A school newspaper reporter decides to randomly survey 18 students to see if they will attend Tet festivities this year. Based on past years, she knows that 11% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. Find the probability that more than 2 students will attend.

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Answer 1

Answer:

Answer:

There is a 13.80% probability that more than 2 students will attend.

Step-by-step explanation:

For each student surveyed, there are only two possible outcomes. Either they will attend the Tet festivities this year, or they will not. This means that we can solve this problem using binomial probability distribution concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)$

In which $C_(n,x)$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And $\pi$ is the probability of X happening.

In this problem, we have that:

11% of students attend Tet festivities, so $p = 0.11$ .

18 students are surveyed, so $n = 18$ .

Find the probability that more than 2 students will attend.

This is $P(X > 2)$ , that is:

$P(X > 2) = 1 - P(X \leq 2)$

In which

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)$

$P(X = 0) = C_(18,0).(0.11)^(0).(0.89)^(16) = 0.1550$

$P(X = 1) = C_(18,1).(0.11)^(1).(0.89)^(15) = 0.3448$

$P(X = 2) = C_(18,2).(0.11)^(2).(0.89)^(14) = 0.3622$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1550 + 0.3448 + 0.3622 = 0.8620$

Finally

$P(X > 2) = 1 - P(X \leq 2) = 1 - 0.8620 = 0.1380$

There is a 13.80% probability that more than 2 students will attend.

Answer 2

Answer:

Final answer:

To find the probability that more than 2 out of 18 randomly chosen students will attend the Tet festivities, given the historical attendance rate of 11%, we use the binomial probability formula. We subtract the probability of 0, 1, or 2 students attending from 1.

Explanation:

The subject matter of this question pertains to the field of probability in mathematics. We are asked to calculate the probability that more than 2 out of 18 students will attend the Tet festivities, given that historically, 11% of students attend.

To solve this, we can use the binomial probability formula:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where n is the total number of trials, in this case, 18 students; k is the number of successes we are interested in, which are more than 2 attendances; p is the probability of success, in this case, 0.11; and C(n, k) is the binomial coefficient calculation, 'n choose k'.

However, since we are interested in more than 2 students attending, we have to subtract from 1 the probability of 0, 1, or 2 students attending. Therefore, the answer would be 1 - P(X=0) - P(X=1) - P(X=2).

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Maybe an answer would be 30=20+n What is the value of the variable?

A smoothie recipe calls for 3 cups of soy milk, 2 frozen bananas and, 1 tablespoon of chocolate syrup. Write a sentence that uses a ratio to describe this recipe.

Answers

Answer:

3:2:1

Step-by-step explanation:

Let a, b, and c be integers. Consider the following conditional statement: If a divides bc, then a divides b or a divides c
Which of the following statements have the same meaning as this conditional statement, which ones are the negations, and which ones are not neither? Justify your answers using logical equivalences or truth tables.
A) If a does not divide b or a does not divide c, then a does not divide bc.
B) If a does not divide b and a does not divide c, then a does not divide bc.
C) If a divides bc and a does not divide c, then a divides b.
D) If a divides bc or a does not divide b, then a divides c. (e) a divides bc, a does not divide b, and a does not divide c.

Answers

Step-by-step explanation:

Given that the logical statement is

"If a divides bc, then a divides b or a divides c"

we can see that a must divide one either b or c from the statement above

A) If a does not divide b or a does not divide c, then a does not divide bc.

This is False because a can divide b or c

B) If a does not divide b and a does not divide c, then a does not divide bc.

this is True for a to divide bc it must divide b or c (either b or c)

C) If a divides bc and a does not divide c, then a divides b.

This is True since a can divide bc and it cannot divide c, it must definitely divide b

D) If a divides bc or a does not divide b, then a divides c.

This is True since a can divide bc and it cannot divide b, it must definitely divide c

E) a divides bc, a does not divide b, and a does not divide c.

This is False for a to divide bc it must divide one of b or c

Statement A is not the same as the original statement.

Statement B is the negation of the original statement.

Statement C is the same as the original statement.

Statement D is not the same as the original statement.

Condition E is not a statement, but a set of conditions without any logical implications.

Given that;

The conditional statement:

If a divides bc, then a divides b or a divides c

A) If a does not divide b or a does not divide c, then a does not divide bc.

This statement is not the same as the original conditional statement.

The original statement states that if a divides bc, then a divides b or a divides c.

However, statement A states the opposite - if a does not divide b or a does not divide c, then a does not divide bc.

So, this is not the same as the original statement.

