Please answer this if you can! (NO EXPLANATION NEEDED!) <3

The Normal distribution is symmetric and ranges from negative to positive infinity, while the Log-normal distribution is skewed and only takes positive values. To select the better fit for data, consider characteristics (positivity and skewness favor Log-normal, symmetry favors Normal), hypothesis testing, visualization, and statistical tests.

Let's analyze each section separately:
a) The major differences between the Normal and Log-normal distributions are:

Normal Distribution: The Normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution that is defined by its mean (μ) and standard deviation (σ). It follows a bell-shaped curve and is often used to model naturally occurring phenomena. The range of values extends from negative infinity to positive infinity.

Log-normal Distribution: The Log-normal distribution is a skewed probability distribution that arises when the logarithm of a random variable follows a normal distribution. It is characterized by its parameters mu (μ) and sigma (σ) of the underlying normal distribution. Unlike the Normal distribution, the Log-normal distribution only takes positive values.

b) Selecting which distribution fits the data better depends on the nature of the data and the research question at hand. Here are a few considerations:

1. Data Characteristics: If the data consists of positive values and the distribution appears to be skewed, the Log-normal distribution might be more appropriate. On the other hand, if the data is symmetric and unbounded, the Normal distribution may be a better fit.

2. Hypothesis Testing: If you have a specific hypothesis to test or a theoretical justification for choosing one distribution over the other, it is advisable to use that distribution.

3. Visualization: Plotting the data and comparing it to the shapes of the Normal and Log-normal distributions can provide visual insights into which distribution aligns better with the data.

4. Statistical Tests: Statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test can be used to assess the goodness-of-fit for each distribution and determine which one provides a better fit to the data.

In summary, selecting the appropriate distribution involves considering the characteristics of the data, the research question, and statistical tests. Visualization and hypothesis testing can further aid in determining the best fit distribution.

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Answer:

In 6 years Diane will be twice as old as Amy. How old are they now? 5. Fred is 4 years older than Barney. Five years ago the sum of their ages was 48 there have a good day:-D

Step-by-step explanation:

The probability that either event will occur is 0.83

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

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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Thus, m∠F =  33º for the corresponding angle measures for each similar triangle ΔABC and ΔDEF.

To start, we know that similar triangles have corresponding angles that are congruent. Therefore, we can set up the following proportion:

m∠BAC/m∠EDF = m∠BCA/m∠DFE

Substituting the given angle measures, we get:
(x² - 5x)/(4x + 36) = (4x - 5)/m∠F

To solve for m∠F, we need to isolate it on one side of the equation. First, we can cross-multiply to get:
(4x - 5)(4x + 36) = (x² - 5x)m∠F

Expanding the left side, we get:
16x² + 116x - 180 = (x² - 5x)m∠F

Next, we can divide both sides by (x² - 5x):
(16x² + 116x - 180)/(x² - 5x) = m∠F

Simplifying the left side, we get:
(4x + 29)/(x - 5) = m∠F

Therefore, m∠F = (4x + 29)/(x - 5).

To check our answer, we can plug in a value for x and find the corresponding angle measures for each triangle. For example, if x = 6:

m∠BAC = (6² - 5(6))º = 16º
m∠BCA = (4(6) - 5)º = 19º
m∠EDF = (4(6) + 36)º = 60º

Using our formula for m∠F, we get:
m∠F = (4(6) + 29)/(6 - 5) = 33º

We can see that this satisfies the proportion and therefore our answer is correct.

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To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:

2y=26, y=13

3x-(13)= -1, 3x=12, x=4

The Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547  .

The Binomial  Distribution formula is

P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ

where ,

n is the number of trials

x is the number of times success occurs

p is the probability of success

q is the probability of failure .

In the given question ;

it is given that

students that are registered for the course = 20

so , n=20

Let x denote the number of students that withdraw without completing the course .

given that 14 % students  withdraw without completing the course ,

hence p = 14% = 0.14

So , q= 1-p = 1-0.14 = 0.86

the probability that 2 or fewer will withdraw from the course is denoted by P(X ≤ 2) and  is calculated using

the formula , P(X≤2)=P(X=0)+P(X=1)+P(X=2)        ...(i)

using Binomial Probability we get

P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ

P(X=0) = C(20,0)*(0.14)⁰*(0.86)²⁰⁻⁰

= C(20,0)*(0.14)⁰*(0.86)²⁰

= 1*1*(0.0489)

= 0.0489

So , P(X=0)=0.0489        ...(ii)

P(X=1) = C(20,1)*(0.14)¹*(0.86)¹⁹

= 20*0.14*0.0569

= 0.1593

So , P(X=1)=0.1593        ...(iii)

P(X=2) = C(20,2)*(0.14)²*(0.86)¹⁸

= 190*0.0196*0.0662

= 0.2465    

So , P(X=2)=0.2465        ...(iv)

Substituting the values of (ii) , (iii) and (iv) in (i) , we get

P(X≤2)=P(X=0)+P(X=1)+P(X=2)

P(X ≤ 2) = 0.0489 + 0.1593 + 0.2465

= 0.4547

Therefore , the Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547   .

