The probabilities are
P1(XT{0,3} = 3) = P(X1 = 3|X0 = 2) = 0.6.
P2(XT{0,3} = 0) = P(X1 = 0|X0 = 1) = 0.5.
E1[T{0,3}] = 10.4 + 2(0.40.6) + 3(0.40.60.6) = 1.6.
E2[T{0,3}] = 10.5 + 2(0.50.5) + 3(0.50.50.5) = 1.875.
(a) To calculate the probability that Markov wins the game, we need to find P1(XT{0,3} = 3). From the given transition diagram, we see that Markov will win the game if he reaches a capital of 3 Rubel.
The only way this can happen is if he starts with a capital of 2 Rubel and wins the first bet. Hence,
P1(XT{0,3} = 3) = P(X1 = 3|X0 = 2) = 0.6.
(b) To calculate the probability that Gombaud wins the game, we need to find
P2(XT{0,3} = 0).
From the given transition diagram, we see that Gombaud will win the game if Markov loses all his money and reaches a capital of 0 Rubel.
The only way this can happen is if Markov starts with a capital of 1 Rubel and loses the first bet. Hence,
P2(XT{0,3} = 0) = P(X1 = 0|X0 = 1) = 0.5.
(c) To find the expected length of the game for Markov to win, we need to calculate E1[T{0,3}]. We can use the formula
E1[T{0,3}] = Σi=1∞ iP1(T{0,3} = i).
Since the game will end in at most 3 rounds, we only need to consider i = 1, 2, 3. We know that the probability of winning in one round is 0.4, the probability of losing in one round is 0.6.
Therefore, E1[T{0,3}] = 10.4 + 2(0.40.6) + 3(0.40.60.6) = 1.6.
(d) To find the expected length of the game for Gombaud to win, we need to calculate E2[T{0,3}].
We can use the formula
E2[T{0,3}] = Σi=1∞ iP2(T{0,3} = i).
Since the game will end in at most 3 rounds, we only need to consider i = 1, 2, 3. We know that the probability of losing in one round is 0.5, and the probability of neither losing nor winning is 0.5. Therefore,
E2[T{0,3}] = 10.5 + 2(0.50.5) + 3(0.50.50.5) = 1.875.
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To compute E2[T{0,3}], we need to find the expected length of the game, specifically the expected number of steps it takes for either Markov or Gombaud to reach a total capital of 0 or 3.
The given one-step transition diagram represents Markov's wealth. From the diagram, we can observe that if Markov has a capital of 0, he will stay at 0 with a probability of 1. Similarly, if Markov has a capital of 3, he will stay at 3 with a probability of 1.
To calculate the expected length of the game, we consider the possible transitions and probabilities from each state. If Markov has a capital of 1, there is a 0.4 probability that he will lose 1 Rubel and end up with 0 capital, and a 0.6 probability that he will win 1 Rubel and reach a capital of 2. If Markov has a capital of 2, there is a 0.3 probability that he will lose 1 Rubel and reach a capital of 1, and a 0.7 probability that he will win 1 Rubel and reach a capital of 3.
We can construct a Markov chain and solve for the expected length of the game using the method of absorbing Markov chains. In this case, states 0 and 3 are absorbing states, meaning once reached, the game ends.
The expected length of the game can be calculated by solving a system of linear equations. Let E2[T{0,3}] represent the expected length of the game starting from state 2 (capital of 2). We can set up the following equations:
E2[T{0,3}] = 0.3 * (1 + E2[T{1,3}]) + 0.7 * (1 + E2[T{2,3}])
E2[T{1,3}] = 0.4 * (1 + E2[T{0,3}]) + 0.6 * (1 + E2[T{2,3}])
E2[T{2,3}] = 1
Solving this system of equations will give us the expected length of the game E2[T{0,3}].
Note: The calculations above assume that the game continues until one of the players reaches a capital of 0 or 3.
