It is the probability distribution used when the population variance is unknown and/or if the sample size is small?

The solution to the system of equations is C0 = 17.7 MPa and C1

= -0.042.

Given the yield criterion equation:

|σ11| = √3(C0 + C1p)

We are given two conditions:

In tension: |σ11| = 30 MPa, p = 10

Substituting these values into the equation:

30 = √3(C0 + C1 * 10)

Simplifying, we have:

C0 + 10C1 = 30/√3

In compression: |σ11| = -31.5 MPa, p = -10.5

Substituting these values into the equation:

|-31.5| = √3(C0 - C1 * 10.5)

Simplifying, we have:

C0 - 10.5C1 = 31.5/√3

Now, we have a system of two equations and two unknowns:

C0 + 10C1 = 30/√3 ---(1)

C0 - 10.5C1 = 31.5/√3 ---(2)

To solve this system, we can use the method of substitution or elimination. Let's use the elimination method to eliminate C0:

Multiplying equation (1) by 10:

10C0 + 100C1 = 300/√3 ---(3)

Multiplying equation (2) by 10:

10C0 - 105C1 = 315/√3 ---(4)

Subtracting equation (4) from equation (3):

(10C0 - 10C0) + (100C1 + 105C1) = (300/√3 - 315/√3)

Simplifying:

205C1 = -15/√3

Dividing by 205:

C1 = -15/(205√3)

Simplifying further:

C1 = -0.042

Now, substituting the value of C1 into equation (1):

C0 + 10(-0.042) = 30/√3

C0 - 0.42 = 30/√3

C0 = 30/√3 + 0.42

C0 ≈ 17.7 MPa

The solution to the system of equations is C0 = 17.7 MPa and C1 = -0.042.

To know more about yield criterion, visit

https://brainly.com/question/13002026

#SPJ11

To complete each ordered pair using the function y = 200 tan(x) on the interval 0° ≤ x ≤ 141°, we need to substitute different values of x within that interval and calculate the corresponding values of y. Let's calculate the ordered pairs by rounding the answers to the nearest whole number:

1. For x = 0°:

  y = 200 tan(0°) = 0

  The ordered pair is (0, 0).

2. For x = 45°:

  y = 200 tan(45°) = 200

  The ordered pair is (45, 200).

3. For x = 90°:

  y = 200 tan (90°) = ∞ (undefined since the tangent of 90° is infinite)

  The ordered pair is (90, undefined).

4. For x = 135°:

  y = 200 tan (135°) = -200

  The ordered pair is (135, -200).

5. For x = 141°:

  y = 200 tan (141°) = -13

  The ordered pair is (141, -13).

So, the completed ordered pairs (rounded to the nearest whole number) are:

(0, 0), (45, 200), (90, undefined), (135, -200), (141, -13).

Learn more about ordered pair here:

brainly.com/question/12105733

#SPJ11

The equation is satisfied for all values of a and b.

The values of a and b can be any non-negative real numbers as long as the product ab is non-negative.


The equation √a + √b = √(a + b) is a special case of a more general rule called the Square Root Property.

According to this property, if both sides of an equation are equal and non-negative, then the square roots of the two sides must also be equal.

To find the values of a and b that satisfy the given equation, let's square both sides of the equation:

(√a + √b)² = (√a + √b)²

Expanding the left side of the equation:

a + 2√ab + b = a + 2√ab + b

Notice that the a terms and b terms cancel each other out, leaving us with:

2√ab = 2√ab

This equation is true for any non-negative values of a and b, as long as the product ab is also non-negative.

In other words, for any non-negative real numbers a and b, the equation √a + √b = √(a + b) holds.

For example:

- If a = 4 and b = 9, we have √4 + √9 = √13, which satisfies the equation.

- If a = 0 and b = 16, we have √0 + √16 = √16, which also satisfies the equation.

So, the values of a and b can be any non-negative real numbers as long as the product ab is non-negative.

To know more about equation refer here:

https://brainly.com/question/13763238

#SPJ11

To find the area of triangle AEB, we use base AB (6 cm) and height 6 cm. Applying the formula (1/2) * base * height, the area is 18 cm².

