Alice is trying to transmit to Bob the answer to a yes-no question, us-ing a noisy channel. She encodes "yes" as 1 and "no" as 0, and sends the appropriatevalue. However, the channel adds noise; specifically, Bob receives what Alice sends plusaN(0,σ2) noise term (the noise is independent of what Alice sends). If Bob receives avalue greater than 1/2 he interprets it as "yes"; otherwise, he interprets it as "no".(a) Find the probability that Bob understands Alice correctly. 2 (b) What happens to the result from (a) if σ is very small? What about if σ is very large? Explain intuitively why the results in these extreme cases make sense.(b) What happens to the result from (a) if σ is very small? What about if σ is very large? Explain intuitively why the results in these extreme cases make sense.

The specific calculations for expected frequencies, chi-square statistic, and critical value depend on the data and the distribution being tested.

In a chi-square goodness-of-fit test, the objective is to determine whether the observed frequencies in different categories significantly differ from the expected frequencies. The test involves calculating the chi-square statistic and comparing it to the critical value from the chi-square distribution at a given significance level.

In this specific case, we have six categories and 500 observations. To perform the chi-square goodness-of-fit test, we need the expected frequencies for each category. The expected frequencies are usually calculated based on a theoretical distribution or an assumed null hypothesis.

Given that the significance level is 0.01, we will compare the calculated chi-square statistic to the critical value at this level. The critical value represents the threshold beyond which we reject the null hypothesis.

Let's assume that the null hypothesis states that the observed frequencies are in line with the expected frequencies. To proceed with the test, we follow these steps:

Specify the null hypothesis (H0) and the alternative hypothesis (Ha):

Null hypothesis (H0): The observed frequencies are consistent with the expected frequencies in each category.

Alternative hypothesis (Ha): There is a significant difference between the observed and expected frequencies in at least one category.

Determine the expected frequencies for each category based on the null hypothesis.

Calculate the chi-square statistic using the formula:

chi-square = Σ((observed frequency - expected frequency)^2 / expected frequency)

Here, we sum over all the categories.

Determine the degrees of freedom (df), which is the number of categories minus 1 (df = number of categories - 1).

Look up the critical value from the chi-square distribution table using the significance level (0.01) and degrees of freedom (df).

Compare the calculated chi-square statistic to the critical value:

If the calculated chi-square statistic is greater than the critical value, we reject the null hypothesis.

If the calculated chi-square statistic is less than or equal to the critical value, we fail to reject the null hypothesis.

Performing these steps will allow us to determine whether there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the observed and expected frequencies in the categories.

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The natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

To find the natural values of n for which the difference (2-2n) - (5n-27) is positive, we need to simplify the expression and then solve for n.

(2-2n) - (5n-27) = 2 - 2n - 5n + 27

= -7n + 29

So, we need to find the natural numbers n for which -7n + 29 > 0.

To do this, we can solve for n as follows

-7n + 29 > 0

-7n > -29

n < 29/7

Since n is a natural number, it must be an integer greater than or equal to 1. Therefore, the natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

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Part A:

For a normally distributed data, population mean = sample mean

From the question, population mean = 34.82

Hence the sample mean = 34.82

The sample standard deviation is given by;

where n = 6, and

Therefore, the sample standard deviation is 2.05.

Part B

The interpretation of the standard deviation of the sampling distribution is that, since the square root of the sample size appears at the denominator, the standard deviation decreases as the sample size increases.

Part C

Hence, the probability is 0.0111.

Answer: Figure D

Figure D is a 180 degree rotation of figure A.

Answer:

y = 2x

Step-by-step explanation:

Slope = \(\frac{y}{x} =\frac{2}{1}\)

Step-by-step explanation:

A o option

-(-45)

hope it helps

Answer:

C

Step-by-step explanation:

A function is constant when the y value does not change when the x value does

The function is constant during section C

Answer:

so he can get brainliest it is c

Step-by-step explanation:

Answer:

4. y = -x + 8

9. y = 3/2x + 15

16. y = 1/2x -5

20. y = -3/5x + 16

13. y = -1/2x + 1

14. y =  3/4x - 2

Step-by-step explanation:

4. 5=3(-1)+b = 8

9. 6=-6(3/2)+b=15

16. \(\frac{1--2}{12-6} =\frac{3}{6} = \frac{1}{2}\)

     -2= (1/2)6 + b = -5

20. \(\frac{19-13}{-5-5}= -\frac{6}{10} =-\frac{3}{5}\)

     19 = -3/5(-5) + b = 16

Step-by-stepAnswer:

explanation:

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Answer:

38.9°

Step-by-step explanation:

The three angles in a triangle add up to 180°. Also, a right triangle has a right angle in it. A right angle is 90°.