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summarize how the high temperature in this city changed over the 15 days
The temperature in this city changed by 7.5 degrees Celcius
How to determine the temperature changeFrom the question, we have the following parameters that can be used in our computation:
Rate of change = 0.5 degree Celcius daily
Number of days = 15
Using the above as a guide, we have the following:
Total change = Rate of change * Number of days
Substitute the known values in the above equation, so, we have the following representation
Total change = 0.5 * 15
Total change = 7.5
Hence, the total change is 7.5 degrees
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Complete question
The temperature of a City changes by 0.5 degree Celcius daily in the month of February. Summarize how the high temperature in this city changed over the 15 days
Determine the solution sets of the system of equations using the Gaussian Elimination method?
x-3y+z=4
2x-8y+8z=-2
-6x+3y-15z=9
Therefore , the solution of the given problem of equation comes out to be x = 73/19 , y = 5/19 and z = 18/19.
Equation: What is it?In a mathematical formula, the equal symbol (=) is used to denote that the statements are equivalent. It is demonstrated that many numerical variables are comparable using mathematical equations, which are statements of reality. The equal sign, for instance, separates the numbers 12 or b + 6 split separate halves of the equation y + 6 = 12. It is possible to calculate how many words each sides of a symbol represents. The meaning of a symbol usually contradicts itself.
Here,
Given :
=> x-3y+z=4....... (1)
=>2x-8y+8z=-2 ........ (2)
=> -6x+3y-15z=9 ......... (3)
Multiply eq (1) by 2 and subtract from eq (2)
=> 2x - 6y + 2z -2x +8y +8z = 8 +2
=> 2y +10z =10
=> y + 5z =5 ..... (4)
and
Multiply eq (2) by 3 and add to eq (3)
=> 6x - 24y +24z -6x + 3y -15z =-6 +9
=> -21y + 9z = 3
=> -7y + 3z =1 ..... (5)
So ,
from eq (4) and (5)
=> y = 5 -5z
=> -7(5-5z) + 3z = 1
=> -35 + 35z + 3z =1
=> 38z = 36
=> z = 36/38
=> z = 18/19
and
=> y = 5 - 5 (18/19)
=> y = 95 -90/19
=> y = 5/19
and
=> x = 4 -z +3y
=> x = 4 - 18/19 +15/19
=> x = 76 -3 /19
=> x = 73/19
Therefore , the solution of the given problem of equation comes out to be x = 73/19 , y = 5/19 and z = 18/19.
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Need help right now please I don’t understand why this question is so hard
Answer:
A:33
B:22
C:74
Step-by-step explanation:
A:
2x2x2=8
5x5=25
8+25=33
B:
7x7=49
3x3x3=27
49-27=22
C:
8x8=64
square root of 100 is 10
64+10=74
i hope this helps :)
In training for a triathlon, Yuna wam 1. 9 mile in the open ocean, which took her 2 hour. For the firt part of her wim, he averaged 1. 4 mile per hour. For the econd part of her wim, he wam againt the current and tarted to tire, o her average peed decreaed to 0. 8 mph
Yuna wam 1.9 miles in the open ocean in two hours, starting off with an average speed of 1.4 mph but decreasing to 0.8 mph. This resulted in a total distance of 2.8 miles.
To calculate Yuna's total distance wimmed, we need to calculate the total time it took her to wim. She wam 1.9 miles in 2 hours, so her average peed for the entire wim wa 1.4 mph.
1.4 mph x 2 hours = 2.8 miles
Therefore, Yuna wam a total of 2.8 miles.
Yuna trained for a triathlon and wam 1.9 miles in the open ocean, which took her two hours. She started off with an average speed of 1.4 mph, but as she got tired and wam against the current her average speed decreased to 0.8 mph. In order to calculate the total distance wimmed, we need to calculate the total time it took her which can be done by multiplying her average speed of 1.4 mph by the two hours. This gives us a total distance of 2.8 miles, which means that Yuna wam a total of 2.8 miles.
Yuna wam 1.9 miles in the open ocean in two hours, starting off with an average speed of 1.4 mph but decreasing to 0.8 mph. This resulted in a total distance of 2.8 miles.
