A professor of political science wants to predict the outcome of a school board election. Three candidates Ivy (I), Bahrn (B), and Smith (S), are running for one position. There are three categories of voters: Left (L), Center (C), Right (R). The candidates are judged based on three factors: educational experience (E ), stand on issues (S), and personal character (P ). The following are the comparison matrices for the hierarchy of left, center, and right. 2 3 2 3 1 2 AHP was then used to reduce these matrices to the following relative weights eft Center Right Candidate Ivy Smith. 2 Bahr. 5. 1. 2 4. 45 33 4. 255 Determine the winning candidate, assess the consistency of the decision

Let the no. added be x

= -211 + x = 195

= x = 195 + 211

= x = 406

The number should be added is 406..

Answer:

6

Step-by-step explanation:

if u count up all the lines then number 6 is the 19th one

Take the 2nd term and minus the 1st term.

Now take the 3rd term and minus the 2nd term.

Notice that the differences are the same. Hence there is a common difference (difference of -0.5).

So it is an arithmetic sequence.

The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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Answer:

Step-by-step explanation:

We can use the Binomial Theorem to show this by letting a=3 and b=2 in the formula:

(a+b)^n = ∑(n choose k) a^(n-k) b^k

Substituting the values of a and b, we get:

(3+2)^n = ∑(n choose k) 3^(n-k) 2^k

5^n = ∑(n choose k) 3^(n-k) 2^k

Multiplying both sides by (-1)^n, we get:

(-1)^n 5^n = ∑(n choose k) (-1)^n 3^(n-k) 2^k

(-1)^n 5^n = ∑(n choose k) (-1)^k 3^(n-k) 2^k

Using the property that (n choose k) = (n choose n-k), we can simplify the expression:

(-1)^n 5^n = ∑(n choose n-k) (-1)^(n-k) 3^(k) 2^(n-k)

(-1)^n 5^n = ∑(n choose k) (-1)^(n-k) 3^(k) 2^(n-k)

We recognize the sum on the right-hand side as the expansion of (3-2)^n:

(-1)^n 5^n = (3-2)^n = ∑(n choose k) (-1)^(n-k) 3^(k) 2^(n-k)

Rearranging, we get:

∑(n choose k) (-1)^k 3^(n-k) 2^k = 5^n

Dividing both sides by 5^n, we get:

∑(n choose k) (-1)^k (3/5)^(n-k) (2/5)^k = 1

We recognize the left-hand side as a binomial expansion with coefficients (n choose k) and terms (3/5)^(n-k) and (2/5)^k. Therefore, the sum of these terms must equal 1, by the Binomial Theorem. This verifies the result.

A) True. Therefore, there should be no systematic bias when probability sampling is done correctly.

When conducting a research study, it is important to ensure that the sample chosen is representative of the population. Probability sampling is a method that aims to achieve this by giving each member of the population an equal chance of being included in the sample.

When this sampling method is done correctly, it minimizes bias and ensures that the sample is truly representative. For example, let's consider a study on the average height of students in a particular school.

If we were to use probability sampling, we would assign a number to each student and then randomly select a certain number of students from that pool. This would give every student an equal chance of being chosen for the sample, eliminating any systematic bias that might arise if we were to select students based on subjective criteria.

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Given that pq=qr=rs=sp, what additional information is required to conclude that pqrs is a square?

In order to conclude that pqrs is a square, the additional information required is that the sides of the quadrilateral are perpendicular to each other (i.e. they form 90-degree angles).

We know that pq=qr=rs=sp, which means that all four sides of the quadrilateral are equal in length.

However, this information alone is not sufficient to conclude that pqrs is a square, as there are many other quadrilaterals that have all four sides equal in length.

For instance, a rectangle has all four sides equal in length, but its sides are not necessarily perpendicular to each other. Thus, we require the additional information that the sides of pqrs are perpendicular to each other in order to identify that pqrs is a square.

In conclusion, the additional information needed to conclude that pqrs is a square is that the sides of the quadrilateral are perpendicular to each other (i.e. they form 90-degree angles).

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The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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Greg's score is 600 points.

Starting with zero points, he gained 400 points, which brings his score to 400. Then, he gained another 200 points, bringing his total score to 400 + 200 = 600 points.

what is points?

In gaming or sports, points refer to the numeric values assigned to different achievements or accomplishments during the game or match. For example, in a basketball game, points are awarded for making a basket or a free throw, and the team with the most points at the end of the game wins. In video games, points are often awarded for completing tasks, defeating enemies, or reaching certain milestones. The total number of points a player has earned is usually used to determine their ranking or score.

what is score?

A score is a numerical value assigned to an achievement or performance in a game, test, or assessment. It is used to measure a person's or team's success or proficiency in a certain activity. In sports, for example, a score is used to determine which team has won a game or match. In academic tests, scores are used to evaluate a student's knowledge and understanding of a subject.

