how many radians in a circle

The approximate probability that out of 1000 poker hands there will be at least 450 with a single pair is 0.035

This is a binomial distribution problem with n = 1000 and p = 0.42. Let X be the number of poker hands with a single pair out of 1000 poker hands.

To find the probability that there are at least 450 poker hands with a single pair, we need to calculate P(X ≥ 450).

Using the normal approximation to the binomial distribution, we have:

μ = np = 1000 × 0.42 = 420

σ = √(np(1-p)) = √(1000 × 0.42 × 0.58) ≈ 16.08

Using the continuity correction, we can approximate P(X ≥ 450) as P(Z ≥ (449.5 - 420)/16.08) where Z is the standard normal distribution.

P(Z ≥ (449.5 - 420)/16.08) = P(Z ≥ 1.814) ≈ 0.035

Therefore, the approximate probability that out of 1000 poker hands there will be at least 450 with a single pair is 0.035.

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In mathematics, the term "orthogonal" refers to a relationship between two objects where they are perpendicular or at right angles to each other.

More generally, it refers to a relationship where two objects are independent or uncorrelated with each other. For example, in Euclidean geometry, two lines are orthogonal if they meet at a right angle. In linear algebra, two vectors are said to be orthogonal if their dot product (also known as inner product) is zero. Similarly, in statistics, two variables are said to be orthogonal if they have a correlation coefficient of zero, indicating that they are uncorrelated.

The term "orthogonal" is also used in various other fields, such as signal processing, computer science, and quantum mechanics, with similar meanings of independence, uncorrelatedness, or perpendicularity.

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1. The Complete table is shown below.

2. The graph likes like parabola whose equation is y= 50x - x².

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

Given:

Length  Width  Area

10            40      400

20             30      600

25             25       625

35             15        525

40              10       400

So, x+ y= 50

y= 50- x

so, area of figure is

= x (50- x)

= 50x - x²

So, we get parabola which is opened downward.

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Kilometers per hour (km/h) and miles per hour (mph) are both units of speed used to measure how fast something is moving.

Kilometers per hour are the standard unit of speed used in most countries that use the metric system, while miles per hour is more commonly used in the United States and other countries that use the imperial system.

To convert km/h to mph, you can multiply the speed in kilometers per hour by 0.621371. This conversion factor is based on the fact that one mile is equivalent to 1.60934 kilometers. Converting between these two units is a common task when traveling, driving, or using fitness trackers or GPS devices.

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Let's call the smaller number "x" and the larger number "y".

We know that:

y + x = 26 (since the total of the two numbers is 26)

and

y = 10 + 3x (since the larger number is 10 more than triple the smaller number)

We can substitute the second equation into the first equation to get:

(10 + 3x) + x = 26

Simplifying, we get:

4x + 10 = 26

Subtracting 10 from both sides, we get:

4x = 16

Dividing both sides by 4, we get:

x = 4

Now that we know x is 4, we can use the second equation to find y:

y = 10 + 3x

y = 10 + 3(4)

y = 22

Therefore, the two numbers are 4 and 22.

Answer:

∠S possibility is 65 degrees and 115 degrees

Step-by-step explanation:

∠S + ∠T + ∠U = 180

Substituting the given values, we get:

∠S + ∠T + 79 = 180

Simplifying, we get:

∠S + ∠T = 101

We also know that the sides of a triangle are related to the angles opposite them by the law of sines:

a/sin A = b/sin B = c/sin C

In this case, we can use the following ratio:

ST/sin S = UT/sin U

Substituting the given values, we get:

ST/sin S = UT/sin 79

ST = s = 56 cm

UT = u = 94 cm

Solving for sin S, we get:

sin S = (ST × sin 79) / UT

sin S = (56 × sin 79) / 94

sin S ≈ 0.906

Taking the inverse sine, we get:

∠S ≈ 65 degrees or ∠S ≈ 115 degrees

Therefore, the possible values of ∠S are approximately 65 degrees and 115 degrees, to the nearest degree.

