How to find probability if 33% of jewels are rubies. if 3 are randomly chosen what is the probability that exactly one is a ruby?

If θ = 1π/6 then six trigonometric functions of θ are: sec(θ), cos(θ), tan(θ), cot(θ), is  \(((2 \sqrt{(3)})\), \(\sqrt(3)/2\), \(\sqrt{(3)}/3\), and \(\sqrt{(3)\), respectively.

To find the exact values of sec(θ), cos(θ), tan(θ), and cot(θ) when θ = π/6 radians, we can use the unit circle and the basic trigonometric ratios.

First, we locate the point on the unit circle corresponding to θ = π/6, which has coordinates\((\sqrt{(3)}/2, 1/2).\)

Then, we can use the definitions of the trigonometric ratios to calculate their exact values:

sec(θ) = 1/cos(θ) = \(2\sqrt3 = (2 \sqrt{(3)})\)

cos(θ) = adjacent/hypotenuse =\(\sqrt{(3)}/2\)

 tan(θ) = opposite/adjacent = \(\sqrt{(3)}/3\)

 cot(θ) = adjacent/opposite = \(\sqrt(3)\)

Therefore, the exact values of sec(θ), cos(θ), tan(θ), and cot(θ) when θ = π/6 are \(((2 \sqrt{(3)})\), \(\sqrt(3)/2\), \(\sqrt{(3)}/3\), and \(\sqrt{(3)\), respectively.

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The area of the octagon is 7/2

To determine the area of the octagon, we need to know that;

From the information given, we have that;

If the corner cut has length 1, then each corner triangle has legs of length   \(\frac{1}{\sqrt{2} }\)

Then, the area would be;

1/2 × 1/√2 × 1/√2 = 1/4

The original square then has side lengths is:

1/√2 + 1/√2 + 1/√2

Add the values

= 3/√2

Total area = (3/√2)²

Expand the bracket

= 9/2

Then subtract the triangles' areas from the square's area to get the octagon's area, we have;

9/2 -  1

Find the lowest common multiply

9 - 2/2

7/2

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The complete question:

An equiangular octagon has four sides of length $1$ and four sides of length $\frac{\sqrt{2}}{2}$, arranged so that no two consecutive sides have the same length. What is the area of the octagon

Answer:

16.85 cm²

Step-by-step explanation:

Find the area of the small circle then subtract the area of the large circle by the small circle

Area of small circle :

πr², where  r = 4cm

π(4²) = 50.27 cm²

67.12 - 50.27 = 16.85 cm²

Katy's house is about 8.1 miles from Camilla's house, measured in a straight line.

we apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

H^2 = west distance^2 + north distance^2

H^2 = 4.6^2 + 6.7^2

H^2 = 21.16 + 44.89

He^2 = 66.05

We take the square root of both sides, we get:

hypotenuse = 8.13

We then can say that  Katy's house is about 8.1 miles from Camilla's house, measured in a straight line.

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Answer:

The domain is all x-values or inputs of a function. hope this helps!

Step-by-step explanation:

(a) To determine whether the number √7 - 5 is constructible, we need to check if it can be obtained using a finite number of operations involving only straightedge and compass.

The square root of 7 is not a rational number, which means it cannot be constructed exactly using straightedge and compass. However, it is possible to construct an approximation of √7 using geometric constructions.

The number 5 is a constructible real number, as it can be obtained by drawing a line segment of length 5 units.

The operation of subtraction is allowed in geometric constructions, so we can construct the number √7 - 5 by subtracting the length of √7 from the length of 5.

Therefore, the number √7 - 5 is constructible.

(b) The number 11 + √13 is also constructible. The number 11 is a constructible real number, and the square root of 13 can be approximated using geometric constructions.

We can construct the number √13 by drawing a line segment of length √13 units.

The operation of addition is allowed in geometric constructions, so we can add the length of √13 to the length of 11.

Therefore, the number 11 + √13 is constructible.

In summary, both (a) √7 - 5 and (b) 11 + √13 are constructible real numbers.

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Answer:

$400

..................

To calculate the margin of error needed to create a 90% confidence interval for the mean, we need to consider the standard deviation, sample size, and the desired confidence level.

The formula to calculate the margin of error is:

Margin of Error = Critical Value * (Standard Deviation / √(Sample Size))

The critical value corresponds to the desired confidence level and is obtained from the standard normal distribution or t-distribution based on the sample size and whether the population standard deviation is known or unknown.

If the population standard deviation (σ) is known, we use the standard normal distribution and the critical value is obtained from the Z-table for the desired confidence level.

If the population standard deviation (σ) is unknown, we use the t-distribution and the critical value is obtained from the t-table for the desired confidence level and degrees of freedom (sample size minus one).

Once we have the critical value, standard deviation, and sample size, we can calculate the margin of error using the formula mentioned above.