To find the area of triangle AEB, we need to determine the length of the base AB and the height of the triangle. Since both square ABCD and triangle AABE is standing on the same base AB, the length of AB remains the same for both.

We are given that BD = 6 cm, which means that the length of AB is also 6 cm. Now, to find the height of the triangle, we can consider the height of the square. Since AB is the base of both the square and the triangle, the height of the square is equal to AB.

Therefore, the height of triangle AEB is also 6 cm. Now we can calculate the area of the triangle using the formula: Area = (1/2) * base * height. Plugging in the values, we get Area = (1/2) * 6 cm * 6 cm = 18 cm².

Thus, the area of triangle AEB is 18 square centimeters.

For more questions on the area of a triangle

https://brainly.com/question/30818408

#SPJ8

Write the symbolic statement ~ (p ^ q ) in words:

"It is not true that the taxes are high and the stove is hot."

Write the symbolic statement ~ (p ^ q ) in words," requires understanding the logical negation and conjunction. Given that p represents "The taxes are high" and q represents "The stove is hot," the symbolic statement ~ (p ^ q) can be translated into words as "It is not true that the taxes are high and the stove is hot.

Therefore, the correct sentence that represents the symbolic statement is A. "It is not true that the taxes are high and the stove is hot."

In logic, the tilde (~) represents negation, indicating the denial or opposite of a statement. The caret (^) symbolizes the logical conjunction, which means "and." By combining these symbols, we can form complex statements and express them in words. Understanding symbolic logic allows us to analyze and reason about the truth values of compound statements, providing a foundation for deductive reasoning and critical thinking.

Learn more about symbolic statement

brainly.com/question/15649055

#SPJ11

To express the algebraic expression [tex]$(x + iy)^2 - (x - x)^2$[/tex] in the rectangular form [tex]$(Z = X + iY)$[/tex] where [tex]$x$[/tex], [tex]$X$[/tex],[tex]$y$[/tex], [tex]$Y$[/tex]are real numbers, we can expand and simplify the expression.

First, let's expand [tex]$(x + iy)^2$[/tex]:

[tex]\[(x + iy)^2 = (x + iy)(x + iy) = x(x) + x(iy) + ix(y) + iy(iy) = x^2 + 2ixy - y^2\][/tex]

Next, let's simplify [tex]$(x - x)^2$[/tex]:

[tex]\[(x - x)^2 = 0^2 = 0\][/tex]

Now, we can substitute these results back into the original expression:

[tex]\[2(x + iy)^2 - (x - x)^2 = 2(x^2 + 2ixy - y^2) - 0 = 2x^2 + 4ixy - 2y^2\][/tex]

Therefore, the algebraic expression [tex]$(x + iy)^2 - (x - x)^2$[/tex] can be expressed in the rectangular form as [tex]$2x^2 + 4ixy - 2y^2$[/tex].

In this form, [tex]$X = 2x^2$[/tex][tex]$Y = 4xy - 2y^2$[/tex], representing the real and imaginary parts respectively.

learn more about real and imaginary parts

https://brainly.com/question/13389642

#SPJ11

The statement "If vectors u and v are orthogonal, then u² + v² = (u - v)²" is not true in general.

To verify the given statement, let's consider two arbitrary 2-dimensional vectors:

Vector u: (u₁, u₂)

Vector v: (v₁, v₂)

The length squared of vector u, denoted as u², is given by:

u² = u₁² + u₂²

According to the statement, if vectors u and v are orthogonal, then:

u² + v² = (u - v)²

Expanding the right side of the equation:

(u - v)² = (u₁ - v₁)² + (u₂ - v₂)²

         = u₁² - 2u₁v₁ + v₁² + u₂² - 2u₂v₂ + v₂²

         = u₁² + u₂² - 2u₁v₁ - 2u₂v₂ + v₁² + v₂²

Comparing this with the left side of the equation (u² + v²), we can see that they are not equal. There is a missing cross term (-2u₁v₁ - 2u₂v₂) on the left side. Therefore, the statement is not true in general.

In other words, if vectors u and v are orthogonal, it does not imply that u² + v² is equal to (u - v)².

