Consider a branching process whose offspring generating function is b(s) = (1/6) + (5/6)s^2. Obtain the probability of ultimate extinction.
Enter your answer as an integer of the form m or a fraction of the form m/n. Do not include spaces.
Answers
Hence, the solution is `q = 1/5` or `0.2`(integer).
Consider the branching process whose offspring generating function is given by `b(s) = (1/6) + (5/6)s^2`.
Formula used: The probability of extinction is given by `q = 1 - p`, where `p` is the probability that the process continues indefinitely.
Suppose the probability generating function for the offspring distribution is `P(s)`.
Then, the generating function for the number of individuals in generation `n` is given by `f_n(s) = P(f_{n-1}(s))`.
The probability of ultimate extinction is the smallest nonnegative solution of `q = P(q)`.
The offspring generating function is `b(s) = (1/6) + (5/6)s^2`.
Therefore, the probability generating function is given by
`P(s) = b(s)
= (1/6) + (5/6)s^2`.
The probability of ultimate extinction is the smallest nonnegative solution of `q = P(q)`.
Therefore, we need to solve the equation `q = (1/6) + (5/6)q^2` for `q`.
Simplifying this equation, we get `5q^2 - 6q + 1 = 0`.
Using the quadratic formula, we get `q = (6 ± √16)/10
= (3/5) or (1/5)`.
Since `q` is the probability of ultimate extinction, it must be less than or equal to 1.
Therefore, `q = 1/5`.
To know more about integer visit:
https://brainly.com/question/15276410
#SPJ11
Related Questions
\( y^{\prime \prime}+3 t y-6 y-2 \) Find \( y(t) \) where \( y(0)=0 \) and \( y^{\prime}(0)=0 \)
Answers
The final solution to the given differential equation with the given initial conditions is:
\(\( y(t) = \frac{1}{21} e^{-6t} + \frac{2}{7} e^{t} - \frac{1}{3} \)\)
To find the solution y(t) for the given second-order ordinary differential equation with initial conditions, we can follow these steps:
Find the characteristic equation:
The characteristic equation for the given differential equation is obtained by substituting y(t) = \(e^{rt}\) into the equation, where ( r) is an unknown constant:
r² + 3r - 6 = 0
Solve the characteristic equation:
We can solve the characteristic equation by factoring or using the quadratic formula. In this case, factoring is convenient:
(r + 6)(r - 1) = 0
So we have two possible values for r :
\(\( r_1 = -6 \) and \( r_2 = 1 \)\)
Step 3: Find the homogeneous solution:
The homogeneous solution is given by:
\(\( y_h(t) = C_1 e^{r_1 t} + C_2 e^{r_2 t} \)\)
where \(\( C_1 \) and \( C_2 \)\) are arbitrary constants.
Step 4: Find the particular solution:
To find the particular solution, we assume that y(t) can be expressed as a linear combination of t and a constant term. Let's assume:
\(\( y_p(t) = A t + B \)\)
where \( A \) and \( B \) are constants to be determined.
Taking the derivatives of\(\( y_p(t) \)\):
\(\( y_p'(t) = A \)\)(derivative of t is 1, derivative of B is 0)
\(\( y_p''(t) = 0 \)\)(derivative of a constant is 0)
Substituting these derivatives into the original differential equation:
\(\( y_p''(t) + 3t y_p(t) - 6y_p(t) - 2 = 0 \)\( 0 + 3t(A t + B) - 6(A t + B) - 2 = 0 \)\)
Simplifying the equation:
\(\( 3A t² + (3B - 6A)t - 6B - 2 = 0 \)\)
Comparing the coefficients of the powers of \( t \), we get the following equations:
3A = 0 (coefficient of t² term)
3B - 6A = 0 (coefficient of t term)
-6B - 2 = 0 (constant term)
From the first equation, we find that A = 0 .
