Consider a random experiment with sample space Ω={0,1,…,}(allnon−negativeintegers)andthe associated collection of events B consisting of all subsets of Ω. Prove that there does not exist an "equilikely" distribution of probabilities for Ω; that is, for any set function, P, such that P(A)=P(B) whenever events A∈B and B∈B have the same number of elements, prove that P does NOT satisfy the axioms of probability (Definition 1.3.1)

The correct alternative hypothesis is: Ha: not all sample mean course ratings are the same.

Since we are comparing the average ratings of the three courses, we should use the sample mean instead of the median. The alternative hypothesis (Ha) should propose a difference between the courses, indicating that not all sample mean course ratings are the same.

This hypothesis will be tested against the null hypothesis, which states that the sample mean course ratings are the same. If we find enough evidence to reject the null hypothesis, it suggests that there is a significant difference in the average ratings among the three courses.

To know more about null hypothesis click on below link:

https://brainly.com/question/19263925#

#SPJ11

The minimized SOP expression for F(A,B,C,D,E) using a five-variable Karnaugh map is D'E' + BCE'. A five-variable Karnaugh map is a graphical tool used to simplify Boolean expressions.

The map consists of a grid with input variables A, B, C, D, and E as the column and row headings. The cell entries in the map correspond to the output values of the logic function for the respective input combinations.

To find the minimized SOP expression, we start by marking the cells in the Karnaugh map corresponding to the minterms given in the function: 2m(4,5,6,7,9,11,13,15,16,18,27,28,31). These cells are identified by their binary representations.

Next, we look for adjacent marked cells in groups of 1s, 2s, 4s, and 8s. These groups represent terms that can be combined to form a simplified expression. In this case, we find a group of 1s in the map that corresponds to the term D'E' and a group of 2s that corresponds to the term BCE'. Combining these groups, we obtain the expression D'E' + BCE'.

The final step is to check for any remaining cells that are not covered by the combined terms. In this case, there are no remaining cells. Therefore, the minimized SOP expression for the given logic function F(A,B,C,D,E) is D'E' + BCE'.

Learn more about combinations here: https://brainly.com/question/29595163

#SPJ11

The sum of vectors a and b in unit-vector notation is (-4.4 m)i + (1.2 m)j + (6.5 m)h.

The magnitude of the vector a + b can be determined using the Pythagorean theorem. The magnitude, denoted as |a + b|, is calculated as the square root of the sum of the squares of the components. In this case, |a + b| = √[(-4.4 m)^2 + (1.2 m)^2 + (6.5 m)^2]. Solving this equation yields |a + b| ≈ 7.35 m.

To determine the direction of a + b relative to the unit vector h^, we can express the vector a + b as a linear combination of unit vectors. In this case, we have (-4.4 m)i + (1.2 m)j + (6.5 m)h = (-4.4 m)i + (1.2 m)j + (6.5 m)(0)i + (6.5 m)(0)j + (6.5 m)(1)h. Therefore, the direction of a + b relative to the unit vector h^ is parallel to the h-axis, with a magnitude of 6.5 m.

Learn more about vectors here:

https://brainly.com/question/30958460

#SPJ11

Answer:

0.43 cubic yards

Explanation:

We know that 1 cubic yard is equivalent to 46656 cubic inches. So, we can convert 19845 cubic inches into cubic yards as:

Therefore, the answer is 0.43 cubic yards

Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

Know more about vector functions here:

https://brainly.com/question/14895420

#SPJ4

It should include 653 medical files in a random sample to be 90% confident that the point estimate will be within 0.01 from p.

To determine the sample size needed for estimating the proportion with a certain level of confidence, we can use the formula:

n = (Z^2 * p * q) / E^2

where:

- n is the required sample size

- Z is the critical value corresponding to the desired confidence level

- p is the preliminary estimate of the proportion

- q = 1 - p

- E is the margin of error

In this case, we want to be 90% confident that the point estimate will be within 0.01 from p. Therefore, the confidence interval is 90%, which corresponds to a critical value Z. The critical value can be obtained from a standard normal distribution table or a statistical calculator. For a 90% confidence level, the critical value is approximately 1.645 (rounded to 2 decimal places).

Given the preliminary estimate p = 0.52 (52% people have blood type B), the margin of error E = 0.01, and the critical value Z = 1.645, we can calculate the required sample size:

n = (1.645^2 * 0.52 * 0.48) / 0.01^2

n ≈ 652.83

Rounding up to the nearest whole number, the required sample size is 653.

Therefore, you should include 653 medical files in a random sample to be 90% confident that the point estimate will be within 0.01 from p.

