Answer:
\(\sqrt{80}\)
80 is the number in the square root
Step-by-step explanation:
\(d = \sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2} } \\d = \sqrt{(4-(-4) )^{2} +(5- 1 )^{2} }\\d = \sqrt{(4+4 )^{2} +4^{2}\\d = \sqrt{8^{2} +4^{2} }\\d=\sqrt{64 +16}\\d=\sqrt{80}\)
square root of 3x+7=x-1
Answer:
you can't find the square root of a negative
Step-by-step explanation:
Find the value of r in the isosceles triangle shown below.
8
8
6
Answer:
r = 6
.....................
While reading about a research study, which of the following would tell you that an association claim is being
made?
a. The presence of a scatterplot or bar graph
b. The measurement of two variables
c. The use of a correlation coefficient
d. The interrogation of internal validity
The answer to this question is c.The use of a correlation coefficient.
The use of a correlation coefficient would tell you that an association claim is being made in a research study. A correlation coefficient is a statistical measure that shows the strength and direction of a relationship between two variables. It ranges from -1 to 1, with 0 indicating no relationship and -1 or 1 indicating a perfect negative or positive relationship, respectively.
A scatterplot or bar graph may be used to visually display the relationship between two variables, but they do not necessarily indicate that an association claim is being made. The measurement of two variables is necessary for any type of research study, but it does not inherently imply that an association claim is being made.
Interrogation of internal validity is a process used to ensure that the study's results accurately reflect the relationship between the variables being studied. It is important for any research study but does not specifically indicate that an association claim is being made.
Therefore,the answer to this question is c.The use of a correlation coefficient.
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what is the answer I need help
Answer:
C
Step-by-step explanation:
The product will be greater than
Why is it important to know the background of a poet.
Answer:
To understand their poems better
Step-by-step explanation:
First you have a general knowledge on why the author made the poem
Second you now have more info to use in order to understand the poems
Third is the same reason why there are people in history books.
3/2x-8=hx+2
This equation will have zero solutions when h=
Because you get zero
Ans=h=3/2
Please mark brainliest
What is the average of the points A, B and C with weights 1, 1
and 1
respectively?
The average of the 3 points A, B, and C is 1/3
How to find the average of the 3 points?We know that for a set of N values {x₁, x₂, ..., xₙ} the average is:
Average = (x₁ + ... + xₙ)/N
Assuming that all the weights are 1.
Here the values (y values) for the 3 points are:
A = -9
B = 2
C = 8
The average of these 3 points is:
average = (-9 + 2 + 8)/3
average = 1/3
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Helppp I will mark brainliestttt
Answer:
2
Step-by-step explanation:
P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }
The solution to the division of the given surd is: \(\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }\)
Division of Surds.The division of surds follows a systemic approach whereby we divide the whole numbers separately and the root(s) are being divided by each other.
Given that:
\(\mathbf{P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }}\)
i.e.
\(\mathbf{=\dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )}{ \frac{4x}{(x-1)^{2} }} }\)
Using the fraction rule:
\(\mathbf{\dfrac{a}{\dfrac{b}{c}}= \dfrac{a\times c}{b}}\)
\(\mathbf{\implies \dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )(x-1)^{2}}{4x}} }\)
By simplification, we have:
\(\mathbf{ =\dfrac{\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{2} }{4x} }\)
\(\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }\)
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Below are the jorsey numbers of 11 players randomly solected from a football tearn Find the range, variance, and standard deviation for the given sample data What do the results teli us? 33747065564739725794150 Range = (Round to one decimal place as needed) Sample standard deviation = (Round to one decimal place as needed) Sample variance = (Round to one decimal place as needed) What do the results tell us? A. Jersey numbers on a football team do not vary as much as expected. B. The sample standard deviation is too large in companson to the range. C. Jersey numbers on a footbas team vary much mofe than expected D. Jersey numbers ate nominal data that are just replacemonts for names, so the resulling statistics are meaningiess:
The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.
