The number of different ways the prizes can be awarded is 161700
How to determine the number of different ways can the prizes be awarded?From the question, we have the following parameters that can be used in our computation:
Total number of people, n = 100Total numbers of winners, r = 3 i.e. the first, the second, the thirdThe number of different ways the prizes can be awarded is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 100 and r = 3
Substitute the known values in the above equation
Total = ¹⁰⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 100!/97!3!
Evaluate
Total = 161700
Hence, the number of ways is 161700
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you are given an array of arrays a. your task is to group the arrays a[i] by their mean values, so that arrays with equal mean values are in the same group, and arrays with different mean values are in different groups. each group should contain a set of indices (i, j, etc), such that the corresponding arrays (a[i], a[j], etc) all have the same mean. return the set of groups as an array of arrays, where the indices within each group are sorted in ascending order, and the groups are sorted in ascending order of their minimum element.
Example
For
a = [[3, 3, 4, 2],
[4, 4],
[4, 0, 3, 3],
[2, 3],
[3, 3, 3]]
the output should be
meanGroups(a) = [[0, 4],
[1],
[2, 3]]
mean(a[0]) = (3 + 3 + 4 + 2) / 4 = 3;
mean(a[1]) = (4 + 4) / 2 = 4;
mean(a[2]) = (4 + 0 + 3 + 3) / 4 = 2.5;
mean(a[3]) = (2 + 3) / 2 = 2.5;
mean(a[4]) = (3 + 3 + 3) / 3 = 3.
There are three groups of means: those with mean 2.5, 3, and 4. And they form the following groups:
Arrays with indices 0and 4 form a group with mean 3;
Array with index 1 forms a group with mean 4;
Arrays with indices 2and 3 form a group with mean 2.5.
Note that neither
meanGroups(a) = [[0, 4],
[2, 3],
[1]]
nor
meanGroups(a) = [[0, 4],
[1],
[3, 2]]
will be considered as a correct answer:
In the first case, the minimal element in the array at index 2 is 1, and it is less then the minimal element in the array at index 1, which is 2.
In the second case, the array at index 2 is not sorted in ascending order.
For
a = [[-5, 2, 3],
[0, 0],
[0],
[-100, 100]]
the output should be
meanGroups(a) = [[0, 1, 2, 3]]
The mean values of all of the arrays are 0, so all of them are in the same group.
Input/Output
[execution time limit] 3 seconds (java)
[input] array.array.integer a
An array of arrays of integers.
Guaranteed constraints:
1 ≤ a.length ≤ 100,
1 ≤ a[i].length ≤ 100,
-100 ≤ a[i][j] ≤ 100.
[output] array.array.integer
An array of arrays, representing the groups of indices
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
public class Mean {
static public void main(String args[])
{
// Initializing variables
int[][] a = new int[100][100]; // Array of arrays for holding the inputs
Map<Integer,ArrayList<Integer>> averagemaps = new HashMap<Integer,ArrayList<Integer>>(); // Map to contain the average and the list of array indexes
List<Integer> averages = new ArrayList<Integer>(); // List of averages of the arrays
Scanner sc = new Scanner(System.in);
// Input for the array of arrays
System.out.println("Enter the number of arrays: ");
int noArrays = sc.nextInt();
for(int i = 0; i < noArrays; i++)
{
System.out.println("Enter the number of elements in the array "+i+":");
int noElements = sc.nextInt();
int sum = 0;
int avg = 0;
System.out.println("Enter the elements of the array "+i+" one by one:");
for(int j = 0; j < noElements; j++)
{
a[i][j] = sc.nextInt(); // Input for each elements in the array.
sum += a[i][j]; // Calculating the sum of the elements in the array.
}
avg = sum/noElements; // calculating average for the array
// checking if the average is inside the list or not
if(!averages.contains(avg))
{
// If the average is not already in the list
// Adding the average into the list
averages.add(avg);
// create an array list to
// hold the list of indices which has the same array
ArrayList<Integer> a1 = new ArrayList<Integer>();
a1.add(i);
// Mapping the average to the list of indices.
averagemaps.put(avg, a1);
}
else
{
// The average is present in the list
// Adding the index to the array list
// mapped to it.
averagemaps.get(avg).add(i);
}
}
// Sorting the index arrays for each average
// in ascending order
Iterator itr=averages.iterator();
int index = 0;
while(itr.hasNext()){
Collections.sort(averagemaps.get(itr.next()));
}
// For sorting the array of indices based on their lowest number
// Since the arrays are in a map, the map needs to be sorted.