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How do you convert base 10 to base 4?
Answer:
First, divide the number by the base to get the remainder. This remainder is the first, ie least significant, digit of the new number in the other base
Then repeat the process by dividing the quotient of step 1, by the new base. ...
Repeat this process until your quotient becomes less than the base
Step-by-step explanation:
ASAP PLEASE
Solve for x.
Enter your answer.
A rectangle with dimensions 12 meters and 5 times x meters, with diagonal length of 37 meters.
The value of x in the rectangle is 7 metres.
How to find the side of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and also parallel to each other.
The rectangle has dimension 12 meters and 5 times x metres, with diagonal length of 37 metres.
Hence, the length x can be found using Pythagoras's theorem.
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
37² = 12² + (5x)²
1369 = 144 + 25x²
1369 - 144 = 25x²
1225 = 25x²
divide both sides by 25
x² = 1225 / 25
x² = 49
square both sides
x = √49
x = 7 metres
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I'm struggling here, i need help before my semester ends
Answer:
Below
Step-by-step explanation:
Cross multiply to get
[3x(x) + (x-2)(x+3) ] / [x(x+3)] <==== simplify
[4x^2 +x -6 ] / (x(x+3)) done.
Find the range for the measure of the third side of a triangle when the measures of the other two sides are 6 ft and 19 ft.
The range of possibilities for the third side of the triangle, after using the triangle inequality theorem is 13 < n < 25.
According to the theorem of triangle inequality, the sum of any two of a triangle's sides must exceed the length of the third side. When we know the lengths of two sides, x and y, we can apply the triangle inequality theorem to estimate the length of the third side, which will be between x + y and x - y.
As a result,
x – y < n < x + y
19 – 6 < n < 19 + 6
13 ft < n < 25 ft
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What is image in maths class 11?
An image may be defined as that point, where the light rays coming from an object meet or appears to meet after reflection or refraction.
In this definition, the word 'object' may be defined as anything from which light rays are coming.
A function f from a set A to a set B is a special relation in
which, every element of set A has unique image in set B.
The function f from A to B is denoted by f : A →
If, f(a) = b, then ‘b’ is called the image of ‘a’ under f and ‘a’
is called the pre image of ‘b’ under f.
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A rectangular park is 80 meters long and 50 meters wide. Give the length and width of another rectangular park that has the same perimeter but a larger area.
Answer:
75 meters long 55 meters wide
Step-by-step explanation:
80*50= 4000
75*55=4125
4125<4000
75+55= 130
80+50=130
A chef can bake 15 pies in 1 hour. What is the rate of pies per minute?
Answer: The chef can bake (a) 0.25 pies/min.
Step-by-step explanation:
1 hour = 60 minutes
1 hour = 15 pies
15=60m
15/60 = 60/60 m
0.25 = m
The rate in pies per minute is 0.25. Therefore, option A is the correct answer.
Given that, a chef can bake 15 pies in one hour.
We need to find the rate in pies per minute.
What is the rate per minute?
Rate per minute was calculated by dividing the number of events observed by the observed minutes in the observation.
Simplify the rate by dividing each number by the greatest common factor.
Here, divide the number of pies by 60 minutes (1 hour=60 minute)
Now, 15/60=0.25 pies/min
The rate in pies per minute is 0.25. Therefore, option A is the correct answer.
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originally by brainly user bhoopendrasisodiya34
Find the decimal form of
5/18.
Answer:
0.28
Step-by-step explanation:5 (numerator) ÷ 18 (denominator) = 0.28
Answer: 0.28
Step-by-step explanation:
You look it up
Can a triangle be formed having the length of sides 2cm 3cm & 5cm justify it?
Can a triangle be formed having the length of sides 2cm 3cm & 5cm.Therefore, this triangle is not possible.