From the third equation, we find that \(\( B = -\frac{1}{3} \).\)
Therefore, the particular solution is:
\(\( y_p(t) = -\frac{1}{3} \)\)
Step 5: Find the complete solution:
The complete solution is given by the sum of the homogeneous and particular solutions:
\(\( y(t) = y_h(t) + y_p(t) \)\( y(t) = C_1 e^{-6t} + C_2 e^{t} - \frac{1}{3} \)\)
Step 6: Apply the initial conditions:
Using the initial conditions \(\( y(0) = 0 \) and \( y'(0) = 0 \),\) we can solve for the constants \(\( C_1 \) and \( C_2 \).\)
\(\( y(0) = C_1 e^{-6(0)} + C_2 e^{0} - \frac{1}{3} = 0 \)\)
\(\( C_1 + C_2 - \frac{1}{3} = 0 \) (equation 1)\( y'(t) = -6C_1 e^{-6t} + C_2 e^{t} \)\( y'(0) = -6C_1 e^{-6(0)} + C_2 e^{0} = 0 \)\( -6C_1 + C_2 = 0 \)\) (equation 2)
Solving equations 1 and 2 simultaneously, we can find the values of\(\( C_1 \) and \( C_2 \).\)
From equation 2, we have \(\( C_2 = 6C_1 \).\)
Substituting this into equation 1, we get:
\(\( C_1 + 6C_1 - \frac{1}{3} = 0 \)\( 7C_1 = \frac{1}{3} \)\( C_1 = \frac{1}{21} \)\)
Substituting \(\( C_1 = \frac{1}{21} \)\) into equation 2, we get:
\(\( C_2 = 6 \left( \frac{1}{21} \right) = \frac{2}{7} \)\)
Therefore, the final solution to the given differential equation with the given initial conditions is:
\(\( y(t) = \frac{1}{21} e^{-6t} + \frac{2}{7} e^{t} - \frac{1}{3} \)\)
Learn more about differential equation here:
https://brainly.com/question/32645495
#SPJ11
can someone help me with this problem? Thank you!
Answers
\(\qquad \sf \dashrightarrow \: 2x - 13 = 9\)
\(\qquad \sf \dashrightarrow \: 2x = 9 +13\)
\(\qquad \sf \dashrightarrow \: 2x = 22\)
\(\qquad \sf \dashrightarrow \: x = 22 \div 2\)
\(\qquad \sf \dashrightarrow \: x = 11\)
x = 11
2x = 13 + 9
2x = 22 |: 2
x = 11
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x)→0.] f(x)=9x−4x3,a=−2 Find the associated radius of convergence R. R=Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x)→0.] f(x)=9x−4x3,a=−2 Find the associated radius of convergence R. R = ____
Answers
To find the Taylor series for f(x) = 9x - 4x^3 centered at a = -2, we can start by finding the derivatives of f(x) and evaluating them at x = -2.
f(x) = 9x - 4x^3
f'(x) = 9 - 12x^2
f''(x) = -24x
f'''(x) = -24
Now, let's evaluate these derivatives at x = -2:
f(-2) = 9(-2) - 4(-2)^3 = -18 - 32 = -50
f'(-2) = 9 - 12(-2)^2 = 9 - 48 = -39
f''(-2) = -24(-2) = 48
f'''(-2) = -24
The Taylor series expansion for f(x) centered at a = -2 can be written as:
f(x) = f(-2) + f'(-2)(x - (-2)) + (f''(-2)/2!)(x - (-2))^2 + (f'''(-2)/3!)(x - (-2))^3 + ...
Substituting the values we calculated, we have:
f(x) = -50 - 39(x + 2) + (48/2!)(x + 2)^2 - (24/3!)(x + 2)^3 + ...
Simplifying, we get:
f(x) = -50 - 39(x + 2) + 24(x + 2)^2 - 4(x + 2)^3 + ...
The associated radius of convergence R for this Taylor series expansion is determined by the interval of convergence, which depends on the behavior of the function and its derivatives. Without further information, we cannot determine the exact value of R. However, in general, the radius of convergence is typically determined by the distance between the center (a) and the nearest singular point or point of discontinuity of the function.
Learn more about Taylor series here: brainly.com/question/32764971
#SPJ11
A woman is rowing a boat across a 60 wide river from west to east. She can row at 2 mph in still water, but the river's current is 5 mph from north to south. To the nearest foot, how far downstream on the east bank will she land?
Answers
Answer:
S, and the other day. I have been a while. I have a great drea the most important things. The may have to pay a fee of the most popular and I will not 66 the most of the most of my life. I was a bit of the best, but the 15th. I have been a while. I am your what is happening in the next couple days 6 the most of the most of the most
Step-by-step explanation:
popular and I will not be hurt by a friend of the day, and the other side, I think I have a great drea, I think I have been a while. I have been in touch. Thanks for the next day delivery. We have a great drea the same time. I was just the right place for the use of the most of the most popular and I am a beautiful person. The comments for your email.
The woman will land on the east bank of the river at a downstream of 37.5 miles.
What is meant by relative velocity ?Relative velocity of an object in motion is defined as the velocity of the object with respect to another object.
Here,
Width of the river, W = 60 miles
Velocity of the boat in still water, Vb = 2 mph
Velocity of river, Vr = 5 mph
Relative velocity of the boat with respect to river in downstream,
Vbr = Vb + Vr
Vbr = 8 mph
Drift of the boat, d = Vr W/Vbr
d = 5 x 60/8
d = 37.5 miles downstream
Hence,
The woman will land on the east bank of the river at a downstream of 37.5 miles.