// There is no function to sort the map, Hence the map is converted to
// a list of entersets.
List<Map.Entry<Integer,ArrayList<Integer>>> list =
new LinkedList<Map.Entry<Integer,ArrayList<Integer>>>(averagemaps.entrySet());
// Using the sort function to sort the list. The list should be sorted based on the minimum
// element in each array.
Collections.sort(list, new Comparator<Map.Entry<Integer,ArrayList<Integer>>>() {
public int compare(Map.Entry<Integer,ArrayList<Integer>> o1,
Map.Entry<Integer,ArrayList<Integer>> o2) {
// since the elements in the arrays are already sorted
// the element in the index 0 will be the smallest element
return (o1.getValue().get(0)).compareTo(o2.getValue().get(0));
}
});
// Converting the list back to a hashmap
averagemaps = new HashMap<Integer,ArrayList<Integer>>();
for (Map.Entry<Integer,ArrayList<Integer>> entry : list) {
averagemaps.put(entry.getKey(), entry.getValue());
}
// Initializing an array of array for the output
// The outer array dimension is defined.
// The inner array dimension can be defined based on the
// size of the indices array
int[][] answer = new int[averages.size()][];
itr = averages.iterator();
// Iterate through the averages lists
while(itr.hasNext())
{
ArrayList<Integer> i = averagemaps.get(itr.next());
Iterator iterr=i.iterator();
answer[index] = new int[i.size()];
int innerindex = 0;
while(iterr.hasNext())
answer[index][innerindex++] = (Integer)iterr.next(); // adding the array of indices into the output array.
index++;
}
// Printing the arrays of arrays.
System.out.print("[ ");
for(int i = 0; i < answer.length; i++)
{
System.out.print("[ ");
for(int j = 0;j < answer[i].length; j++)
System.out.print(answer[i][j]+ ", ");
System.out.println("]");
}
System.out.println("]");
}
}
Output:
Enter the number of arrays:
4
Enter the number of elements in the array 0:
3
Enter the elements of the array 0 one by one:
-5
2
3
Enter the number of elements in the array 1:
2
Enter the elements of the array 1 one by one:
0
0
Enter the number of elements in the array 2:
1
Enter the elements of the array 2 one by one:
0
Enter the number of elements in the array 3:
2
Enter the elements of the array 3 one by one:
-100
100
[ [ 0, 1, 2, 3, ]
]
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Hi please do these three or you can just do one, two problems for me so, I can look back at it if I need help cuz I don't really get this and please explain how you got the answer don't just tell me the answer.
Write each decimal as a fraction in simplest form
Say it, Write it, Simply it.
1. 0.5 = ?
2. 0.7 = ?
3. 0. 875 = ?
Answer:
1) [tex]\dfrac{1}{2}[/tex]
2) [tex]\dfrac{7}{10}[/tex]
3) [tex]\dfrac{7}{8}[/tex]
Step-by-step explanation:
Any decimal can be written as a fraction by just putting the given number over 1.
For example, take the first problem.
0.5 can be written as:
[tex]\dfrac{0.5}{1}[/tex]
Then, to simplify it, multiply both the top and bottom by 2.
[tex]\dfrac{0.5 \times 2}{1 \times 2}[/tex]
[tex]= \dfrac{1}{2}[/tex]
The reason this doesn't change the value of the fraction is because any number over itself is 1. Look at the 2's we just multiplied by in the numerator and denominator. We are really just multiplying the entire fraction by 2/2, which equals 1. Here's a way of writing the above step that makes it clearer:
[tex]\dfrac{0.5}{1} \times \dfrac{2}{2}[/tex]
[tex]=\dfrac{1}{2}[/tex]
So, the answer to the first problem is [tex]\dfrac{1}{2}[/tex].
