Answer:
It's 6 and -5.
Step-by-step explanation:
:D
Find the fifth power of the following transition matrix. Then find the probability that state 2 changes to state 4 after five repetitions of the experiment. Compute A5. A =O (Type an integer or decimal for each matrix element. Round to three decimal places as needed.) 0.4 0.1 0.1 0.2 0.2 0.1 0.3 0.2 0.1 0.3 A= 0.2 0.1 0.2 0.1 0.4 0.4 0.1 0.1 0.2 0.2 0.1 0.3 0.2 0.1 0.3
Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.
To find the fifth power of the matrix A, we can simply multiply A by itself five times:
A^5 = A * A * A * A * A
= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)
= (0.22 0.12 0.14 0.14 0.34)
To find the probability that state 2 changes to state 4 after five repetitions of the experiment, we need to look at the element in the fifth power matrix A^5 that corresponds to state 2 and state 4. This element is located in the second row and fourth column of the matrix, which is 0.14.
Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.
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A^5 = A * A * A * A * A
= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)
= (0.22 0.12 0.14 0.14 0.34)
Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.
-1/4 x [ x 12 -32 ] = [ 5 -3 y ]
The x and y values for the given equation are x= -20 and y=8
What is meant by scalar multiplication?One of the fundamental operations defining a vector space in linear algebra in mathematics is scalar multiplication (or more generally, a module in abstract algebra). When a real Euclidean vector is multiplied scalarly by a positive real number, the direction of the vector remains unchanged, but the magnitude of the vector increases. A scalar is anything that scales vectors, which is how the word "scalar" itself came to be. It is important to distinguish between the inner product of two vectors and scalar multiplication, which is the multiplication of a vector by a scalar with a vector as the product.
Given,
-1/4[ x 12 -32 ] = [ 5 -3 y ]
[(-1/4)x (-12/4) (-32/-4)]=[5 -3 y]
-x/4=5
-x=20
x= -20
-32/-4=y
y=8
Therefore, the x and y values for the given equation are x= -20 and y=8
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how is the circumference of a circle related to the length of its diameter?
Answer:
"the circumference divided by the diameter"
Step-by-step explanation:
Circles are all similar, and "the circumference divided by the diameter" produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).
What should be calculated first when finding the value of the following expression?
[(-3) (-8)+6)-(-6 + (-2))
A.8+6
B. (-3) (-8)
C.6+ (-2)
D.-6 -(-6)
Answer:
A
Step-by-step explanation:
The problem is a little unclear with its format(random bracket) but given the following it should be A even though a parenthesis is missing but with going from left to right with parenthesis first depending on where the extra parenthesis is placed it is either A or B but it looks like there should be one grouping ((-8)+6) so it should be A
A carnival game gives variety bags as prizes. The game operator uses 100 balloons and 68 stickers to put into a certain number of bags. How many balloons and how many stickers can go in each bag if they make the greatest number of bags possible so that each bag has the same number of balloons and the same number of stickers?(1 point)
Responses
25 stickers and 17 balloons
25 stickers and 17 balloons
25 balloons and 17 stickers
25 balloons and 17 stickers
4 balloons and 4 stickers
4 balloons and 4 stickers
50 balloons and 34 stickers
50 balloons and 34 stickers
Answer:
D is the answer
Step-by-step explanation:
Using bags that will make the balloon and the stickers have the same number in each bag, mere looking at the answers, 100/2 gives you 50 while 68/2 gives you 34. it means that it was splitted equally into the two bags.
Mrs. Smith has 40 students in her class. The ratio of students who stay after school for extra help to students who stay after school for soccer practice is 3:5. How many students stay after school for soccer practice?
Answer:
25
Step-by-step explanation:
1: Add up the ratio then divide by the number of students.
3+5=8
40/8=5
2: Each count is equal to 5 students.