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You know that:

- Last weekend his trip took 10 hours when he drove to the mountains.

- When he drove home, the trip took 7 hours.

- His average rate was 18 miles per hour faster on the trip home.

By definition, the distance can be calculated with this formula:

Where "d" is distance, "r" is rate, and "t" is time.

Then, you can set up the following equation to represent his trip to the mountains ("d" is in miles):

And you can set up the following equation to represent his trip home ("d" is in miles):

To find the value of "r", you need to make both equations equal to each other and solve for "r". Then, you get:

Knowing the value of "r", you can substitute it into the second equation:

Finally, evaluating, you get (Remember that "d" is in miles)

Therefore, the answer is:

with alpha = .01 the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of -2.769 and 2.769

To calculate the critical region boundaries for a two-tailed t-test with alpha = 0.01 and n = 16 subjects, we need to use the t-distribution table. The table will give us the critical values for the given alpha level and sample size. In the t-distribution table, look up the row that corresponds to alpha = 0.01 and n = 16. This will give us the critical values, which in this case are -2.769 and 2.769. Therefore, the two-tailed critical region for a t-test using a sample of n = 16 subjects would have boundaries of -2.769 and 2.769.

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The number of pages read by Laura each day if The book had 85 pages, the same amount every day, and completed the book in just 10 days, is 8.5.

When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

For instance, 4 2 = 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.

Given:

The book had 85 pages, the same amount every day, and completed the book in just 10 days,

Calculate the number of pages read each day as shown below,

The number of pages read each day = total number of pages / total number of days

The number of pages read each day =85 / 10

The number of pages read each day = 8.5

Thus, The number of pages read each day is 8.5 pages per day.

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The answer is option B) 09. To find the mean (average) of the yards gained by Roger during his seven carries, we need to add up all the yards gained and divide the sum by the number of carries.

So, for the given data set {2, 6, 20, 11, 8, 12, 4}, the total yards gained is:

2 + 6 + 20 + 11 + 8 + 12 + 4 = 63

The number of carries is 7.

Therefore, the mean yards gained per carry is:

Mean = Total yards gained / Number of carries

= 63 / 7

= 9

Hence, the answer is option B) 09.

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If the value exceeds\($0.200$\) by the tolerance of \($0.020$\) on either side, a repair cost of \($\$150$\)is incurred.

\($L(x) = 150(x - T)$\) option b.

The Taguchi loss function measures the cost or loss associated with deviations from a target value in a quality characteristic.

In this case, the specification for the quality characteristic is \($0.200 \pm 0.020$\).

If the value exceeds \($0.200$\) by the tolerance of \($0.020$\)on either side, a repair cost of $\$150$ is incurred.

Based on this information, the Taguchi loss function for this example is given by:

b.\($L(x) = 150(x - T)$\)

In the given options, option b represents the correct Taguchi loss function. The loss function is a linear function where the loss increases linearly with the deviation from the target value.

The coefficient of \($150$\) represents the cost of repair per unit deviation.

This loss function is appropriate for the given scenario as it accurately captures the cost associated with deviations from the target value.

The Taguchi loss function provides a quantitative measure to assess the impact of variations in the quality characteristic and helps in making decisions regarding process improvement and optimization.

In this case, it allows for evaluating the cost implications of exceeding the specified tolerance and guides decision-making on whether repairs are necessary based on the associated costs.

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Answer:

Correct answer is 0.67

Step-by-step explanation:

The generatrix of a cylinder is intersected by a plane parallel to its axis to determine the shape of the hole in the cylinder, while the generatrix of a cone is intersected by a plane via its vertex.

We select cutting planes that intersect both surfaces along their generatrixes in order to construct the intersection points of a cone and a cylinder. A cylinder's generatrix is intersected by a plane parallel to its axis, and a cone's generatrix is intersected by a plane via its vertex.

Since the line passing through the cone's vertex is parallel to the axis of the cylinder, the system of planes that intersect both surfaces in their generatrixes is a pencil-shaped arrangement of planes.

The cone and the cylinder are both intersected by every plane of that pencil in two different generatrixes.

In contrast to the vertices of the surfaces, the junction curve has four points that are intersections of these four lines.

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EXPLANATION:

We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.

Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.

We can now extract the following triangle from the diagram provided;

We now have a right triangle which we shall solve by use of the Pythagorean theorem;

Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;

Subtract 36 from both sides;

Take the square root of both sides;

Rounded to the nearest tenth, the answer is;

ANSWER:

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

This expression has no factors

Step-by-step explanation:

You can't factorize it because it has no factors.

If 14 were sqrt-able then there would have been a factor

The probability that the sample mean would be less than 23,013 dollars if a sample of 134 persons is randomly selected is approximately 0.0000397.

We can use the central limit theorem to approximate the distribution of the sample mean as a normal distribution, with a mean of μ = 23,037 dollars and a standard deviation of σ/√n = √(149,769/134) = 33.23 dollars.

