Answer:
Below
Step-by-step explanation:
x^6 -16x^2 = x^2 ( x^4 - 16 ) is one possibility
( you didn't include choices)
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.
To learn more about volume visit:
https://brainly.com/question/13084284
#SPJ4
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.
the country of transylvania contains 2.3 million people (vampires not included) and covers 800,000 square miles. in the year after the last census, the crude birth rate was 48 out of 1000 and the crude death rate was 47 out of 1000. 1. what is the population growth rate (r)? 2. in how many years will the population of transylvania double?
In 700 years the population of Transylvania will double
What is growth rate ?
the typical annual rate of population change during a particular period for a certain nation, region, or geographic area. In most cases, a factor of 100 is used to describe the ratio between the annual growth in population size and the total population for the year.
Growth rate equals Absolute Change divided by Previous Value. Calculate the percentage of change: Percent of change = Growth rate x 100 is the formula that may be used to calculate the percent of change.
To calculate in how many years the population of Transylvania double
= 70 / 0.1
= 700 years
To learn more about growth rate from the given link
https://brainly.com/question/12081555
#SPJ4
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.
To learn more about linear regression :
brainly.com/question/17844286
#SPJ4
find an equation of variation in which y varies directly as x and the following is true. yequals 21.25 when xequals 4.25
Answer:
y = 5x
Step-by-step explanation:
the equation of variation in which y varies directly as x is
y = kx ← k is the constant of variation
to find k use the given y = 21.25 when x = 4.25
21.25 = 4.25k ( divide both sides by 4.25 )
5 = k
y = 5x ← equation of variation
A hot-air balloon travels 2,016 miles in
96 hours. It travels the same number
of miles each hour. How many miles
does the balloon travel in 1 hour?
Answer: 21 miles
Step-by-step explanation:
We know that it travels 2016 miles in 96 hours.
So we just need to get 2016 divided by 96 = 21 miles/ per hour
If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!
Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.
What is the miles?
Mile is a customary unit used for measuring length or distance. More About Mile Mile is denoted by the symbol 'mi'.
Here given that,
A hot-air balloon travels [tex]2,016[/tex] miles in [tex]96[/tex] hours. It travels the same number of miles each hour.
As we know that it travels [tex]2016[/tex] miles just only in [tex]96[/tex] hours.
[tex]\frac{2016}{96}=21[/tex] miles/ per hour
Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.
To know more about the miles
https://brainly.com/question/833967
#SPJ2
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.
Learn more about expected payback here;
https://brainly.com/question/28819723
#SPJ4
in a family with 3 children, excluding multiple births, what is the probability of having 2 boys and 1 girl ? assume that a girl is as likely as a boy at each birth
The probability of having 2 boys and 1 girl would be [tex]\frac{3}{8}[/tex]
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given that:
family with 3 children.
Condition: Girl is as likely as a boy at each birth.
s will be the sample space.
The sample space has 8 elements:
s = {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}
n(s) = [tex]\frac{1}{8}[/tex]
We need 2 boys and 1 girl, regardless of order,
sample space for 2 boys and 1 girl, regardless of order would be 3.
s = 3
Then, probability will be
[tex]Probability \ of\ having\ 2 \ boys\ and \ 1\ girl =\frac{3}{8}[/tex]
Hence, The probability of having 2 boys and 1 girl would be [tex]\frac{3}{8}[/tex]
To know more about Probability visit,
https://brainly.com/question/24756209
#SPJ4
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, ]
]
To know more about arraylist check the below link:
https://brainly.com/question/8045197
#SPJ4
what is the maximum number of electrons in an atom that can have the given sets of quantum numbers n=4?
The maximum number of electrons in an atom that can have the given sets of quantum numbers n=4 is 32.
In the given question we have to find the maximum number of electrons in an atom that can have the given sets of quantum numbers n=4.
As we know that;
A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound). One of the three main types of particles within an atom is an electron that is bonded to it; the other two are protons and neutrons. The nucleus of an atom is made up of electrons, protons, and neutrons altogether.
So the maximum number of electrons in an atom is;
Number of Electron = 2*n^2
Number of Electron = 2*(4)^2
Number of Electron = 2*16
Number of Electron = 32
To learn more about electron in atom link is here
brainly.com/question/13993867
#SPJ4
a radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=15e^(-0,02t) where m(t) is measured in kilograms.
a. Find the mass at time t=3
b. How much of the mass remains after 20 days?
For the given data, a) The mass at the time t = 3 is 14.13 kg. and b) The mass remaining after 20 days is 10.05 kg.
What is radioactive decay?
The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay.
The Radioactive Formula is given by
[tex]N = N_{0} e^{-\lambda T}[/tex]
Given, [tex]m(t) = 15e^{-0.02t}[/tex]
where m(t) is measured in kilograms
a) To find the mass at time t=3, then
m(3) = [tex]15e^{-0.02*3}[/tex] = [tex]15e^{-0.06}[/tex] = 14.13 kg
Therefore, the mass at the time t=3 is 14.13 kg.
b) To find how much of the mass remains after 20 days,
m(20) = [tex]15e^{-0.02*20}[/tex] = [tex]15e^{-0.4}[/tex] = 10.05 kg
Therefore, the mass remaining after 20 days is 10.05 kg.
