Let ξ1, ξ2, ξ3, ... be the interarrival times of the pure renewal process {N(t) : t ≥ 0}.
Then, the renewal-type equation for the expected number of arrivals up to time t, denoted by H(t) or m(t), is given by:
H(t) = E[N(t)] = E[1 + N(t − ξ1)] = 1 + E[N(t − ξ1)]
The last equality follows from the memoryless property of the exponential distribution, which implies that N(t − ξ1) has the same distribution as N(t), shifted by a time of ξ1.
Let F(x) be the cumulative distribution function (cdf) of ξ1, and let f(x) = F'(x) be its probability density function (pdf). Then, we have:
H(t) = 1 + ∫_0^t H(t − x) f(x) dx
This is the renewal-type equation for H(t) or m(t), with the function D(t) = f(t). The interpretation of this equation is that the expected number of arrivals up to time t is the sum of the first arrival (which occurs with probability 1) and the expected number of arrivals up to time t − ξ1, weighted by the probability density of ξ1.
The integral term represents the expected number of arrivals up to time t − x, given that the first arrival occurred at time x, and is weighted by the probability density of the interarrival time x.
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W(-7,-4), X(1,-6), Y(5,-13), Z(1,-12) is this a parallelogram or not?
The polygon given, based on the vertices of the points on the polygon, is not a parallelogram.
Why is the shape not a parallelogram ?Parallelograms are such that there are two vertical parallel lines and two horizontal parallel lines. What this means is that two points on the parallelogram will share the same position on the x axis, and the other two points will share the position on the y - axis.
For instance, the vertices of a parallelogram would be P(−4,0), Q(0,4), R(4,0), and S(0,−4) where you see that two points share the same x coordinates and two share the same y coordinates.
This is not the same with W(-7,-4), X(1,-6), Y(5,-13), Z(1,-12) so this is not a parallelogram.
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How do you find the mirror image of a curve with respect to a line?
Finding the mirror image of a curve with respect to a line is a relatively straightforward task.
What is mirror image?Mirror image is an exact reflection of an object or an image as seen in a mirror. It is an image that is flipped from left to right, with the left side of the image becoming the right side and vice versa. This type of reflection is also known as a lateral inversion. In art and photography, mirror images are often used for aesthetic purposes and to create symmetry.
Firstly, you need to determine the line of reflection. This can be identified by using the angle bisector of the two lines that form the curve. Once you have identified the line of reflection, draw a line perpendicular to it. This is the axis of symmetry.
Next, draw a line parallel to the axis of symmetry. This line will serve as the mirror line. Now, you can start plotting the points of the curve with respect to the mirror line. To do this, take the midpoint of the curve and reflect it across the mirror line. Then, take the points on either side of the midpoint, and reflect them across the mirror line as well. Repeat this process for all the points on the curve.
Finally, connect the reflected points to form the mirror image of the curve. This will give you the same curve, just flipped across the mirror line. It is important to note that the mirror image of the curve will be a mirror reflection of its original shape, but its orientation may be different.
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5) Kim and Matt each improved their yards by planting grass sod and ornamental grass. They
bought their supplies from the same store. Kim spent $32 on 4 ft² of grass sod and 4 bunches of
ornamental grass. Matt spent $29 on 8 ft² of grass sod and 1 bunch of ornamental grass. Find the
cost of one ft² of grass sod and the cost of one bunch of ornamental grass.
Therefore , the solution to the given problem of equation comes out to be $12 for a geranium and $11 for a square foot of grass.
Explain the equation.When connecting two statements, a mathematical equation uses its equal sign (=) to denote equivalence. An equation in algebra is a claim that establishes the comparability of two equations. For instance, the formula 5x + 5 = 14 establishes a link between the two integers. The spaces seen between phrases with either front of a letter are used to form a mathematical connection. The lone variable so the only outcome are frequently the symbol. For instance, 8x - 4 = 2.
Here,
To start, you should underline and group pertinent information. Sort the products according to the individual who purchased them. We can give each of the two purchased things a constant or letter as there are only two of them:
Kim
5 feet by 2 feet (X for short) of grass
10 geraniums, designated as "Y" geraniums; total cost: $175
Matt
9 ft 2 of grass (let's call it grass X).
Four geraniums, designated as Y.
$147 in total
Now that the data has been split, you may create two equations: one for Matt and one for Kim.
Kim
5x + 10y = $175
Matt 9x plus 4y = $147
Observe how the numbers remained constant, but I eliminated the units and substituted X or Y depends on just what we assigned. We can start solving now.
