2. Give the degree of x2 - 17x + 2x - 5.00

a. The expected value of the sum of all incurred but as yet

b. Unreported claims at time t is λt times the expected value of a single claim amount.

Probability is a branch of mathematics that deals with measuring the likelihood of an event occurring. It involves quantifying the chances of different outcomes of a random experiment, such as flipping a coin, rolling a die, or drawing a card from a deck.

According to the given information:

(a) Let N(t) be the number of claims incurred up to time t, and let S be the set of times when claims are incurred but not yet reported. Then, the probability that there are exactly n incurred but as yet unreported claims at time t is given by:

P(N(t) - |S| = n) = P(N(t) = n + |S|) × P(|S|)

Since the occurrence of claims follows a Poisson process with rate λ, the probability of n + |S| claims in time t is:

P(N(t) = n + |S|) = ( + |S| / (n + |S|)!)

The distribution of the time until a claim is reported, G, gives the probability that a claim is reported within some time interval after it is incurred. The probability that a claim is incurred but not reported by time t is given by:

P(|S|) = P(G > t)

Putting all these pieces together, we get:

P(N(t) - |S| = n) = ( + |S| / (n + |S|)!) ×) × P(G > t)

(b) Let X_i denote the claim amount for the i-th incurred but as yet unreported claim. Then, the total claim amount for all incurred but as yet unreported claims at time t is:

Y(t) = Σ_i= - |S| X_i

We can find the expected value of Y(t) by using the law of total expectation:

E(Y(t)) = E[E(Y(t) | N(t), S)]

Given N(t) and S, the expected value of Y(t) is just the sum of the expected values of the claim amounts for the unreported claims:

E(Y(t) | N(t), S) = Σ_i= E(X_i)

Since the claim amounts are independent and identically distributed according to F, we have:

E(X_i) = E(F)

Thus, we get:

E(Y(t)) = E[E(Y(t) | N(t), S)] = E[(n + |S|)E(F)] = λt × E(F)

Therefore, the expected value of the sum of all incurred but as yet unreported claims at time t is λt times the expected value of a single claim amount.

To know more about Probability visit:

https://brainly.com/question/30034780

#SPJ1

Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

To know more about Relation, visit

https://brainly.com/question/30056459

#SPJ11

We can easily identify the dependent and independent (free) variables by looking at the matrix after converting augmented matrix.

When we convert the augmented matrix of a system of equations into reduced row-echelon form, we can easily identify the dependent and independent (free) variables by looking at the matrix. The columns that contain leading 1's correspond to the variables that are dependent on the others. The columns that do not contain leading 1's correspond to the variables that are independent or free.

For example, if we have a matrix in reduced row-echelon form that looks like this:

1 0 2 | 3
0 1 -1 | 2
0 0 0 | 0

We can see that the first and second columns have leading 1's, so the variables corresponding to those columns (in this case, x1 and x2) are dependent on each other. The third column does not have a leading 1, so the variable corresponding to that column (in this case, x3) is independent or free.

In general, we can say that the number of independent variables is equal to the number of columns without leading 1's, and the number of dependent variables is equal to the number of columns with leading 1's. By identifying the dependent and independent variables, we can then use this information to solve the system of equations using substitution or elimination.

Learn more about augmented matrix here:

https://brainly.com/question/30153510

#SPJ11

The probability of event B, P(B), is 0.1667.

To find the probability of event B, we can use the formula for the probability of the intersection of two independent events:

P(A and B) = P(A) * P(B)

We are given that P(A and B) = 0.10 and P(A) = 0.6.

Let's substitute these values into the formula:

0.10 = 0.6 * P(B)

To solve for P(B), we divide both sides of the equation by 0.6:

0.10 / 0.6 = P(B)

Simplifying the division:

P(B) ≈ 0.1667

Therefore, the probability of event B, P(B), is approximately 0.1667.

know more about probability here:

https://brainly.com/question/13604758

#SPJ8

Answer:

a=4, b=11

Step-by-step explanation:

You have to complete the square.

x²-8x+5 = (x-4)²-16 +5 = (x-4)² - 11

The result of 297,060 divided by 0.0004839 is approximately 6.1429 x 10⁸ or 614,290,000 in standard notation.