Learn more about interval here: brainly.com/question/32278466

#SPJ11

(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

5/2

Step-by-step explanation:

tan&= 2/5(p/b)

here,

p=2,b=5

cot&=b/p

=5/2

The assumptions of an ANOVA (Analysis of Variance) include:

1. Independence: The observations within and between groups must be independent of each other, meaning the outcome of one observation should not influence the outcome of another.
2. Same or similar variance: The variances of the populations from which the samples are drawn should be approximately equal. This is also known as homogeneity of variance or homoscedasticity.
The options "at least 5 in each group" and "at least 10 in each group" are not assumptions of ANOVA. However, having an adequate sample size in each group is essential for the validity and power of the statistical test, but there is no specific requirement of 5 or 10 in each group. It is generally recommended to have a balanced design, with equal or nearly equal sample sizes across all groups.

To know more about ANOVA visit:

https://brainly.com/question/30763604

#SPJ11

Answer:

C 4 loaves

Step-by-step explanation:

Answer:

Approximately 16%

Step-by-step explanation:

To solve this problem using the empirical rule, we need to first standardize the value of 170 pages using the mean and standard deviation provided:

z = (x - k) / o

where x is the value we want to find the probability for (170 pages), k is the mean (195 pages), and o is the standard deviation (25 pages).

So,

z = (170 - 195) / 25 = -1

Now, we can use the empirical rule, which states that for a normal distribution:

- About 68% of the data falls within 1 standard deviation of the mean

- About 95% of the data falls within 2 standard deviations of the mean

- About 99.7% of the data falls within 3 standard deviations of the mean

Since we know that the distribution is normal, and we want to find the probability that a randomly selected book has fewer than 170 pages (which is one standard deviation below the mean), we can use the empirical rule to estimate this probability as follows:

- From the empirical rule, we know that about 68% of the data falls within 1 standard deviation of the mean.

- Since the value of 170 pages is one standard deviation below the mean, we can estimate that the probability of randomly selecting a book with fewer than 170 pages is approximately 16% (which is half of the remaining 32% outside of one standard deviation below the mean).

Therefore, the probability that a randomly selected book has fewer than 170 pages is approximately 16%.

0.00634 in scientific notation is: 6.34 × 10⁻³  

To write extremely big or extremely small numbers, use scientific notation. When a number in the range of 1 to 10 is multiplied by a power of 10, the result is represented in scientific notation.

The default base value ought to be 10. The exponent must be an integer that is not zero; hence, it may be either positive or negative. The coefficient's absolute value should be less than 10, although it might be larger than or equal to 1. The whole and decimal numbers that make up coefficients might be positive or negative.

Thus, the given number 0.00634 in scientific notation is expressed as : 6.34 × 10⁻³  

To know more about scientific notation refer to:

https://brainly.com/question/1767229

#SPJ1

Answer:

i would like to  say you divide but not shure im just starting 8th grade but good luck

Step-by-step explanation:

Answer:

y = -15

Step-by-step explanation:

All you have to do is 51 divided by -3.4 and it equals -15. Inverse operations in short terms. And if you substitute -15 for y it will fir.

Answer:

-3.4y = 51

y = 51/-3.4

y = 510/-34

y = -15

We can see that the measure that changes the most when the value of 82° is changed to 94° is the mean. The new mean temperature is 82.3°

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Before the change, the measures are:

IQR = 105 - 61 = 44°

Range = 105 - 57 = 48°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 81.4°

Median = the middle value, which is 84°

After the change, the list becomes:

58, 61, 71, 77, 91, 100, 105, 102, 95, 94, 66, 57

IQR = 102 - 61 = 41°

Range = 105 - 57 = 48°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 94 + 66 + 57) / 12 = 82.3°

Median = the middle value, which is still 84°

Hence, we can see that the measure that changes the most when the value of 82° is changed to 94° is the mean. The new mean temperature is 82.3°

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ1

Answer:

  (d)  Median 84°

Step-by-step explanation:

You want to know the effect on various statistics of changing the value 82 to 94 in the data ...

  {57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105}

Changing a middle value in the list will have no effect on either the range or the IQR.

Changing a value from 82 to 94 adds 12 to the total of the 12 data values. This will increase the mean by 12/12 = 1 degrees to about 81.4.

The median value is currently the average of 77 and 82. Replacing 82 with 94, changes the order so that the median will be the average of 77 and 91. That is the median will increase by 9/2 = 4.5 degrees.

The measure that changes the most is the median. Its new value is 84°, choice D.

<95141404393>

Answer:

176/90

1.9556

Step-by-step explanation:

2 9/10 - 1 7/18

29×9-17×5/90

261-85/90

176/90

1.9556

Answer is 1.9556

3b^3+2b^2+13b+14

Just add like terms

If u have any questions just ask

The equation of the parabola using vertex form in the graph is given as; y = (-19/9)(x + 3)².