To learn more about radioactive decay
https://brainly.com/question/5391767
#SPJ4
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
To know more about the expression:
https://brainly.com/question/14083225
#SPJ1
X is 19 units to the left of 0. Use the drop-down menus to complete the statement about −X.
Options:
-19
-9
0
9
19
The value of ''- X'' will be;
⇒ - X = 19
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
X is 19 units to the left of 0.
Now,
Since, X is 19 units to the left of 0.
Hence, The value of X = - 19
So, We get;
The value of - X = - (- 19)
= 19
Thus, The value of ''- X'' will be;
⇒ - X = 19
Learn more about the number line visit:
https://brainly.com/question/24644930
#SPJ1
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!
Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?
I Need Help!
Answer: $117
Step-by-step explanation: 1st subtract 3 then divide by 2 then subtract 3 again and divide by 2 again
Sort the following polygons in order of increasing perimeter.
Answer:
rectangle, square, triangle
Step-by-step explanation:
Given the coordinates of the vertices of a rectangle, triangle, and square, you want to sort them in order of increasing perimeter.
Side lengthsIn general, the length of a side can be found using the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
This shows you that if the x-coordinates are the same, the distance is the positive difference of the y-coordinates, and vice versa.
The attachment shows the side lengths for the figures, computed using this formula. Each row shows the distance from the point on that row to the point on the next row. (You will notice the last point is a copy of the first point.)
PerimeterThe perimeter of each figure is the sum of the side lengths. This is the number below the Distance column in each of the tables.
In increasing order, the perimeters are ...
Rectangle: 10Square: 12Triangle: ~19.06__
Additional comment
When the computations are repetitive, it is often convenient to let a spreadsheet do them. The formula can be entered once and copied where needed. The problem then reduces to one of data entry, which you generally have to do for any but mental arithmetic.
1.2.what are the complex eigenvalues of the matrix a that represents a rotation of jr3 through the angle () about a pole u?
A rotation matrix has two complex eigenvalues e−iθ and eiθ.
These are matched by complicated eigenvectors.
We are aware that the rotational axis is represented by the eigenvector with the eigenvalue 1 in it. how to demonstrate that the angle of rotation is represented by the complex eigenvalue.
It is simple to compare it with a rotation matrix for rotation about the x, y, or z axes, but how can one draw this conclusion for a general R that belongs to SO (3).
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ with respect to the positive x axis about the origin of a two-dimensional Cartesian Plane.
To learn more about matrix
https://brainly.com/question/28180105
#SPJ4
find the f-test statistic to test the claim that the population variances are equal. both distributions are normal. the standard deviation of the first sample is 2.1971 7.32 is the standard deviation of the second sample.
the f-test statistic to test the claim that the population variances are equal is F test = 2.54
We are given two samples
Standard deviation of the first sample = 2.1971
Standard deviation of the second sample = 7.32
F test statistic = Variance of the Larger sample/ Variance of the smaller sample
Variance = (Standard deviation)²
Variance for the first sample = 2.1971²
= 4.8272
Variance for the second sample = 7.32² = 53.5824
F test = 53.5824/4.8272
= 11.100
Therefore, the F test approximately = 11.100
learn more about of F -test here
https://brainly.com/question/17256783
#SPJ4
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.
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.
To know more about ratio check the below link:
https://brainly.com/question/2328454
#SPJ4
Solve for x. Show your steps
The value of x is -7.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given the equation as
[tex]8^{x + 3} = 2 ^{x - 5}[/tex]
Solving the equation as;
[tex]8^{x + 3} = 2 ^{x - 5}\\\\2^{3(x + 3)} = 2 ^{x - 5}[/tex]
Then we have;
3x + 9 = x - 5
2x = -14
x = -7
The value of x is -7.
Learn more about equations here;
brainly.com/question/25180086
#SPJ1
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.
Learn more about confidence intervals, by the following link.
https://brainly.com/question/17097944
#SPJ4
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
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.
To learn more about probability link is here
brainly.com/question/26911497
#SPJ4
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.
Learn more about reflections here:
https://brainly.com/question/12463306
#SPJ1
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
To learn more about rate, please check: https://brainly.com/question/21734785
#SPJ1
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 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].
if angles of a triangle are congruent then are the sides also congruent
Answer:
yes
Step-by-step explanation:
You want to know if the sides are congruent in a triangle with congruent angles.
Law of sinesThe Law of Sines tells us the sides of a triangle are proportional in length to the sines of the opposite angles.
If the angles are congruent, their sines are equal, and the sides are congruent.
Congruent anglesA triangle with congruent angles has all angles 60°. Such a triangle is called an equilateral triangle. The name "equilateral" refers to the fact that the sides are the same length.