I'll take the x out of Kim's equation. the following steps:
1) 5x + 10y = $175 Rewriting the equation
2) If you'd want to perform y first, 5x = $175 - 10y (again, you can still do y first as we're trying to isolate x). That's exactly how I did it.)
3) (5x)÷5 = ($175 - 10y)÷5 (divide both aspects of the equation by 5)
4) 5x + 10y = $175
=>5x + 10($12) = $175
5x + 10($12) = $175
Add the value of y = $12 to Kim's equation to get 5x + $120 = $175.
5) 5x = $175 - $120
=> 5x = $55
=> x = $11
x = $11
Therefore , the solution to the given problem of equation comes out to be $12 for a geranium and $11 for a square foot of grass.
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help!
im scared to get this wrong!
Question 1(Multiple Choice Worth 2 points) (Graphing Linear Equations LC) Which of the following graphs has a slope of negative two thirds and a y-intercept of 2? graph of a line passing through the points 0 comma 2 and 3 comma 0 graph of a line passing through the points 0 comma 2 and 2 comma negative 1 graph of a line passing through the points 0 comma 3 and 2 comma 0 graph of a line passing through the points 0 comma 3 and 3 comma 1 Question 2(Multiple Choice Worth 2 points) (Graphing Linear Equations MC) Which graph represents the equation y equals one half times x minus 1? graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1 graph of a line passing through the points negative 2 comma 0 and 0 comma 1 graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2 graph of a line passing through the points negative 4 comma 0 and 0 comma 2 Question 3(Multiple Choice Worth 2 points) (Graphing Linear Equations MC) A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory. Sunglasses Inventory Number of Days Total Amount of Sunglasses 2 54 5 48 7 44 10 38 Which of the following graphs shows the relationship given in the table? graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50 graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49 graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56 graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1
1. The graph that has a slope of -2/3 and a y-intercept of 2 is given as follows:
Graph of a line passing through the points (0,2) and (3,0).
2. The graph that represents the equation y = 0.5x - 1 is given as follows:
Graph of a line passing through the points (-2,-2) and (0,-1).
3. The graph that represents the relation is given as follows:
Graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point (0,58) and (1, 56).
How to model a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the change in y when x is increased by one.b is the intercept, representing the value of y when x = 0.For the graph that has a slope of -2/3 and a y-intercept of 2, we have that:
The intercept of 2 means that the function passes through (0,2).The intercept of -2/3 means that the function passes through (3,0), as when x increases by 3, y decays by 2.The y-intercept and the slope of the equation y = 0.5x - 1 is given as follows:
-1, meaning that the function passes through the point (0,-1).
When x = -2, the value of the function is given as follows:
y = 0.5(-2) - 1
y = -1 - 1
y = -2.
Hence the other point is (-2,-2).
For the relation in item 3, we have that when x increases by 3, y decays by 6, hence the slope m is given as follows:
m = -6/3
m = -2.
Hence:
y = -2x + b.
When x = 2, y = 54, hence the intercept b is given as follows:
54 = -2(2) + b
b = 58.
Hence the function is:
y = -2x + 58.
The points are:
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How do you identify the factors of the terms of an expression?
A single mathematical phrase is referred to as a term. It might be a single number (positive or negative), a single variable (a letter), or a combination of variables multiplied but never added or subtracted. A factor is a number that divides another number by itself and leaves no residue.
What is algebraic expression?An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the words 4m and 5 are separated by the arithmetic sign + and m is the variable of the provided expression.
Here,
A term refers to a single mathematical phrase. It might be a single integer (positive or negative), a single variable (a letter), or a mixture of variables that have been multiplied but never added or subtracted. A factor is a number that divides another number by itself with no remainder.
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Standardized tests for certain subjects, given to high
school students, are scored on a scale of 1 to 5. Let X
represent the score on a randomly selected exam. The
distribution of scores for one subject's standardized
test is given in the table.
Score
Probability
Mark this and return
For the given values the probability less than 3 equals 0.38.
What is meant by 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.
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.
Given,
the probability of different scores
Probability of score less than 3 equals
= P(score 1) + P(score 2)
= 0.18 + 0.20
= 0.38
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Shelby is thinking of a secret number. She tells her brother that it is divisible by 3 and tells
her friend that it is divisible by 11. If Shelby is telling the truth to both of them, what is the
smallest secret number that Shelby could be thinking of?l
Answer:
33!
Step-by-step explanation:
We can use the opposite of division (multiplication) to find what this number could be.
These are the multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, etc.
There are the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, etc.
As you can see, the lowest number that is both a multiple of 3 and 11 is 33.