We can repeat these steps for the second problem.
[tex]0.7 = \dfrac{0.7}{1}[/tex]
But this time, multiply by 10/10 instead of 2/2. Remember that 10/10 is still equal to 1.
[tex]= \dfrac{0.7}{1} \times \dfrac{10}{10}[/tex]
[tex]= \dfrac{7}{10}[/tex]
So, the answer to the second problem is [tex]\dfrac{7}{10}[/tex].
Finally, repeat the steps from the previous problems.
[tex]0.875 = \dfrac{0.875}{1}[/tex]
But this time, multiply by 1,000/1,000.
[tex]= \dfrac{0.875}{1} \times \dfrac{1,000}{1,000}[/tex]
[tex]= \dfrac{875}{1,000}[/tex]
And this time, some extra simplification is necessary. Divide by 25/25.
[tex]= \dfrac{875}{1,000} \div \dfrac{25}{25}[/tex]
[tex]= \dfrac{35}{40}[/tex]
Then, divide by 5/5.
[tex]= \dfrac{35}{40} \div \dfrac{5}{5}[/tex]
[tex]= \dfrac{7}{8}[/tex]
So, the answer to the third problem is [tex]\dfrac{7}{8}[/tex].
A linear regression assumes a. no relationship between X and Y b. a linear relationship between X and Y c. Unequal variance d. a negative relationship between X and Y
A linear regression assumes a linear relationship between X and Y.
Option B is correct.
What is a linear regression?
Linear regression analysis is used to predict the value of a variable based on the value of another variable. When data has only 1 independent feature then it’s called simple linear regression.
This assumption says that independent and dependent features are having linear relationship. To check this assumption, we can use a scatter plot and a scatter plot should look like the left graph in the attached image.
Hence, we assume that there is a linear relationship between X and Y.
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2.859 + 7.31
I have to line up the decimals
Answer: 10.169
Step-by-step explanation: To add decimals like this we have to line up them in order.
2.859
+
7.31 =
10.169
Above I have to line them up in order.
If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!
Please help me asap!
Answer:
6pi
Step-by-step explanation:
1.) Figure out the total circumference of the circle. The circumference of a circle is equal to 2*pi*r, which is equal to 8pi.
2.) Figure out the portion of the circle that the arc is by using the angle. Since the angle is 90 degrees, and the total measure in a circle is 360 degrees, that means that the cut out part is 90/360, which is 1/4 of the circle.
3.) Now, since the cut out part is 1/4, that means that the remaining part is 3/4 of the circle.
4.) Now, we multiply 8pi * 3/4, which is equal to 6pi.
As the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000, what happens to the probability of getting between 40% and 60% heads? What happens to the probability of getting exactly 50% heads?
answer choices
a. Both of those probabilities increase.
b. Both of those probabilities decrease.
c. The first probability increases, but the second one decreases.
d. The first probability decreases, but the second one increases.
Both of those probabilities decrease, hence Option (B) is the correct answer.
Given, the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000.
we have to find the effect on the probability of getting exactly 50% heads.
In 10 tosses,
we have to get heads 5 times,
P(X = 5) = (1/2)^5(1/2)^5
P(X = 5) = (1/2)^10
In 100 tosses,
we have to get heads 50 times,
P(X = 50) = (1/2)^50(1/2)^50
P(X = 50) = (1/2)^100
and so on.
It is clear that the probability of getting 50% heads decreases.
Also, Probability of getting heads between 40% and 60% decreases.
Hence, both of those probabilities decrease.
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-(9m + 7) algebra question please help me!!
How do you divide Powers with the same base?How dou you raise quotients(fractions) to a power(exponents)
consider the following time series. t 1 2 3 4 5 6 7 yt 121 111 106 99 95 93 88 (a) construct a time series plot. what type of pattern exists in the data? the time series plot shows a seasonal pattern. the time series plot shows a linear trend. the time series plot shows a nonlinear trend. the time series plot shows a horizontal pattern. (b) use simple linear regression analysis to find the parameters for the line that minimizes mse for this time series. (round your answers to two decimal places.) b0
The time series plot is attached below
The parameters for the line that minimizes mse for this time series 119.714 - 4.9286t
What is time series ?
