What would be the result of executing the following code? int[] x = {0, 1, 2, 3, 4, 5}

Probability Theory

P (K) =\(\frac{n (K) }{n (S)}\)

P(K) : probability of selected K

n (K) : number of occurence of K

n (S) : number of all occurence

In question is not contain information about the number of students who curry a gun, knife, or other weapon and the number of all students. so, we can desribe that :

n (A) : the number of occurence of students who curry a gun

n (B) : the number of occurence of students who curry a knife

n (C) : the number of occurence of students who curry other weapon

and the number of all students is n ( A U B U C) -> union of sets

how many randomly selected student? in question, there is no specific about the student. so, we can answer with :

1) probability of students who curry a gun

P (A) = \(\frac{n (A) }{n (AUBUC)}\)

2) probability of students who curry a knife

P (B) = \(\frac{n (B) }{n (AUBUC)}\)

3) probability of students who curry other weapon

P (C) = \(\frac{n (C) }{n (AUBUC)}\)

and if question want to estimate with percentage, we can multiply with 100%. example :

1) percentage of probability of students who curry a gun

P (A) = \(\frac{n (A) }{n (AUBUC)}\) x 100%

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Geometric Sequence :

Every term in a geometric sequence is obtained by multiplying the term before it by the same number.  \(A_{n}\) = \(a_{}\) \(r^{n-1}\) is the general term for it. The common ratio is denoted by the number 'r'. Any term in the sequence can be used to find it by dividing it by the term before it.

'a' is the first term of the sequence, n is the  \(n^{th}\) term.

Given geometric sequence :

7 , -21 , 63 , ....

Here, first term = a = 7

common ratio = r = \(\frac{-21}{7}\) = -3

n = 15.

Then, \(15^{th}\) term =  \(A_{15}\) = 7 x \((-3)^{15-1}\)

                                    = 7 x \((-3)^{14}\)  =  7 x 4,782,969

                                    = 33,480,783 .

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The graph of the sine function f(x) = sin(400πx) is given by the image at the end of the answer.

The sine function in this problem is defined as follows:

f(x) = sin (y × 2πx).

In which the relevant variable for the graph is the variable y, which is the number of cycles in a single second of the wave.

In this problem, it is states that the note has a frequency of 440 Hz, meaning that it has 440 cycles in one second, thus the equation is:

f(x) = sin (440 × 2πx).

f(x) = sin (880πx).

The function is not multiplied by any value, hence the amplitude is of 1, meaning that the function oscillates between 0 and 1, and also there is not any phase shift or vertical shift, meaning that it oscillates between -1 and 1 starting at the origin.

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The equivalent fractions here are: 14/18 ,  21/27 , 28/36 , 35/45 , 42/54.

Given, the number 7/9

7/9 = (7/9 × 2/2) = 14/18

7/9 = (7/9 × 3/3) = 21/27

7/9 = (7/9 × 4/4) = 28/36

7/9 = (7/9 × 5/5) = 35/45

7/9 = (7/9 × 6/6) = 42/54

hence the equivalent fractions here are:

14/18 , 21/27 , 28/36 , 35/45 , 42/54

Equivalent fractions are those fractions that reflect the same value even if they may have distinct numerators and denominators. For instance, the fractions 9/12 and 6/8 are comparable as both, when simplified, equal 3/4.

When reduced to their most basic form, all equivalent fractions become the same fraction.

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Answer:

x = 3

Step-by-step explanation:

I hope this helps!

Answer:

x = 3

Step-by-step explanation:

I hope this helps

Answer:

neither

Step-by-step explanation:

Parallel lines need to have the same slope.

Perpendicular lines have opposite reciprocal slopes.

-5/2 and -2/5 are opposite reciprocals nor are they equal.

Answer:

Step-by-step explanation:

y=-2x-9

subtract both sides by 2x

Answer:

37

Step-by-step explanation:

substitute the given values for x and y into the expression

4x² + 2y

= 4(3)² + 2(\(\frac{1}{2} \) )

= 4(9) + 1

= 36 + 1

= 37

Answer:

i don't know i need help with this one too

Step-by-step explanation:

1) The sample proportion is 0.14 (7 left-handed students out of 50 total students surveyed).
2) The hypothesized proportion po is 0.10 (the usual proportion of left-handed students).
3) The sample size n is 50 (the number of students surveyed).
4) The test statistic z is 1.32.