Can 2cm 5cm and 3cm make a triangle?In a triangle, the sum of the lengths of either two sides is always greater than the third side. Given that, the sides of the triangle are 2 cm, 3 cm, 5 cm. Hence, this triangle is not possible.When the two legs of an isosceles right triangle are congruent to one another and the non-right angles are both 45 degrees, the triangle is known as a 45 45 90 triangle. When the two legs of an isosceles right triangle are congruent to one another and the non-right angles are both 45 degrees, the triangle is known as a 45 45 90 triangle. The Pythagorean theorem can frequently be used to locate the missing legs or hypotenuse of 45 45 90 triangles. The sides' to the hypotenuse's ratio.To learn more about triangle refer to:
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Find the missing values
Answer:
x = 5 ft
Step-by-step explanation:
Volume of a right square pyramid = V = x²h/3
66.7 = x²(8/3)
x² = 66.7(3/8) = 25
x = √25 = 5
What is HJ? correct answer gets brainliest
For the given line segment, the value of HJ is 32 and hence option a is the correct answer.
What is a line segment?Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places.
Given that:
GJ = 56
[tex]\frac{GH}{HJ} =\frac{3}{4}[/tex]
The line segment GHJ = GJ can be written as follows:
GJ= GH +HJ
From the given ratio we know that:
GH = 3x and
HJ = 4x
Thus, the value of GJ = 3x + 4x
GJ = 7x
56 = 7x
x = 8
Substitute the value of x = 8 in GH = 3x and HJ = 4x.
GH= (3)(8) = 24
HJ = (4)(8) = 32
Hence the value of HJ = 32 and option a is the correct answer.
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what are the coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down, given T(-1,-1), U (-1,2), and V(2,1)?
The coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down can be found by following the transformation sequence.
What are the coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down, given T(-1,-1), U (-1,2), and V(2,1)?The first transformation to be applied is the dilation with a scale of 5. This transformation enlarges the coordinates of the original points by a factor of 5. The coordinates of T, U, and V become (5(-1,-1)), (5(-1,2)), and (5(2,1)) respectively. The coordinates of the dilated points are (T’(-5,-5)), (U’(-5,10)), and (V’(10,5)).The next transformation to be applied is the translation 3 units right and 2 units down.This transformation adds 3 to the x-coordinate and subtracts 2 from the y-coordinate of each point. After the translation, the coordinates of T’, U’, and V’ become (T’(-2,-7)), (U’(-2,8)), and (V’(13,3)) respectively.Therefore, the coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down are (13,3).The coordinates of V' can be found by first applying the dilation with scale 5 to the original points, followed by a translation 3 units right and 2 units down. Using the coordinates of T, U, and V as starting points, the coordinates of the points after the dilation with scale 5 can be found. T(-1,-1) becomes (-5,-5), U(-1,2) becomes (-5,10), and V(2,1) becomes (10,5). Applying the translation of 3 units right and 2 units down to the new points, the coordinates of V' can be found. T(-5,-5) becomes (-2,-7), U(-5,10) becomes (-2,8), and V(10,5) becomes (13,3). Therefore, the coordinates of V' are (13,3).To learn more about a dilation and a translation refer to:
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Find the missing values so that the area of the product is equal to the
area of its sum.
On solving the provided question, we can say that here, in the equation = (2x+3y)(3y-3)=12x+3y-15. so the missing values are = 3y
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here, in the equation
(2x+3y)(3y-3)=12x+3y-15
so the missing values are
3y
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A tring i placed on the outide of a clock going clockwie from 12to 9. The clock ha a radiu of 6 inche. What i the length of the tring
The length of the string is 37.7 inches string is placed on the outside of a clock going clockwise from 12 to 9.
To calculate the length of the string, first, start with the fact that the circumference of a circle is equal to pi multiplied by the diameter. The diameter of the clock is 12 inches, so then the circumference is 12π or 37.7 inches.
Since the string is going around the outside of the circle, the length of the string is equal to the circumference which is 37.7 inches. To get this answer, take the radius (6 inches) of the clock and double it to get the diameter (12 inches).