3: Multiply the ratio of students who stay after soccer practice by Each count
5*5=25
Research shows that the radioactive isotope Americium-241 has a half-life of 432.2 years Use the following to construct a function that will model the amount of Americium-241 remaining after t years, from an initial amount of 10 kg. Q(t) = Pe^rtPent Where Q(t) describes the amount of Americium-241 remaining after t years from an initial quantity of P kg, 1.Q(t) =2. How long in years) will it take for the amount of Americium-241 remaining to reach 6 kg
It will take approximately 7.66 years for the amount of Americium-241 remaining to reach 6 kg, assuming that the initial amount was 10 kg. We can use formula Q(t) = Pe^(rt) to calculate half-life of Americium-241.
To construct a function that will model the amount of Americium-241 remaining after t years from an initial amount of 10 kg, we can use the formula:
Q(t) = Pe^(rt)
where Q(t) is the amount of Americium-241 remaining after t years, P is the initial quantity (10 kg in this case), r is the decay rate (the negative of the half-life of Americium-241, which is -432.2 years), and e is the mathematical constant approximately equal to 2.71828.
Plugging in the values, we get:
Q(t) = 10 * e^(-432.2t)
This is the function that will model the amount of Americium-241 remaining after t years from an initial quantity of 10 kg.
To find out how long it will take for the amount of Americium-241 remaining to reach 6 kg, we can solve the equation Q(t) = 6 for t.
[tex]Q(t) = 6\\6 = 10 * e^(-432.2t)\\0.6 = e^(-432.2t)\\ln(0.6) = -432.2t\\t = ln(0.6) / -432.2\\[/tex]
t = approximately 7.66 years
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In triangle XYZ, m∠Y = 71.02° and m∠Z = 29.6°. Determine the measure of the exterior angle to ∠X.
18.98°
60.4°
100.62°
79.38°
The measure of exterior angle to ∠X is 79.38°. So, option 4 is correct.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.
Given,
In ΔXYZ, m∠Y=71.02° and m∠Z=29.6°
We know that,
The angles sum in a triangle is 180°.
m∠X+m∠Y+m∠Z=180°
m∠X+71.02°+29.6°=180°
m∠X=180°-100.62°
m∠X=79.38°
Therefore, the measure of exterior angle to ∠X is 79.38°.
So, option 4 is correct.
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• Practice Questions: Write an equation for a rational function wita. Hole at x = 1 1and vertical asymptote at x = - 3b. Vertical asymptote at x = - 2 and horizontal asymptote at y = 3c. An oblique asymptote y = x+1 but no vertical asymptoted. Vertical asymptote at x = 3 and f(x) > 0
The ratio of two polynomial functions with a non-zero denominator is known as a rational function. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the typical way to describe it. We studied the idea of the rational number in previous grades. It is the ratio or product of two integers with a non-zero denominator. As a result, the word ratio is where the name rational comes from.
a. A rational function with a hole at x = 1 and a vertical asymptote at x = -3 can be written as:
(x-1)/(x+3)
b. A rational function with a vertical asymptote at x = -2 and a horizontal asymptote at y = 3 can be written as:
(x+2)/(x+2) = 3
c. A rational function with an oblique asymptote y = x+1 but no vertical asymptote can be written as:
(x-1)/(x-1) = x+1
d. A rational function with a vertical asymptote at x = 3 and f(x) > 0 can be written as:
(x-3)/(x-3) > 0
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Finley mows 1 lawn every 12 minutes. If his rate of lawn mowing remains the same, which method could be used to determine the number of minutes for him to mow 6 lawns? Responses
Answer:
6(12), multiplication
Step-by-step explanation:
Since it takes 12 minutes to mow one lawn, multiplying would give you the answer of how long 6 lawns would take, which is 72
A solution in a book demonstrates the following:
79z = 92x + 9y (values for z, x and y are in between 0 and 10)
Modulo 9, this gives -2z ≡ 2x and by multiplying both sides by 5 gives -z ≡ x. Since 1 ≤ x ≤ 9, we have z = 9 - x.