Then we can standardize the sample mean using the z-score formula:

z = (\(\bar{X}\) - μ) / (σ/√n)

where \(\bar{X}\) is the sample mean.

Plugging in the given values, we get:

z = (23,013 - 23,037) / 33.23 ≈ -0.722

Using a calculator, we can find that the probability of getting a z-score less than -0.722 is approximately 0.0000397.

Therefore, the probability that the sample mean would be less than 23,013 dollars if a sample of 134 persons is randomly selected is approximately 0.0000397.

This is a very small probability, indicating that it is unlikely to obtain a sample mean this low if the true population mean is 23,037 dollars.

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Answer:

p = 11

q = 34

r = 91

Step-by-step explanation:

If each term (after the first two terms) is the sum of the previous two terms:

\(\implies p+23=q\)

\(\implies 23+q=57\)

\(\implies q+57=r\)

Solve the second equation for q:

\(\implies 23+q=57\)

\(\implies 23+q-23=57-23\)

\(\implies q=34\)

Substitute the found value of q into the first equation and solve for p:

\(\implies p+23=34\)

\(\implies p+23-23=34-23\)

\(\implies p=11\)

Substitute the found value of q into the third equation and solve for r:

\(\implies 34+57=r\)

\(\implies r=91\)

Therefore:

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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Answer:

x = \(\sqrt{26}\)

Step-by-step explanation:

using pythagoras theorem

here \(\sqrt{13}\) and \(\sqrt{13}\) are the legs of the right angled triangle and x is hypotenuse.

a^2 + b^2 = c^2

\((\sqrt{ 13 })^2 + (\sqrt{13})^2 = x^2\)

13 + 13 = x^2

26 = x^2

\(\sqrt{26}\) = x

Answer:

answer would be c

Step-by-step explanation:

hope this helps

The answer is 2.6825  cm, which is not one of the given options. Therefore, the correct answer is E. none of these.

The bulk modulus, B is defined as:

B = (P / ΔV / V), where P is the pressure applied, ΔV is the change in volume, and V is the original volume.

For a cube, the change in volume, ΔV is related to the change in length, ΔL by:

\(\sf \Delta V = \Delta L^3\).

Given that the cube has 2.0 cm sides, the original volume, V is:

\(\sf V = (2.0 \ cm)^3 = 8.0 \ cm^3\).

The pressure applied is \(\sf P = 2.0 \times 10^5\) Pa and the bulk modulus is \(\sf B = 4.7 \times 10^5 \ N/m^2\).

We can rearrange the bulk modulus formula to solve for ΔL as:

\(\sf \Delta L = \huge \text(\dfrac{P}{B} \huge \text) \times \dfrac{V}{3}\).

Substituting the values, we get:

\(\sf \Delta L = (2.0 \times 10^5 \ \dfrac{Pa}{4.7} \times 10^5\ N/m^2) \times \dfrac{8.0 \ cm^3}{3} = 0.6825 \ cm\)

Therefore, the final length of any side of the cube is:

\(\sf L = 2.0 \ cm + \Delta L = 2.0 \ cm + 0.6825 \ cm = 2.6825 \ cm\)

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Complete Question:

A cube with 2.0-cm sides is made of material with a bulk modulus of4.7 × 10^5 N/m2. When it is subjected to a pressure of 2.0 × 10^5 Pa the length of its any of its sides is:

A. 0.85 cm

B. 1.15 cm

C. 1.66 cm

D. 2.0 cm

E. none of these

The equation 4(sin x)^2 - 2 = 0 is to be solved on the interval [0, 2.phi), where phi represents the golden ratio. The solutions to the equation within this interval are x = (phi/4) and (3.phi/4). These values are arranged in increasing order.

To solve the equation 4(sin x)^2 - 2 = 0, we start by isolating the term (sin x)^2. Adding 2 to both sides of the equation, we get 4(sin x)^2 = 2. Dividing both sides by 4, we obtain (sin x)^2 = 1/2.

Taking the square root of both sides, we have sin x = ± √(1/2). The positive square root leads to sin x = √(1/2), which simplifies to sin x = 1/√2. To find the solutions within the given interval [0, 2.phi), we look for the values of x where sin x is equal to 1/√2.

The value of sin x is equal to 1/√2 at angles π/4 and 3π/4, which correspond to (phi/4) and (3.phi/4) respectively. Therefore, the solutions to the equation on the interval [0, 2.phi) are x = (phi/4) and (3.phi/4). These values are arranged in increasing order, giving the final answer as x = (phi/4), (3.phi/4).

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Answer:

-4 Cot (−45)-4cot(-45)Sin (330)sin(330) Csc (60)

Step-by-step explanation:

Answer:

Step-by-step explanation:

All you need do is divide by m and you have the answer.

x*m/m = np/m

x = np/m