Let X and Y be discrete random variables with finite sample spaces {x1,...,xK} and {y1,...,yK], and let pij = [X = xi and Y = Yj]. Use the definition of E[], V ar(), and summation notation , to show E[aX + bY + c] = aE[X] + bE[Y] + c Var(aX + bY + c) = aVar(X) + 2abCov(X, Y) + b2 Var(Y) If X and Y are independent, then E[X]y = y] = E [X], for any y.

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Answer:

2

Step-by-step explanation:

The question is asking what the value of f(x), or y, is when x equals -2.

When x = -2, y = 2. Therefore, f(-2) = 2.

Answer:

d=7.4

d= =square 1.

Step-by-step explanation:

Answer:

7.4 meters

Step-by-step explanation:

Solve for the radius:

\(A=\pi r^2\)

\(42.71=\pi r^2\)

\(\frac{42.71}{\pi}=r^2\)

\(\sqrt{\frac{42.71}{\pi}}=r\)

Solve for the diameter:

\(d=2r\)

\(d=2\sqrt{\frac{42.71}{\pi}}\)

\(d\approx7.4\)

Therefore, the diameter of the circle is about 7.4 meters

expression: 20 - n

numbers of balloons left = total balloons - popped balloons

numbers of balloons left = 20 - n

Answer:

20 - n balloons remained

Explanation:

Finding how much balloons remained:

20 - n balloons remained.

The function g(x) that satisfies the given PDF of Y is g(x) = Y = 3x².

To find the function g(x), we need to use the transformation method. We know that Y = g(X), so we can use the following formula:

fY(y) = fX(x) * |dx/dy|

where fX(x) is the PDF of X, and |dx/dy| is the absolute value of the derivative of g(x) with respect to y.

In this case, X is a uniform random variable with parameters 0 and 1, so its PDF is:

fX(x) = 1 for 0 <= x <= 1, 0 otherwise.

Now we need to find g(x) such that fY(y) = 3y² for 0 <= y <= 1, 0 otherwise. Let's set g(x) = Y = 3x².

Then, we can find the derivative of g(x) with respect to y:

dy/dx = 6x

|dx/dy| = 1/|dy/dx| = 1/6x

Now we can substitute fX(x) and |dx/dy| into the formula:

fY(y) = fX(x) * |dx/dy|
fY(y) = 1 * 1/6x
fY(y) = 1/6(√y)

We can see that this matches the desired PDF of Y, which is 3y² for 0 <= y <= 1, 0 otherwise.

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Answer:

The length will be multiplied by 2.

Step-by-step explanation:

By looking at the first and third ratio, we know that the no. of birck have been multiplied by 2 and the length has also been multiplied by 2 .

So when the number of bricks is multiplied by 2, the length is multiplied by 2

Answer:

Step-by-step explanation:

Using the table we observe the points

The number of bricks doubled

The length is doubled accordingly

So the answer is 2

By using binomial distribution, it can be calculated that

a)  If 9 men are randomly selected for a study of traffic signal perceptions, the probability that between 2 and 4 inclusive of them have this type of color blindness is 0.1907

b) Mean number that are color blind = 16.2

c)  Standard deviation of the number that are color blind = 3.8395

d)  27 is a significantly high number that would perhaps suggest that the given percentage of men that are color blind (i.e., 9%) is not correct.

What is Binomial Distribution?

Binomial distribution is a discrete probability distribution whose Probability mass function is given by

P(X = x) = \({n \choose x} p^x q^{n-x}\), where p is the probability of success and q is the probability of failure

a)P(X = 2) = \({9 \choose 2}(0.09)^2(1 - 0.09)^7=0.1507\)

P(X = 3) =  \({9 \choose 3}(0.09)^3(1 - 0.09)^6=0.0348\\\)

P(X = 4) = \({9 \choose 4}(0.09)^4(1 - 0.09)^5=0.0052\)

Total probability = 0.1507 + 0.0348 + 0.0052 = 0.1907

b) n = 180

Mean number that are color blind = 180 \(\times\) 0.09 = 16.2

c)  Standard deviation of the number that are color blind = \(\sqrt{180 \times 0.09 \times 0.91} = 3.8395\)

d) Let us calculate \(16.2 \pm 2 \times 3.8395\)

16.2 + 2 \(\times\) 3.8395 = 23.88
16.2 -  2 \(\times\) 3.8395 = 8.52

27 does not lie in the interval (8.52, 23.88)

So, 27 is a significantly high number that would perhaps suggest that the given percentage of men that are color blind (i.e., 9%) is not correct.

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Answer:

420 is the answer

Step-by-step explanation:

15/2 * 56L =

l = 15/2 = 7.5

7.5 * 56 = 420

Answer:

420

Step-by-step explanation:

Attached below

The threshold price F * for insurance is F * = c1c2. If F >F *, it would not be rational for Nick to purchase insurance. If F < F *, it would be rational for Nick to purchase insurance as it provides a net benefit.