To find the range, we need to subtract the smallest number from the largest number in the sample. So, the range is:
94 - 15 = 79
To find the sample variance and standard deviation, we first need to find the mean of the sample. We can do this by adding up all the numbers and dividing by the total number of players:
(33 + 74 + 70 + 65 + 56 + 47 + 39 + 72 + 57 + 94 + 15) / 11 = 54.18
Next, we need to find the difference between each number and the mean, square them, and add them up. This gives us the sum of squares:
[(33 - 54.18)^2 + (74 - 54.18)^2 + (70 - 54.18)^2 + (65 - 54.18)^2 + (56 - 54.18)^2 + (47 - 54.18)^2 + (39 - 54.18)^2 + (72 - 54.18)^2 + (57 - 54.18)^2 + (94 - 54.18)^2 + (15 - 54.18)^2] = 15864.4
The sample variance is then calculated by dividing the sum of squares by the total number of players minus one:
15864.4 / 10 = 1586.44
Finally, we can calculate the sample standard deviation by taking the square root of the variance:
√1586.44 ≈ 39.83
The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.
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Check that the trinomial is a perfect square trinomial
HELPPPPP!!!!!!!!
As a result, x²-18x+81 is a perfect square trinomial and can be represented as (x-9)².
WHAT ARE SOME OTHER PERFECT SQUARE TERMINAL EXAMPLES?Perfect square trinomials are illustrated by the following:
x²+6x+9
=(x+3)²
x²-10x+25
=(x-5)²
4x²+12x+9
=(2x+3)²
a²+2ab+b²=(a+b)²
The quadratic expression is a perfect square trinomial if it can be expressed in this way.
As an illustration,
let's determine whether x²-18x+81 is a perfect square trinomial:
The square of x is the first term, x².
The square of 9 is the final term (81).
Its result 2(x)(-9)=-18x is
twice as long as the middle term.
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A bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble. What is the probability that the marble is red or blue?
The probability that the marble is red or blue is 0.6923 or 69.23% if the bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble.
What is probability?It 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.
We have the total number of marbles = 5+4+4 =13
Total number of red and blue marble = 5+4 = 9
The probability that the marble is red or blue = 9/13 = 0.6923 or
= 69.23%
Thus, the probability that the marble is red or blue is 0.6923 or 69.23% if the bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble.
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CAN SOMEONE CHECK MY ANSWERS FOR ME RQ?
1. Addition:
a. x - 5 = 10
b. s - 4 = 6
c. y - 11 = 24
d. t - 8 = 9
2. Subtraction:
a. x + 2 = 10
b. s + 4 = 6
c. y + 17 = 24
d. t + 3 = 118
3. Multiplication
a. 1/5 x = 10
b. 1/2 s = 8
c. 1/2 t = 6
d. 1/4 y = 20
4. Division
a. 4x = 36
b. 13x = 52
c. 5x = 25
d. 10x = 120
5. Mixed Practice
a. x + 9 = 7
b. 23 - y = 44
c. s + 19 = 26
d. m - 40 = 20
e. z + 100 = 100
f. x + 22 = 23
g. s - 4 = 96
h. 1/4 x = 4
i. 24x = 3
j. 1/10 x = 50
k. 1/11y = 33
l. t + 14 = 16
m. t - 1 = 16
n. 1/2 q = 8
o. 15t = 24
My answers:
1.
A.15
B.10
C.35
D.17
2.
A.8
B.2
C.7
D.115
3.
A.50
B.16
C.12
D.80
4.
A.9
B.4
C.5
D.12
5.
A.-2
B.-21
C.7
D.60
E.0
F.1
G.100
H.16
I.1/8
J.500
K.636
L.2
M.17
N.16
O.8/5
Answer:
All looks good but Problem 5 K
363
Step-by-step explanation:
33 x 11 = 363
Answer: I only saw one mistake. On your mixed practice, K is wrong. It is 363, not 636.
hope this helps!
please give brainliest!
Pentagon ABCDE is reflected across the line shown and then rotated
72 clockwise about its center to create congruent pentagon FGHIJ.
Label the vertices of FGHU in the correct positions on the image.
Answer:
rotate it once to the right and you will get the vertices
Step-by-step explanation:
biometric authentication system using fingerprints returns a value between 0 and 1 for each attempted match. The system was tested with 1000 genuine fingerprints and 1000 imposter fingerprints. The histogram shows the numbers of genuine and imposter attempts for different ranges. Ex: 88 of the 1000 genuine fingerprints returned a value of n between 0.5 and 0.4, while only 3 imposter fingerprints returned a value in the same range.