A time series is a group of data points that have been indexed chronologically in mathematics. A time series is most frequently a sequence captured at a series of equally spaced moments in time. As a result, it is a collection of discrete-time data.
These four elements are: -Secular trend, which describes movement over time; -Seasonal variations, which depict seasonal changes; -Cyclical fluctuations, which relate to periodic but not seasonal variations; -Irregular variations, which are additional nonrandom sources of variations in series.
t' = 28 / 7
= 4
Y' = 700 / 7
= 100
∑(t - t') (y - y') = -138
∑(t - t')² = 28
b1 = -138 / 28
= -4.9286
b0 = Y' - b1t'
= 100 - (-4.9286*4)
= 119.714
[tex]T_{t}[/tex] = 119.714 - 4.9286t
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f(x) = x; g(x) = -x + 3 what is the transformation (for algebra 1)
There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
The transformation of f(x) to g(x) is,
f(x) is reflected over the x-axis and then shifted 3 steps to the right.
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
f(x) = x
g(x) = -x + 3
g(x) is the transformation of f(x).
When f(x) is reflected along the x-axis we get,
g(x) = -x
Now,
g(x) is shifted 3 steps to the right we get,
g(x) = -x + 3
Thus,
The transformation of f(x) to g(x) is,
f(x) is reflected over the x-axis and then shifted 3 steps to the right.
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What is the slope of a line perpendicular to the line whose equation is
4x+10y=-140.
Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]4x+10y=-140\implies 10y=-4x-140\implies y=\cfrac{-4x-140}{10} \\\\\\ y=\cfrac{-4x}{10}-\cfrac{140}{10}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-14\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies {\Large \begin{array}{llll} \cfrac{5}{2} \end{array}}}}[/tex]
The sampling distribution for a goodness of fit test is the a. Poisson distribution b. t distribution c. normal distribution d. chi-square distribution
The chi-square distribution serves as the sampling distribution for the goodness of fit test since it quantifies how well the distribution derived from the data fits the empirical distribution.
What is sampling distribution?The sampling distribution is the probability distribution of a statistic that is obtained by repeated sampling of a certain population. The mean or mode of a population's mean or mode of a variable is one example of the many different choices for a statistic that are described in this passage. The sampling distribution of a proportion is obtained by repeating your survey or poll for each possible sample of the population. For instance, instead of asking 1,000 cat owners what cat food they prefer, you could conduct a number of polls.
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3. a pair of 6-sided dice is thrown. someone tells you that both the dice are showing an even number. with this information, what is the probability of the total (when you sum up the dice) being equal to 8?
The probability of the total being equal to 8 is 1/9 or 11.11%.
To calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8. Since both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6). Therefore, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.
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line has a slope of –
5 and includes the points (5,–
7) and (2,p). What is the value of p?
Answer:
p=8
Step-by-step explanation:
y= -5x + b
( -7) = -5(5) + b
-7= -25+b
add 25 both sides
-7+25=-25+25+b
18=b
y= -5x+18
p=-5(2)+18
p=8
The admission fee to play virtual reality is $12. It cost an additional x dollar to rent virtual reality equipment to play in the games. The total cost for 8 people to play virtual reality with equipment is $400. How much will it cost for one person to rent virtual reality equipment?
Answer:
$38
Step-by-step explanation:
400 ÷ 8 = 50 per person plus admission
minus admission
50 - 12 = 38
Find the volume of the solid obtained by revolving equilateral triangle of side length 2 around one of its sides. Sketch a diagram and indicate which method you are using: Washer Method Shell Method
The volume of the solid formed by revolving an equilateral triangle around any of its sides of length 2 is π /√3 units .
From the diagram we can see that the washer method will be used to calculate the are of the solid formed.
The solid formed is in the form of a cone.
Volume of a cone = 1/3 πr²h
Here the radius of the cone = diameter / 2 = 2/2 = 1 units.