The black bear population at that national park in 25 years would be 2973 approx, according to the considered model.

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

According to the model, the relationship between the elapsed time t, in years, since the beginning of the study, and the black bear population B(t) is:

B(t) = 2500 * 2^0.01t

Here, if we take t = 25 years elapsed, the value of B(t) comes out as:

B(25) = 2500 * 2^0.01*25

B(25) = 2973

Thus, the black bear population be at that national park in 25 years would be 2973 approx, according to the considered model.

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Answer:

B(25) = 2500 * 2^0.01*25

B(25) = 2973

Step-by-step explanation:

Approximately 50% of the values in a distribution lie between the 25th percentile and the 75th percentile.

The interquartile range (IQR) is the range between the 25th percentile (Q1) and the 75th percentile (Q3) of a distribution. The IQR contains the middle 50% of the data.

Therefore, approximately 50% of the values in a distribution lie outside the IQR, with 25% of the values below Q1 and 25% of the values above Q3. The remaining 50% of the values lie within the IQR, with approximately 25% of the values between Q1 and the median, and 25% of the values between the median and Q3.

So, approximately 50% of the values in a distribution lie outside the IQR, and approximately 50% of the values lie within the IQR, which includes the values between the 25th and 75th percentile.

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A left-skewed histogram is a frequency distribution in which the data is concentrated towards the right side of the histogram, with a tail stretching towards the left.

A left-skewed histogram is a kind of frequency distribution where the data is concentrated towards the right side of the histogram, with a tail extending towards the left. It is otherwise called a negatively skewed histogram or a left-tailed histogram. In a left-skewed histogram, the mean is not exactly in the middle, demonstrating that the information is slanted toward the lower end of the conveyance. This can happen when the information has a lower bound or a base worth, which makes the tail of the dispersion be pulled towards the left. Left-skewed histograms can be helpful in examining information that has a characteristic lower cutoff or floor, for example, response times, reaction rates, or pay levels.

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Using the inequality 38+4x≤61 shown to represent the situation, based on the solution that x ≤ 5.75, the true statement is A. Sam went on at most 5 rides.

Inequality is an algebraic statement showing that two or more mathematical expressions are unequal.

Inequalities are represented as:

The total amount Sam has to spend at the amusement park = $61

The entrance fee = $20

The unit cost of a game = $3

The unit cost of a ride = $4

The total number of games Sam plays = 6

The amount spent on games = $18 ($3 x 6)

The total known cost = $38 ($20 + $18)

Let the number of rides Sam goes on = x

38 + 4x ≤ 61

Thus, the correct statement about the inequality is Option A.

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Answer:

5.90551 inches

Step-by-step explanation:

To solve for the number of inches, we can use this equation:

15 × 0.393701 = 5.90551

Therefore, for every 15 cm, it is equivalent to 5.90551 inches.

The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.

A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.

2/5 = (2 × 2) / (5 × 2) = 4/10

Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.

The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.

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Solving the equation explicitly for y and differentiating we get y' = -1/(x - 1)²

Differerentiation is the process of finding the derivative of a function.

Since we have the equation 1/x + 1/y = 1, to solve explicitly for y, we make y subject of the formula.

So, 1/x + 1/y = 1

1/y = 1 - 1/x

y = 1/(1 - 1/x)

To find y', we differentiate y with respect to x.

So, y' = dy/dx

= d[1/(1 - 1/x)]/dx

Let u = 1 - 1/x  

So,y' = d(1/u)/dx

= d(1/u)/du × du/dx

Now,

So, substituting these into dy/dx, we have that

y' = = d(1/u)/du × du/dx

= -1/u² × 1/x²

= -1/(ux)²

= -1/[(1 - 1/x)x]²

= -1/(x - 1)²

So, y' = -1/(x - 1)²

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After converting 6.25% into fraction we get 16/256 or 1/16.