Note: Since you haven't provided specific data or the sample size, I cannot calculate the exact margin of error. However, with the appropriate values, you can follow the steps outlined above to determine the margin of error for a 90% confidence interval for the mean.

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To calculate the margin of error needed to create a 90% confidence interval for the mean, we need to know the sample size (n), the standard deviation (σ), and the critical value corresponding to a 90% confidence level.

The formula for the margin of error is given by:

Margin of Error = Critical Value * Standard Error

The critical value for a 90% confidence level depends on the distribution of the sample. If we assume a normal distribution, the critical value is approximately 1.645.

The standard error is calculated as the standard deviation divided by the square root of the sample size:

Standard Error = σ / √n

By substituting the appropriate values into the formula, we can calculate the margin of error. However, without specific values for the sample size and standard deviation, it is not possible to provide the exact margin of error.

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The probability of two or more events happening simultaneously is 0.36.

The probability of two or more events happening simultaneously depends on the number of events and the type of relationship between them. If the events are independent, meaning that the occurrence of one event does not affect the probability of the other event happening.

The probability of two or more events happening simultaneously can be calculated using the formula for the sum of probabilities:

P(A or B) = P(A) + P(B) - P(A and B)

Where A and B are two events. If we have n independent events with the same probability of 20%, the probability of two or more events happening simultaneously can be calculated as follows:

P = 1 - P(none of them happen) = 1 - (1 - 0.2)ⁿ

For n = 2, we have:

P = 1 - (1 - 0.2)² = 1 - 0.64 = 0.36

So, the chance that two events with a 20% probability will happen simultaneously is 36%. The chance for three or more events is even higher.

It's important to note that if the events are dependent, the calculation will be different. The relationship between the events can significantly impact the final probability.

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The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

Answer:

\(\frac{7x}{8}-\frac{1}{40}\)

Step-by-step explanation:

\((\frac{3x}{4}-\frac{5}{8})+(\frac{x}{8}+\frac{3}{5})\)

By combining the like terms,

= \((\frac{3x}{4}+\frac{x}{8})+(\frac{3}{5}-\frac{5}{8})\)

= \((\frac{6x}{8}+\frac{x}{8})+(\frac{3}{5}\times \frac{8}{8}-\frac{5}{8}\times \frac{5}{5} )\)

= \(\frac{7x}{8}+(\frac{24}{40}-\frac{25}{40})\)

= \(\frac{7x}{8}-\frac{1}{40}\)

Therefore, by solving the given expression we find the answer as \(\frac{7x}{8}-\frac{1}{40}\).

Answer:

\(k<1, k>5\)

Step-by-step explanation:

\(3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5\)

Answer:

  yes

Step-by-step explanation:

You want to know if the quadrilateral can be proven to be a parallelogram if opposite angles are congruent.

The angles of a quadrilateral have a sum of 360°. If there are two pairs of congruent angles, the sum of angles of each pair must be 180°. If adjacent angles are supplementary, then opposite sides are parallel. A quadrilateral with opposite sides parallel is a parallelogram.

Yes, the figure can be proven to be a parallelogram.

Linear regression is a technique used in statistics and machine learning to understand the relationship between two variables and how one affects the other.

In this case, we are interested in understanding the relationship between sales and seasonality. We can use linear regression to create a model that predicts sales based on seasonality. Here's how we can do it First, let's plot the data to see if there is a relationship between sales and seasonality.

We can see that there is a clear pattern that repeats every year. This indicates that there is a strong relationship between sales and seasonality. We can use the following equation: y = mx + b, where y is the dependent variable (sales), x is the independent variable (seasonality), m is the slope of the line, and b is the intercept of the line.

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Answer:

600045

Step-by-step explanation:

Answer:

Hmm the answer might be 600045

Step-by-step explanation:

So what you do is that you add them up using your calculator or brain.

Answer:

Hi,

Step-by-step explanation:

\((fog)(x)=g(f(x))=g(3x+2)=(3x+2)^2+1=9x^2+6x+5\)

Answer:

hi

Step-by-step explanation:

The series ∑[n=1 to ∞] \(8e^n\) / (3n(n+1)) is convergent.

To determine whether the series ∑[n=1 to ∞] \(8e^n\) / (3n(n+1)) is convergent or divergent, we can apply the ratio test.

Using the ratio test, we calculate the limit as n approaches infinity of the absolute value of the ratio of the (n+1)-th term to the n-th term:

lim(n→∞) |\((8e^(^n^+^1^) / (3(n+1)(n+2))) / (8e^n / (3n(n+1)))\)|

Simplifying the expression:

lim(n→∞) |\((8e^(^n^+^1^) * 3n(n+1)) / (8e^n * 3(n+1)(n+2))\)|

The common factors cancel out:

lim(n→∞) |e * n / (n+2)|

As n approaches infinity, the ratio tends to e, which is a finite non-zero value.

Since the ratio is a constant (e), which is less than 1, the series is convergent by the ratio test.

