The objective function for a LP model is 3 X1 + 2 X2. If X1 = 20 and X2 = 30, what is the value of the objective function?
0
120
60
50

a) For chi-squared distribution with v=3 degrees of freedom, the statistic that can be constructed using Xi's is:

X2 = Σ i=1 3 (Xi − i)2 / 3.

X2 has chi-squared distribution with 3 degrees of freedom.

b) For t-distribution with v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

T = (X1 − 1) / [(X2/2)0.5].

T has t-distribution with 2 degrees of freedom.

c) For F-distribution with v1=1 and v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

F = [(X1 − 1)/1] / [(Σi=2 to 3 Xi2) / 2].

F has F-distribution with 1 and 2 degrees of freedom.

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Answer:

A.3.  x = 72°    y = 90°

Step-by-step explanation:

The sum of the interior angles in a polygon is (n-2)*180, where n is the number of angles.  In this diagram, we have:

Hexagon n=6):  (6-2)*180° = 720°

Pentagon (n=5):  (5-2)*180° = 540°

Triangle (n=3):  (3-2)*180° = 180°

Square (n=4):     (4-2)*180° = 360°

In this case, all are either regular or equilateral, so the angles will all be the same within each polygon.

Hexagon:  (720°/6) = 120°

Pentagon:  (540°/5) = 108°

Triangle = 60°

Square = 90°

Refer to the attached diagram for the calculations.

By adding up the angles we know that are adjacent to x and y, and setting the total to 360°, we can calculate the missing angles x and y.

x = 72°

y = 90°

I started the problem for B3, but am not certain how to find the angles for the isosceles triangles without more information.

The decimals of a square root that would be rounded to an approximate value are √3 = 1.732 and √5 = 2.23

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The decimals are equivalent to a square root.

Example:

√5 = 2.23

This can be rounded to 2.

√3 = 1.732

This can be rounded to 1.7 or 2.

Thus,

The decimals of a square root are √5 = 2.23 and √3 = 1.732.

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Answer:

the answer is A

Step-by-step explanation:

A = 4/3x-5

Answer:

Step-by-step explanation:

B

The  probability of getting at least 12 successes is approximately 0.035, or 3.5% (rounded to the nearest tenth of a percent).

This is a binomial distribution problem with $n=90$ trials and probability of success $p = 1/6$, since getting a six on a single roll is a success. We are interested in finding the probability of getting at least 12 successes.

To calculate this probability, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. In this case, the event of interest is getting at least 12 successes, so the complement event is getting 11 or fewer successes.

We can use the binomial probability formula to calculate the probability of getting 11 or fewer successes:

$P(X \leq 11) = \sum_{k=0}^{11} {90 \choose k} \left(\frac{1}{6}\right)^k \left(\frac{5}{6}\right)^{90-k} \approx 0.965$

Therefore, the probability of getting at least 12 successes is:

$P(X \geq 12) = 1 - P(X \leq 11) \approx 0.035$

So the probability of getting at least 12 successes is approximately 0.035, or 3.5% (rounded to the nearest tenth of a percent).

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The total surface area of the triangular prism is: 111 ft²

To find the total surface area of the given triangular prism, we will find the area of all the surfaces and add it up.

Formula for the area of a rectangle is:

Area = Length * Width

Area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Total Surface area = 2(¹/₂ * 3 * 7) + (7 * 5) + (8 * 5) + (3 * 5)

Total Surface area = 21 + 35 + 40 + 15

Total Surface area = 111 ft²

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There are two stiff transforms to use:

The fact that the real domain is the domain of quadratic functions makes it possible to identify the solution set.

Thus, we must decide which rigid transformations to apply to f(x) in order to produce g(x). Rigid transformations are transformations applied to geometric loci in the field of Euclidean geometry so that Euclidean distances within the latter are conserved (x).

Following thorough consideration, we come to the conclusion that the two stiff transformations listed below must be used:

Vertical translation 7 units to the plus side.

reflection along the y = 5 line.