1) The sample proportion is calculated by dividing the number of left-handed students by the total number of students surveyed. In this case, 7 left-handed students out of 50 gives a sample proportion of 7/50 = 0.14.
2) The hypothesized proportion (p₀) is the usual proportion of left-handed students, which is given as 0.10.
3) The sample size (n) is the total number of students surveyed, which is 50.
4) The test statistic (z) can be calculated using the formula: z = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). In this case, z = (0.14 - 0.10) / sqrt((0.10 * (1 - 0.10)) / 50) = 0.04 / sqrt(0.09 / 50) ≈ 0.943.
To calculate the test statistic z, we use the formula:

z = (sample proportion - hypothesized proportion) / standard error

The standard error is calculated as:

standard error = sqrt((po * (1-po)) / n)

Plugging in the values, we get:

standard error = sqrt((0.10 * (1-0.10)) / 50) = 0.0499

Then,

z = (0.14 - 0.10) / 0.0499 = 1.32

Since the calculated z-value of 1.32 is greater than the critical value of 1.645 (using a significance level of 0.05 for a two-tailed test), we can conclude that there is not enough evidence to reject the null hypothesis that the proportion of left-handed students at the school is the same as the usual proportion of 0.10.

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Answer:

This would be QUADRATIC

Answer:

.8  or 8/10 or 4/5

Step-by-step explanation:

A. the 95% confidence interval for the average value of y when x = 2 is (4.9241, 5.4283).
B. The 95% prediction interval for some value of y to be observed in the future when x = 2 is (4.6619, 5.4576).

(a) To find a 95% confidence interval for the average value of y when x = 2, use the provided information:

Predicted Value for New Obs 1 (x = 2): 5.1762
SE Fit: 0.0926

Now, apply the formula for confidence intervals:

CI = Predicted Value ± (t-value * SE Fit)

For a 95% confidence interval and degrees of freedom = 4 (6 points - 2 parameters), the t-value is approximately 2.776 (using a t-table).

CI = 5.1762 ± (2.776 * 0.0926)

CI = (5.1762 - (2.776 * 0.0926), 5.1762 + (2.776 * 0.0926))
CI = (4.9241, 5.4283)

So, the 95% confidence interval for the average value of y when x = 2 is (4.9241, 5.4283).

(b) To find a 95% prediction interval for some value of y to be observed in the future when x = 2, use the information provided:

95.0% PI: (4.6619, 5.4576)

The 95% prediction interval for some value of y to be observed in the future when x = 2 is (4.6619, 5.4576).

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The coefficient of x^10 in (1 x x^2 x^3 ...)^n is C(n, 10), or "n choose 10".

The expression (1 x x^2 x^3 ...) represents an infinite geometric series with a common ratio of x. The sum of an infinite geometric series with a common ratio of x and a first term of 1 is given by:

sum = 1 / (1 - x)

To find the coefficient of x^10 in (1 x x^2 x^3 ...)^n, we need to find the coefficient of x^10 in the expansion of (1 / (1 - x))^n. We can use the binomial theorem to expand this expression as follows:

(1 / (1 - x))^n = C(n, 0) + C(n, 1)x + C(n, 2)x^2 + ... + C(n, n)x^n

where C(n, k) is the binomial coefficient "n choose k", which gives the number of ways to choose k items from a set of n items. The coefficient of x^10 in this expansion is given by C(n, 10), since the term x^10 only appears in the (n-10)th term.

Therefore, the coefficient of x^10 is C(n, 10), or "n choose 10".

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Answer:

The correct option is;

2.81

Step-by-step explanation:

The critical value \(Z_{\alpha /2}\), is found from the z score table as follows, where the the confidence level is 99.5

Therefore, we have α = 1 - 99.5/100 = 1 - 0.995 = 0.005

α/2 = 0.0025

The critical value is thus found from the z-score table value of 1 - 0.0025 = 0.9975

From the z-table, we can find the 0.9975 score on the row  with z = 2.8 where 0.9975 can be located under the 0.1 column giving the critical value as 2.81

Answer: h= V/2πr^2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

51 x $31 an hour = $1581 is his gross earnings for the week

The probability that the team will win at most 4 out of 5 games is 8/9.

To calculate the probability of winning at most 4 out of 5 games, we need to find the probability of winning 0, 1, 2, 3, or 4 games.

The probability of winning exactly k games out of 5 is given by the binomial distribution formula:

P(X = k) = (5 choose k) * (2/3)^k * (1/3)^(5-k)

Where "n choose k" is the binomial coefficient, representing the number of ways to choose k items from a set of n items. In this case, it represents the number of ways to win k games out of 5.

Using this formula, we can calculate the individual probabilities:

P(X = 0) = (5 choose 0) * (2/3)^0 * (1/3)^5 = (1) * (1) * (1/243) = 1/243

P(X = 1) = (5 choose 1) * (2/3)^1 * (1/3)^4 = (5) * (2/3) * (1/81) = 10/243

P(X = 2) = (5 choose 2) * (2/3)^2 * (1/3)^3 = (10) * (4/9) * (1/27) = 40/243

P(X = 3) = (5 choose 3) * (2/3)^3 * (1/3)^2 = (10) * (8/27) * (1/9) = 80/243

P(X = 4) = (5 choose 4) * (2/3)^4 * (1/3)^1 = (5) * (16/81) * (1/3) = 80/243

To find the probability of winning at most 4 out of 5 games, we sum up these probabilities:

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = (1/243) + (10/243) + (40/243) + (80/243) + (80/243) = 8/9.