Multiply the diameter by pi (3.14) to get the circumference (37.7 inches) and then the length of the string is the same as the circumference.
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Correct question.
A string is placed on the outside of a clock going clockwise from 12 to 9. The clock has a radius of 6 inches. What is the length of the string?
What is the rule of the sequence 2 4 6?
The rule of the sequence 2 4 6 is that each term is obtained by adding 2 to the previous term.
In an arithmetic sequence, the rule is that each term is obtained by adding a fixed value (common difference) to the previous term. In this case, the common difference of the sequence 2 4 6 is 2. So, 2 is added to the first term (2) to get the second term (4), and 2 is added to the second term (4) to get the third term (6).
It is also possible to express the rule of the sequence by using the formula of an arithmetic sequence, which is a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the number of the term.
In this case, a_1 = 2, d = 2, so the rule of the sequence is a_n = 2 + (n-1)2 = 2n, where n is the number of the term.
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What is the area in square units of triangle def?
Triangle DEF is an isosceles triangle, with two sides of length 8 and one side of length 10.
We can use Heron's Formula to calculate the area of the triangle. Heron's Formula is A = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter, or half of the perimeter, and a, b, and c are the lengths of the sides of the triangle.
The semiperimeter of triangle DEF is (8+8+10)/2 = 16. Substituting these values into Heron's formula yields A = √(16(16-8)(16-8)(16-10)) = √(256(8)(8)(6)) = √11520 = 107.3.
Therefore, the area of triangle DEF is 107.3 square units.
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What is the domain of f x 4 x +1?
The domain of f(x) = 4x + 1 is all real numbers.
The domain of a function is the set of all input values for which the function is defined. As the expression f(x) = 4x + 1 does not contain any restrictions on the values of x, the domain of this function is all real numbers.
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is f(x) = 4x + 1, which does not have any restrictions on the values of x, thus the domain of this function is all real numbers. This means that all real numbers are valid input values, including negative numbers, positive numbers, fractions, irrational numbers, and all other real numbers. This means that regardless of the input value, the output will always be a real number. Thus, the domain of this function is all real numbers.
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Krista was assigned a homework problem that stated there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents. To solve this problem, she wrote the system of equations that is shown below.
0.40 x + y = 45. x + 0.55 y = 18.75.
Which explains the error that Krista made?
Krista was assigned a homework problem that stated there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents. To solve this problem, she wrote the system of equations that is shown below.
0.40 x + y = 45. x + 0.55 y = 18.75.
Which explains the error that Krista made?
Krista put 0.40 in the first equation meant for the number of stamps.
Krista did not use the correct decimal to represent the total cost of the stamps.
Krista mistakenly put 45 in the first equation when it should have been in the second equation.
Krista put 0.55 in the second equation meant for the value of stamps.
Krista put 0.40 in the first equation meant for the number of stamps. Therefore, option A is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, Krista was assigned a homework problem that stated there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents.
Let 40 cents stamps be x and 55 cents stamps be y.
Now, x+y=45 --------------(I)
0.40x+0.55y=18.75 --------------(II)
System of equations Krista written are
0.40x+y=45 and x+0.55y=18.75
Therefore, option A is the correct answer.
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How would the graph change if she already had $5 saved AND started saving $2.50 a week? Use the color blue
to represent this situation on the graph provided. Write the equation of the line represented in the graph.
Describe how the components of the equation represent the situation.
The linear function to model this problem is y = 2.50x + 5
What is Linear FunctionA linear function is a type of mathematical function that describes a straight line. A linear function is defined by an equation of the form:
y = mx + c
Where y is the dependent variable (the variable being measured or predicted), x is the independent variable (the variable being used to make the prediction or explanation), m is the slope of the line (the rate of change of y with respect to x), and c is the y-intercept (the value of y when x is zero).
The linear function to model this problem is given as;
y = 2.50x + 5
We can use a graphing calculator to represent this.