To find the threshold price F *  for insurance where Nick is indifferent over buying insurance, we need to determine the point at which Nick's expected utility is the same whether he purchases insurance or not.

Let's consider the two scenarios:

1. No insurance purchased (F' = 0):
In this case, if Nick consumes c1 chocolate bars in period 1 and c2 chocolate bars in period 2, his utility function becomes U(c1;c2;0) = c1c2.

2. Insurance purchased (F' = F):
If Nick purchases insurance by paying F upfront, his utility function becomes U(c1;c2;F) = c1c2 - F.

Now, let's find the threshold price F * by comparing the expected utilities for both scenarios:

1. No insurance:
The expected utility without insurance is the utility multiplied by the probability of not having his chocolate stolen (1 - 0.25 = 0.75):
E(U(c1;c2;0)) = 0.75 * (c1c2)

2. Insurance:
The expected utility with insurance is the utility multiplied by the probability of not having his chocolate stolen, minus the cost of insurance (F), multiplied by the probability of having his chocolate stolen (0.25):
E(U(c1;c2;F)) = 0.75 * (c1c2) + 0.25 * (c1c2 - F)

To find the threshold price F *, we set the expected utilities equal to each other and solve for F:
0.75 * (c1c2) = 0.75 * (c1c2) + 0.25 * (c1c2 - F)

By simplifying the equation, we get:
0 = 0.25 * (c1c2 - F)

Solving for F gives us:
F = c1c2

Therefore, the threshold price F * for insurance is F * = c1c2.

Now let's consider the scenarios when F > F * and F < F *:

- F > F *:
If the price of insurance (F) is greater than the threshold price (F *), it means that the cost of insurance is higher than the expected loss from chocolate being stolen. In this case, it would not be rational for Nick to purchase insurance because he would be paying more than the potential loss.

- F < F *:
If the price of insurance (F) is less than the threshold price (F *), it means that the cost of insurance is lower than the expected loss from chocolate being stolen. In this case, it would be rational for Nick to purchase insurance as it provides a net benefit by reducing the potential loss.

In summary, the threshold price F * for insurance is F * = c1c2. If F > F *, it would not be rational for Nick to purchase insurance. If F < F *, it would be rational for Nick to purchase insurance as it provides a net benefit.

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The correct answer is d. The plurality winner does not need to achieve a set percentage of the vote.

In a plurality voting system, the candidate who receives the most votes is declared the winner, regardless of whether they have a majority or a specific percentage of the total vote. Unlike in a majority voting system where a candidate needs to secure over 50% of the vote to win, a plurality winner only needs to have the highest number of votes among all the candidates. This means that even if the plurality winner receives less than 50% or even 25% of the total vote, they can still emerge as the winner as long as they have more votes than any other candidate. The plurality winner's victory is determined by having the highest vote count, without a specific threshold or percentage requirement.

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Answer:

I'd say probably 6, as 3 + 3 = 6, and 3 is the middle number.

**EDIT**

It's a 7, because there are 6 ways of rolling this value, making it the most probable.

Answer:

No solutions

Step-by-step explanation:

Let's simplify the equation first.

12y + 48 - 4y = 8(y-6) becomes 8y + 48 = 8y - 48 (You can probably see why it has no solutions already)

Now let's subtract 8y from both sides.

48 = -48. No solutions

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Answer:

Ich weiß nicht =13

die Antwort -2 -4 (6p-5)

Step-by-step explanation:

False. In statistical process control (SPC), the mean and the standard deviation serve different purposes and are not interchangeable.

The mean, often denoted as μ, represents the central tendency or average of a set of data points. It provides information about the typical or expected value of the process under consideration.

The mean is commonly used as a reference point in SPC to monitor and control the process performance. Control charts, which are a fundamental tool in SPC, typically plot the mean of the process data over time to detect any shifts or trends.

On the other hand, the standard deviation, often denoted as σ, is a measure of the dispersion or variability of the data points around the mean. It provides insights into the spread or consistency of the process. The standard deviation is not used as a substitute for the mean in SPC; rather, it is used to calculate control limits on control charts.

Control limits help identify when the process is exhibiting unusual variation that may indicate a special cause or a deviation from the desired performance.

In summary, the mean and the standard deviation are distinct statistical measures, each with its own role in SPC. They provide complementary information and should not be used interchangeably.

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The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

Step-by-step explanation:

17

Answer: 19.52 seconds

Step-by-step explanation:

9.2 seconds + 10.32 seconds = 19.52 seconds

The standard deviation of the given sample, which is the average of 100 independent normal random variables with a population standard deviation of 3, is 0.3.

To calculate the standard deviation of the sample, we can use the formula:

Standard Deviation of Sample = Population Standard Deviation /                  \(\sqrt{}\)(Sample Size)

In this case, the population standard deviation is given as 3, and the sample size is 100.