To express 297,060 divided by 0.0004839 in scientific notation, we can represent it as:

297,060 / 0.0004839 = 6.1429 x 10⁸

In standard notation, the result is approximately:

614,290,000

To know more about standard notation,

https://brainly.com/question/30224384

#SPJ11

For the function\(f(x) = 2/(x²+25)\), the power series is given by;\(f(x) = 2 * 1/(25(1 + (x²/25)))\)

This is similar to \(f(x) = a / (1 + bx²)\) where a = 2 and b = 1/25;∴ \(1 + bx² = 1 + x²/25\)

∴ \(f(x) = 2(1 + (-1/25)x² + (-1/25)(-3/25)x^4 + (-1/25)(-3/25)(-5/25)x^6 + ... )\)∴ \(f(x) = Σ(-1)ⁿ(3,5,7,...)x^(2n) / 25ⁿ , (-5/5 < x < 5/5)\), where 5/5 = 1

Therefore the power series of \(f(x) = 2/(x²+25) is;$$f(x) = \sum_{n=0}^{\infty} (-1)^n \frac{3 \cdot 5 \cdot 7 ... (2n-1)}{25^n} x^{2n} $$\)

The interval of convergence is\($$ -1 < \frac{x^2}{25} < 1 $$ $$ -5\)

Learn more about power series

https://brainly.com/question/29896893

#SPJ11

Answer:

4 1/2 tiles are needed to cover this area

Step-by-step explanation:

Mathematically, the area of a parallelogram is the product of the base and the height

We have this as;

24 * 10 = 240 cm^2

So the area of a tile is this

The number of tiles that will cover the given area will be;

1080/240 = 4.5 tiles

Answer:

94 ft

Step-by-step explanation:

Rewriting input as fractions if necessary:

3/2, 3/8, 5/6, 3/1

For the denominators (2, 8, 6, 1) the least common multiple (LCM) is 24.

Therefore, the least common denominator (LCD) is 24.

Answer:

0.75

Step-by-step explanation:

Answer:

A 1

Step-by-step explanation:

8x11=88

1x11=11

The given table represents the counts from three independent random samples taken from three major cities regarding whether teenagers consumed a soft drink in the past week.

By summing up the counts of teenagers who consumed a soft drink from all three cities and dividing it by the total number of teenagers surveyed, we can calculate the overall proportion. Dividing this proportion by the total number of teenagers and multiplying by 100 will give us the percentage of teenagers who consumed a soft drink.

For example, if the first city had a count of 150 teenagers who consumed a soft drink out of a total of 300 surveyed, the second city had 200 out of 400, and the third city had 180 out of 350, the overall proportion would be (150 + 200 + 180) / (300 + 400 + 350) = 530 / 1050. Multiplying this by 100, we find that approximately 50.48% of teenagers consumed a soft drink in the past week based on the combined sample.

Learn more about Dividing here:

https://brainly.com/question/15381501

#SPJ11

A research center conducted a national survey about teenage behavior. Teens were asked whether they had consumed a soft drink in the past week. The following table shows the counts for three independent random samples from major cities. Baltimore Yes 727 Detroit 1,232 431 1,663 San Diego 1,482 798 2,280 Total 3,441 1,406 4,847 No 177 904 Total (a) Suppose one teen is randomly selected from each city's sample. A researcher claims that the likelihood of selecting a teen from Baltimore who consumed a soft drink in the past week is less than the likelihood of selecting a teen from either one of the other cities who consumed a soft drink in the past week because Baltimore has the least number of teens who consumed a soft drink. Is the researcher's claim correct? Explain your answer. (b) Consider the values in the table. (i) Baltimore Detroit San Diego 0 0.1 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Relative Frequency of Response (ii) Which city had the smallest proportion of teens who consumed a soft drink in the previous week? Determine the value of the proportion. (c) Consider the inference procedure that is appropriate for investigating whether there is a difference among the three cities in the proportion of all teens who consumed a soft drink in the past week. (i) Identify the appropriate inference procedure. (ii) Identify the hypotheses of the test.

Answer:

To represent geometrically √x on a number line:

To represent geometrically √4.5 on a number line:

Draw:

Draw a line perpendicular to AC at point B.

Let O be the midpoint of AC:

\(\implies \sf O=\dfrac{-4.5+1}{2}=-1.75\)

Draw a semicircle with center O and radius OA

\(\implies \sf OA=\dfrac{AC}{2}=\dfrac{5.5}{2}=2.75\)

Let point D be where the semicircle intersects with the perpendicular line

\(\implies \sf BD=\sqrt{AB}=\sqrt{4.5}\)

Draw an arc with center B and radius BD from point D to the number line.

\(\implies \sf BE=\sqrt{4.5}\)

⇒ Point E is \(\sf \sqrt{4.5}\) on the number line.