Range of n Genuine Imposter fingerprints fingerprints
1>n>0.9 192 0
.9 2 n>0.8 188 0.82 n>0.7 176 0.72 n>0.6 158 0.6 2 n>0.5 133 0.52 n>0.4 88 0.42 n>0.3 49 0.32 n>0.2 15 29 0.22 n>0.1 1 319 0.12 n>0 643 (a) Determine the threshold value of n such that less than 1% of imposter attempts are accepted. How many false alarms are generated as a result? (b) Determine the threshold value of n such that less than 1% of genuine attempts are rejected. How many imposter attempts are accepted as a result? (c) Determine the threshold value of n such that no genuine attempts are rejected. How many imposter attempts are accepted as a result?
To determine the threshold value of n such that less than 1% of imposter attempts are accepted, we need to find the value of n for which the cumulative percentage of imposter attempts is 1%. From the histogram, we can see that the number of imposter attempts for values of n greater than 0.4 is 0. Therefore, we need to consider the values of n less than or equal to 0.4.
Let's calculate the cumulative percentage of imposter attempts for each range of values of n:
For n > 0.4: 0%
For n > 0.3: (0 + 29) / 1000 = 2.9%
For n > 0.2: (0 + 29 + 15) / 1000 = 4.4%
For n > 0.1: (0 + 29 + 15 + 319) / 1000 = 35.3%
For n > 0: (0 + 29 + 15 + 319 + 643) / 1000 = 97.2%
We can see that the cumulative percentage of imposter attempts is already above 1% for n > 0.2. Therefore, the threshold value of n should be set to 0.2 to ensure that less than 1% of imposter attempts are accepted.
The false alarm rate is the percentage of genuine attempts that are incorrectly rejected. In this case, since we are setting the threshold at 0.2, we can calculate the false alarm rate as the percentage of genuine attempts with a value of n less than or equal to 0.2:
For n <= 0.2: (88 + 133 + 158 + 176 + 188 + 192) / 1000 = 0.935
Therefore, the false alarm rate is 93.5%, which means that almost all genuine attempts will be incorrectly rejected.
To determine the threshold value of n such that less than 1% of genuine attempts are rejected, we need to find the value of n for which the cumulative percentage of genuine attempts is 99%. From the histogram, we can see that the number of genuine attempts for values of n less than or equal to 0.2 is 39. Therefore, we need to consider the values of n greater than 0.2.
Let's calculate the cumulative percentage of genuine attempts for each range of values of n:
For n > 0.2: (39 + 15 + 1) / 1000 = 5.5%
For n > 0.3: (39 + 15 + 1 + 49) / 1000 = 6.4%
For n > 0.4: (39 + 15 + 1 + 49 + 88) / 1000 = 14.2%
For n > 0.5: (39 + 15 + 1 + 49 + 88 + 133) / 1000 = 27.8%
For n > 0.6: (39 + 15 + 1 + 49 + 88 + 133 + 158) / 1000 = 43.6%
For n > 0.7: (39 + 15 + 1 + 49 + 88 + 133 + 158 + 176) / 1000 = 61.4%
For n > 0.8: (39 + 15 + 1 + 49 + 88 + 133 + 158 + 176 + 188
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Identify the rule that correctly describes each
sequence.
12, 8, 4, 0, -4, ...
Each term is 4 more than the previous term.
Each term is 4 less than the previous term.
Each term is 1/2 the previous term.
Each term is 2/3 the previous term.
6, 12, 24, 48, 96, ...
Each term is 6 more than the previous term.
Each term is 12 more than the previous term.
Each term is 1/2 the previous term.
Each term is 2 times the previous term.
COMPLETE
COMPLETE
here’s the answers
Answer:
Each term is 4 less than the previous term.
Step-by-step explanation:
If this helps you mark as brainlist!
Answer:
B and D are your answers for that whole page
Step-by-step explanation:
Identify the rule that correctly describes each sequence.
12, 8, 4, 0, –4, …
Each term is 4 more than the previous term.
This Is the right one: Each term is 4 less than the previous term.
Each term is 1/2 the previous term.
Each term is 2/3 the previous term.
6, 12, 24, 48, 96, …
Each term is 6 more than the previous term.
Each term is 12 more than the previous term.
Each term is 1/2 the previous term.
This is the right one: Each term is 2 times the previous term.
Determine the Rankine-Hugoniot condition, based on conservation of mass, for the speed of a shock for the equation ut+u2ux=0. (b) Solve the initial value problem u(0,x)={a,b,x<0,x>0, when (i)∣a∣>∣b∣, (ii) ∣a∣<∣b∣. Hint: Use Exercise 2.3.15 to determine the shape of a rarefaction wave.