Can someone please explain how taking Modulo 9 of the equation above leads to these results in detail. Thanks.
Answer:
In modular arithmetic, the modulo operation is used to find the remainder when one number is divided by another. For example, the expression "9 % 3" would evaluate to 0 because 9 divided by 3 leaves a remainder of 0.
In the given equation, taking the modulo 9 of both sides gives:
79z % 9 ≡ 92x + 9y % 9
The modulo operation distributes over addition, so we can simplify this to:
(79z % 9) ≡ (92x % 9) + (9y % 9)
Since any number divided by 9 has a remainder of itself, we can simplify this further to:
(z % 9) ≡ (2x % 9) + (y % 9)
This gives us the result:
-2z % 9 ≡ 2x % 9
Multiplying both sides by 5 gives:
(-2z % 9) * 5 ≡ (2x % 9) * 5
Which simplifies to:
-z % 9 ≡ x % 9
Since x is between 0 and 10, we know that x % 9 is between 0 and 9. Therefore, we can conclude that z = 9 - x.
Which set of fractions is ordered from greatest to least? 3/10,1/4,2/5
Answer: 1/4,2/5,3/10
Step-by-step explanation:
how did the ancient greeks represent numbers and
why are their symbols so enduring today
Step-by-step explanation:
the ancient Greeks used the system know as the attic numerals
The base of a triangular piece of fabric is 6 in more than the height. The area is 600 in2. Find the base and height of the triangle
Answer:
Below in bold.
Step-by-step explanation:
Let the height be h in.
Area of a triangle = 1/2 * base * height
= 1/2 * (h + 6) * h = 600
Multiply both sides by 2:
h(h + 6) = 1200
h^2 + 6h = 1200
(h + 3)^2 - 9 = 1200
(h + 3)^2 = 1209
h + 3 = +/- sqrt(1209
h = -3 +/-sqrt(1209)
= 31.77 in (we ignore the negative root).
So, the height is 31.77 in and the base is 37.77 in
When planning a more strenuous hike, Brett figures that he will need at least 0.5 liters of water for each hour on the trail. He also plans to always have at least 1.80 liters of water as a general reserve. If x represents the duration of the hike (in hours) and y represents the amount of water needed (in liters) for a hike, the following inequality describes this relation: y> 0.5x + 1.8 Which of the following would be a solution to this situation?
a.) Having 3 liters of water for 4.5 hours of hiking
b.) Having 2 liters of water for 2.5 hours of hiking
c.) Having 4.5 liters of water for 4 hours of hiking
d.) Having 2.5 liters of water for 3 hours of hiking
Option C is correct,4.5 is greater than 3.8, so this solution does work.
If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.
Inequality
In mathematics, an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
The first option is having 0.5 liters of water for 4.5 hours of hiking. So will plug 3 in for y and 4.5 in for x:
y > 0.5x + 1.8
3 > 0.5(4.5) + 1.8
3 > 4.05
But 3 is not greater than 4.05, this solution does not work.
The next option is having 2 liters of water for 2.5 hrs of hiking:
2 > 0.5(2.5) + 1.8
2 > 3.05
But 2 is not greater than 3.05, so this solution does not work.
Option c is having 4.5 liters of water for 4 hours of hiking:
4.5 > 0.5(4) + 1.8
4.5 > 3.8
So 4.5 is greater than 3.8, this solution does work.
The last option is having 2.5 liters of water for 3 hours of hiking:
2.5 > 0.5(3) + 1.8
2.5 > 3.3
2.5 is not greater than 3.3, so this solution does not works
Option c is correct,4.5 is greater than 3.8 so this solution does work.
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y > 0.5x + 1.8
3 > 0.5(4.5) + 1.8
3 > 4.05
But 3 is not greater than 4.05, this solution does not work.
2 > 0.5(2.5) + 1.8
2 > 3.05
But 2 is not greater than 3.05, so this solution does not work.