90° + 51.1° + x = 180°

141.1 + x = 180°

subtract 141.1°

x = 38.9°

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

444211111111154545

Step-by-step explanation:

The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:

Now, find g(k(1)), it means, g(-7):

(g°k)(1)=573.

The empirical probability of drawing the cards will be 6 / 55.

The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.

Given that a card is drawn one at a time from a well-shuffled deck of 52 cards. In 13 repetitions of this experiment, 1 king is drawn.

The number of kings in a well-shuffled deck consists of 52 cards which is 4.

The number of ways of drawing consists of 4 kings in 13 repetitions which is ¹³C₄.

In 13 repetitions, 2 kings are drawn by ¹³C₂ ways,

The empirical probability will be calculated as,

P(E) = ¹³C₂ / ¹³C₄

P(E) = [ (13!) / (13-2)! ] ÷ [ (13!) / ( 13-4)!(4!) ]

P(E) = ( 4 x 3 ) / ( 11 x 10)

P(E) = 6 / 55

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Hi,

if it's 11:24, it wil be 12:13

✅(◠‿◕)

The best description of the sample selected by the administrator is Stratified Random Sample that is option D is correct.

Stratified Random Sampling is the method of sampling in which data of population or any other demographic study is divided into smaller subgroups or subdivisions and then measurements are carried out. These subdivisions are known as Strata. The subdivisions are made on the basis of the attributes of the people of the population such as their income statement or their educational qualifications. This type of sampling technique is also known as random or quota random sampling technique. This sampling technique is also used in determining the life expectancy data. It allows researchers to develop a sample of a small area that represents the entire area.

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Complete Question:

as part of a demographic study, a college administrator needed to survey a sample of students from the college. from each major offered at the college, the administrator randomly selected 5 percent of the students with that major to participate in the survey. which of the following is the best description of the type of sample selected by the administrator?

a)cluster sample

b)convenience sample

c)simple random sample

d)stratified random sample

e)systematic random sample

Answer:

2g+7

Step-by-step explanation:

g represents gails age

2 times gails age

2g

7 more than is addition

2g+7

Once the specific rides are selected based on popularity and shortest travel time, you can compute the total travel time by summing the travel times between the rides, including the time from the entrance to the first ride and from the last ride to the exit.

What is the distance?

Distance refers to the amount of space between two objects or points. It is a measure of the length of the path traveled by an object or a person from one point to another. The most common units of distance are meters, kilometers, feet, miles, and yards.

Based on the two criteria mentioned (popularity and shortest travel time), the selection of 4 rides would depend on the specific information available regarding popularity and travel times.

Since I do not have access to the information about the rides, I am unable to make a specific recommendation for the 4 rides to select.

However, I can provide a general approach to selecting the rides based on the given criteria:

1. Popularity: Identify the rides that are most popular based on factors such as visitor ratings, reviews, or attendance numbers. Choose the top 4 rides that are consistently mentioned as popular choices.

2. Shortest travel time: Determine the travel time between each ride location, including the entrance and exit.

Calculate the time it takes to move between each ride and consider the shortest overall travel route. Select the 4 rides that minimize the total travel time.

Hence, Once the specific rides are selected based on popularity and shortest travel time, you can compute the total travel time by summing the travel times between the rides, including the time from the entrance to the first ride and from the last ride to the exit.

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The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

\((y-1.5)^2\)

Step-by-step explanation:

I’m guessing you want a perfect square trinomial.

b=-3

\(\frac{b}{2}=-1.5\)

\((-1.5)^2=2.25\)

You need to add 2.25 to the binomial to create a perfect square trinomial.