Plugging these values into the formula, we have:

Standard Deviation of Sample \(\sigma= 3 / \sqrt{100}\)

\(\sigma = 3 / 10\\ \sigma = 0.3\)

Therefore, the standard deviation of the sample is 0.3. This value represents the spread or variability of the sample's data points around the mean. It indicates the average amount by which each data point differs from the sample's mean value.

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Answer:

Answer:

33% is the discount

Step-by-step explanation:

You need to add the prices so i can caculate the discounts.

Plz give brainliest

The linear function is y = (-1/2)x + 4.

What is a linear function?

A linear function whose graph is a straight line and which is represented by an equation of the form y = ax + b where a and b are constants, a does not equal zero, and x is any real number.

Here, we have

Given,

A linear function has an x-intercept of 8 and a y-intercept of 4.

So, The two points on the line are (8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 - 8).

slope(m) = -4/8.

slope(m) = -1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Hence, the linear function is y = (-1/2)x + 4.

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The length of the radius of circle o is 18 cm.

Circle o has a circumference of 36π cm.

What is the length of the radius, r?

Circle o has a circumference of 36π cm.

The length of the radius of the circle is determined by the following formula;

\(\rm Circumference = 2\pi r\)

Substitute all the values in the formula;

\(\rm Circumference = 2\pi r\\ \\ 36\pi =2\pi r\\ \\ r = \dfrac{36\pi }{2\pi }\\ \\ r = 18 \ cm\)

Hence, the length of the radius of circle o is 18 cm.

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Answer:

18 cm

Step-by-step explanation:

on edge

Answer:

a=?,b=?,c=1

1=ab

1xab

=ab

1=a,1=b

=a=1,b=1

Answer:

(9x+2)^2

Step-by-step explanation:

Step-by-step explanation:

⎡02413524−6⎦⎥⎥⎤ and B=⎣⎢⎢⎡−10021030−1⎦⎥⎥⎤

∴4A=⎣⎢⎢⎡081641220816−24⎦⎥⎥⎤ and 6B=⎣⎢⎢⎡−600126080−6⎦⎥⎥⎤ 

⇒4A−6B=⎣⎢⎢⎡0−(−6)8−016−04

Sarah left work at 5:20 p.m. on Friday. She work d) 5 1/3 hrs after noon.

To calculate the hours, we know that noon is 12:00 PM, so we have to find the difference between 12 PM and 5:20 PM. We know that clock resets at 12, so she works 5 hours 20 mins after noon.

We can write 5 hours 20 mins as

5 20/60

= 5 1/3 because in 1 hour there are 60 minutes.

Hence, the answer is 5 1/3.

Equal hours, also known as equinoctial hours, were defined as 124 of a day measured from noon to noon; small seasonal changes in this unit were subsequently smoothed out by making it 124 of a solar day.

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Answer:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

The radioactive decay of a substance is given by the following formula:

\(mass(t) = mass(0)*e^{-\lambda*t}\)

Since the element has a half life of 12 minutes, this means that after this time the mass of the element will be half of it was originally, therefore:

\(\frac{mass(0)}{2} = mass(0)*e^{-\lambda*12}\)

\(\frac{1}{2} = e^{-\lambda*12}\)

\(ln(\frac{1}{2}) = -12*\lambda\\\lambda = -\frac{ln(0.5)}{12} =0.0577623\)

Therefore the mass of the element is given by:

\(mass(t) = mass(0)*e^{-0.0577623*t}\)

If the initial mass is 760 g and the final mass is 15 g, we have:

\(mass(t) = mass(0)*e^{-0.0577623*t}\\\\15 = 760*e^{-0.0577623*t}\\\\e^{-0.0577623*t} = \frac{15}{760}\\\\ln(e^{-0.0577623*t}) = ln(\frac{15}{760})\\\\-0.0577623*t = ln(\frac{15}{760})\\\\t = \frac{ln(\frac{15}{760})}{-0.0577623}\\\\t = 67.9555\)

The time it'd take for the element to have 15 g of mass is approximately 68 min.

The mean is 18.6.

Given the following information; z = 2.25, x = 22.2, and σ = 1.6, to find the mean, we have to apply the formula for z-score. z = (x - μ)/σWhere; z-score is represented by z, the value of X is represented by x, the mean is represented by μ and the standard deviation is represented by σSubstituting the values into the equation above;2.25 = (22.2 - μ)/1.6Multiplying both sides of the equation by 1.6, we have;1.6(2.25) = (22.2 - μ)3.6 = 22.2 - μ Subtracting 22.2 from both sides of the equation;3.6 - 22.2 = - μ-18.6 = - μ Multiplying both sides of the equation by -1, we have;μ = 18.6

Simply said, a z-score, also known as a standard score, informs you of how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve. Z-scores range from -3 standard deviations, which would fall to the extreme left of the normal distribution curve, to +3 standard deviations, which would fall to the far right. You must be aware of the mean and population standard deviation in order to use a z-score.

The z-score can show you how that person's weight compares to the mean weight of the general population.

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