B) If a does not divide b and a does not divide c, then a does not divide bc.

This statement is actually the negation of the original conditional statement.

The original statement states that if a divides bc, then a divides b or a divides c.

The negation of this statement would be that if a does not divide b and a does not divide c, then a does not divide bc.

So, statement B is the negation of the original statement.

C) If a divides bc and a does not divide c, then a divides b.

This statement is the same as the original conditional statement. It states that if a divides bc and a does not divide c, then a divides b.

This is equivalent to the original statement, which states that if a divides bc, then a divides b or a divides c.

D) If a divides bc or a does not divide b, then a divides c.

This statement is not the same as the original conditional statement.

The original statement states that if a divides bc, then a divides b or a divides c.

However, statement D states that if a divides bc or a does not divide b, then a divides c.

This is a different condition altogether, so it is not equivalent to the original statement.

E) a divides bc, a does not divide b, and a does not divide c.

This is not a statement but rather an additional condition specified.

It describes a scenario where a divides bc, a does not divide b, and a does not divide c.

However, it doesn't provide any logical implications or conclusions like the conditional statements we have been discussing.

Therefore, we get;

Statement A is not the same as the original statement.

Statement B is the negation of the original statement.

Statement C is the same as the original statement.

Statement D is not the same as the original statement.

Condition E is not a statement, but a set of conditions without any logical implications.

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Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.

Answers

Answer:

r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

-4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

(3x^5-8x^4-10x^2+4x) divided by (2x^3)

Answers

Answer: 3x^4-8x^3-10x+4x/2x^2

Step-by-step explanation: JUST SOLVE IT

A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 12. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 14. Test the claim that the population means are different. Use level of significance 0.01.What distribution does the sample test statistic follow? Explain.

Answers

Answer:

We reject the null hypothesis that the population means are equal and accept the alternative hypothesis that the population means are different.

Step-by-step explanation:

We have large sample sizes $n_(1) = 49$ and $n_(2) = 64$ , the unbiased point estimate for $\mu_(1)-\mu_(2)$ is $\bar{x}_(1) - \bar{x}_(2)$ , i.e., 12-14 = -2.

The standard error is given by $\sqrt{(\sigma^(2)_(1))/(n_(1))+(\sigma^(2)_(2))/(n_(2))}$ , i.e.,

$\sqrt{((3)^(2))/(49)+((4)^(2))/(64)}$ = 0.6585.

We want to test $H_(0): \mu_(1)-\mu_(2) = 0$ vs $H_(1): \mu_(1)-\mu_(2) \neq 0$ (two-tailed alternative). The rejection region is given by RR = {z | z < -2.5758 or z > 2.5758} where -2.5758 and 2.5758 are the 0.5th and 99.5th quantiles of the standard normal distribution respectively. The test statistic is $Z = \frac{\bar{x}_(1) - \bar{x}_(2)-0}{\sqrt{(\sigma^(2)_(1))/(n_(1))+(\sigma^(2)_(2))/(n_(2))}}$ and the observed value is $z_(0) = (-2)/(0.6585) = -3.0372$ . Because -3.0372 fall inside RR, we reject the null hypothesis.

The test statistic follow a standard normal distribution because we are dealing with large sample sizes.

Final answer:

In this scenario of comparing two independent samples and given that the sample sizes are large, the sample test statistic follows the Standard Normal distribution or Z-distribution. The Z-test statistic representing the difference in sample means (in units of standard error) is compared with critical values for a two-tailed test at 0.01 significance level to determine if there's sufficient evidence to reject the null hypothesis that the two population means are equal.

Explanation:

The test in your question pertains to a hypothesis testing scenario featuring two independent samples. This scenario typically involves two population means given that population standard deviations are known. The distribution followed by the sample test statistic in such cases is the Standard Normal distribution or Z-distribution, as the sample sizes (n1 = 49, n2 = 64) are sufficiently large. To test the claim that population means are different (at a significance level of 0.01), you'd typically construct a Z-test statistic that represents the difference in sample means (x1 - x2) in units of its standard error. The Z-test statistic is calculated as follows:

$Z = \frac{x_1 - x_2}{\sqrt{(\sigma_1^2)/(n_1) + (\sigma_2^2)/(n_2)}}$

Here, x1 and x2 are the sample means, σ1 and σ2 are the population standard deviations and n1 and n2 are the samples sizes. The resulting Z-score can be compared with critical Z-scores for a two-tailed test at the given level of significance (0.01) to determine whether or not the null hypothesis (two population means are equal) can be rejected.

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