For the given question;

The curve on the graph in the vertex form is defined by the the equation;

y = a( x – h) 2 + k

Where, (h,k) are the vertex of the curve.

From the graph.

Vertex (h,k) = (-3, 0)

Point = (x, y) = (0, -19)

Put the values in the curve.

y = a( x – h)² + k

-19 = a( 0 – (-3))² + 0

Solving.

a = -19/9

Now, the put the value of a in the equation of parabola.

y = (-19/9)(x + 3)² + 0

y = (-19/9)(x + 3)²

Thus, the equation of the parabola in the graph is given as; y = (-19/9)(x + 3)².

To know more about parabola, here

https://brainly.com/question/13009188

#SPJ13

Answer:

87°

Step-by-step explanation:

if an angle is complementary that means that equals 90°.

and we know one part of the angles, so then we take 90° - 3° and we get 87°.

Answer:

The measure of its complementary angle is 87°

Step-by-step explanation:

We know this because the sum of two complementary angles is always equal to 90°, so:

90 - 3 = 87

Therefore, your final answer will be 87°

Answer:

The degree of f(x) is even, and the leading coefficient is negative. There are  3 real zeros, and 1 relative minimum values.

Step-by-step explanation:

We have the graph of f(x).

First, since both end behaviors are the same, our function must be an even-degree.

Second, since both end behaviors are going towards negative infinity, this means that the leading coefficient of our function must be negative.

The real zeros are whenever the graph touches or crosses the x-axis. We can see that this happens three times. I've circled them in blue in the image below.

Finally, relative minimum values are the lowest points in a graph, and then happen between a decreasing and then an increasing curve.

From, the graph, we only have one relative minimum value. This is circled in black in the image below.

Note that the arrows whether the curve is decreasing or increasing. We can see that the curve to the left of the minimum is decreasing, while the curve to the right of the minimum is increasing.

So, our solution is:

The degree of f(x) is even, and the leading coefficient is negative. There are  3 real zeros, and 1 relative minimum values.

And we're done!

9,603.75 cm² is the area of the given triangle.

So, the perimeter of the triangle is 392 cm.

Then, let the rest 2 sides be x, where x = x.

Now, we know that the rest 2 equal sides are of length 98.5 cm.

Now, calculate the area as follows:

Therefore, 9,603.75 cm² is the area of the given triangle.

Know more about triangles here:

https://brainly.com/question/28889256

#SPJ1

The answer choice which represents a table which represents a linear and proportional relationship is; Choice C ; whose y-intercept is 0.

With respect to relationships, two variables are said to be proportional if the y-intercept of the relation between them is 0.

here, we have,

The answer represents a linear relationship that is also proportional

Hence, y = kx represents a proportional relationship where k is the constant of proportionality.

Read more on proportional relationship;

brainly.com/question/21302696

#SPJ1

Answer:

You would need 16 pounds of apples!

Step-by-step explanation:

The table goes up by 3 for pounds of apples so you would do 10+3 which equals 13 and then add another three to get 16! Hope this helps.

The numbers of nickels in a boys bank is 1 less that twice the number of dimes. if the total value of the coins in the bank is at least 4.37. There are smallest 87 number of coins are dimes

Nickel:

The nickel is a five-cent coin minted by the United States Mint. Made of cupronickel (75% copper, 25% nickel), this piece has been published since 1866. It has a diameter of 21.21 mm (0.835 inches) and a thickness of 1.95 mm (0.077 inches). The

Dine:

Dime is a dime in U.S. terminology, officially called a "one cent". The name was first authorized by the Money Act of 1792.

The dime is the smallest in diameter and thinnest US coin currently minted for circulation at 0.705 inches (17.91 millimeters) and 0.053 inches (1 inch) in diameter.

According to the question:

We know that 1 Nickel = $0.05

and                  1 Dime = $ 0.10

Let Nickel be denoted as N

and, Dime be denoted as D

Now,

N +D = 1 - 2D  

⇒ N + 3D = 1          ------------------------- (1)

And,

0.05N +0.10D = 4.37 ------------------------- (2)

solving the equation (1) and (2), we get,

N = 261

putting N = 261 in equation (1), we get,

D = 87

Therefore,  there are total 261 nickel and 87 Dimes

Learn more about Dimes:

https://brainly.com/question/16439760

#SPJ4

Answer:

D

Step-by-step explanation:

25

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

To learn more about check and saving accounts visit;

https://brainly.com/question/20984186

#SPJ4

Answer:

m=0

Step-by-step explanation:

\(m=\frac{Rise}{Run}=\frac{y_1-y_0}{x_1-x_0}=\frac{5-5}{7-(-8)}=0\\m=0\)