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Answer:

The correct answer is $5,29

Step-by-step explanation:

The unit price helps us determine the price for a single unit of something that has been purchased in a group.

In this case we have a package of 5 pairs of insulated gloves, which includes 5 pairs and costs 29.45.

We want to know what the unit price is, that is, how much does a single pair of gloves cost.

To determine this we simply divide the total price by the number of gloves:

29.45 / 5 = 5.29

In this way we can confirm that the unit price of a pair of insulated gloves is $ 5.29.

Answer:

Each pair of gloves is $5.29

Step-by-step explanation:

Answer:

Integers: 32,33,34,35

Step-by-step explanation:

Consecutive means back-to-back, with a difference of 1

Therefore this can be represented with the following equation (where x is the first number), and we can set this equal to the sum

\(x+(x+1)+(x+2)+(x+3)=134\\4x+6=134\\4x=128\\x=32\)

Therefore since x = 32, all four integers are:

\(32,33,34,35\)

If we check this, we can see that their sum equals to 134

\(32+33+34+35 = 134\)

Hope this helps!

Answer:

If x < -12, then (-x) > 12, and we have:

x - (-12) = x + 12

So, the simplified expression without using the absolute value symbol is:

x + 12

Step-by-step explanation:

Answer:

Since x is less than -12, then x-(-12) = x+12.

Here is a table of values for x and x-(-12):

x | x-(-12)

-13 | -1

-14 | -2

-15 | -3

...

Step-by-step explanation:

The arithmetic mean of the two fractions is 68/35.

The arithmetic mean can be calculated using the mentioned formula -

Arithmetic mean = sum of the numbers / frequency of numbers.

Sum of the fractions = 2/5 + 4/7

Performing division of the two numbers

Sum of the fractions = (14 + 20)/35

Sum of the fractions = 34/35

Arithmetic mean = (34/35)/2

Rewriting the average

Arithmetic mean = (34 × 2)/35

Performing multiplication on Right Hand Side of the equation

Arithmetic mean = 68/35

Hence, the Arithmetic mean is 68/35.

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Answer:

A screenshot of the graph is attached. :)

Answer:

D

Timon chewed six gumballs in two hours today and six gumballs in three hours yesterday.

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A function is represented by every input has only one output. Let’s look at each of the answer choices:

A. Input 4 notebooks, cost is $20 and input 5 notebooks, cost is $25. This is a function

B. Input 1 hour, charge is $20 and input 2 hours, charge is $40. This is a function

C. Input 1 hour, drove 50 miles and input 2 hours, drove 100 miles. This is a function.

D. Input 6 gum balls chewed, chewed in 2 and 3 hours. This is NOT a function. The input does not have only one output.

I hope this helps! :)

Answer:

5:3

Step-by-step explanation:

if there are 8 buttons in the tin. 5 of which are white. this leaves with 3 other buttons which are green. therefore the ratio will be 5:3

Answer:

20/27

Step-by-step explanation:

Answer:

A. B is correct

B. A is correct

C. B is correct

Step-by-step explanation:

Area of triangle: A = 1/2bh

A. Area of each triangle: A = 1/2 x 11.5 x 12 = 69

Total surface areas = 4(area of triangle) + area of square = 4(69) + 12^2 = 420

So A is incorrect and B is correct

B. Area of triangle: A = 1/2 x 13.9 x 16 = 111.2

Surface area = 4(area of triangle) = 4(111.2) = 444.8

So A is correct and B is incorrect

C. Area of triangle with base of 10: A = 1/2 x 10 x 7 = 35

Area of triangle with base of 8.1: A = 1/2 x 8.1 x 16 = 64.8

Total surface areas = 2(area of triangle base of 10) + 2(area of triangle base of 8.1) + area of rectangle = 2(35) + 2(64.8) + (10x8.1) = 280.6

So A is incorrect and B is correct.

12/1      if its a whole number you always just put a 1 under it as a fraction.