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The value of the angle x of the given pentagon is: x = 36°

The formula to find the interior angle of a regular polygon is:

θ = 180(n - 2)/n

where n is number of sides of polygon

In this case we have a pentagon which has 5 sides. Thus:

θ = 180(5 - 2)/5

θ = 540/5

θ = 108°

Now, the sides of the pentagon are equal and as such the triangle formed ΔBDC is an Isosceles triangle where:

∠BDC = ∠DBC

Thus:

x = (180 - 108)/2

x = 72/2

x = 36°

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Answer:

i believe so

Step-by-step explanation:

Answer:

To be honest I don't understand this question

Answer:

3367.11 cm³ ≈ 3240 cm³

Step-by-step explanation:

Volume = Area hexagon x height

Area hexagon = 374.12

374.12 x 9 = 3367.08 ≈ 3367.11 ≈ 3240

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The average time it takes to rent a video tape is 0.141 minutes.

Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.

Thus, the average time it takes to rent a video tape is 0.141 minutes.

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The particular solution satisfying the initial conditions is y(t) = (1/2)*cos(2t) - (1/8)*sin(2t) + (1/4)t - 1/2 and the graph has been plotted.

The given differential equation is y′′ + 4y = (t − ) − (t − 2). To solve this equation, we will first find the general solution to the homogeneous part, y′′ + 4y = 0, and then find a particular solution to the non-homogeneous part, (t − ) − (t − 2).

The characteristic equation for the homogeneous part is obtained by assuming the solution is of the form. Substituting this into the equation, we get r² + 4 = 0. Solving this quadratic equation, we find two complex roots: r = ±2i. Therefore, the general solution to the homogeneous part is y_h(t) = c₁cos(2t) + c₂sin(2t), where c₁ and c₂ are arbitrary constants.

To find a particular solution to the non-homogeneous part, we will use the method of undetermined coefficients. Since the non-homogeneous part contains terms (t − ) and (t − 2), we assume a particular solution of the form y_p(t) = At + B, where A and B are constants to be determined.

Taking the derivatives, we have y′_p(t) = A and y′′_p(t) = 0. Substituting these into the differential equation, we get 0 + 4(At + B) = (t − ) − (t − 2). Equating the coefficients of the like terms on both sides, we get 4A = 1 and 4B = -2.

Solving these equations, we find A = 1/4 and B = -1/2. Thus, the particular solution is y_p(t) = (1/4)t - 1/2.

The general solution to the original differential equation is given by the sum of the homogeneous and particular solutions: y(t) = y_h(t) + y_p(t).

y(t) = c₁cos(2t) + c₂sin(2t) + (1/4)t - 1/2.

We are given the initial conditions y(0) = 0 and y′(0) = 0.

Substituting these values into the general solution, we get:

y(0) = c₁cos(0) + c₂sin(0) + (1/4)*0 - 1/2 = 0.

This equation simplifies to c₁ - 1/2 = 0, which gives c₁ = 1/2.

Differentiating the general solution with respect to t, we get:

y′(t) = -2c₁sin(2t) + 2c₂cos(2t) + 1/4.

Substituting t = 0 and y′(0) = 0 into the above equation, we have:

y′(0) = -2c₁sin(0) + 2c₂cos(0) + 1/4 = 0.

This equation simplifies to 2c₂ + 1/4 = 0, which gives c₂ = -1/8.

Therefore, the particular solution satisfying the initial conditions is:

y(t) = (1/2)*cos(2t) - (1/8)*sin(2t) + (1/4)t - 1/2.

The graph will show how the solution varies with the input value t. It will illustrate the oscillatory nature of the cosine and sine functions, along with the linear term (1/4)t, which represents a gradual increase. The initial condition y(0) = 0 ensures that the graph passes through the origin, and y′(0) = 0 implies the absence of an initial velocity.

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Answer:

$299

Step-by-step explanation:

\((\frac{207}{9} )(13)=\frac{2691}{9}}} =299\)

Hope this helps

Let's solve for v.

v=−7i+11

Answer:v=−7i+11

Step-by-step explanation: Hope you understand. Hope this help :)

Let's simplify step-by-step.

11i+7j

There are no like terms.

Answer:=11i+7j

Answer:

42.50 ÷ 8.50 = p

Step-by-step explanation:

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The correct option is for the value of c,  such that f(c) is the average value of the function on the interval [0, 2], is D.

The average value of a function on an interval [a, b] is given by:

R = (f(b) - f(a))/(b - a)

Here the interval is [0, 2], then:

f(2) = √(2 + 2) = 2

f(0) = √(0 + 2) = √2

Then here we need to solve the equation:

√(c + 2) = (f(2) - f(0))/(2 - 0)

√(c + 2) = (2 + √2)/2

Solving this for c, we will get:

c = [ (2 + √2)/2]² - 2

c = 0.9

Them tjhe correct option is D.

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