Learn more about orthogonal

brainly.com/question/32196772

#SPJ11

In order to compute the annual dollar changes and percent changes for each item, we need to follow these steps:

1. Identify the items for which we need to compute the changes.
2. Determine the dollar change for each item by subtracting the previous year's value from the current year's value. If the value has decreased, add a minus sign in front of the change to indicate a decrease.
3. Calculate the percent change for each item by dividing the dollar change by the previous year's value and multiplying by 100. Round your percentage answers to one decimal place.
4. Repeat steps 2 and 3 for each item.

For example, let's say we have the following items:

Item A:
Previous year's value = $100
Current year's value = $120

Item B:
Previous year's value = $500
Current year's value = $400

Item C:
Previous year's value = $1000
Current year's value = $1100

To compute the changes:

1. Item A:
Dollar change = $120 - $100 = $20
Percent change = ($20 / $100) * 100 = 20%

2. Item B:
Dollar change = $400 - $500 = -$100
Percent change = (-$100 / $500) * 100 = -20%

3. Item C:
Dollar change = $1100 - $1000 = $100
Percent change = ($100 / $1000) * 100 = 10%

By following these steps, you can compute the annual dollar changes and percent changes for each item in the given information. Remember to round the percentage answers to one decimal place.

To know more about annual dollar  here

https://brainly.com/question/28449645

#SPJ11

The test statistic is z = -1.60

To test the claim that the percentage of readers who own a personal computer is different from the reported percentage, we can use a hypothesis test. Let's define our null hypothesis (H0) and alternative hypothesis (H1) as follows:

H0: The percentage of readers who own a personal computer is equal to 34%.

H1: The percentage of readers who own a personal computer is different from 34%.

We can use the z-test statistic to evaluate this hypothesis. The formula for the z-test statistic is:

[tex]z = (p - P) / \sqrt_((P * (1 - P)) / n)_[/tex]

Where:

p is the sample proportion (30% or 0.30)

P is the hypothesized population proportion (34% or 0.34)

n is the sample size (360)

Let's plug in the values and calculate the test statistic:

[tex]z = (0.30 - 0.34) / \sqrt_((0.34 * (1 - 0.34)) / 360)_\\[/tex]

[tex]z = (-0.04) / \sqrt_((0.34 * 0.66) / 360)_\\[/tex]

[tex]z = -0.04 / \sqrt_(0.2244 / 360)_\\[/tex]

[tex]z= -0.04 / \sqrt_(0.0006233)_[/tex]

[tex]z = -0.04 / 0.02497\\z = -1.60[/tex]

Rounding the test statistic to two decimal places, the value is approximately -1.60.

Learn more about test statistics:

https://brainly.com/question/30458874

#SPJ11

The expression "n" as the subject is given by:

n = (2 - 3K)/(K - 3)

To make "n" the subject in the expression K = 3n + 2/n + 3, we can follow these steps:

Multiply both sides of the equation by (n + 3) to eliminate the fraction:

K(n + 3) = 3n + 2

Distribute K to both terms on the left side:

Kn + 3K = 3n + 2

Move the terms involving "n" to one side of the equation by subtracting 3n from both sides:

Kn - 3n + 3K = 2

Factor out "n" on the left side:

n(K - 3) + 3K = 2

Subtract 3K from both sides:

n(K - 3) = 2 - 3K

Divide both sides by (K - 3) to isolate "n":

n = (2 - 3K)/(K - 3)

Therefore, the expression "n" as the subject is given by:

n = (2 - 3K)/(K - 3)

Learn more about expression here

https://brainly.com/question/30265549

#SPJ11

To find out the amount Tim takes home each month on his monthly paycheck after all taxes (federal and state) and insurance costs are paid, we need to subtract the deductions from his monthly paycheck. After paying all federal, state, and insurance taxes and premiums, Tim's monthly take-home pay is therefore X – $200.

Given that Tim has another $200 deducted from his monthly paycheck each month for insurance and state taxes, we can subtract this amount from his monthly paycheck to find the amount he takes home.

Let's say Tim's monthly paycheck before deductions is X dollars.

First, we subtract $200 (deductions for insurance and state taxes) from X:

X - $200 = Amount Tim takes home each month on his paycheck after deductions.

Therefore, the amount Tim takes home each month on his paycheck after all taxes (federal and state) and insurance costs are paid is X - $200.