Answer:

9x² - 42x + 49

Step-by-step explanation:

Given

(3x - 7)² = (3x - 7)(3x - 7)

Each term in the second factor is multiplied by each term in the first factor, that is

3x(3x - 7) - 7(3x - 7) ← distribute both parenthesis

9x² - 21x - 21x + 49 ← collect like terms

= 9x² - 42x + 49

If you survey 25 randomly chosen college students from your local college to name their diet preference. The estimated the number of students at the college who prefer to be a vegetarian is 1600.

Assuming out of the 25 surveyed students 10 students prefer to be vegetarian.

So,

Proportion of vegetarian students in the sample = (Number of vegetarian students in the sample) / Sample size

Proportion of vegetarian students in the sample = 10 / 25

Proportion of vegetarian students in the sample = 0.4

Now let find the estimated number of students

Estimated number of vegetarian students = Proportion of vegetarian students in the sample * Total number of students

Estimated number of vegetarian students = 0.4 * 4000

Estimated number of vegetarian students = 1600

Therefore 1600 students at the college prefer to be vegetarian.

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Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

When graphing frequency distributions, bar charts are most commonly used to depict simple descriptions of categories for a single variable.

Bar charts provide a visual representation of the frequencies or counts of different categories or classes of a variable.

A bar chart consists of a series of rectangular bars, where the length or height of each bar represents the frequency or count of the corresponding category. The categories are displayed on the horizontal axis, while the frequency or count is shown on the vertical axis. Each bar is separate and distinct, allowing for easy comparison between categories.

The use of bar charts is particularly effective when working with categorical or discrete variables. Categorical variables represent data that can be divided into distinct groups or categories, such as colors, types of animals, or levels of satisfaction. By using a bar chart, we can clearly visualize the distribution of data across these categories.

Bar charts have several advantages that make them suitable for displaying frequency distributions. Firstly, they are easy to understand and interpret. The length or height of each bar directly corresponds to the frequency or count, making it straightforward to identify the relative magnitudes of the categories. Additionally, the spacing between the bars allows for clear differentiation between categories, enhancing readability.

Furthermore, bar charts facilitate the comparison of frequencies or counts across different categories. By aligning the bars side by side, we can easily assess the differences in frequencies or counts between categories. This visual comparison is especially useful for identifying dominant or minority categories, patterns, or trends within the data.

Bar charts also allow for additional visual enhancements to convey additional information. For example, different colors can be used to represent different categories, making it easier to distinguish between them. Labels can be added to the bars or axes to provide further context or explanation. These visual cues help in enhancing the overall clarity and communicability of the graph.

It is worth noting that bar charts are most appropriate when dealing with discrete or categorical variables. For continuous variables, a histogram is commonly used to depict the frequency distribution. Histograms are similar to bar charts, but the bars are connected to form a continuous distribution to represent the frequency or count of data within specific intervals or bins.

In conclusion, when graphing frequency distributions, bar charts are the most commonly used method to depict simple descriptions of categories for a single variable. Bar charts provide a clear and intuitive visual representation of the frequencies or counts of different categories, facilitating easy comparison and interpretation of the data. Their simplicity and versatility make them a valuable tool in data analysis and visualization.

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The value of b in the quadratic function affects the position of the axis of symmetry by determining the position of the vertex of the graph and the direction in which the graph opens.

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Answer:

value of b

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

5x - (x+3)2

5x - (2x+6)

5x - 2x -6

3x - 6

3(2) - 6

6 - 6

0

Hope it helps and let me know if you want an explanation <3 :)

Answer:

it is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remove the brackets

-90 - 27i - 66 - 34i                              

Combine like terms

- 90- 66 - 27i - 34i

-156 - 61i

There are 23 small prints, 264 medium prints ,188 large prints and 42 extra large prints which are being sold by Mr. Carandang.

Given that there is total sales of 1790 prints of one of the drawings by Mr, Caradang. Out of which 1273 unframed prints, 152 were small, 544 were medium. Out of the framed prints 23 were small,42 were extra large. Out of large prints 188 were framed, 496 were unframed.

We are required to find the number of small prints,medium prints, large .extra large in total and  total framed print of the drawings.

Total framed print=Small print+Medium print+Large print+Extra large print

=23+264+188+42

=517

Unframed print:

Small=152

Medium=544

Large=496

Extra large=81

Total unframed print=Small+Medium+large+extra large

=152+544+496+81

=1273.

Hence there are 23 small prints, 264 medium prints ,188 large prints and 42 extra large prints which are being sold by Mr. Carandang.

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