The percentage means divied by hundred.

A fraction consists of two parts one is the numerator and other is denominator.

Where the number which is written in upper most part of the line is called numerator, and the number bottom most part of the line is called denominator.

To convert a percentage into a fraction divide the percentage by 100,

And simplify the resulting fraction.

So,

To convert 6.25% to a fraction,

We divide 6.25 by 100:

6.25% ÷ 100 = 0.0625

Divide by 0.0625

0.0625 ÷ 0.0625 = 1

1 ÷ 0.0625 = 16

Therefore,  After simplification 6.25% is equal to 16/256 or 1/16.

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The correct option is A: A linear pair is two adjacent, supplementary angles.

Supplementary angles are a pair of angles whose measures add up to 180 degrees. In other words, if we place two angles side by side, and their measures add up to 180 degrees, then they are said to be supplementary.

For example, if we have an angle with a measure of 120 degrees, then its supplementary angle would have a measure of 60 degrees, since 120 + 60 = 180. It's important to note that the two angles in a pair of supplementary angles do not have to be adjacent, meaning they can be located anywhere in a figure, as long as their measures add up to 180 degrees.

Supplementary angles play an important role in geometry and mathematics, especially when it comes to solving problems involving angles. For instance, if we know that two angles are supplementary, and we know the measure of one of the angles, we can easily calculate the measure of the other angle by subtracting the known measure from 180 degrees.

In addition, supplementary angles are often used in real-life situations, such as when designing buildings, bridges, or other structures that require precise measurements of angles. Overall, understanding the concept of supplementary angles is crucial for anyone who wants to study and understand geometry and mathematics.

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The community developed the 8 Values Test to assess a person's political position in light of eight essential political tenets. I am standing at 5 in the 8 value test.

The "8 values test" is a political assessment tool that compares and contrasts eight political philosophies: capitalism vs. socialism, traditionalism vs. progressivism, nationalism vs. globalism, libertarianism vs. authoritarianism, democracy vs. elitism, pacifism vs. militarism, ecology vs. production, and decentralization vs. centralization.

The exam generates a political compass based on their responses and presents them on a graph.

The 8 Values Political Test is distributed under the terms of the MIT License.

The 8 Values Political Test is not interchangeable with the Political Compass Test, a registered trademark of Pace News Ltd, or the Political Coordinates Test, a creation of IDRlabs.

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Right triangle side lengths can be achieved in a few different ways. You can utilise various relationships or laws to discover the remaining side depending on what is offered.

Presented with two sides

The simplest way is to use the Trigonometry if you are aware of two additional right triangle sides:

a² + b² = c²

If leg an is the omitted side, change the equation such that an is still on one corner and compute the scale factor of that number:

a = √(c² - b²)

Leg b is equal to (c2 - a2) if foot b is unknown.

The formula for a deficient hypotenuse is c = (a2 + b2).

A right triangle has one symmetry boundary line if it is isosceles, meaning that its two different sides have an identical length. Otherwise, the triangle won't have any symmetries lines.

However, not all right-angled triangles are identical. If all of their angles have the same length as well as the relation of two among their angles is the same, then they are similar.

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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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The mean weight of a randomly chosen vehicle is 3500 pounds.

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean.

We are given that the weight of a randomly chosen american passenger car is a uniformly distributed random variable ranging from 1,749 pounds to 4,039 pounds.

Let X= weight of the passenger car

a/q, X is u(1,749, 4,039)

we know that mean= a+b/2

so a=1,749, b=4,039

hence, mean=1,749 +4,039/2

mean=3500 pounds

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Answer: in two years you'll have 686.94

At the end of the fourth minute, the point 'g' would be at the position of 9605961 on the line segment TS.

As per the question, at the end of the first minute,  g covers 1/100th of the remaining segment, which is 1/100 × 10000000 = 100000 units. Therefore, the position of point g would be at 10000000 - 100000 = 9900000 at the end of first minute.

