Let P(n) be the set of all partitions of the positive integer n. For all (a₁,..., ak), B = (B₁, ...) = P(n), define (a) Show that (P(n), ≤) is a partially ordered sets (b) Draw its Hasse diagram of (P(6),≤). Is (P(n), ) a lattice for all n?

Answer:

I think it is the last answer.

Step-by-step explanation:

There can only be one vertex.

Answer:[tex]2355.31\ cm^3[/tex]

Step-by-step explanation:

Given

diameter of the cone is  [tex]d=23\ cm\quad [r=\frac{d}{2}=11.5\ cm][/tex]

The height of the cone is  [tex]h=17\ cm[/tex]

The volume of a cone is  [tex]V=\dfrac{1}{3}\pi r^2h[/tex]

Insert the values

[tex]\Rightarrow V=\dfrac{1}{3}\times \dfrac{22}{7}\times 11.5^2\times 17=2355.309\\\\\Rightarrow V\approx 2355.31\ cm^3[/tex]

Thus, the volume of the cone is [tex]2355.31\ cm^3[/tex]

Answer:

8 ft

Step-by-step explanation:

Given:

Volume = 401.92

radius = 4 feet

Volume of cylinder: [tex]\pi[/tex]r^2h

3.14 * 4^2 * h = 401.92 cubic feet

3.14 * 16 * h = 401.92 cubic feet

50.24 * h = 401.92

h = 8 ft

The density function of Y, denoted as [tex]f_Y[/tex](y), is given by [tex]f_Y[/tex](y) = 2y × φ(y²), where φ(y) is the standard normal density function.

To find the density function of Y = √|X|, we need to calculate the cumulative distribution function (CDF) of Y and then differentiate it to obtain the density function.

Start with the CDF of Y:

[tex]f_Y[/tex](y) = P(Y ≤ y) = P(√|X| ≤ y)

Since X is normally distributed with mean 0 and variance 1, we know that X follows a standard normal distribution.

We can rewrite the CDF of Y in terms of X:

[tex]f_Y[/tex](y) = P(-y ≤ √|X| ≤ y) = P(X ≤ y²) - P(X ≤ -y²)

Using the standard normal distribution table, we can find the probabilities:

[tex]f_Y[/tex](y) = Φ(y²) - Φ(-y²)

Differentiating the CDF with respect to y, we obtain the density function of Y:

[tex]f_Y[/tex](y) = d/dy[[tex]f_Y[/tex](y)] = d/dy[Φ(y²) - Φ(-y²)]

Simplifying the derivative, we get:

[tex]f_Y[/tex](y) = 2y × φ(y²)

where φ(y) is the standard normal density function.

Thus, the density function of Y is [tex]f_Y[/tex](y) = 2y × φ(y²), where φ(y) is the standard normal density function.

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Answer:

50m^2

Step-by-step explanation:

This question seems extremely odd to me. I don't really even understand what's being asked.

As far as exponential functions go, it's missing an exponent for one. The dependent variable is missing. This essentially saying f(x) = -4 or y = -4. Which is fine, but is definitely not an exponential function and in a very odd and incomplete form to begin with.

Answer:

624.5 feet

Step-by-step explanation:

Calculation to determine how many feet from the boat is the parasailor

Based on the information given we would make use of Pythagorean theorem to determine how many feet from the boat is the parasailor using this formula

a²+b²=c²

First step is to plug in the formula by substituting the given value

500²+b²=800²

Second step is to evaluate the exponent

250,000+b²=640,000

Third step is to substract 250,000 from both side and simplify

250,000+b²-250,000=640,000-250,000

b²=390,000

Now let determine how many feet from the boat is the parasailor

Parasailor feet=√b²

Parasailor feet=√390,000

Parasailor feet=b=624.49

Parasailor feet=b=624.5 feet (Approximately)

Therefore how many feet from the boat is the parasailor will be 624.5 feet

Answer: Sorry I don't know the answer but I recommend an app that will help you is called Mathpapa is really helpful and have helped me get A on test and homework

Step-by-step explanation: is htis one https://www.mathpapa.com/algebra-calculator.html

Answer:

60 +24 = 84

Step-by-step explanation:jjjjjhjhjhj

6 x 4 +5 x 12

Answer:

x > − 2

Step-by-step explanation:

If your motive was to solve for x thats your answer, if not good luck!