High school and college students were surveyed to choose a favorite movie genre: action, drama, or comedy. 23% of the students in the survey chose comedy, and 43.1% of the students in the survey were high school students. From the sample, it is found that 13.2% were high school students who chose drama, and 23% were high school students who chose action. 11.5% were college students who chose action, and 29.3% were college students who chose drama.
Which of the following is a correct two-way relative frequency table for the data?
Movie Preference
Action Drama Comedy Row totals
High School 23.0% 13.2% 6.9% 43.1%
College 11.5% 29.3% 16.1% 56.9%
Column totals 34.5% 42.5% 23% 100%
Movie Preference
Action Drama Comedy Row totals
High School 23.0 13.2 6.9 43.1
College 11.5 29.3 16.1 56.9
Column totals 34.5 42.5 23 100
Movie Preference
Action Drama Comedy Row totals
High School 23.0 13.2 6.9 43.1%
College 11.5 29.3 16.1 56.9%
Column totals 34.5% 42.5% 23% 100%
Movie Preference
Action Drama Comedy Row totals
High School 23.0 13.2 6.9 0.431
College 11.5 29.3 16.1 0.569
Column totals 0.345 0.425 0.23 1
Note that the correct Two-way relative frequency table for the data is: (Option A) which is given as follows.
Movie Preference
Action Drama Comedy Row Totals
High School 23.0% 13.2% 6.9% 43.1%
College 11.5% 29.3% 16.1% 56.9%
Column totals 34.5% 42.5% 23% 100%
See the tabularized format attached.
What is a Two-Way Relative Frequency Table?Tables of two-way relative frequency indicate percentages rather than counts. They are useful for determining whether or not two variables are related.
Thus, the first choice is the accurate depiction of a two-way frequency table since it shows the percentage of students in each group (high school and college) who picked each movie genre (action, drama, comedy), as well as row and column totals that sum up to 100%. The other three selections are incorrect because they lack percentages or column and row totals.
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Which graph represents (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis-pairs that make the equation y = 3x-2y=3x−2y, equals, 3, x, minus, 2 true?
The graph of linear equation y = 3x - 2 have a slope of 3 and y intercept of -2
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The linear equation is in the form:
y = mx + b
where m is the rate of change and b is the y intercept.
Given that the graph of y = 3x - 2 is shown. It passes through the point (0, -2) and (1, 1)
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Which set of numbers can represent the side lengths in inches of an acute triangle ?a. 4, 5, 7b. 5, 7, 8,c. 6, 7, 10d. 7, 9, 12
5 , 7 , 8 represent the side of acute angled triangle.
The correct answer is set B.
Now, According to the question:
We use the following result:
When given 3 triangle sides then to determine if the triangle is acute angled , right angled or obtuse angled.
First find Square all 3 sides, then Sum the squares of the 2 shortest sides and then Compare the sum to the square of the last side.
if sum > Square of last side ⇒ it is Acute Triangle
if sum = Square of last side ⇒ it is Right Triangle
if sum < Square of last side ⇒ it is Obtuse Triangle
a). 4 , 5 , 7
[tex]4^2 = 16 , 5^2 = 25 , 7^2 = 49[/tex]
16 + 25 = 41
∵ 41 < 49
⇒ It is an Obtuse Triangle.
b). 5 , 7 , 8
[tex]5^2 = 25 , 7^2 = 49 , 8^2 = 64[/tex]
25 + 49 = 74
∵ 74 > 64
⇒ It is an acute Triangle.
c). 6 , 7 , 10
[tex]6^2 = 36 , 7^2 = 49 , 10^2 = 100[/tex]
36 + 49 = 85
∵ 85 < 100
⇒ It is an Obtuse Triangle.
d). 7 , 9 , 12
[tex]7^2 = 49 , 9^2 = 81 , 12^2 = 144[/tex]
49 + 81 = 130
∵ 130 < 144
⇒ It is an Obtuse Triangle.
Therefore,5 , 7 , 8 represent the side of acute angled triangle.
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Can a triangle be formed with side lengths of 3/4 7?
Answer:
NO
Step-by-step explanation:
Assuming the correct question is "Can a triangle be formed with side lengths of 3, 4 and 7?"
The sum of the length of any two sides of a triangle is greater than the length of the third side
3 + 4 = 7
so your answer is NO
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 1 of 5: State the null and alternative hypotheses.
The null hypothesis is H0: u = 447, the alternative hypothesis is given as: H1: u ≠ 447
What is a null and alternative hypothesis?A null hypothesis is a statement that there is no significant difference between two groups or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a significant difference or relationship between the groups or variables.
In statistical hypothesis testing, we test the null hypothesis against an alternative hypothesis. If the data provides enough evidence against the null hypothesis, we can reject it in favor of the alternative hypothesis.