It is important to note that we don't have the value of X, Tim's monthly paycheck before deductions. If you have the value of X, you can substitute it into the equation to find the amount Tim takes home.

To know more about "Insurance":

https://brainly.com/question/25855858

#SPJ11

The general solution to the given differential equation is:

y = y_c + y_p = C_1 + C_2x^3 + 1/x - 1/(8x^5)

We assume a solution of the form y_c = x^r. Plugging this into the homogeneous equation, we get:

r(r-1)x^r - 2rx^r + 2x^r = 0

r^2 - 3r = 0

This quadratic equation has two roots: r = 0 and r = 3. Therefore, the complementary solution is:

y_c = C_1x^0 + C_2x^3 = C_1 + C_2x^3

Next, we need to find the particular solution, which we assume as:

y_p = u_1(x)y_1(x) + u_2(x)y_2(x)

Here, y_1(x) = 1 and y_2(x) = x^3. To find u_1(x) and u_2(x),

formulas:

u_1(x) = -∫(y_2(x)f(x))/(W(x)) dx

u_2(x) = ∫(y_1(x)f(x))/(W(x)) dx

where f(x) = 1/x and W(x) is the Wronskian of y_1 and y_2.

Calculate:

u_1(x) = -∫(x^3/x)/(x^6) dx = -∫(1/x^2) dx = -(-1/x) = 1/x

u_2(x) = ∫(1/(x^3))/(x^6) dx = ∫(1/x^9) dx = -1/(8x^8)

Finally, the particular solution is given by:

y_p = (1/x)(1) + (-1/(8x^8))(x^3) = 1/x - 1/(8x^5)

Therefore, the general solution to the given differential equation is:

y = y_c + y_p = C_1 + C_2x^3 + 1/x - 1/(8x^5)

learn more about differential equation

https://brainly.com/question/32645495

#SPJ11

Mathematics is an interesting subject that is constantly evolving and changing. Researching different areas of Mathematics Teaching can help to advance teaching techniques and increase the knowledge base for both students and teachers.

There are several researchable areas of Mathematics Teaching. One area of research is in the development of new teaching strategies and methods.

Another area of research is in the creation of new mathematical tools and technologies.

A third area of research is in the evaluation of the effectiveness of existing teaching methods and tools.

A fourth area of research is in the identification of key skills and knowledge areas that are essential for success in mathematics.

Finally, a fifth area of research is in the exploration of different ways to engage students and motivate them to learn mathematics.

Overall, there are many different researchable areas of Mathematics Teaching.

By exploring these areas, teachers and researchers can help to advance the field and improve the quality of education for students.

To learn more on Researching :

https://brainly.com/question/25257437

#SPJ11

Coupon STRIPS can be created from the given T-bond by removing the coupon payments from the bond and selling them as individual securities. Let's calculate how many coupon STRIPS can be created from this T-bond.

The bond has a 5% coupon, which means it will pay $5 million in interest every year. Over a period of 29 years, the total interest payments would be $5 million x 29 years = $145 million.

The par value of the bond is $100 million. After deducting the interest payments of $145 million, the remaining principal value is $100 million - $145 million = -$45 million.

Since there is a negative principal value, we cannot create any principal STRIPS from this bond. However, we can create coupon STRIPS equal to the number of coupon payments that will be made over the remaining life of the bond.

Therefore, we can create 29 coupon STRIPS of $5 million each from this T-bond. These coupon STRIPS will be sold separately and will not include the principal repayment of the bond.

Learn more about T-bond

https://brainly.com/question/15176473

#SPJ11

The given statement is false. A square matrix A (m × n) has an eigenvalue λ if there is a nonzero vector x in Rn such that Ax = λx.

If the only eigenvalue of A is zero, it is called a zero matrix, and all its entries are zero. The matrix A is a scalar matrix with an eigenvalue λ if it is diagonal, and each diagonal entry is equal to λ.The matrix A will not necessarily be zero if 0 is its only eigenvalue. To prove the statement is false, we will provide an example; Let A be the following 3 x 3 matrix:

{0, 1, 0} {0, 0, 1} {0, 0, 0}A=0

is the only eigenvalue of A, but A is not equal to 0. The statement "If 0 is the only eigenvalue of A (matrix M3x3 (C)), then A = 0" is false. A matrix A (m × n) has an eigenvalue λ if there is a nonzero vector x in Rn such that

Ax = λx

If the only eigenvalue of A is zero, it is called a zero matrix, and all its entries are zero.The matrix A will not necessarily be zero if 0 is its only eigenvalue. To prove the statement is false, we can take an example of a matrix A with 0 as the only eigenvalue. For instance,

{0, 1, 0} {0, 0, 1} {0, 0, 0}A=0

is the only eigenvalue of A, but A is not equal to 0.

