suppose that the decision maker obtained the probabilities p(s1) = 0.65, p(s2) = 0.15, and p(s3) = 0.20. use the expected value approach to determine the optimal decision.

To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:

1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n

Solution:

1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.

2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.

Now, we need to verify that the product of these series converges:

3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)

4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.

5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.

In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and

summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.

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Answer:

Point q would be located at (10,5)

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The maximum value of the objective function is 4 at the vertex (4, 0), and the minimum value is -8 at the vertex (0, -4). The optimal solutions for the given LP problem are Maximum: p = 4 at x = 4 and y = 0 and Minimum: p = -8 at x = 0 and y = -4.

Maximize and minimize p = x + 2y

subject to:

x + y ≥ 4

x + y ≤ 10

x - y ≤ 4

x - y ≥ -4

First, let's graph the feasible region defined by the given constraints:

Plotting the lines:

x + y = 4 (solid line)

x + y = 10 (solid line)

x - y = 4 (solid line)

x - y = -4 (solid line)

The feasible region is the area that satisfies all the constraints and is bounded by the lines on the graph.

Upon examining the feasible region, we can observe that it is a bounded region.

To find the optimal solution, we need to evaluate the objective function p = x + 2y at the vertices (corner points) of the feasible region.

Now, let's find the vertices of the feasible region by solving the intersection points of the lines:

1. Intersection of x + y = 4 and x + y = 10:

Subtracting the equations, we get 0 = 6, which is not possible. No intersection point exists for these lines.

2. Intersection of x + y = 4 and x - y = 4:

Adding the equations, we get 2x = 8, x = 4. Substituting x = 4 into x + y = 4, we get 4 + y = 4, y = 0. The first vertex is (4, 0).

3. Intersection of x - y = 4 and x - y = -4:

Adding the equations, we get 2x = 0, x = 0. Substituting x = 0 into x - y = 4, we get -y = 4, y = -4. The second vertex is (0, -4).

Now, we evaluate the objective function at each vertex:

p(4, 0) = 4 + 2(0) = 4

p(0, -4) = 0 + 2(-4) = -8

The maximum value of the objective function is 4 at the vertex (4, 0), and the minimum value is -8 at the vertex (0, -4).

Therefore, the optimal solutions for the given LP problem are Maximum: p = 4 at x = 4 and y = 0 and Minimum: p = -8 at x = 0 and y = -4.

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Answer:

Step-by-step explanation:

Decrease

Percent decrease

The Measure of angle A is 120°, Measure of angle C = 120° and the Measure of angle D is 60°

In a parallelogram, opposite angles are congruent. Therefore, if the measure of angle A is 120°, then the measure of angle C is also 120°.

Since angle A and angle C are opposite angles, their adjacent angles are also congruent. This means that the measure of angle B is equal to the measure of angle Z.

Now, let's consider angle D. In a parallelogram, the sum of the measures of adjacent angles is always 180°. Since angle C is 120°, the adjacent angle D must be:

180° - 120°

= 60°.

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Answer:

20%

Step-by-step explanation:

Profit = 24000 - 20000 = 4000

\(Profit \: percent = \frac{4000 \times 100}{20000} \\ = \frac{400000}{20000} \\ = 20\%\)

Answer:I think the answer is 112

Step-by-step explanation:

Answer:

Step-by-step explanation:

9000 is 60% of what number?

9000=0.6*X

9000/0.6=X

X=$15000

Solution

Now

Add and subtract

Answer:

C, hope this helps :)

Answer:\(x\leq 2\)

Step-by-step explanation:

Answer:

A= 2w^2 + 11w +12

Step-by-step explanation:

(w + 4)(2w + 3) = l x b = A

2w^2 + 3w +8w +12 = A

A= 2w^2 + 11w +12

Answer:

A = 2 1/2 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 3 * 5/6

A = 5/2 ft^2

A = 2 1/2 ft^2

Answer:

A=2.5 ft^2

Step-by-step explanation:

A=3

A=3(5/6)

A=2.5 ft^2

Answer:

$68.85

Step-by-step explanation:

76.50/10=7.65

76.50-7.65=68.85

Answer:

1) 800 (read the both) 2) 2200 (read exactly one)

Step-by-step explanation:

Find the people (families) who read neither of them

4000/100*25= 1000

It means that the rest 4000-1000= 3000 families read the newspapers at least  in one language  from the pointed languages. 4000/1oo*50= 2000 - readers in Nepali

4000/100*45= 40*45=1800 - readers in English.