To represent geometrically √8.3 on a number line:

Draw:

Draw a line perpendicular to AC at point B.

Let O be the midpoint of AC:

\(\implies \sf O=\dfrac{-8.3+1}{2}=-3.65\)

Draw a semicircle with center O and radius OA

\(\implies \sf OA=\dfrac{AC}{2}=\dfrac{9.3}{2}=4.65\)

Let point D be where the semicircle intersects with the perpendicular line

\(\implies \sf BD=\sqrt{AB}=\sqrt{8.3}\)

Draw an arc with center B and radius BD from point D to the number line.

\(\implies \sf BE=\sqrt{8.3}\)

⇒ Point E is \(\sf \sqrt{8.3}\) on the number line.

The solution of the given system of equations 8x+3y=5 and 3x-2y=5 is x = 1 and y = -1

In this question we have been given a system of equations.

8x+3y=5                 ..........(1)

and 3x-2y=5           ..........(2)

We need to find the solution of the given system of equations.

As right hane side of both equations is equal, we equate LHS of both equations.

so, we get,

8x + 3y = 3x - 2y

⇒ 8x - 3x = - 2y - 3y

⇒ 5x = - 5y

⇒ x = - y                      .............(3)

By substituting x = - y in equation (1), we get,

8 ( - y ) + 3y = 5

⇒ - 8y + 3y = 5

⇒ - 5y = 5

⇒ y = - 1

Substitute above value of y in equation (3)

⇒ x = - (- 1)

⇒ x = 1

Therefore, x = 1 and y = -1 is solution of given equations.

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Answer:

I dont know I just really need points. Please Mark Brainliest

Step-by-step explanation:

Sorry

Answer:

1.C      2.  576 feet

Step-by-step explanation:

Percentage of part time employees = (part-time employees/total employees) * 100 = (6/60) * 100 = 1/10 * 100 = 10%

Work Shown:

n(A only) = number of items inside set A only

n(A only) = 12

n(A and B) = 16

n(B only) = 20

n(A or B) = n(A only) + n(A and B) + n(B only)

n(A or B) = 12 + 16 + 20

n(A or B) = 48

n(Total) = n(A only) + n(A and B) + n(B only) + n(Not A, not B)

n(Total) = 12+16+20+24

n(Total) = 72

P(A or B) = n(A or B)/n(Total)

P(A or B) = 48/72

P(A or B) = 0.67 approximately

The proper format for scientific notation is a x 10^b , 6.75 × 10⁹ is the scientific notation for 6,750,000,000.

The proper format for scientific notation is a x 10^b where a is a number or decimal number.

Given number is 6,750,000,000, we need to write in scientific notation.

To write the number to scientific notation, we need to follow few rules, Move the decimal so there is one non-zero digit to the left of the decimal point.

The number of decimal places you move will be the exponent on the . If the decimal is being moved to the right, the exponent will be negative.

If the decimal is being moved to the left, the exponent will be positive.

6,750,000,000 = 6.75 × 10⁹

Therefore 6.75 × 10⁹ is scientific notation for 6,750,000,000.

To learn more on scientific notation click:https://brainly.com/question/1705769

#SPJ1

Answer:

55.00

Step-by-step explanation:

basically I subtracted 84.25 from 75.49 and I got 8.76. So I too kthat answer and subtracted 8.76 from 63.76. So the answer is 55.00

The value of a is -4 from the given system of linear equations.

The system of given equations are ax+12y=-6 and 2x-6y=4.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here, ax+12y=-6 -------(I) and 2x-6y=4 -------(II)

Given, no solution for the system

So, (a1/a2) = (b1/b2) ≠ (c1/c2)

Now, a/2 = 12/(-6)

a=-4

Hence, the value of a is -4 from the given system of linear equations.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ1

I need help on the same one!!

Answer:

5

Step-by-step explanation:

The slope is given by

m = ( y2-y1)/(x2-x1)

We can use any two sets of points.  I like to use the first and the last

m = (15-0)/(4-1)

m = (15/3)

   = 5

Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Workers in an office of 90 staff were asked their favorite type of takeaway. The results are summarised in the table.

Take-away             Frequency            Angle

   Pizza                         29                       a

   Curry                          9                        b

Fish & chips                 24                        c

  Kebab                        16                        d

   Other                         12                       e

The angles on the pie chart are calculated by multiplying the table by 4. Then the angles will be

∠a = 4 x 29 = 116°

∠b = 4 x 9 = 36°

∠c = 4 x 24 = 96°

∠d = 4 x 16 = 64°

∠e = 4 x 12 = 48°

Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ1

f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6.

f(x) is concave up on the interval -6 ≤ x ≤ 0.