To know more about matrix visit:

https://brainly.com/question/29132693

#SPJ11

False: If hog is surjective, then h and g are both non-empty, and hog is surjective. True: If hog is surjective, then for every element u in U, there exists an element s in S such that hog(s)=h(g(s))=u.  False: If hog is injective and g is surjective, then for every element s in S and t,t′ in T, hog(s)=h(t)=h(t′) implies t=t′.

a) False: If hog is surjective, then h and g are both non-empty, and hog is surjective. However, even if hog is surjective, there is no guarantee that h is surjective. This is because hog could map multiple elements in S to a single element in U, which means that there are elements in U that are not in the range of h, and so h is not surjective. Therefore, the statement is false.

b) True: If hog is surjective, then for every element u in U, there exists an element s in S such that hog(s)=h(g(s))=u. This means that g(s) is in the range of g, and so g is surjective. Therefore, the statement is true.

c) False: If hog is injective and g is surjective, then for every element s in S and t,t′ in T, hog(s)=h(t)=h(t′) implies t=t′. Suppose that there exist elements t,t′ in T such that h(t)=h(t′). Since g is surjective, there exist elements s,s′ in S such that g(s)=t and g(s′)=t′. Then, we have hog(s)=h(g(s))=h(t)=h(t′)=h(g(s′))=hog(s′), which implies that s=s′ since hog is injective. However, this does not imply that t=t′, since h could map multiple elements in T to a single element in U, and so h(t)=h(t′) does not necessarily mean that t=t′. Therefore, the statement is false.

Learn more about surjective at https://brainly.com/question/13656067

#SPJ11

To find the area under the standard normal curve to the right of z=2.25, you can use the z-table or a calculator such as the ALEKS calculator. The z-table provides the cumulative probability up to a given z-score.

1. Using the z-table, locate the row corresponding to 2.2 and the column corresponding to 0.05. The intersection of this row and column gives the area to the left of z=2.25, which is 0.9878.

2. Subtract this value from 1 to find the area to the right of z=2.25:
  1 - 0.9878 = 0.0122

Therefore, the area under the standard normal curve to the right of z=2.25 is approximately 0.0122.

To find the area under the standard normal curve between z=−2.48 and z=−, we can use the same approach:

1. Using the z-table, locate the row corresponding to -2.4 and the column corresponding to 0.08. The intersection of this row and column gives the area to the left of z=-2.48, which is 0.0066.

2. Subtract this value from the area to the left of z=0 (0.5000) to find the area between z=−2.48 and z=−:
  0.5000 - 0.0066 = 0.4934

Therefore, the area under the standard normal curve between z=−2.48 and z=− is approximately 0.4934.

To know more about "Cumulative Probability":

https://brainly.com/question/27856123

#SPJ11

The attack rate for the people who ate the shrimp salad and fell ill is approximately 10.50%.

To calculate the attack rate for the people who ate the shrimp salad and fell ill, we need to divide the number of people who ate the shrimp salad and fell ill by the total number of people who ate the shrimp salad, and then multiply by 100 to express it as a percentage.

Given information:

Total number of passengers = 1,780

Total number of crew members = 240

Total number of people who ate the shrimp salad and fell ill = 212

Total number of people who ate the shrimp salad = Total number of passengers + Total number of crew members = 1,780 + 240 = 2,020

Attack Rate = (Number of people who ate shrimp salad and fell ill / Number of people who ate shrimp salad) * 100

Attack Rate = (212 / 2,020) * 100

Attack Rate ≈ 10.50

Learn more about percentage

https://brainly.com/question/32197511

#SPJ11

Playoffs are a competition where participants compete against specific opponents in a structured format, but it is not a requirement for every contestant to meet every other participant in turn.