2000+1800= 3800- the special amount, that consists of 1) only Nepali readers

2) only English readers 3) the readers in two languages (but the were counted twice, because we considered them in the group of Nepali readers and group of English readers)

The real quantity of only Nepali readers, only English readers and both language readers is 3000.

S0 3800-3000= 800 people - read in two languages

3000-800=2200 families read exactly one kind of these papers

Answer:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

Answer:

6000

Step-by-step explanation:

Interest of 3% a year of principal of 200,000 = 6000

monthly payment of 843 also includes a portion of amortization of the principal itself, which you can ignore cause the question only asked for the interest portion.

this is an unclear question cause it didn't say PER YEAR interest paid.  you only need to remember interest% * principal = ANNUAL interest payment $.  Then you can divide that over 12 months, which is 500$ per month.

Answer:

x = - 1 or x = - \(\frac{2}{3}\)

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

3x² + 5x + 2 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × 2 = 6 and sum = + 5

the factors are 3 and 2

use these factors to split the x- term

3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(3x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - \(\frac{2}{3}\)

To measure out exactly 1 gallon of water we need exactly six possible number of moves.

To measure out exactly 1 gallon of water using two jugs, one with a 3-gallon capacity and one with an 5-gallon capacity, you can follow some steps

Fill the 5-gallon jug with water completely. Pour the water from the 5-gallon jug into the 3-gallon jug, leaving 2 gallons of water in the 5-gallon jug.

Empty the 3-gallon jug completely. Pour the 2 gallons of water from the 5-gallon jug into the empty 3-gallon jug.

Fill the 5-gallon jug with water again. Pour water from the 5-gallon jug into the 3-gallon jug until it is full, which will leave exactly 1 gallon of water in the 5-gallon jug.

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The  requried rationalized form of 1/(7-3√2) is (7+3√2)/31.

To rationalize the denominator, we need to eliminate the radical in the denominator. To do this, we can multiply the numerator and denominator by the conjugate of the denominator, which is 7+3√2:

1/(7-3√2) * (7+3√2)/(7+3√2) = (7+3√2)/(49-18) = (7+3√2)/31

Therefore, the rationalized form of 1/(7-3√2) is (7+3√2)/31.

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Answer:

(C) 30πcm

Step-by-step explanation:

In order to find circumference you use the formula C (circumference)=2(pi)(r) in which r is the radius. In this case, two and 15 are thirty so to find the circumference all you have is the equation 30 times pi centimeters is equal to the Circumference.

Given

Answer

Which is triangle 2

The three points to plot for the equation 2y = 3x + 11 are (0, 5.5), (1, 7), and (-1, 4).

To graph the equation 2y = 3x + 11, we can choose any three points that satisfy the equation. Let's select three points and plot them on a coordinate plane:

Point 1:

Let's set x = 0 and solve for y:

2y = 3(0) + 11

2y = 0 + 11

2y = 11

y = 11/2 = 5.5

So, the first point is (0, 5.5).

Point 2:

Let's set x = 1 and solve for y:

2y = 3(1) + 11

2y = 3 + 11

2y = 14

y = 14/2 = 7

The second point is (1, 7).

Point 3:

Let's set x = -1 and solve for y:

2y = 3(-1) + 11

2y = -3 + 11

2y = 8

y = 8/2 = 4

The third point is (-1, 4).