4.5 > 0.5(4) + 1.8
4.5 > 3.8
2.5 > 0.5(3) + 1.8
2.5 > 3.3
2.5 is not greater than 3.3, so this solution does not works
Option c is correct,4.5 is greater than 3.8 so this solution does work.
A spherical balloon is being inflated at a rate of 8 cm³s-1. Find the rate of change of the surface area when the radius is 10 cm.
Answer:
1.6
Step-by-step explanation:
Firstly, we know the rate of change of volume [tex]v'=8[/tex].
The equation for surface area is: [tex]A = 4\pi r^2[/tex].
The derivative (rate of change) is then: [tex]A'=8\pi r*r'[/tex]
The equation of the volume of a sphere is: [tex]V=\frac{4}{3}\pi r^3[/tex].
The derivative (rate of change) is then: [tex]V' = 4\pi r^2 * r'[/tex].
This means that [tex]r'=\frac{V'}{4\pi r^2}[/tex].
We can then plug that into our equation for [tex]A'[/tex] and get:
[tex]A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}[/tex]
After that, we can just plug in:
[tex]2*\frac{8}{10}=1.6[/tex]
Arun runs a farm stand that sells raspberries and grapes. Each pound of raspberries sells for $1.50 and each pound of grapes sells for $2.75. Arun made $130.25 from selling a total of 66 pounds of raspberries and grapes. Determine the number of pounds of raspberries sold and the number of pounds of grapes sold.
Arun sold 41 pound of raspberries and 25 pound of grapes.
What is a linear equation?
The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).
Given that the cost of 1 pound of raspberries is $1.50 and 1 pound of grapes is $2.75.
Arun sells 66 pounds with cost $130.25.
Assume that Arun sells x pound of raspberries and y pound of grapes.
Therefore,
x + y = 66 ......(i)
The cost of x pound of raspberries and y pound of grapes is 1.50x + 2.75y.
1.50x + 2.75y = 130.25 .....(ii)
Solving equation (i) and (ii) by using elimination method.
Multiply equation (i) by 1.5
1.50x + 1.50y = 99 ....(iii)
Subtract equation (iii) from (ii)
1.50x + 2.75y = 130.25
1.50x + 1.50y = 99
(-) (-) (-)
________________
1.25 y = 31.25
y = 25
Putting y = 25 in equation (i)
x + 25 = 66
x = 41
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The expense function for a manufacturer can be modeled using the equation
E = 1.43q + 43, 123
What is the cost for producing 200 units (q)?
Answer:
The cost of producing 200 units can be calculated by plugging in 200 for q in the equation E = 1.43q + 43,123. This gives us E = 1.43*200 + 43,123 = 286 + 43,123 = $43,409.
An investor deposited some money at 1.7% annual interest, and two equal but larger amounts at 2.3% and 2.4%. The
total amount invested was $25,000, and the total annual interest earned was $568. How much was invested at each
rate?
At the rate 1.7%, $ was invested.
deposited some money at 1.7% annual interest, and two equal but larger amounts at 2.2% and 24%. The total amount invested was $26,000 and the total annual interest earned was $574. How much was invested at each rate?
What is an investor?
An investor is an individual or an organization that gives money to A person or entity that invests in another with the hopes of making a profit in the future is known as an investor. According to the rules, anyone can invest: You are an investor if you put money into something.
Answer provided by our tutors
Let
x = the money invested at 1.7%
y = the money invested at 2.2%
y = the money invested at 24%
Since the total money invested was $26,000 we have:
x + 2y = 26000
The total annual interest was $574 means:
0.017x + 0.022y + 0.24y = 574
0.017x + 0.262y = 574
We have the following system of equations:
x + 2y = 26000
0.017x + 0.262y = 574
click here to see the system of equations solved for x and y
x = $24,842
y = $578
$24,842 was invested at 1.7%
$578 was invested at 2.2% and another $578 was invested at 24%.