Height of the cone is calculated using the Pythagoras theorem of a right angled triangle
radius² + height² = side ²
or, height² = 4 - 1
or, height = √3
Volume of the cone = 1/3 πr²h
Substituting the values we get:
V = 1/3 π 1²√3 = π /√3
Therefore the volume of the cone thus formed is π /√3 cubic units.
A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic form in the plane, or any combination of the above plus all the enclosed points, depending on the author.
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Use point-slope form to write the equation of a line that passes through the point
(-8, 8) with slope 3.
Answer:
y -8 = 3(x+8)
Step-by-step explanation:
y-8 = 3(x-(-8)
y - 8 = 3(x+8)
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
After solving the given expression the values for x will be equal to x = 1 and x = 13.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given information in the question,
The given equation is,
(x - 7)² = 36
x - 7 = √36
x = ±6
Then the values for x will be,
x1 = 6 + 7 = 17
x2 = -6 + 7 = -1
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Find the sum of 2/5+1/6 please i need this
Answer:
7/30 is your answer.
Step-by-step explanation:
Answers:
Q
Step-by-step explanation:
A waterfall has a height of 1000 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The
height, h, of the pebble after t seconds is given by the equation h=-161² +16t+1000. How long after the pebble is thrown will it hit the
ground? Use a graphing calculator to solve the problem.
seconds after it is thrown.
The pebble will hit the ground about
(Round to one decimal place as needed.)
Ok, so, this implies h=0 when the pebble hits the ground.
So, - 16t^2 + 24t + 1300 = 0
If we find t, we obtain two solutions, one negative and one positive, so the positive is correct.
Then, t = 9.7950 s
Therefore, it would take about 9.7950 seconds for the pebble to hit the ground.
Someone help me at h.w
Answer:
12. impact
13. environment
14. unique
15, destination
16. provide
17. designed
19. local
20. conservation
Step-by-ste1p explanation:
ur welcome
4.) numbers is a game in which you bet $1 on any 3-digit number from 000 to 999. if your number comes up, you get $500. find the expected payback.
Mathematically, the expected payback is $9.5.
Below, this is further discussed.
What is the anticipated return?
In general, the likelihood times the value are multiplied together to calculate the projected payback.
E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....
We have two different repayment alternatives in this situation.
Winning
The payback is $500 - $10 = $490
x_1 = 490
The likelihood of winning is one in a thousand (since the choices are 0 to 999)
p(x 1) = 1/1000
Losing
Due to the fact that the person did not win anything, they actually lost $8.
x _2 = -10
The other 999 numbers are regarded as losing numbers because there is only one number that can win.
p(x 2) = 999/1000
E(x) = p(x 1)*x 1 + p(x 2)*x 2 = (1/1000)* 490+ is the expected payback as a result.
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Question is below! Please answer will mark brainliest!
Answer:
315 children attend the play.
Answer:
c=315
Step-by-step explanation:
we know c is equal to 21a so we can insert it into the second equation
a+21a=330
22a=330
/22. /22
a=15
now we inset a to find c
21(15)=c
315=c
Hopes this helps please mark brainliest
Hi, todays question is requested from a middle schooler the question is- A jet travels 650 miles in 3 hours,At this rate how far can the jet fly in 9 hours. And a separate answer for 6 hours.Use Details
The distance the jet can fly in 9 hours is 1950 miles.
The distance the jet can fly in 6 hours is 1300 miles.
What are the distances the jet can fly?The first step is to determine the rate of the jet. The rate measures how fast the jet travels with respect to time. It is the total distance travelled divided by the total time.
Rate = distance / time
Rate = 650 / 3
Rate = 216.67 miles per hour
Distance travelled = rate x time
Distance travelled in 9 hours = 216.67 miles per hour x 9 = 1950 miles
Distance travelled in 6 hours = 216.67 miles per hour x 6 = 1300 miles
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problem: report error alice and bob each have a certain amount of money. if alice receives $n$ dollars from bob, then she will have $4$ times as much money as bob. if, on the other hand, she gives $n$ dollars to bob, then she will have $3$ times as much money as bob. if neither gives the other any money, what is the ratio of the amount of money alice has to the amount bob has?
The ratio of the amount of money alice has to the amount bob has 31:9.
Assume the following:
Alice's amount = P
Bob's amount = Q
Amount received = n
If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.