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Answer:

Here,

<1 = 120° [linear pair]

<2 = 60° [Vertically Opposite Angles]

<3 = 90° [linear pair]

<4 = 90° [Vertically Opposite Angles]

<5 = 30° [Angle sum property of triangle]

<6 = 150° [linear pair of <5]

45 was divided by 10^1 (or simply 10) to obtain 4.5.

To determine the power of 10 by which 45 was divided to obtain 4.5, we can set up the equation:

45 ÷ 10^x = 4.5

Here, 'x' represents the power of 10 we are trying to find. To solve for 'x', we can rewrite the equation:

45 = 4.5 * 10^x

Next, we can divide both sides of the equation by 4.5:

45 / 4.5 = 10^x

10 = 10^x

Since 10 raised to any power 'x' is equal to 10, we can conclude that 'x' is 1.

Therefore, 45 was divided by 10^1 (or simply 10) to obtain 4.5.

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To solve a differential equation with exponential equations, start by isolating the dependent variable and any coefficients that may exist on either side of the equation. Next, take the natural logarithm of both sides of the equation and use the properties of logarithms to simplify the equation. Solve for the dependent variable. Finally, take the exponential of both sides of the equation and simplify it to get the solution.

For example, consider the differential equation dy/dx = 2y.

Isolate the dependent variable to get y = dx/2.

Then, take the natural logarithm of both sides to get ln(y) = ln(dx/2).

Use the property ln(a/b) = ln(a) - ln(b) to get ln(y) = ln(dx) - ln(2).

Solve for ln(y) to get ln(y) = ln(dx) - ln(2).

Then, take the exponential of both sides to get \(y = e^{ln(dx) - ln(2)}\) and simplify to get the solution \(y = (dx/2) e^{ln(dx)}\).

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Answer:

18 degrees Fahrenheit

Step-by-step explanation:

Given

\(F = 32 + 1.8C\)

Required

Determine change in F if change in C is 10

A 10 degrees change in C is represented as: C + 10

The equivalent change in F is F + x, where x represents the change in F

So: If \(F = 32 + 1.8C\)

Then

\(F + x = 32 + 1.8(C + 10)\)

Open brackets

\(F + x = 32 + 1.8C + 18\)

Collect Like Terms

\(F + x = 32 + 18+ 1.8C\)

\(F + x = 50+ 1.8C\)

Make x the subject

\(x = 50+ 1.8C - F\)

Recall that: \(F = 32 + 1.8C\)

So:

\(x = 50+ 1.8C - F\) becomes

\(x = 50 + 1.8C - (32 + 1.8C)\)

Open Bracket

\(x = 50 + 1.8C - 32 - 1.8C\)

\(x = 50 - 32+ 1.8C - 1.8C\)

\(x = 50 - 32\)

\(x = 18\)

Hence:

A change of 10 degrees Celsius will bring a change of 18 degrees Fahrenheit

Answer:

18 degrees Fahrenheit

Step-by-step explanation:

I got it right on Khan Academy

Answer:

You Answer is C. 738

Step-by-step explanation:

L x W x H

A= 2 w  l   h  l  h  w  = 2  18 13.5 4  13.5 4 18  =  738

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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The present value of the loan, rounded to the nearest cent, is $37,196.88.

To calculate the present value of a loan, we can use the formula for the present value of an ordinary annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r),

where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is $3,400, the interest rate is 5.19% compounded semi-annually, and the loan term is 7 years, which is equivalent to 14 semi-annual periods.

First, let's convert the interest rate to its semi-annual equivalent by dividing it by 2. So, the interest rate per semi-annual period is 5.19% / 2 = 2.595%.

Now, we can plug these values into the formula:

PV = $3,400 * ((1 - (1 + 0.02595)^(-14)) / 0.02595).

Calculating this equation, we find that the present value of the loan is approximately $37,196.88 when rounded to the nearest cent.

Therefore, the present value of the loan, rounded to the nearest cent, is $37,196.88.

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