No, it is not true that playoffs are a competition in which each contestant meets every other participant, usually in turn.

Playoffs typically involve a series of elimination rounds where participants compete against a specific opponent or team. The format of playoffs can vary depending on the sport or competition, but the general idea is to determine a winner or a group of winners through a series of matches or games.

In team sports, such as basketball or soccer, playoffs often consist of a bracket-style tournament where teams are seeded based on their performance during the regular season. Teams compete against their assigned opponents in each round, and the winners move on to the next round while the losers are eliminated. The matchups in playoffs are usually determined by the seeding or a predetermined schedule, and not every team will face every other team.

Individual sports, such as tennis or golf, may also have playoffs or championships where participants compete against each other. However, even in these cases, it is not necessary for every contestant to meet every other participant. The matchups are typically determined based on rankings or tournament results.

In summary, playoffs are a competition where participants compete against specific opponents in a structured format, but it is not a requirement for every contestant to meet every other participant in turn.

for such more question on competition

https://brainly.com/question/2891218

#SPJ8

"the probability that a student plays video games given that the student is female." is an example of a conditional probability.The correct answer is option C.

A conditional probability is a probability that is based on certain conditions or events occurring. Out of the options provided, option C is an example of a conditional probability: "the probability that a student plays video games given that the student is female."

Conditional probability involves determining the likelihood of an event happening given that another event has already occurred. In this case, the event is a student playing video games, and the condition is that the student is female.

The probability of a female student playing video games may differ from the overall probability of any student playing video games because it is based on a specific subset of the population (female students).

To calculate this conditional probability, you would divide the number of female students who play video games by the total number of female students.

This allows you to focus solely on the subset of female students and determine the likelihood of them playing video games.

In summary, option C is an example of a conditional probability as it involves determining the probability of a specific event (playing video games) given that a condition (being a female student) is satisfied.

For more such questions probability,click on

https://brainly.com/question/251701

#SPJ8

The Laplace transform of the function F(s) = 2s² + 40s + 168 / (2 (s-2) (s² + (s² + 4s+20)) is 2/s² + 40/s + 168 / ((s-2) (2s³ + 16s - 40)).

The Laplace transform of the function F(s) can be determined by using the linearity property and applying the corresponding transforms to each term.

The given function F(s) is expressed as F(s) = 2s² + 40s + 168 / (2 (s-2) (s² + (s² + 4s+20)).

To calculate the Laplace transform of F(s), we can split the function into three parts:

1. The first term, 2s², can be directly transformed using the derivative property of the Laplace transform. Taking the derivative of s², we get 2, so the Laplace transform of 2s² is 2/s².

2. The second term, 40s, can also be directly transformed using the derivative property. The derivative of s is 1, so the Laplace transform of 40s is 40/s.

3. The third term, 168 / (2 (s-2) (s² + (s² + 4s+20)), can be simplified by factoring out the denominator. We get 168 / (2 (s-2) (2s² + 4s+20)).

Now, let's consider the denominator: (s-2) (2s² + 4s+20). We can expand the quadratic term to obtain (s-2) (2s² + 4s+20) = (s-2) (2s²) + (s-2) (4s) + (s-2) (20) = 2s³ - 4s² + 4s² - 8s + 20s - 40 = 2s³ + 16s - 40.

Thus, the denominator becomes (s-2) (2s³ + 16s - 40).

We can now rewrite the expression for F(s) as F(s) = 2/s² + 40/s + 168 / ((s-2) (2s³ + 16s - 40)).

Therefore, the Laplace transform of F(s) is 2/s² + 40/s + 168 / ((s-2) (2s³ + 16s - 40)).

To know more about Laplace transforms and their properties, refer here:

https://brainly.com/question/31689149#

#SPJ11

There are 134,596 ways to select a committee of six persons from a dib with 24 members.

To solve this problem, we can use the concept of combinations. A combination is a selection of items without regard to the order. In this case, we want to select six persons from a group of 24.

The formula to calculate the number of combinations is given by:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of items and r is the number of items we want to select.

Applying this formula to our problem, we have:

C(24, 6) = 24! / (6! * (24-6)!)

Simplifying this expression, we get:

C(24, 6) = 24! / (6! * 18!)