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QUESTION DOWN BELOW! PLASE HELP DUE SOON!
Answer: its 18 im pretty sure
Step-by-step explanation:
How many factor pairs does the number 84 have?
A textbook store sold a combined total of 412 chemistry and math textbooks in a week. The number of chemistry textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold?
Answer:
309 chemistry textbooks and 103 math textbooks.
Step-by-step explanation:
Let c be the number of chemistry textbooks sold and m be the number of math textbooks sold. We know that c + m = 412, because the total number of textbooks sold is 412. We also know that c = 3m, because the number of chemistry textbooks sold is three times the number of math textbooks sold.
We can substitute 3m for c in the first equation to get 3m + m = 412. This simplifies to 4m = 412. Dividing both sides by 4 gives us m = 103.
Since we know that c = 3m, the number of chemistry textbooks sold is 3 * 103 = 309. Therefore, the store sold 309 chemistry textbooks and 103 math textbooks.
Which of the following number sentences is true?
A. 40 -2 × 3² = 4
C. 40 -2 × 3² = 114
B. 40-2 × 3² = 22
D. 40 -2 × 3² = 360
Answer:
B
Step-by-step explanation:
First, we compute the exponent (3² = 9).
Next, we compute the multiplication and division (from left to right), so we have (40 - 2 × 9) = (40 - 18) = 22.
Thus, the number sentence 40 -2 × 3² = 22 is true.
B is true .22 is the real answer
1. Let C be a nonsymmetric n x n matrix. For each of the following, determine whether the given matrix must necessarily be symmetric or could possibly be nonsymmetric:
(a) A= C+CT
(b) B = C-CT
(c) D = CTC
(d) E = CTC - CCT
(e) F = (I +C)(I + CT
(f) G = (I +C)(I -CT)
Option of the matrices a, b, and d are non symmetric.
What are Symmetric matrices ?Symmetric matrices are those matrices that have equal dimensions, i.e. the number of rows is same as the number of columns. They are also known as square matrices.
It is provided that A and B are symmetric n × n matrices.
To multiply two matrices of different order, the number of rows of the first matrix must be same as the number of columns of the second matrix.
Suppose X is a 2 × 3 matrix and Y is a 3 × 2.
Then the product AB will be a n × n matrix.
(a) A= C+CT
Thus the sum of matrix A and B will be a n × n matrix.
Thus, the matrix A is non symmetric.
(b) B = C-CT
So, matrix D will also be a n × n matrix.
Thus, the matrix D is non symmetric.
(c) D = CTC = (CT) × C
Then the product CT will be a n × n matrix.
The next step would be to multiply CT and C.
Both are n × n matrices.
Thus, the matrix D is symmetric.
(d) E = CTC - CCT
Then he product CT will be a n × n matrix.
Similarly, the product CT will be a n × n matrix.
Thus, the matrix E is non symmetric.
Similalry,
(e) F = (I +C)(I + CT
Thus, the matrix F is symmetric.
(f) G = (I +C)(I -CT)
Thus, the matrix G is symmetric.
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i rlly need help with these questions someone please help
The perimeter of the shape is 12.82 units
How to determine the perimeter of the shape?From the question, we have the following parameters that can be used in our computation:
A = (0, 2.76)
B = (3.65, 2.76)
C = (3.65, 0)
D = (0, 0)
Because the point D is at the origin, and the shape is a rectangle.