(a). The speed of the shock wave can be determined by setting [u]s = 0.
(b). The initial value problem u(0,x)={a,b,x<0,x>0 has been solved.
(a) To determine the Rankine-Hugoniot condition for the speed of a shock, we consider the conservation of mass across the shock wave.
The given equation is:
ut + u^2ux = 0
The Rankine-Hugoniot condition for the conservation of mass is: [u]s = 0
where [u]s represents the jump in fluid velocity across the shock wave.
In this case, the equation is already in conservative form, so we can directly apply the Rankine-Hugoniot condition. Therefore, the speed of the shock wave can be determined by setting [u]s = 0.
(b) Now let's solve the initial value problem u(0, x) = {a, b} for two cases:
(i) |a| > |b|:
In this case, we have a shock wave. The solution will consist of a shock wave moving to the right with velocity s.
(ii) |a| < |b|:
In this case, we have a rarefaction wave. To determine the shape of the rarefaction wave, we can use Exercise 2.3.15, which involves solving the characteristic equations for the given PDE.
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\(\sf 2x+6x=-24\)
Answer:
\( \sf{ \dfrac{8x}{8} = \dfrac{ - 24}{8} }\)
Step-by-step explanation:
\( \sf{ \longmapsto \: x = - 3}\)
-XxItzAdiXxYour ceiling is 230 centimeters high, you want the tree to have 50 centimeters of space with the ceiling. How tall must the tree be? (In centimeters)
To determine the height the tree should be, we need to subtract the desired space between the ceiling and the tree from the total height of the room. The tree must be 280 centimeters tall to leave 50 centimeters of space between its top and the ceiling.
Given that the ceiling is 230 centimeters high and we want 50 centimeters of space between the tree and the ceiling, we can calculate the required height as follows:
Total height of the room = Ceiling height + Space between ceiling and tree
Total height of the room = 230 cm + 50 cm
Total height of the room = 280 cm
Therefore, the tree must be 280 centimeters tall to leave 50 centimeters of space between its top and the ceiling.
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your village community group is putting a new fence around the park .you offer to help and measure the distance around the park as 337 metres. each fence panel is 550cm across .how many fence panels do you need
Explanation:
Perimeter of the park
= 337 m
= 33700 cm
Length of each fence panel
= 550 cm
Number of fence panel required
= Perimeter of the park/Length of each fence panel
= 33700 cm/550 cm
= 33700/550
= 3370/55
= 674/11
= 61 3/11
So, we will need 61 3/11 fence panels.
P.S. — 61 3/11 means 61 whole and 3/11. I have attached its picture, so that you understand.
PLEASE HELP ME ANSWER ASAP
L = k/f, where k is the variational constant, is the formula for the inverse variation.
Inverse proportionsA mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.
Using the variables length of violin 'l' and frequency of vibration 'f'
If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:
l α 1/f
l = k/f
Hence the formula for the inverse variation is l = k/f where k is the constant of variation.
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compute each sum or differences
3/8 + 7/12
By finding a common denominator, we can rewrite the sum as:
3/8 + 7/12 = 9/24 + 14/24 = 23/24
How to find the sum between the two fractions?Here we want to find the sum between two fractions that have different denominators.
To sum them, we need to find a common denominator, so we need to find a common multiple between 8 and 12.
We know that:
8*3 = 24
12*2 = 24
Then we can multiply and divide the first fraction by 3:
3/8*(3/3) = 9/24
7/12*(2/2) = 14/24
Then the sum will give:
9/24 + 14/24 = 23/24
That is the outcome.
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Find the limit, if it exists, for (x^2 + y^2 - 2x - 2y)/ (x^2 + y^2 - 2x + 2y +2) according to (x, y) (1,-1)
If does not exist, explain,
Therefore, the limit of the given expression as (x, y) approaches (1, -1) does not exist because the expression becomes undefined at that point.
To find the limit of the given expression as (x, y) approaches (1, -1), we can substitute the values of x and y into the expression and see if it simplifies to a single value.
Let's substitute x = 1 and y = -1 into the expression:
\([(x^2 + y^2 - 2x - 2y) / (x^2 + y^2 - 2x + 2y + 2)] = [(1^2 + (-1)^2 - 2(1) - 2(-1)) / (1^2 + (-1)^2 - 2(1) + 2(-1) + 2)]\)
Simplifying the numerator and denominator, we get:
[(1 + 1 - 2 - (-2)) / (1 + 1 - 2 + 2 - 2)]
= (2 + 2) / 0
Here, we have a division by zero in the denominator, which means the expression is undefined.
