Use the following information for the next two questions: • A portfolio consists of 16 independent risks. • For each risk, losses follow a Gamma distribution, with parameters 0 = 250 and a = 1. The Central Limit Theorem: Suppose that X is a random variable with mean u and standard deviation and suppose that X, X2...., Xy are independent random variables with the same distribution as X (i.e. Independent and Identically Distributed or IID assumption). Let Y = X2, X2..... X... Then E[Y] = nu and Var(Y) = ng2. As n increases, the distribution of Y approaches a normal distribution Nínu, no4). This is also known as normal approximation. (a) Without using the Central Limit Theorem, determine the probability that the aggregate losses for the entire portfolio will exceed 6,000. (b) Using the Central Limit Theorem, determine the approximate probability that the aggregate losses for the entire portfolio will exceed 6,000.

Answer:

12

Step-by-step explanation:

Answer:

50 %

Step-by-step explanation:

Given that :

Total Number of beads in necklace = 58

Number of Blue beads = 29

Percentage of blue beads on necklace :

(Number of Blue beads / total number of beads) * 100%

(29 / 58) * 100%

0.5 * 100%

50%

Blue beads is 50% of total number of beads

Answer:

23 años

Step-by-step explanation:

Para resolver la situación, consideremos que x es la edad de la persona. Sabemos que dentro de seis años esta tendrá el doble de la edad que tenía hace cuatro años. La edad dentro de 6 años se puede expresar como x+6 y esto será igual al doble de la edad que tenía hace cuatro años, lo que se puede expresar como 2(x-4). De acuerdo a esto:

x+6=2(x-4)

x+6=2x-8

6+8=2x-x

x=14

Ahora que sabemos que la edad de la persona es 14 años, le sumamos 9 y esto da como resultado 23 y esta es la edad que la persona tendrá en 9 años.

Answer:

4, 8, 12, 13

In order to find the mean you must add all of the values together and then divide by the number of numbers. 4 + 8 + 12 + 13 = 37

Now we divide: 37 ÷ 4 = 9.25

So the mean is 9.25

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Answer:

x²+2x-35=0

Step-by-step explanation:

Solve this eqn for the answer

Answer:

First answer lol

Step-by-step explanation:

is the domain by any chance x ≥-2?

Dr. Hellsing is in the process of establishing a norm-referenced assessment.

Norm-referenced assessment is a method that evaluates an individual's aptitude in comparison with the outputs of a larger, representative sample of test takers from the corresponding population. This technique ranks persons on a scale relative to each other instead of objectively evaluating their actual abilities.

Therefore, by giving the exam to a significant group of high school graduates, Dr. Hellsing will be able to generate standards to interpret separate test scores and equate them to the outcome of others in the same demographic.

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Answer:

The last choice (3,2), because both lines pass through this point.

Step-by-step explanation:

For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.

Answer: (3, 2), because both lines pass through this point

Step-by-stepexplanation:

This can be solved by substitution. The graph will show the same result.

A  linear function that represents the profit generated from selling the manufactured kayaks is P(x) = $575x - $480x.

Profit is the total selling price of an item less the cost price.

Profit = selling price - cost price.

A linear function is a function that has a single variable raised to the power of 1. An example is x + 2 The variable x is raised to the power of 1. 2 is the constant terms.

P(x) = $575x - $480x.

Where x represents the number of manufactured kayaks sold

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Answer:

Slope = 0

Step-by-step explanation:

Slope = \(\frac{y_{2} -y_{1}}{x_{2}-x_{1}}\)

Slope = \(\frac{-10 -(-10)}{-19-(-7)}\) = 0

Also, just by looking at these points you can determine that the slope is zero because the y value does not change between these points.

Answer: B. The rotation of a line is a pair of parallel lines.

Step-by-step explanation: In geometry, a rotation refers to the transformation of an object around a fixed point called the center of rotation.  When a line is rotated, it does not result in a pair of parallel lines. Instead, a line remains a line after a rotation, but its orientation changes.  A rotation simply changes the direction or angle of the line while keeping its length and shape intact.

On the other hand, a pair of parallel lines refers to two lines in the same plane that never intersect, regardless of any transformations applied to them.  The rotation of a line does not change its parallel nature with any other line.

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The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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The printer that has a better rate of cost per page would be = printer B.

For printer A:

The number of pages printed = 100

The cost for the printed pages = $26.99

Cost per page = 26.99/100 = $0.27/page

For printer B:

The number of pages printed = 275

The cost for the printed pages = $67.99

Cost per page =67.99/275

= 0.25

Therefore the printer that has a better rate of cost per page would be = printer B

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Answer: 3:00 p.m

Step-by-step explanation: the longest movie is 120 minutes/2 hours, so the 2 hours plus 1:00=3:00 since the movies start at the same time

Answer:

the like terms were not grouped together.

Answer:

Your right!! Good Job!!

Step-by-step explanation:

Could you give me brainliest please? I only need one more :)

The solution is :

There are 240 students in the school.

Here, we have,

Givens

55% of the total number of students in a school are girls.

Equation

55/100 * x = 132

Solution

Multiply both sides of the equation  by 100

55/100x * 100  = 132 * 100

55x = 13200                        [  Divide by 55  ]

55x/55  = 13200/55

x = 240

Hence, The solution is :

There are 240 students in the school.

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complete question:

Of the students at milton middle school, 132 are girls. if 55% of the students are girls, how many total students are there at milton middle school?