At the end of second minute, g covers another 1/100th of the remaining segment, which is 1/100 × 9900000 = 99000 units. So, the position of point g would be now 9900000 - 99000 = 9801000.

On the third minute's end ,  g would covers another 1/100th of the remaining segment, which is 1/100 × 9801000 = 98010 units. Therefore, the position of point g would be at 9801000 - 98010 = 9702990.

For fourth minute's end, point g covers another 1/100th of the next remaining segment, which is 1/100 × 9702990 = 97029 units. Therefore, the final position of point g would be at 9702990 - 97029 = 9605961 units.

Therefore, at the end of the fourth minute, point g would be finally at the position of 9605961 on the line segment TS.

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The correct question is :

imagine a line segment ts of length 10000000 and point g moving from t=10000000 toward s=0, so that it cuts 1/100th of the remaining segment each minute. For example, at the the end of first minute g1 is at 99,00,000. Where is g at the end of fouth minute (g4) ?

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Answer: you

Step-by-step explanation:

Answer:

Step-by-step explanation:

Try putting it in Y= in the calculator

1) All the angles are,

∠ 1 = 72°

∠ 2 = 54°

∠ 3 = 54°

∠ 4 = 72°

2) All the angles are,

∠1 = 59°

∠2 = 90°

∠3 = 90°

∠ 4 = 31°

3) All the angles are,

∠ 1 = 22°

∠ 2 = 68°

∠ 3 = 68°

∠ 4 = 90° (right angle)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

1) From first figure,

⇒ ∠ 3 = 54°   (Two sides are equal hence two angles are also equal)

Hence, We get;

∠3 + ∠4 + 54° = 180°

54° + ∠4 + 54° = 180

∠4 = 180 - 108

∠4 = 72°

Hence, We get;

∠ 1 = ∠ 4

∠ 1 = 72°

And, ∠2 = ∠3 = 54°

2) From second figure,

∠ 4 = 90 - 59°

      = 31°

And, We have;

∠1 = 59°

And, Diagonal bisect each other.

Hence,

∠ 2 = ∠ 3 = 90°

3) From third figure,

∠ 2 = 68°

Hence, 2 ∠ 1 = 180 - 136°

2 ∠ 1 = 44°

∠ 1 = 22°

And, We have;

Since, ∠ 2 = 68°

Hence, ∠ 3 = 68°

And. ∠ 4 = 90° (right angle)

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The two angles in the ratio of 5:18 are 50° and 130° respectively. To determine this, we can use the fact that the sum of the angles in any quadrilateral is 360°.

Therefore,

where x and y are the two angles in the ratio of 5:18.

We can then solve for x and y by setting up the proportion

and then solving for x and y.

This gives us

Therefore, the two angles in the ratio of 5:18 are 50° and 130°.

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a) With V=0 at infinity, what is the electric potential at corner A  is -5.07 μC and corner B is = +2.48 μC.

b) The amount of work is required to move a charge from B to A along a diagonal of the rectangle is -2.59 μC.

c) Yes, this work increase the electric potential energy of the three-charge system inside the rectangle but not on a diagonal and outside the rectangle.

The electric potential at a point in a rectangle can be calculated using the electric potential equation. In the given figure, we have a rectangle with sides of length 4.34 cm and 18.5 cm, with charges q1 = -5.07 μC and q2 = +2.48 μC.

=> -5.07 + 2.48 = -2.59

To find the electric potential at corner A and corner B, we must first calculate the electric field from the two charges.

If V=0 at infinity, then the electric potential at corner A and corner B can be calculated using the electric potential equation given by V = ∫E⋅dr.

The amount of work required to move the same charge q3 from point B to point A along a path that is inside the rectangle but not on a diagonal and outside the rectangle will be different.

This is because the path of the charge will determine the electric field and electric potential at each point.

If the path is longer and passes through areas of higher electric potential, then more work will be required to move the charge

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