P + n = 4(Q - n)
P + n = 4Q - 4n
P = 4Q - 4n - n
P = 4Q - 5n - - - - (1)
If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob
P - n = 3(Q + n)
P - n = 3Q + 3n
P = 3Q + 3n + n
P = 3Q + 4n - - - - - - (2)
Equating both equations - (1) and (2)
4Q - 5n = 3Q + 4n
4Q - 3Q = 4n + 5n
Q = 9n
Express P in terms of n, use either equation (1) or (2)
From equation 2:
P = 3Q + 4n
Substituting Q = 9n
P = 3(9n) + 4n
P = 27 + 4n
P = 31n
Alice's amount = P, Bob's = Q
Ratio = P:Q
31 : 9
Hence, the ratio of the amount of money alice has to the amount bob has 31:9.
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if zero is included in a confidence interval for paired data, what does this mean about the average difference?
It means that if you run your experiment again you have a good chance of finding no difference between average differences.
What is a confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contains the parameter's true value is what is meant by the confidence level.
If zero is included in a confidence interval for paired data.
It means that if you rerun your experiment you have a good chance of finding no difference between groups.
When performing your statistical test, you will also see that the p-value in each of these situations is high, indicating that the null hypothesis—that there is no association between the variables or difference between the groups—could have produced the same findings.
Hence, finding no difference between average differences.
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what's the probability of rolling an even number on the dice
1.) 0.5
2.) 0.2
3.) 0.4
Answer:
it would have a 50% or 0.5 probability of rolling an even number on the dice
Step-by-step explanation:
A dice has six numbers, three have them are odd and three are even so we would calculate it as 3/6.
In a class, there are 30 students who like chocolate, 25 students who like vanilla, and12 students who like neither. If there are 55 people in the class, how many students
like chocolate and vanilla?
12 students like chocolate and vanilla, if there are 55 people in the class.
In the given question, in a class, there are 30 students who like chocolate, 25 students who like vanilla, and 12 students who like neither.
If there are 55 people in the class, then we have to find how many students like chocolate and vanilla.
The number of students who like chocolate, n(C)=30
The number of students who like vanilla, n(V)=25
The number of students who like neither chocolate and vanilla, n(C∪V)′=12
Total number of students, n(U)=55
Now,
The number of students who like vanilla or chocolate;
n(C∪V) = n(U)-n(C∪V)’
n(C∪V) = 55-12
n(C∪V) = 43
Since, we have to find how many students like chocolate and vanilla, if there are 55 people in the class. So
n(C∩V)=n(C)+n(V)- n(C∪V)
n(C∩V)=30+25- 43
n(C∩V)=12
Hence, 12 students like chocolate and vanilla, if there are 55 people in the class.
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George has been selling 5,000 t-shirts per month for $8. 50. When he increased the price to $9. 50, he sold only 4,000 t-shirts. What is the demand elasticity? if his marginal cost is $4 per shirt, what is his desired markup and what is his initial actual markup? was raising the price profitable?.
Demand elasticity came in at -4.6154. The actual markup was 0.2167 as opposed to the desired markup of 0.5789. The increase was therefore not profitable.
What is division?A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
The demand elasticity,
=[(Q1-Q2)/(Q1+Q2)] / [(P1-P2)/(P1+P2)]
[(8000-5000)/(8000+5000)] / [(9.5-10.5)/(9.5+10.5)]
[(3000/13000)] / [-1/20}
60000/-13000
=-4.6154
The desired markup,
(9.5-4) / 9.5
= 0.5789
The actual markup,
1/4.6154
= 0.2167
The demand elasticity was -4.6154. The desired markup was 0.5789 and actual markup was 0.2167. Hence, The increment was not profitable.
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consider the correlation between heights of fathers and mothers and the heights of their sons. refer to the accompanying technology output. should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? why or why not?
Yes, the multiple regression equation should be used for predicting the height of a son based on the height of his father and mother because the P-value in the ANOVA table is very low.
What is multiple regression equation?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A single dependent variable and numerous independent variables can be analyzed using the statistical approach known as multiple regression. In order to forecast the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
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