The collection of x-values necessary for the function to exist is represented by the solution set.  Due to the fact that both functions are quadratic equations, the entire real domain is described by their solutions.

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The missing length of the triangle using Pythagoras theorem is; x = 3

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The right angle triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

The formula to find the sides is;

hypotenuse² = opposite + adjacent²

We are given;

Hypotenuse = 5

Opposite = x

adjacent = 4

Thus;

5² = x² + 4²

x² = 5² - 4²

x² = 25 - 16

x = √9

x = 3

We conclude that it is the missing length of the triangle

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Answer:

FH, GF, GH

hmmmmmmmmmmm

Answer:

A)

The simplest way to solve A is by checking 1st digit one-by-one.

selecting 1 as 1st digit, we have 2 ways

1324 and 1423

selecting 2 as 1st digit, we have 3 ways

2143, 2314, and 2413

selecting 3 as 1st digit, we have 3 ways

3142, 3241, and 3412

selecting 4 as 1st digit, we have 2 ways

4132 and 4231

=> 2 +3 + 3 + 2 = 10 ways in total.

B)

Use the same strategy as A)

selecting 1st digit that is greater than 6, there are 3 digits: {9, 8, 7}

selecting 9 as 1st digit => 967, 968

selecting 8 as 1st digit => 867, 869

selecting 7 as 1st digit => 768, 769

=> 3 x 2 = 6 ways

selecting 1st digit that is smaller than 6, there are 5 digits: {5, 4, 3, 2, 1}

selecting 5 as 1st digit => 565, 564, 563, 562, 561, 560

similarly, selecting 4, 3, 2, 1, there are 6 ways to select that last digit

=> 5 x 6 = 30 ways

=> 30 + 6 = 36 ways in total

C)

a 7-digit snakelike number starts with digit 9 (the largest digit)

=> 2nd digit is smaller than 9

=> 3rd digit is larger than 2nd digit

=> 4th digit is smaller than 3rd digit

=> 5th digit is larger than 4th digit

=> 6th digit is smaller than 5th digit

=> 7th digit is larger than 6th digit (this is impossible because 0 is smallest digit)

Answer:

Exact Form-9+√69÷6

Decimal form-2.88443731

Step-by-step explanation:

Answer:

60 seconds

Step-by-step explanation:

The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

Step-by-step explanation:

Answer:

0.013

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

Given n = 6, p = 0.69, and r = 0 or 1:

P = ₆C₀ (0.69)⁰ (1−0.69)⁶⁻⁰ + ₆C₁ (0.69)¹ (1−0.69)⁶⁻¹

P = (1) (1) (0.31)⁶ + (6) (0.69) (0.31)⁵

P = 0.013

(a) The graph of f(x) is increasing on the intervals (-∞, 0) and (2, ∞), and decreasing on the interval (0, 2).

(b) The local maximum occurs at x = 0 and the local minimum occurs at x = 2.

(c) The graph of f(x) is concave up on the interval (1, ∞) and concave down on the interval (-∞, 1).

(d) The point of inflection occurs at x = 1.

(a) To find the intervals on which the graph of f(x) is increasing or decreasing, we need to analyze the sign of the derivative of f(x).

Step 1: Find the derivative of f(x).

f'(x) = d/dx(x³ - 3x²) = 3x² - 6x

Step 2: Set the derivative equal to zero and solve for x to find critical points.

3x² - 6x = 0

Factor out common terms:

3x(x - 2) = 0

This gives two critical points: x = 0 and x = 2.

Step 3: Determine the sign of the derivative in different intervals.

We choose test points within each interval and evaluate the derivative at those points.

Test x = -1:

f'(-1) = 3(-1)² - 6(-1) = 3 + 6 = 9 (positive)

Test x = 1:

f'(1) = 3(1)² - 6(1) = 3 - 6 = -3 (negative)

Test x = 3:

f'(3) = 3(3)² - 6(3) = 27 - 18 = 9 (positive)

Based on these results, we can determine the intervals of increasing and decreasing.