Now let's calculate the factorial terms:

24! = 24 * 23 * 22 * 21 * 20 * 19 * 18!

6! = 6 * 5 * 4 * 3 * 2 * 1

Substituting these values into the formula, we have:

C(24, 6) = (24 * 23 * 22 * 21 * 20 * 19 * 18!) / (6 * 5 * 4 * 3 * 2 * 1 * 18!)

Simplifying further, we can cancel out the common terms in the numerator and denominator:

C(24, 6) = (24 * 23 * 22 * 21 * 20 * 19) / (6 * 5 * 4 * 3 * 2 * 1)

Calculating the values, we get:

C(24, 6) = 134,596

Therefore, there are 134,596 ways to select a committee of six persons from a dib with 24 members.

To know more about "dib  members "

https://brainly.com/question/4658834

#SPJ11

The minimum possible value of x, assuming that x is a whole number, is 63

From the question above,, Volume of ethanol used = n = 10 ounces

Volume of water used = w = 8x ounces

C (volume percent concentration) should be less than or equal to 16%.

That is, C ≤ 16% (or C/100 ≤ 0.16)

From the given formula, we know that:

100n C = -% n+w

Rearranging this formula, we get:C = -100n / n+w

Now substituting the given values, we get:

C = -100(10) / 10 + 8x

Simplifying this equation, we get:C = -1000 / (10 + 8x)

We need to find the minimum possible value of x for which C ≤ 16%

Substituting the value of C, we get:

-1000 / (10 + 8x) ≤ 0.16

Multiplying both sides by (10 + 8x), we get:-1000 ≤ 1.6(10 + 8x)

Simplifying this equation, we get:1000 ≤ 16x + 160

Dividing both sides by 16, we get:62.5 ≤ x

Learn more about chemical solution at

https://brainly.com/question/32511210

#SPJ11

Answer:

21

Step-by-step explanation:

b - 2a - c

(9) -2(-3) - (-6)

9 + 6 + 6

21

Helping in the name of Jesus.

The answer is:

Work/explanation:

To evaluate further, plug in -3 for a, 9 for b and -6 for c

[tex]\bf{b-2a-c}[/tex]

[tex]\bf{9-2a-c}[/tex]

[tex]\bf{9-2(-3)-(-6)}[/tex]

Simplify

[tex]\bf{9-2(-3)+6}[/tex]

[tex]\bf{9-(-6)+6}[/tex]

[tex]\bf{9+6+6}[/tex]

[tex]\bf{9+12}[/tex]

[tex]\bf{21}[/tex]

In the given prisoner's dilemma game, players have two choices: cooperate (C) or defect (D). The payoffs for each combination of actions are represented by the variables g and ℓ, where g>0 and ℓ>0.

Now, let's consider a twist in the game. If a player chooses a different action in the second period compared to the first period, they incur a cost of ε. The players aim to maximize the sum of their payoffs over the two periods, with a discount factor of δ=1.

The question asks us to show that there is always a subgame perfect equilibrium where both players play (D,D) in both periods, given that g<1 and ℓ<1.

To prove this, we can analyze the incentives for each player and the possible outcomes in the game.

1. If both players choose (C,C) in the first period, they both receive a payoff of ℓ in the first period. However, in the second period, if one player switches to (D), they will receive a higher payoff of g, while the other player incurs a cost of ε. Therefore, it is not in the players' best interest to choose (C,C) in the first period.

2. If both players choose (D,D) in the first period, they both receive a payoff of g in the first period. In the second period, if they both stick to (D), they will receive another payoff of g. Since g>0, it is a better outcome for both players compared to (C,C). Furthermore, if one player switches to (C) in the second period, they will receive a lower payoff of ℓ, while the other player incurs a cost of ε. Hence, it is not in the players' best interest to choose (D,D) in the first period.

Based on this analysis, we can conclude that in the subgame perfect equilibrium, both players will choose (D,D) in both periods. This is because it is a dominant strategy for both players, ensuring the highest possible payoff for each player.

In summary, regardless of the values of g and ℓ (as long as they are both less than 1), there will always be a subgame perfect equilibrium where both players play (D,D) in both periods. This equilibrium is a result of analyzing the incentives and outcomes of the game.