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The number of students increased by 25% between last year and this year. Last year there were 280 students.
Answer:
11.2
Step-by-step explanation:
Define Chi square test OR Tests of significance based on Chi-Square. A: -Various tests of significance described previously have mostly applicable to only quantitative data and usually to the data which are approximately normally distributed. It may also happens that we may have data which are not normally Inference: (i) If Z0 ≤ Ze we accept the H0 (ii) If Z0 >Ze we reject the H0 Example: A test of the breaking strengths of two different types of cables was conducted using samples of n1 = n2 = 100 pieces of each type of cable. Do the data provide sufficient evidence to indicate a difference between the mean breaking strengths of the two cables? Use 0.01 level of significance. x = 1925 and sigm = 40 and X2 = 1905, sigma = 30
The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.
The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.
To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.
Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.
To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.
Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.
If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.
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Abdul takes classes at both westside community college and pinewood community college. at westside, class fees are $ 98 per credit hour, and at pinewood, class fees are $ 115 per credit hour. abdul is taking a combined total of 12 credit hours at the two schools.
Abdul is taking a combined total of 12 credit hours at both Westside Community College and Pinewood Community College. At Westside, the class fee is $98 per credit hour, and at Pinewood, the class fee is $115 per credit hour.
To find the total cost of Abdul's classes, we can multiply the number of credit hours by the respective class fees at each college and then add the results together.
At Westside, the cost of 12 credit hours would be 12 x $98 = $<<12*98=1176>>1176.
At Pinewood, the cost of 12 credit hours would be 12 x $115 = $<<12*115=1380>>1380.
Adding the two totals together, Abdul's combined class fees would be $1176 + $1380 = $<<1176+1380=2556>>2556.
So, the main answer to your question is: The combined total cost of Abdul's classes at Westside Community College and Pinewood Community College is $2556.
In summary, Abdul is taking 12 credit hours at Westside Community College and Pinewood Community College. By multiplying the number of credit hours by the respective class fees at each college, we find that the cost at Westside is $1176 and the cost at Pinewood is $1380. Adding these two totals together, Abdul's combined class fees amount to $2556.
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Mary bought 6 tickets to a basketball game. She paid a total of $228. Write an equation to represent this situation.
Answer:
6(x)=228
Step-by-step explanation:
Answer:
228/6
Step-by-step explanation:
she is dividing the 228 dollars among the six tickets to get the answer
you can also put 228 divided by 6
Dave learned a total of 10 appetizer recipes over the course of 5 weeks of culinary school.
After how many weeks of culinary school will Dave knov a total of 12 appetizer recipes?
Assume the relationship is directly proportional.
Answer:
4.8
Step-by-step explanation:
Answer:
6 weeks
Step-by-step explanation:
(12/10)5 = 6 weeks
what is the finest grain property in statistics
The finest-grain property simply means that all possible distinguishable outcomes are identified separately in probability statistics.
The requirement that outcomes be mutually exclusive says that if one outcome occurs, then no other outcome also occurs.
An outcome is often called a finest grain result of the model in the sense that an outcome ω contains no subsets other than the empty set ϕ and the singleton subset {ω}. A sample space is a set of all the possible outcomes or sample points, denoted as Ω. An outcome ω is often called a finest grain result when even {ω} contains no proper subsets. The outcomes in the sample space are mutually exclusive and collectively constitute the entire sample space.
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In a village the number of houses and the number of flats are in the ration9:5 the number of flats and the number pf bungalows are in the ratio 10:3 there are 30 bungalows in the village. How many houses are there in the village?
Answer: 180 houses
Step-by-step explanation:
From the question, we are informed that in a village the number of houses and the number of flats are in the ratio 9:5 while the number of flats and the number of bungalows are in the ratio 10:3 and that there are 30 bungalows in the village.
Since the ratio of the number of flats and the number of bungalows are in the ratio 10:3 and there are 30 bungalows in the village, the number of flats will be:
= 10/3 × 30
= 10 × 10
= 100 flats
Since we are told that the ratio of the number of houses to the number of flats are in the ratio 9:5 and we've gotten the number of flats as 100, then the number of houses will be:
= 9/5 × 100
= 9 × 20
= 180 houses