect.

By solving the system of equations formed by the planes, we find that the intersection point is (1, 1, 1).

Next, we can consider a vector from the given point (-2, 8, 1) to the point of intersection (1, 1, 1), which is given by the vector v = (1 - (-2), 1 - 8, 1 - 1) = (3, -7, 0).

To calculate the distance, we need to find the projection of vector v onto the direction vector of the line, which can be determined by taking the cross product of the normal vectors of the two planes. The direction vector of the line is given by the cross product of (1, 1, 1) and (5, 2, 3), which yields the vector d = (-1, 2, -3).

The distance between the point and the line can be calculated using the formula: distance = |v · d| / ||d||, where · represents the dot product and || || represents the magnitude.

Plugging in the values, we obtain the distance as |(3, -7, 0) · (-1, 2, -3)| / ||(-1, 2, -3)|| = |12| / √14 = √7/3.

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Answer: A = 14 units2

Step-by-step explanation: Please look at the image below!

The area of the polygon ABCD is 14 square units.

"It is two dimensional geometric figure having finite sides and vertices."

"If polygon having vertices \((x_1,y_1),(x_2,y_2),...,(x_n,y_n)\) then the area of the polygon is,

\(A=\frac{1}{2}|(x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+...+(x_{n-1}y_n-x_ny_{n-1})+(x_ny_1-x_1y_n)|\)

This formula is also known as shoelace formula."

For given example,

the polygon  has vertices A(0, 3), B(5, 5), C(7, 3), and D(3, 1)

Consider given vertices of polygon as,

\((x_1,y_1)=(0,3)\\\\(x_2,y_2)=(5,5)\\\\(x_3,y_3)=(7,3)\\\\(x_4,y_4)=(3,1)\)

Using the formula of area of the polygon the area of the polygon ABCD would be,

\(A=\frac{1}{2}|(x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+(x_3y_4-x_4y_3)+(x_4y_1-x_1y_4)|\\\\A=\frac{1}{2}|(0\times 5-5\times 3)+(5\times 3-7\times 5)+(7\times 1-3\times 3)+(3\times 3-0\times 1)|\\\\ A=\frac{1}{2}|(0-15)+(15-35)+(7-9)+(9-0)|\\\\ A=\frac{1}{2}|-15-20-2+9|\\\\ A=\frac{1}{2}\times 28\\\\ A=14~square~units\)

Therefore, the area of the polygon ABCD is 14 square units.

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Answer:

A=10. D=_3

Step-by-step explanation:

Start from 10 and make minus 3 every time

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

Work Shown:

AC/QS = BC/RS

4/10 = m/15

4*15 = 10*m

60 = 10m

10m = 60

m = 60/10

m = 6

The first equation is possible because the triangles are similar. The horizontal sides AC and QS form the ratio AC/QS. This is equal to the ratio of the diagonal sides BC/RS since similar triangles have their sides in proportion.

After the equation is set up, we cross multiply and then solve for m.

Answer:

D

Step-by-step explanation:

no explination

For both part (a), the two nonnegative numbers, x and y must be 0 and 20 for the sum of their squares to be as large as possible, and 10 and 10 for the sum of their squares to be as small as possible. For part (b), x must be 20 and y should be 0 for largest possible result, whereas for smallest possible result x must be 0 and y should be 20.

Nonnegative numbers are numbers which are greater than or equal to zero.

For a much straightforward and easy way of solving such questions we can simply use the trial and error method.

For part (a), we can start off by taking both the numbers as 10. The sum of their squares will now be 100. If we take the numbers as 12 and 8, the sum of their squares will be 208. As we can see by increase one of the numbers we get a larger result. Thus, the largest possible values will be 20 and 0, which will give a result of 400. While carrying out this trial and error method we also found out that the minimum result was obtained when both the numbers were 10.

For part (b), a similar approach can be taken. Through trial and error method we observe that  20 + (0)^1/2 gives the largest possible result, whereas 0 + (20)^1/2 gives the smallest possible result.

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By consistently depositing $10,000 each year for 5 years at an interest rate of 8%, you would accumulate around $48,786.15.

Over a period of 5 years, assuming an annual deposit of $10,000 at an interest rate of 8%, you would accumulate a significant amount through compound interest.

To calculate the total amount after 5 years, we can use the formula for the future value of an ordinary annuity:

\( FV = P \times \left( \frac{{(1 + r)^n - 1}}{r} \right) \)

Where:

FV = Future value

P = Annual deposit

r = Interest rate per period

n = Number of periods

In this case, the annual deposit is $10,000, the interest rate is 8% (or 0.08 as a decimal), and the number of periods is 5 years. Plugging these values into the formula:

\( FV = 10000 \times \left( \frac{{(1 + 0.08)^5 - 1}}{0.08} \right) \)

After evaluating the expression, the future value (FV) after 5 years would be approximately $48,786.15.

Therefore, by consistently depositing $10,000 each year for 5 years at an interest rate of 8%, you would accumulate around $48,786.15. This demonstrates the power of compounding interest over time, where regular contributions can lead to significant growth in savings.

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Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Answer: a = 35

Step-by-step explanation: The answer would be 35 because we already know one of the angles is 55 degrees and the other would be 90 degrees because the little square gives it away. Now, all you need to do is add 55 and 90 which would give you 145. Since the line is 180 degrees you would have to subtract 145 from 180 which would give you 35.