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Those activities that enable a person to describe in the detail the system that solves the need is called "System design".

The method of defining the components of a system consists, modules, and components, the various interfaces of those components, and the data that flows through that system is known as system design.

Some key features regarding the system design are-

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The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

hi you can solve this sum by 4×side formula

Step-by-step explanation:

plz solve and check you equation

Step-by-step explanation:

\( \frac{dA}{dx} = 3 {(x - 1)}^{2} \\A = ∫3 {(x - 1)}^{2}dx \\ = ∫3 {x}^{2} - 6x + 3 \: dx \\ = \frac{3 {x}^{3} }{3} - \frac{6 {x}^{2} }{2} + 3x + c \\ = {x}^{3} - 3 {x}^{2} + 3 + c\)

Now substitute in A=10 and X=3, to find the value of c

\(10 = {3}^{3} - 3 {(3)}^{2} + 3(3) + c \\ c = 1\)

Hence,

\(A = {x}^{3} - 3 {x}^{2} + 3x + 1\)

The solution set is empty: {}. To solve the equation |x² + x - 2| = x + 3, we can consider two cases: when the expression inside the absolute value is positive, and when it is negative. Let's solve each case separately:

Case 1: x² + x - 2 is positive (x² + x - 2 > 0):

To find the values of x that satisfy this inequality, we can factorize the quadratic expression:

x² + x - 2 = (x + 2)(x - 1)

For the expression to be positive, both factors must have the same sign. Considering the signs of each factor:

(x + 2) > 0 => x > -2

(x - 1) > 0 => x > 1

Since both factors must be positive, we can take the intersection of the two intervals: x > 1.

Case 2: x² + x - 2 is negative (x² + x - 2 < 0):

Again, factorizing the quadratic expression:

x² + x - 2 = (x + 2)(x - 1)

For the expression to be negative, the factors must have opposite signs. Considering the signs of each factor:

(x + 2) < 0 => x < -2

(x - 1) > 0 => x > 1

Since the factors have opposite signs, we can take the union of the two intervals: x < -2 or x > 1.

Combining the solutions from both cases, we have:

x > 1 or x < -2

Now let's verify the solutions by substituting them back into the original equation:

For x > 1:

|x² + x - 2| = x + 3

Substituting x = 2:

|2² + 2 - 2| = 2 + 3

|4 + 2 - 2| = 5

|4| = 5

4 = 5 (Not true)

For x < -2:

|x² + x - 2| = x + 3

Substituting x = -3:

|-3² - 3 - 2| = -3 + 3

|-9 - 3 - 2| = 0

|-14| = 0

14 = 0 (Not true)

Since neither solution satisfies the equation, there are no valid solutions to the equation |x² + x - 2| = x + 3.

Therefore, the solution set is empty: {}

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Answer:

x=1. (1, 2)

x=2. (2, 5)

Step-by-step explanation:

i hope this helps :)

Answer:

23 =x

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

132 = x+109

132 -109 = x

23 =x

Answer:

x = 23°

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Let's solve for value of x,

→ x + 109° = 132°

→ x = 132° - 109°

→ [ x = 23° ]

Thus, the value of x is 23°.

Answer:

pq= 12 cm

Step-by-step explanation:

I believe PQ would be 12 cm.

Answer:

Domain: (-infinite, -8) U (-8, 2) U (2, +infinite)

Step-by-step explanation:

The graphs never intersect with the lines x=-8 and x=2 so -8 and 2 cannot be included in the domain.

Use "[]" for included and "()" for excluded.

The domain will go from far left to -8 => (-infinite, -8).

Then, the domain will go from -8 to 2 => (-8, 2).

Last, the domain will go from 2 to +infinite => (2, +infinite).

Divide the 5% of Spanish by 40% male:

0.05 / 0.40 = 0.125

Change to a percent by multiplying by 100:

0.125 x 100 = 12.5%

The answer is a. 12.5%

The probability of the student studying Spanish, if you know the students male will be 12.5%.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that in a certain group of students, the probability of a randomly chosen student being male is 40%, the probability of the students studying Spanish is 18%, and the probability of the student being male who studies Spanish is 5%.

The probability of the student studying Spanish, if you know the student male will be calculated as below:-

Divide the 5% of Spanish by 40% of males:

0.05 / 0.40 = 0.125

Change to a percent by multiplying by 100:

0.125 x 100 = 12.5%

Therefore, the probability of the student studying Spanish, if you know the students male will be 12.5%.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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