Answer:

the answe is A.{-8,-4,0,4,8}

The differences obtained using the Austrian algorithm are: (a) 7424, (b) 4302, (c) 420, and (d) 681.

To find the differences using the Austrian algorithm, we subtract the second number from the first number in each case. Let's calculate the differences for the given values:

(a) 7729 - 305:

The difference is 7729 - 305 = 7424.

(b) 4818 - 516:

The difference is 4818 - 516 = 4302.

(c) 1010 - 590:

The difference is 1010 - 590 = 420.

(d) 1433 - 752:

The difference is 1433 - 752 = 681.

Therefore, the differences are:

(a) 7424

(b) 4302

(c) 420

(d) 681

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Answer:

1. the possible outcomes are any of the seven days of the week

2. 1/7 chance of choosing Wednesday

3. 2/7 chance of choosing Saturday or Sunday

\(\mathbb{PROBLEM:}\)

\( \\ \)

A day is chosen from a week.

1. What are the possible outcomes?

2. What is the chance of choosing Wednesday?

3. Find the probability of selecting weekends.

\( \\ \)

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

\(\mathbb{SOLUTION:}\)

\( \\ \)

1. What are the possible outcomes?

2. What is the chance of choosing Wednesday?

\(\tt\underline\red{ \: \: \frac{1}{7} \: \: }\)

3. Find the probability of selecting weekends.

\(\tt\underline\red{ \: \: \frac{2}{7} \: \: } \)

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

♥️

It is not possible to get a very strong correlation just by chance when there is no relationship between the two variables. False

Correlation measures the strength and direction of the linear relationship between two variables. A high correlation coefficient indicates a strong relationship between the variables, while a low or near-zero correlation suggests a weak or no relationship.

A strong correlation implies that changes in one variable are associated with predictable changes in the other variable. Therefore, a high correlation cannot occur by chance alone without an underlying relationship between the variables.

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The control limits for 3-sigma x chart are

Upper Control Limit - 3.807 inches

Lower Control Limit - 2.291 inches

The control limits for the 3-sigma R-chart are Upper Control Limit- 2.373 inches

X-double bar = Sum of observations (x-bar) / Total number of observations

X-double bar = 73.17 / 24

X-double bar = 3.049

R-bar = Sum of observations (R) / Total number of observations

R-bar = 24.97 / 24

R-bar = 1.040

(a) The Upper Control Limit (UCLx) and Lower Control limit (LCLx) for the 3-sigma x-bar chart is calculated as,

UCLx = X-double bar + (A2 x R-bar)

LCLx = X-double bar - (A2 x R-bar)

From the table of factors for computing the control chart limits (3-sigma),

For n = 4 (4-pieces of precision cut wire)

A2 = 0.729

Putting these values in the above formulas, we get,

UCLx = 3.049 + (0.729 x 1.040)

UCLx = 3.807 inches

LCLx = 3.049 - (0.729 x 1.040)

LCLx = 2.291 inches

Based on the x-bar chart, the wire cutting process has been out of control, because the observation at 19th hour (4.51) lie outside the computed upper control limit and lower control limit.

(b) The Upper Control Limit (UCLr) and Lower Control limit (LCLr) for the 3-sigma  R-chart is calculated as,

UCLr = D4 x R-bar

LCLr = D3 x R-bar

From the table of factors for computing the control chart limits (3-sigma),

For n = 4 (4-pieces of precision cut wire)

D3 = 0, D4 = 2.282

Putting these values in the above formulas, we get,

UCLr = 2.282 x 1.040

UCLr = 2.373 inches

LCLr = D3 x R-bar

LCLr = 0 x 1.040

LCLr = 0 inches

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The length of the radius of circle O is 4 units

From the question, we have the following parameters that can be used in our computation:

Circle O

The equation of the circle O is then given as

(x + 7)2 + (y + 7)2 = 16.

Express the exponents in the above equation properly

So, we have the following representation

(x + 7)² + (y + 7)² = 16.

Express 16 as the square of 4

This gives

(x + 7)² + (y + 7)² = 4²

The standard equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where the length of the radius is r

By comparison. we have

r = 4

Hence, the radius is 4 units

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Answer:

44

Step-by-step explanation:

A circle is 360 degrees.

145 +136 + 35= 316

360-316= 44

44 Degrees