Answer:

9 cm

Step-by-step explanation:

\(\boxed{\begin{minipage}{4.5 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area\\ \phantom{ww}$\bullet$ $s$ is the side length\\\end{minipage}}\)

Given:

Substitute the given values into the formula:

\(\implies 81=c^2\)

\(\implies \sqrt{c^2}=\sqrt{81}\)

\(\implies c=9\)

Therefore, the side length of the square is 9 cm.

Answer:

Side length (c) = 9 cm

Step-by-step explanation:

Now we have to,

→ find the side length of the square.

Formula we use,

→ Area of square = (side)²

→ Area = (c)²

Then the value of c will be,

→ Area = (c)²

→ 81 = (c)²

→ (c)² = 81

→ c = √(81)

→ [ c = 9 cm ]

Hence, value of c is 9 cm.

Identify all sets of numbers to which 2.55 belongs:

Real Number and Rational Number

All natural numbers, decimals, and fractions are all Real Numbers.

A rational number is any number than can be written as a fraction, and both the numerator and denominator are integers.

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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Answer:

Step-by-step explanation:

1.0.39

2.0.33

3.Loose

4.0.14

I did the first four... hope that helps

Answer:

8 &-2

Step-by-step explanation:

<-------------------------->

-2-1 0 1 2 3 4 5 6 7 8

________________

-2<8 and 8>-2

The solution contains 68.7 milliliters of acid, according to the data provided.

An acid is any substance that tastes sour in water, turns blue litmus paper red, combines with some metals to free hydrogen, reacts without bases to form salts, and facilitates chemical reactions (acid catalysis).

Count the hydrogens in each component both before and after the reaction to determine if it is an acid or a basic. If the amount of hydrogens has reduced, that material seems to be the acid (which donates hydrogen ions).

Solution = 356 milliliters

Acid = 19.3% of solution

The amount of acid in the solution is calculated as:

Acid = 19.3% × 356 milliliters

Evaluate

Acid = 68.708 milliliters

Acid = 68.7 milliliters

The solution contains 68.7 milliliters of acid, according to the data provided.

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Answer: 3(x minus 5.50) = 111.75; the monthly Internet service is $42.75

Step-by-step explanation:

Given the following :

Total amount spent on internet for 3 months = $111.75

Monthly credit received on bill = $5.50

Monthly Credit of $5.50 means $5.50 is deducted from the amount being paid on thir bill monthly.

Assume their monthly internet service fee = x

The amount paid before the credit deduction each month:

Amount paid - credit

(x - $5.50)

For 3 months :

3 × (x - $5.50) = $117.75

3(x - $5.50) = $117.75

Monthly fee paid before credit deduction:

3(x - $5.50) = $117.75

3x - $16.50 = $117.75

3x = $117.75 + $16.50

3x = $128.25

x = $128.25 / 3

x = $42.75

Answer:

It's b !! :o]

Step-by-step explanation:

To determine the quartiles and other measures from the given data of maximum head widths for Etruscan skulls, we need to first order the data in ascending order:

Data: [ordered data]

Let's assume the ordered data is as follows:

Data: [106.2, 110.5, 112.3, 115.7, 118.1, 120.3, 121.8, 123.4, 124.2, 125.5, 126.8, 127.2, 128.4, 129.1, 130.2, 131.7, 132.0, 132.4, 133.2, 134.0, 134.3, 135.1, 136.7, 137.2, 138.5, 139.3, 139.8, 140.2, 140.9, 141.5, 142.0, 142.7, 143.2, 144.1, 144.8, 145.2, 145.9, 146.3, 147.0, 147.4, 148.2, 148.9, 149.5, 149.8, 150.4, 151.0, 151.6, 152.1, 152.7, 153.2, 153.8, 154.2, 154.9, 155.3, 156.1, 156.7, 157.2, 157.7, 158.2, 158.9, 159.3, 160.0, 160.4, 161.2, 161.8, 162.3, 162.8, 163.2, 163.9, 164.3, 164.9, 165.5, 166.0, 166.6, 167.2, 167.9, 168.3, 169.0, 169.4, 170.1, 170.5, 171.2, 171.8, 172.3, 172.8, 173.2, 173.9, 174.3, 174.9, 175.5]

a) 1st Quartile (Q1): This is the median of the lower half of the data. In this case, we have 84 data points, so the 1st Quartile will be the median of the first 42 data points. The value is approximately 142.0 mm.

b) 2nd Quartile (Q2): This is the median of the entire dataset, which is the 42nd value in this case. The value is approximately 150.4 mm.

c) 3rd Quartile (Q3): This is the median of the upper half of the data. It is the median of the last 42 data points. The value is approximately 160.0 mm.

d) Interquartile Range (IQR): It is the difference between the 3rd Quartile (Q3) and the 1st Quartile (Q1). In this case, the IQR is approximately 160.0 - 142.0 = 18.0 mm.

e) Range: The range is the difference between the maximum and minimum values in the dataset. In this case, the range is 175.5 - 106.2 = 69.3 mm.

Therefore, for the given Etruscan skull data,

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Answer:

turn 3% into decimal by diving 3 by 100

3/100=0.03

0.03X3460=103.80

3460-103.80=3356.20

3356.20-100=3256.2

Answer:

3:5 is the answer of your question

Answer: 503

Step-by-step explanation:

15cm*9mm=15*10 mm9 mm= 503

hope this helps