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479

According to the question,

we have to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)

Here,

Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.

And Y is the number of days that pass up to and including the first time the car encounters a red light, i.e.,

The distribution here is a geometric one, where

P(Y = 3)

= P(Not red light in initial 2 lights) x P(red light in third light)

= [(1 - 0.35)² X 0.35]

= 0.1479

so, the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479.

Note:

mean and variance of this question is not possible to find out.

the complete question ends till the probability to find the first red light on the third day.

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The mean and standard deviation of the z-scores for pulse rates of women can be calculated using the formula z = (x - μ) / σ, where x represents the original pulse rate, μ represents the mean, and σ represents the standard deviation.

In this case, the mean of the original pulse rates is 77.5 beats per minute, and the standard deviation is 11.6 beats per minute. To convert these pulse rates to z-scores, we subtract the mean from each pulse rate and divide by the standard deviation.

The mean of the z-scores will be 0, as subtracting the mean from each value results in a mean of 0. The standard deviation of the z-scores will be 1, as dividing by the standard deviation ensures that the z-scores have a standard deviation of 1.

Therefore, the values of the mean and standard deviation after converting the pulse rates of women to z-scores are a mean of 0 and a standard deviation of 1.

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In 15 minutes, a water pump capable of pumping 13.2 gallons of water per minute will remove a total of 198 gallons of water from the pool.

If a water pump can pump 13.2 gallons of water in a pool every minute, we can calculate the amount of water it will remove in 15 minutes by multiplying the pumping rate by the duration. Therefore, 13.2 gallons/minute x 15 minutes = 198 gallons. During the 15-minute period, the water pump will continue to operate at a constant rate, removing water from the pool. Each minute, 13.2 gallons of water will be pumped out. When we multiply this rate by the duration of 15 minutes, we find that a total of 198 gallons of water will be removed from the pool. It's important to note that this calculation assumes a constant pumping rate without any interruptions or changes in efficiency.

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The probability that y takes a value less than 1/3 is approximately 0.11.

We are given that the cumulative distribution function (cdf) of the random variable y is defined as:

F(x) = { 0, x ≤ 0

\(x^2,\) 0 < x < 1

1, x ≥ 1

We want to find the probability that the random variable y takes a value less than 1/3, i.e., P(y < 1/3).

Since F(x) is the cdf of y, we have:

P(y < 1/3) = P(y ≤ 1/3) = F(1/3)

To find F(1/3), we need to consider two cases:

Case 1: 0 ≤ 1/3 < 1

In this case, we have:

F(1/3) = (1/3\()^2\) = 1/9

Case 2: 1/3 ≥ 1

In this case, we have:

F(1/3) = 1

Therefore, the probability that y takes a value less than 1/3 is:

P(y < 1/3) = F(1/3) = 1/9

Rounding off to the second decimal place, we get:

P(y < 1/3) ≈ 0.11

Therefore, the probability that y takes a value less than 1/3 is approximately 0.11.

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Full Question

Let y be a random variable with cdf F(x) = { 0, x 0 Find P(x < 1/3) (round off to second decimal place).

The factor of the polynomial is option (D) (2x+5)^2 is the correct answer.

In this question,

Factorization is the breaking or decomposition of an entity (i.e.,) a number, a matrix, or a polynomial into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

The polynomial is \(4x^{2} +20x+25\)

The above polynomial can be factored as

⇒ \(4x^{2} +20x+25=0\)

⇒ \((2x)^{2}+2(2x)(5)+5^{2}\)

⇒ \((2x+5)^{2}\)

Hence we can conclude that the factor of the polynomial is option (D)(2x+5)^2 is the correct answer.

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Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

What is an Algebraic Expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.

Given,

Total money Preston have = $15

He buys the ticket for = $6.50

And, two snacks = $1.75 each

so the cost of two snacks is = 1.75 * 2 = $3.5

Total cost for ticket and snacks = $3.5 + $6.50 = $10

Now, he spent money on snacks and ticket $10 and he have total money $15 so,

Preston left with = $15 - $10

                           = $5

Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

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The linear equation of the line shown in the graph will be 3y +x= 0.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

As we can observe in the given graph of lines,

the given line passes through the point (0, 0) origin and (-6, 2).

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

Since y-intercept is the value of y in line at x = 0

in our case, b = 0

since, slope = (y - y')/(x -x')

Slope = (2-0)/(-6-0)

Slope = 2/-6

Slope = -1/3

thus,

the equation of the line shown in the graph will be y = -1/3x

the equation of the line shown in the graph will be 3y +x= 0.

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Answer:

x > 16

Step-by-step explanation:

As a result, the radian measure of the relevant center angle is around 3.07 radians.

An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference.

Here,

The formula for the length of an arc in a circle is given by:

Arc Length = (Central Angle / 2π) * Circumference

We know the Arc Length and the Radius of the circle, so we can find the Central Angle as follows:

Arc Length = (Central Angle / 2π) * 2π * Radius

66/5 * π = (Central Angle / 2π) * 2π * 22

66/5 * π = Central Angle * 22

Central Angle = (66/5 * π) / 22

The radian measure of an angle is equal to the ratio of the length of the arc that it intercepts to the radius of the circle. Hence, the radian measure of the central angle is given by:

Central Angle (in radians) = Arc Length / Radius

= (66/5 * π) / 22

So, the radian measure of the corresponding central angle is approximately 3.07 radians.

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