Kindly find the attached graph below
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Use the quadratic formula to find the solutions to the quadratic equation
below.
x-5x-4 = 0
O A. x =
O
-5+√41
2
B. x = 5±√41
O c. x =
C.
-5+√/29
D. x = 5√2
Answer:
A, B
Step-by-step explanation:
[tex]x^2-5x-4=0 \\ \\ x=\frac{5 \pm \sqrt{(-5)^2-4(1)(-4)}}{2}[/tex]
On simplifying, the correct answers are A and B.
What is a equivalent expression for 4x - 7y - 5z + 6 and -3x - 8y - 4 - 8/7z
The equivalent expressions for the expressions are
4x - 7y - 5z + 6 = 2(2x + 3) - 7y - 5z-3x - 8y - 4 - 8/7z = -3x - 4(2y - 1 - 2/7z)How to determine the equivalent expressionsFrom the question, we have the following parameters that can be used in our computation:
4x - 7y - 5z + 6 and -3x - 8y - 4 - 8/7z
Solving the first expression, we have
4x - 7y - 5z + 6
Rewrite as
4x + 6 - 7y - 5z
Factor out 2
2(2x + 3) - 7y - 5z
Solving the second expression, we have
-3x - 8y - 4 - 8/7z
Factor out 4
-3x - 4(2y - 1 - 2/7z)
Hence, the equivalent expression is -3x - 4(2y - 1 - 2/7z)
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which is the proper way to enter the following piece wise function into Desmos
The proper way to enter the piece-wise function into Desmos is given as follows:
y = 5x - 1 {x < -2}.y = x - 4 {x ≥ -2}.What is a piecewise function?A piecewise function is a function that has different definitions, based on the input of the function.
The definitions for this problem are given as follows:
Left of x = -2.Right of x = -2.The correct command to enter an interval in Desmos is between {}, hence the intervals are given as follows:
Left of x = -2 -> {x < -2}.Right of x = -2 -> {x ≥ -2}.The definitions of f(x) are entered using y = f(x), hence the correct option is given by the second option.
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If a1 = 4 and an = -3an-1 - 4 then find the value of a3
The 3rd term in the given sequence is 45
What is sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given that, first and nth term of a sequence a₁ = 4 and aₙ = 3aₙ₋₁ + n
a₁ = 4
aₙ = 3aₙ₋₁ + n
So, a₂ = 3a₂₋₁ + 2
= 3a₁ + 2
= 3×4+2
= 14
Therefore,
a₃ = 3a₋₁ + 3
= 3a₂ + 3
= 14×3+3
= 45
Hence, a₃ = 45
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Which equation represents a linear function?
�
=
1
�
y=
x
1
�
=
2
�
−
−
3
y=2x−−3
�
=
5
�
3
+
8
y=5x
3
+8
�
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2
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+
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y=x
2
+2x+1
Answer:
[tex]y = 2x - - 3[/tex]
That's the answer. Hope this helps
Please could you give me brainliest
What base value means?
There are some means for value. There are:
In mathematics and computing, a base value refers to the number of unique digits or symbols used in a numeral system.In other numeral systems, a different base value is used.In computer science, a base value is also used in the representation of data in different formats.BASE VALUEIn mathematics and computing, a base value refers to the number of unique digits or symbols used in a numeral system. For example, the most common base value used in everyday life is base 10, which uses the digits 0 through 9 to represent numbers. In this system, the number "42" represents the value 4 x 10¹ + 2 x 10⁰, or 42.In other numeral systems, a different base value is used. For example, in base 2, also known as binary, only the digits 0 and 1 are used. In this system, the number "1010" represents the value 1 x 2³ + 0 x 2² + 1 x 2¹ + 0 x 2⁰, or 10 in base 10.In computer science, a base value is also used in the representation of data in different formats. For example, in binary data, the base value is 2, while in hexadecimal data, the base value is 16. Understanding the base value and how to convert between numeral systems is important in computer science, as it helps in the understanding of how data is stored and processed by computers.Learn more about Base Value Explanation here:
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