Intervals of increasing: (-∞, 0) and (2, ∞)

Intervals of decreasing: (0, 2)

(b) Local extrema occur at the critical points of the function. From part (a), we found the critical points x = 0 and x = 2.

To determine if these critical points are local extrema, we can analyze the sign of the derivative around these points.

For x = 0:

f'(-1) = 9 (positive) to the left of 0

f'(1) = -3 (negative) to the right of 0

Since the derivative changes sign from positive to negative, x = 0 is a local maximum.

For x = 2:

f'(1) = -3 (negative) to the left of 2

f'(3) = 9 (positive) to the right of 2

Since the derivative changes sign from negative to positive, x = 2 is a local minimum.

(c) To find the intervals of concavity for the graph of f(x), we need to analyze the sign of the second derivative, f''(x).

Step 1: Find the second derivative of f(x).

f''(x) = d/dx(3x² - 6x) = 6x - 6

Step 2: Set the second derivative equal to zero and solve for x to find any inflection points.

6x - 6 = 0

6x = 6

x = 1

Step 3: Determine the sign of the second derivative in different intervals.

Test x = 0:

f''(0) = 6(0) - 6 = -6 (negative)

Test x = 2:

f''(2) = 6(2) - 6 = 6 (positive)

Based on these results, we can determine the intervals of concavity.

Intervals of concave up: (1, ∞)

Intervals of concave down: (-∞, 1)

(d) The point of inflection occurs at x = 1 since the second derivative changes sign from negative to positive at that point.

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Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

Mean reversion refers to the tendency of asset prices or economic variables to move back to their average or mean level over time. The mean-reverting level, x1, for a time series can be calculated using statistical methods like moving averages or exponential smoothing. These techniques estimate the average value or trend of the data.



The interpretation of x1 depends on the context. If the current value is above x1, it suggests a potential future decrease, reverting back to x1. Conversely, if the current value is below x1, it indicates a potential future increase, also reverting back to x1. The deviation from x1 provides insights into the strength or speed of the mean reversion process.



Therefore, Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

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Answer:

the correct answer is the second one

Step-by-step explanation:

I will add a photo of my solution, because there's a lot to type here

Answer:

6 packages

Step-by-step explanation:

30/5 is 6

Answer:

the answer is 6

Step-by-step explanation:

30 divided by 5

Using the division operation, the number of 2/3's in 3 is 4

3 ÷ 2/3

change the sign to multiplication and take inverse of 2/3

3 × 3/2 = 9/2 = 4.5

We need only the whole number value .

Therefore, the number of 2/3's in 3 is 4.

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9514 1404 393

Explanation:

1. ΔABC ≅ ΔDEF . . . . . 1. SAS postulate*

_____

The two given congruent sides are either side of the given congruent angle, so the SAS postulate applies. The objective appears to be irrelevant.

Answer:

\(\huge\boxed{\sf V = 4778.4\ cm\³}\)

Step-by-step explanation:

Given:

Height = 27 cm

Radius = 13 cm

Formula:

\(Volume \ of \ cone \ V = \frac{1}{3} \pi r^2h\)

Solution:

V = 1/3 (3.14)(13)²(27)

V = (3.14)(169)(9)

V = 4778.4 cm³

\(\rule[225]{225}{2}\)

Hope this helped!

Based on the information provided, Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Yes, he is correct. Here's an explanation:

A triangular prism has two triangular bases and three rectangular faces. When a triangular prism is lying on a rectangular face, it means that one of its rectangular faces is on the bottom. If Mateo draws a line along the length of this rectangular face, he is creating a parallel cross-section of the triangular prism.

This is because the line he drew is parallel to the triangular base of the prism, and the two bases are also parallel to each other. A parallel cross-section is created when a plane cuts through a solid parallel to its base, and in this case, Mateo's line fulfills this condition.