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5/4+2/8+13/6=????????
Answer:
88/24. Mixed number: 3 16/24
Step-by-step explanation:
First, you want to find the LCM (Least Common Multiple) for the denominator. The LCM is 24. 24 divided by 4 is 6, so 6 x 5 is 30. 24 divided by 8 is 3, so 2 x 3 is 6. 24 divided by 6 is 4, so 4 x 13 is 52. All of the fractions’ denominators now have the same number, which makes it easier to add. So, 30/24 + 6/24 + 52/24 = 88/24. Your welcome :)
Answer:
this question has 3 answers according to decimal point your answer will be written as 3.67
According to mixed numbers your answer will be 3 written as whole number,2written as numerator and 3 written as denominator.
According to improper fraction your answer will be 11 written as numerator and 3 written as denominator
What is the difference between total revenue and total cost Mcq?
The difference between total revenue and total costs is: gross profit.
What is total cost also known as?Every element of production has a total cost that, depending on whether it has fixed costs or variable costs, includes the total opportunity cost (benefits from the next-best alternative) of each factor. Marginal cost is the added sum of the costs resulting from adding one more unit of output. Total cost is the collective term for all costs associated with manufacturing, including both fixed and variable costs. The total cost, as used in economics, is the sum of all expenses incurred in the production of a good.
Revenue is the entire sum of money that a business receives for items sold or services rendered during a specific period of time. The direct expenses incurred during the manufacture of the products a business sells are known as the cost of goods sold.
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What are the formulas for Class 6?
A formula is an expression that instructs the computer how to mathematically process a given value. Some of the formulas for class 6 as explained.
Define the term formulas and its types?Algebra, decimals, ratios, proportions, geometry, and mensuration are just a few of the crucial Math formulas for Class 6 that students must adhere to.
Closure Property of Multiplication a × bAssociativity of Addition: (a + b) + c = a + (b + c)Associativity of Multiplication: a × (b × c) = (a × b) × cDistributive of Multiplication over Addition: a × (b + c) = a × b + a × cDistributive of Multiplication over Subtraction: a × (b – c) = a × b – a × cExistence of Multiplicative Identity: a + 0 = a = 0 + aExistence of Multiplicative Identity: a × 0 = 0 = 0 × aUnit Multiplication: a × 1 = a = 1 × aTo know more about the formulas, here
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Please help me with these fractions!!
Answer: b = 2 19/30 c = 3 13/30
Step-by-step explanation:
1 4/5 + 5/6
= 1 49/30
= 2 19/30
2 1/10 + 1 2/3
= 3 13/30
Answer:
b)
[tex]2 \times \frac{19}{30} [/tex]
c)
[tex]3 \times \frac{23}{30} [/tex]
Step-by-step explanation:
b)
x - 5/6 = 1 × 4/5
x - 5/6 = 9/5
x = 5/6 + 9/5
x = (25+54)/30
x = 79/30 (or 2×19/30)
c)
x - 2 × 1/10 = 1 × 2/3
x - 21/10 = 5/3
x = 21/10 + 5/3
x = (63+50)/30
x = 113/30 (or 3×23/30)
11.3>b4.3 Solve the inequality
Answer:
Step-by-step explanation:
b<11.3/4.3
Susie AnnaMarie makes $12 per hour cutting grass and $14 per hour tutoring. One weekend, she worked a total of 14 hours and made $184.
Answer: This is a system of equations problem. We can set up the following equations:
x + y = 14 (where x is the number of hours Susie spent cutting grass and y is the number of hours Susie spent tutoring)
12x + 14y = 184 (where 12x represents the amount of money Susie made cutting grass and 14y represents the amount of money Susie made tutoring)
We can solve for x and y using different methods such as substitution or elimination.
By substitution:
x + y = 14
12x + 14y = 184
We know that y = 14-x.
so we can substitute it in second equation.
12x + 14(14-x) = 184
12x + 196 - 14x = 184
-2x = -12
x = 6
y = 14-x = 14-6 = 8
So Susie worked 6 hours cutting grass and 8 hours tutoring.
You can cross check by putting the values in the first equation x+y = 14.
Step-by-step explanation:
Write the equation of the line in standard form:
1/2y=-4/5x-2
The standard form of the equation is 8x+5y = -20.
What is standard form of the equation?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.
Here the given equation is
=> [tex]\frac{1}{2}y=\frac{-4}{5}x-2[/tex]
=> [tex]\frac{1}{2}y=\frac{-4x-10}{5}[/tex]
=> 5y = 2(-4x-10)
=> 5y = -8x-20
=> 8x+5y = -20.