To know more about prisoner's dilemma here

https://brainly.com/question/33721898

#SPJ11

Answer:

One fraction: 23/7

Mixed number: 3 2/7

a) The simplified expression to represent the number of sweets Jack has left after eating 2c sweets is: [tex]\displaystyle 9c-2c[/tex].

b) To find how many sweets Jack has left if [tex]\displaystyle c=3[/tex], we substitute [tex]\displaystyle c=3[/tex] into the expression: [tex]\displaystyle 9(3)-2(3)=27-6=21[/tex].

Therefore, if [tex]\displaystyle c=3[/tex], Jack has 21 sweets left.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answers:

(a)  7c

(b)  21

============================

Explanation:

Start with 9c and subtract off 2c to get 9c-2c = 7c.

We can think of it like 9 candies - 2 candies = 7 candies. Replace each "candies" with "c" so things are shortened.

Afterward, plug in c = 3 to find that 7c = 7*3 = 21

If g¹ (f(x)) = 16x² + 8x + 6and g(x) = x²+5 then (f - g) (-2) = 4(-2) - (-2)² - 4= -8 - 4 - 4= -16 and  g¹ (f(x)) = 16x² + 8x + 6.

Given that f(x) = 4x + 1 and g(x) = x² + 5

a) Find (f-g) (-2)(f - g) (x) = f(x) - g(x)

Substitute the values of f(x) and g(x)f(x) = 4x + 1g(x) = x² + 5(f - g) (x) = 4x + 1 - (x² + 5) = 4x - x² - 4

On substituting x = -2, we get

(f - g) (-2) = 4(-2) - (-2)² - 4= -8 - 4 - 4= -16

b) Find g¹ (f(x))f(x) = 4x + 1g(x) = x² + 5

Let y = f(x) => y = 4x + 1

On substituting the value of y in g(x), we get

g(x) = (4x + 1)² + 5= 16x² + 8x + 1 + 5= 16x² + 8x + 6

Therefore, g¹ (f(x)) = 16x² + 8x + 6

Learn more about g¹ (f(x)) at https://brainly.com/question/32930384

#SPJ11

(a) The amount of the investment at the end of 4 years with semiannual compounding is $25,432.51.

(b) The amount of the investment at the end of 4 years with quarterly compounding is $25,548.02.

(c) The amount of the investment at the end of 4 years with monthly compounding is $25,575.03.

(d) The amount of the investment at the end of 4 years with continuous compounding is $25,584.80.

To calculate the amount of the investment at the end of 4 years with different compounding methods, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount of the investment

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Let's calculate the amounts for each compounding method:

(a) Semiannual Compounding:

n = 2 (compounded twice a year)

A = 23000(1 + 0.06/2)^(2*4) = $25,432.51

(b) Quarterly Compounding:

n = 4 (compounded four times a year)

A = 23000(1 + 0.06/4)^(4*4) = $25,548.02

(c) Monthly Compounding:

n = 12 (compounded twelve times a year)

A = 23000(1 + 0.06/12)^(12*4) = $25,575.03

(d) Continuous Compounding:

Using the formula A = Pe^(rt):

A = 23000 * e^(0.06*4) = $25,584.80

In summary, the amount of the investment at the end of 4 years with different compounding methods are as follows:

(a) Semiannual compounding: $25,432.51

(b) Quarterly compounding: $25,548.02

(c) Monthly compounding: $25,575.03

(d) Continuous compounding: $25,584.80

Learn more about Investment

brainly.com/question/17252319

#SPJ11

In a class of 147 students, where 95 are taking math (M), 73 are taking science (S), and 52 are taking both math and science, the probability of 1 student picked at random taking math or science or both is 0.7891.

According to the given data:

Total number of students in the class = 147

Number of students taking math = 95

Number of students taking science = 73

Number of students taking both math and science = 52

We need to subtract the number of students who are taking both math and science from the sum of the number of students taking math and science to avoid the double counting. This gives us: 95 + 73 - 52 = 116

P (taking math or science or both) = 116/147

P (taking math or science or both) = 0.7891

Therefore, the probability of taking math or science or both is 0.7891.

To know more about probability, refer here:

https://brainly.com/question/30881224

#SPJ11