To determine where f(x) is concave up or concave down, we need to calculate the second derivative of f(x):

f(x) = x √(\(x^2\) + 36)

f'(x) = √\(x^2\) + 36) + \(x^2\) √(\(x^2\) + 36)

f''(x) = (x (\(x^2\) +72) )/((\(x^2\)+36)\(^(3\)/2))

To find where f(x) is concave up or concave down, we need to find where f''(x) > 0 (concave up) or f''(x) < 0 (concave down).

f''(x) = 0 when x = 0 or x = +/-6.

Thus, f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6, and concave up on the interval -6 ≤ x ≤ 0.

The inflection point for this function is at x = 0.

To find the minimum and maximum for this function, we need to look at the endpoints and critical points of the interval -5 ≤ x ≤ 6.

f(-5) = -5√61 and f(6) = 6√72, so the minimum occurs at x = -5 and the maximum occurs at x = 6.

Therefore:

f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6.

f(x) is concave up on the interval -6 ≤ x ≤ 0.

The inflection point for this function is at x = 0.

The minimum for this function occurs at x = -5.

The maximum for this function occurs at x = 6.

To know more about   inflection point, here

https://brainly.com/question/25918847

#SPJ4

The approximate value of the integral using the midpoint rule with n=4 is 5.8571 (rounded to four decimal places).

The area under a simple curve can be roughly estimated using the midpoint rule, commonly referred to as the rectangle method or mid-ordinate rule. The midpoint approach provides a better approximation than the left rectangle or right rectangle sum, which are two other ways for approximating the area.

We need to use the midpoint rule with n=4 to approximate the integral of 8 sin(√(x)) dx.

The midpoint rule formula for approximating a definite integral is:

∫[a,b] f(x) dx ≈ Δx [f(x1/2) + f(x3/2) + ... + f(x(n-1/2))]

where Δx = (b-a) / n is the width of each subinterval, and xi/2 = (xi-1 + xi) / 2 is the midpoint of the i-th subinterval.

For n=4, we have Δx = (b-a) / n = (1-0) / 4 = 0.25, and the endpoints of the subintervals are:

x₀ = 0, x₁ = 0.25, x₂ = 0.5, x₃ = 0.75, x₄ = 1

The midpoints of the subintervals are:

x1/2 = 0.125, x3/2 = 0.375, x5/2 = 0.625, x7/2 = 0.875

Now we can apply the midpoint rule formula:

∫[0,1] 8 sin(√(x)) dx ≈ Δx [f(x1/2) + f(x3/2) + f(x5/2) + f(x7/2)]

where f(x) = 8 sin(√(x)).

Plugging in the values, we get:

∫[0,1] 8 sin(√(x)) dx ≈ 0.25 [f(0.125) + f(0.375) + f(0.625) + f(0.875)]

Using a calculator, we can evaluate each term and sum them up:

f(0.125) ≈ 2.4774

f(0.375) ≈ 5.6382

f(0.625) ≈ 6.8171

f(0.875) ≈ 5.4946

∫[0,1] 8 sin(√(x)) dx ≈ 0.25 [2.4774 + 5.6382 + 6.8171 + 5.4946] ≈ 5.8571

Therefore, the approximate value of the integral using the midpoint rule with n=4 is 5.8571 (rounded to four decimal places).

Learn more about midpoint rule on:

https://brainly.com/question/20888347

#SPJ4

The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, the equation for the parent linear value function, f(x)=x, that has been transformed by,

a) Reflecting across the -axis, vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left :-

Rule for reflection across x-axis = y = f(x) → y = -f(x)

After reflection,

f(x) = -x

And there is a vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left

f(x) = -4(x+4)+5

Therefore, the function will be f(x) = -4(x+4)+5

b) Vertical shrink by a scale factor of 14 and a horizontal shift O units right.

For vertical shrink = f(x)/14 = x/14

For horizontal shift = (x-o)/14

Therefore, the function will be f(x) = (x-o)/14

c) Reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left.

Rule for reflection across x-axis = y = f(x) → y = -f(x)

f(x) = -x

For a vertical shift of 4 units up and a horizontal shift 7 units left =

f(x) = (-x-7)+4

Hence, The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4

For more references on transformations. click;

https://brainly.com/question/11709244

#SPJ1