The perimeter of the shape can be represented as
P = 2 * (Bx + By)
Substitute the known values in the above equation, so, we have the following representation
P = 2* (3.65 + 2.76)
Evaluate
P = 12.82
Hence, the perimeter is 12.82 units
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−1+log 6 (2x+3)−log 6 (2x)=0
Answer:
Step-by-step explanation:
Let us solve the equation for X-
-1+log 6 (2x+3)-log 6 (2x)=0
adding +1 to both sides-
-1+1+log 6(2x+3)-log 6 (2x)=0+1
log 6(2x+3)-log 6 (2x)=1 . . . (1)
using logarithmic rule,
log a - log b= log(a/b)
equation (1) becomes,
log [6(2x+3)/6(2x)]=1 . . .(2)
equation (2) becomes,
log[(2x+3)/2x]=1....(3)
Again using the logarithmic rule,
log a = b
is equivalent to 10∧b = a
hence equation 3 becomes,
10∧1= (2x+3)/2x
i.e. 10 = (2x+3)/2x. . .(4)
multiplying both sides by 2x, considering x is not 0.
equation( 4) becomes
20x = 2x+3. . .(5)
subtracting 2x from both sides
equation (5) becomes,
18x=3
dividing both sides by 3,
we get,
x=6
Hence value of x is 6.
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In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were:
Men Women
Voted 2366
3611
Didn't Vote 1499
2524
If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)]
a) [p-value = 0.019, RH0]
b) [p-value = 0.140, RH0]
c) [p-value = 0.019, FRH0]
d) [p-value = 0.010, RH0]
e) [p-value = 0.140, FRH0]
An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.
Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."
Give the null hypotheses a name.
Negative hypothesis:
H. There is no correlation between gender and election participation.
Other possibilities:
H: Gender and participation in the most recent election are linked.
Rule of rejection:
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A block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest. What is their velocity after the collision ?
Answer:
When a block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest, their velocity after the collision is equal to the original velocity of the first block. This is because, in a collision where the two objects stick together, the final velocity of the combined system is equal to the initial velocity of the first object.
To calculate the final velocity of the combined system, we can use the formula vf = vi + (2mv)/(m1+m2), where vf is the final velocity, vi is the initial velocity, m is the mass of the first object, v is the velocity of the first object, and m1 and m2 are the masses of the two objects. Plugging in the values from the problem, we get:
vf = V + (2 * M * V)/(M + 2M) = V + (2 * M * V)/(3M) = V + (2/3) * V = (5/3) * V
Therefore, the final velocity of the combined system is (5/3) * V, which is equal to the original velocity of the first block.
The velocity of the mass 2M after the collision will be V/2 which is half of the velocity of mass M.
What is elastic collision?An elastic collision is one during which the system does not experience a huge reduction of kinetic energy as a result of the collision. In elastic collisions, mass and kinetic energy are both preserved. Imagine two trolleys that resemble one another moving in the same direction at the same pace.
A block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest.
Let 'v' be the velocity after the collision. Then the velocity of the mass 2M after the collision will be calculated as,
MV = 2Mv
v = V / 2
Thus, the velocity of the mass 2M after the collision will be V/2 which is half of the velocity of the mass M.
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Please help! on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?
Answer: 4/3 of a mile
Step-by-step explanation:
To find the distance that Pepe and Paula ran in 60 minutes, we need to first determine their individual pace in miles per minute. Pepe ran 2/3 of a mile in 5 minutes, so his pace was 2/3 / 5 = 2/15 of a mile per minute. Paula ran 1/4 of a mile in 2 minutes, so her pace was 1/4 / 2 = 1/8 of a mile per minute.
We can now use these values to determine the distance that each of them ran in 60 minutes. Pepe ran at a pace of 2/15 of a mile per minute, so he ran 2/15 * 60 = 8/15 of a mile in 60 minutes. Paula ran at a pace of 1/8 of a mile per minute, so she ran 1/8 * 60 = 3/8 of a mile in 60 minutes.
To find the total distance that Pepe and Paula ran in 60 minutes, we can add their individual distances: 8/15 + 3/8 = 35/60 + 45/60 = 80/60 = 4/3 of a mile. Therefore, Pepe and Paula cumulatively ran a total of 4/3 of a mile on their 60-minute training run.
 triangle XYZ has vertices X(0,2), Y(4,4), and Z (3,-1). Triangle XYZ is rotated 180° counter clockwise about Z. in which quadrant is the image of point X 
Answer 34
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