Hence the standard form of the equation is 8x+5y = -20.
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3. The outside temperature decreases
by 7°F in 3 hours.
Part A
How would you represent the
temperature change as a unit rate?
Express your answer as an integer.
poir
poi
Part B
If the temperature continues to
decrease at this rate, what will be
the change in temperature after 5
hours?
Answer:
Part A: 2
Part B: 10° F
Step-by-step explanation:
Part A
The rate of change is calculated by dividing the difference in temperature by the time.
rate of change = (7°F)/(3 1/2 hours)
rate of change = 7/3.5
rate of change = 2
Answer: 2
Part B
The rate of change tells us that each hour that passes, the temperature decreases by 2° F.
In 5 hours, 5 × 2 = 10, so the change in temperature will be 10° F.
Answer: 10° F
5y+30x=45 and 6y-x=546y−x=54
The solution of the given equations is x = 0, y=9. The value of x and y will satisfy the given equations.
What is an equation?
A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Given a system of equations is
5y+30x=45 ........(i)
6y-x=54 .......(ii)
Applying the elimination method to solve the equations.
Multiply equation (ii) by 30 and with equation (i):
5y + 30x=45
180y - 30x = 1620
_______________
185y = 1665
Divide both sides by 185:
y = 1665/185
y = 9
Putting y = 9 in equation (ii)
6×9-x=54
54 - x = 54
-x = 54 - 54
x = 0
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help with this please
y = 2х-4
6x-3y = 12 (Needs [x,y] solution)
Answer:
Can't be answered, as written.
Step-by-step explanation:
Please check the equations. As written, they are the same:
y=2x-4 and 6x-3y=12
The second, 6x-3y=12, can be rewritten:
-3y = -6x + 12
y = 2x - 4 is the same as the first equation.
========
I'll do an example based on a different first equation. Let's try:
y = 4x-4 and 6x-3y=12
There are two equations and 2 unknowns. We can solve this in either of two ways: Mathematically and Graphically. Let's try both.
Mathematically.
Pick either equation and isolate one of the variables (x or y)
I'll chose the first, since the variable y is already isolated. (the efficient approach)
y = 4x-4
Take the second equation and use the definition of y provided by the first equation in place of y is the second:
6x-3y = 12
6x-3(4x-4) = 12 [Substituted the value of y given in the first equation]
6x - 12x + 12 = 12
-6x=0
x= 0
Use x = 0 in either equation to find y:
y = 4x-4
y=4*(0)-4
y = -4
The solution (where the lines intersect) is (0,-4)
We can also solve this graphically.
Plot the two lines and look for their intersection. The attached graph shows that to be (0,-4).
2y - 8 = 6x
y = 3x + 2
need solution please help
Answer:
No solution.
Step-by-step explanation:
2y-8=6x
y=3x+2
--------------
2(3x+2)-8=6x
6x+4-8=6x
6x-4=6x
6x-6x=4
0=4
What operation would you use to solve 10=6y
The operation you would use to solve [tex]6y=10[/tex] is division because we want to get the variable by itself. We use division because it' is the inverse of multiplication. So to solve [tex]6y=10[/tex], I would be dividing.
[tex]6y=10[/tex]
Divide both sides by 6(get the variable by itself):
[tex]\dfrac{6y}{6} =\dfrac{10}{6}[/tex]
[tex]=1.666667[/tex]
Help with part A and part B Please! ASAP
A: you're finding the area where he needs carpet so you do 30x20 and 10x10 and then add those together B: you're seeing how much it would cost to carpet the bedroom so you take the answer from problem A and multiply it by 3
What are the factors of substitution?
The factors of substitution are separating a polynomial into its component polynomials.
Factoring polynomials mean separating a polynomial into its constituent polynomials. Sometimes, when polynomials are particularly complicated, it is easiest to substitute a simple term and factor it down.
This is a quick technique to use with complicated polynomials, particularly if subsets of that polynomial repeat.
For example, we need to factorise (x − y)(x − y − 1) − 20
Let S = x − y. Then substituting S in for x − y for ease of computation, we get
(x − y)(x − y − 1) − 20
= (S)(S − 1) − 20
= S² − S − 20
=(S − 5)(S + 4)
=(x − y − 5)(x − y + 4).
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Liquid A has a density of 0.6g/cm
Liquid B has a density of 1.5g/cm
126 of liquid a and 126 of liquid b are mixed to make liquid c
Find the density of liquid c
0.6×1.5=0.9 I know this answer come my home
expression equivalent to 11(x - y)
Answer: 11 x - 11 y
Step-by-step explanation: 11 (x - y) 11 x - 11 y