Answer:

Step-by-step explanation:

The statement Joe's salary of $35,060$⁢35,060 is 1.401.40 standard deviations above the mean is false.

To determine if the statement is true or false, we need to calculate the number of standard deviations Joe's salary of $35,060 is above the mean.

Given:

Mean salary = $28,600

Standard deviation = $4,400

Joe's salary = $35,060

To calculate the number of standard deviations above the mean, we can use the formula:

Number of standard deviations = (X - μ) / σ

Where:

X is the value we want to compare (Joe's salary)

μ is the mean

σ is the standard deviation

Plugging in the values, we have:

Number of standard deviations = (35,060 - 28,600) / 4,400

= 6,460 / 4,400

≈ 1.4727

Therefore, Joe's salary of $35,060 is approximately 1.4727 standard deviations above the mean, not 1.40.

The statement is false.

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Answer:

length=2.5feet

Step-by-step explanation:

Volume =Base area * height

6/60=(4*length) * 6/6

10=4length

length=10÷4

=2.5feet

The length of the pyramid is 7.5 feet.

'A rectangular pyramid is a type of pyramid with the base shaped like a rectangle but the sides are shaped like a triangle. A pyramid usually has triangular sides but with different bases.'

According to the given problem,

Volume = 60 cubic feet

Height = 6 feet

Width of rectangular base = 4 feet

Let the length be x,

Volume =[tex]\frac{L * W * H}{3}[/tex]

⇒ 60 = [tex]\frac{x*6*4}{3}[/tex]

⇒ 180 = 24x

⇒ x = [tex]\frac{180}{24}[/tex]

⇒ x =[tex]\frac{45}{6}[/tex] = 7.5

Hence, we can conclude that the value of the length of the rectangular base is 7.5 feet.

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Answer:

(5,7) , (2, -3) , (2,4)

Step-by-step explanation:

your first number, the x, is the horizontal number. The second, y, is the vertical number. So if you look at A, the x is 5, and you then have to go up to 7 to reach the intercept

Answer:

339.36 cm^2

Step-by-step explanation:

14*12.12=169.68

169.68/2=84.84

84.84= the area of one triangle

(84.84)4=339.36

I'm pretty sure, but check my math if it's wrong

Answer:

6336 feet = 0.3476 nautical leagues

The probability of P(X ≤ 2) is  0.0135

We have the information available from the question:

Binomial variable is X

the value of n = 5

and, the value of p = 0.4

We are given to compute the probability P(X [tex]\leq[/tex] 2) and round the answer to five decimal places.

The binomial distribution formula is given by:

[tex]P(X)=nCx(p)^x(1-q)^n^-^x[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)!x!}[/tex]

We have to find the probability:

P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)

P(X = 1) = [tex]5C1(0.4)^1(1-0.4)^5^-^1[/tex] = 0.0026

P(X= 2) =[tex]5C2(0.4)^2(1-0.4)^5^-^2[/tex] = 0.0109

P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)

P(X [tex]\leq[/tex] 2) = 0.0026 + 0.0109

P(X [tex]\leq[/tex] 2) =  0.0135

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Answer: just figure out how many 8s are in 36 then multiply that by 66 :):)

Step-by-step explanation:

Answer:

8th term would be .9375

10th term would be .234375

Step-by-step explanation:

Answer:

56.52

Step-by-step explanation:

C = 2 x pi x r

r = 9

C = 2 x pi x r

multiply 2 by 9

C = 18 x pi

C = 56. 52

Answer:

0.625 : 1

Step-by-step explanation:

5 : 8

→ Divide both sides by 8 to get it to 1

(5 ÷ 8) : (8 ÷ 8)

→ Simplify

0.625 : 1

Step-by-step explanation:

[tex]180 - 130 = 50[/tex]

Answer:

2.9 litres

or

2 14/15 litres

Step-by-step explanation:

To determine the amount of water Sam drinks in an hour, divide the total amount drunk by the number of hours

Amount drank in an hour = total litres drunk / time

[tex]2\frac{1}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex]

[tex]\frac{11}{5}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{44}{15}[/tex] = 2[tex]\frac{14}{15}[/tex] litres

By finding the square root of 1089, we determine that it is equal to 33. Multiplying 3 by 33 results in 99, which is the equivalent expression to 3√1089.