Therefore, Mateo is correct in representing the parallel cross-section of the triangular prism by drawing a line along the length of a rectangular face.

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Answer:

3

Step-by-step explanation:

The paragraph above describes a randomized experiment.

In this study, a researcher wanted to examine the effect of drinking on the ability to play darts.

To test this, he conducts a randomized experiment.

A randomized experiment is a study where researchers randomly allocate participants to groups, to ensure that each person has an equal chance of being assigned to each group.

In the experiment, the researcher randomly assigned 20 dart players to groups by flipping a coin for each player.

Summary: The paragraph above describes a randomized experiment. The participants who drink beer are the experimental group, the participants who drink soda are the control group. Flipping a coin to decide which player gets which drink is an example of random assignment.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Question 9: The standard error of the mean (SEM) is 0.0912 and the 95% confidence interval is (5.0213, 5.3787).

Question 10: This confidence interval indicates that we can be 95% confident that the true mean of acid rain in Winnipeg is between 5.0213 and 5.3787.

Question 11: The 90% and 99% confidence interval for the data is (5.0499, 5.3501) and (4.9650, 5.4350) respectively.

Question 12: As the confidence interval increases from 90% to 95% to 99%, the width of the interval also increases. This means that the range of values that we can be confident contains the true mean becomes larger.

Question 9:

The standard error of the mean (SEM) is calculated as:

SEM = s / √n

where s is the standard deviation of the sample and n is the sample size.

Assuming that the standard deviation and sample size from assignment #2 are 0.5 and 30, respectively, the SEM can be calculated as follows:

SEM = 0.5 / √30

SEM = 0.0912

The 95% confidence interval around the sample mean estimate can be calculated as:

CI = mean +/- (1.96 * SEM)

Assuming that the sample mean from assignment #2 is 5.2, the 95% confidence interval can be calculated as follows:

CI = 5.2 +/- (1.96 * 0.0912)

CI = 5.2 +/- 0.1787

CI = (5.0213, 5.3787)

Question 10:

This confidence interval indicates that we can be 95% confident that the true mean of acid rain in Winnipeg is between 5.0213 and 5.3787. In other words, if we were to take multiple samples from the population and calculate the mean for each sample, 95% of those means would fall within this confidence interval.

Question 11:

The 90% confidence interval can be calculated as:

CI = mean +/- (1.645 * SEM)

CI = 5.2 +/- (1.645 * 0.0912)

CI = 5.2 +/- 0.1501

CI = (5.0499, 5.3501)

The 99% confidence interval can be calculated as

CI = mean +/- (2.576 * SEM)

CI = 5.2 +/- (2.576 * 0.0912)

CI = 5.2 +/- 0.2350

CI = (4.9650, 5.4350)

Question 12:

As the confidence interval increases from 90% to 95% to 99%, the width of the interval also increases. This means that the range of values that we can be confident contains the true mean becomes larger. This pattern emerges because a higher confidence level requires a larger margin of error to account for more variability in the data. As a result, the confidence interval becomes wider to ensure that the true mean is captured within the interval with a higher level of confidence.

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The given relation that is a function is the fourth graph which shows a U- shaped curve.

The graph of a quadratic function is a U-shaped curve called a parabola, which can either face upwards or downwards depending on the value of "a". If "a" is positive, the parabola faces upwards, and if "a" is negative, the parabola faces downwards.

The coefficient "a" determines the width and direction of the parabola, while the constants "b" and "c" determine its position on the coordinate plane. This therefore shows that the fourth graph is a function.

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Answer:

y = 1/2

x = 2

Step-by-step explanation:

7^2y × 3^x = 7 × 9

7^2y × 3^x = 7^1 × 3²

7^2y = 7^1 so y = 1/2

3^x = 3² so x = 2

The day when the sun is highest in the sky varies depending on the location within the United States. However, generally speaking, the highest point of the sun is reached on the summer solstice, which falls around June 20-21 each year.

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