To simplify the expression, we need to find the square root of 1089. The square root of 1089 is 33 because 33 * 33 = 1089.

Now, multiplying 3 by √1089 gives us 3 * 33, which equals 99. Therefore, the expression 3√1089 is equivalent to 99.

When we have a cube root (∛) in the original expression, we need to find the number that, when multiplied by itself three times, equals the given value. However, in this case, we have a square root (√) in the expression, which means we need to find the number that, when multiplied by itself once, equals the given value.

By finding the square root of 1089, we determine that it is equal to 33. Multiplying 3 by 33 results in 99, which is the equivalent expression to 3√1089.

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Answer:

The next three terms of the sequence are 17, 21 and 25.

The 300th term of the sequence is 1197.

Step-by-step explanation:

The statement describes an arithmetic progression, which is defined by following formula:

[tex]p(n) = p_{1}+r\cdot (n-1)[/tex] (1)

Where:

[tex]p_{1}[/tex] - First element of the sequence.

[tex]r[/tex] - Progression rate.

[tex]n[/tex] - Index of the n-th element of the sequence.

[tex]p(n)[/tex] - n-th element of the series.

If we know that [tex]p_{1} = 1[/tex], [tex]n = 2[/tex] and [tex]p(n) = 5[/tex], then the progression rate is:

[tex]r = \frac{p(n)-p_{1}}{n-1}[/tex]

[tex]r = 4[/tex]

The set of elements of the series are described by [tex]p(n) = 1 + 4\cdot (n-1)[/tex].

Lastly, if we know that [tex]n = 300[/tex], then the 300th term of the sequence is:

[tex]p(n) = 1 + 4\cdot (n-1)[/tex]

[tex]p(n) = 1197[/tex]

And the next three terms of the sequence are:

n = 5

[tex]p(n) = 1 + 4\cdot (n-1)[/tex]

[tex]p(n) = 17[/tex]

n = 6

[tex]p(n) = 1 + 4\cdot (n-1)[/tex]

[tex]p(n) = 21[/tex]

n = 7

[tex]p(n) = 1 + 4\cdot (n-1)[/tex]

[tex]p(n) = 25[/tex]

The next three terms of the sequence are 17, 21 and 25.

The 300th term of the sequence is 1197.

If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the variance is greater than 15. Otherwise, if the calculated chi-square value is less than or equal to the critical chi-square value, we fail to reject the null hypothesis.

To test the hypothesis that the variance for the number of ounces of ice cream consumed per month is greater than 15, we can use a chi-square test for variance.

The null and alternative hypotheses for this test are as follows:

Null Hypothesis (H0): The variance for the number of ounces of ice cream consumed per month is equal to or less than 15.

Alternative Hypothesis (H1): The variance for the number of ounces of ice cream consumed per month is greater than 15.

Given a random sample of 23 people with a standard deviation of 4.4 ounces, we can calculate the sample variance as [tex]s^2 = (4.4)^2[/tex] = 19.36.

To perform the chi-square test, we calculate the test statistic as follows:

chi-square = (n - 1) × [tex]s^2[/tex] / [tex]\sigma^2[/tex]

where n is the sample size, [tex]s^2[/tex] is the sample variance, and [tex]\sigma^2[/tex] is the hypothesized population variance (15 in this case).

Substituting the values, we get:

chi-square = (23 - 1) × 19.36 / 15 = 29.44

Next, we compare this test statistic to the critical value from the chi-square distribution table with (n - 1) degrees of freedom (22 degrees of freedom in this case) at the given significance level (alpha = 0.05).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the variance for the number of ounces of ice cream consumed per month is greater than 15.

Otherwise, if the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis.

Performing the chi-square test with the given values, we compare the test statistic (29.44) to the critical value from the chi-square distribution table.

If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that the variance for the number of ounces of ice cream consumed per month is greater than 15. Otherwise, we fail to reject the null hypothesis.

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