To learn more about relative velocity, click:
https://brainly.com/question/19260269
#SPJ3
In space, how many planes can be perpendicular to a given line at a given point on that line in space?
A. 1
B.0
C. 3
D. infinitely many
Answers
In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.
The correct answer is Option D.
The key concept here is that a plane is defined by having at least three non-collinear points.
When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.
Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.
Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.
The correct answer is Option D.
For more such questions on perpendicular
https://brainly.com/question/1202004
#SPJ8
How do you answer this? (this is for slopes.)
Answers
Answer:
\(y= 2x + 4\)
Step-by-step explanation:
We are given an equation of \(2x-y+3 =-1\) and we need to put into \(y = mx+b\) form.
First, we subtract 3 on both sides to get the variables all on one side.
\(2x-y+(3 - 3)=(-1 -3)\\\\\)
\(2x-y = -4\)
We need to now isolate y on its own so we subtract \(2x\) on both sides.
\((2x-2x)-y=(-4-2x)\)
\(-y=-2x-4\)
We almost done! We then need to divide the invisible negative on both sides which is a -1.
\(\frac{-y}{-1}=\frac{-2x-4}{-1}\)
\(y=2x+4\)
When we divide the the negatives together, we know that two negatives divided together is a positive. Therefore, we get our answer \(y=2x+4\)
Hoped this helped!
Use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers. f(x)=x^3-5x^2-61x-55???
Answers
The polynomial function f(x) = x³ - 5x² - 61x - 55 has the following
Real zeros: x = -5, x = -1, and x = 11.
To find the rational zeros of a polynomial, we use the rational zeros theorem. We look at the factors of the leading coefficient and the factors of the constant coefficient.
The states that if a polynomial function is defined as P(x) = anxn + an-1xn-1 + ... + a1x + a0 with integers, then each rational zero of the polynomial can be expressed in the form p/q where p is a factor of a0 and q is a factor of an.
For example, if P(x) = 2x³ - 5x² + 3x + 6 then p can be any factor of 6 and q can be any factor of 2.
The factors of the leading coefficient, 1, and the factors of the constant coefficient, -55, are: ±1, ±5, ±11, ±55. So the possible rational zeros are: ±1, ±5, ±11, ±55, ±1/1, ±5/1, ±11/1, ±55/1, ±1/1, ±5/1, ±11/1, ±55/1.
Simplifying the results, we have that the potential rational zeros are: ±1, ±5, ±11, ±55, ±1, ±5, ±11, and ±55.
By testing each possible rational zero, we find that x = -5, x = -1, and x = 11 are the real zeros of f(x).
Hence, using synthetic division, we get:
(x + 5)(x + 1)(x - 11) = x³ - 5x² - 61x - 55
Thus, the function can be factored over the real numbers as
f(x) = (x + 5)(x + 1)(x - 11).
To learn more about Rational Zero Theorem: https://brainly.com/question/31070385
#SPJ11
a student is trying to solve the system of two equations given below:equation P: y + z = 6equation Q: 5y + 9z = 1Which of the following is a possible step used in eliminating the y-term?A: (y + z = 6) × 9B: (y + z = 6) × -5C: (5y + 9z = 1) × 9D: (5y + 9z = 1) × 5
Answers
we have the system
y + z = 6 ------> equation P
5y + 9z = 1 -----> equation Q
i will solve by elimination
step 1
Multiply the equation P by -5
so
(y + z = 6) *-5
-5y-5z=-30
adds equation Q
-5y-5z=-30
5y + 9z = 1
------------------
5z+9z=-30+1
therefore
the answer is the option Bsuppose p, q,and r are three independent and identically distributed poisson random variables with mean k. let w = 20p – 5q 10r. if the coefficient of variation of w is 0.8739, find k.
Answers
If the coefficient of variation of w is 0.8739, then the value of k is 1.1.
Given that, P, Q and R are three independent and identically distributed Poisson random variables with mean k.
Here,
\(E(P)=E(Q)=E(R)=k\)
\(V(P)=V(Q)=V(R)=k\)
Let \(W=20p-5Q+10R\)
\(= 20E(P)-5E(Q)+10E(R)\)
\(= 20k-5k+10k\)
\(= 25k\)
\(V(W)=V(20p-5Q+10R)\)
\(=400V(P)+25V(Q)+100V(R)\)
\(= 400k+25k+100k\)
\(= 525k\)
We know that, coefficient of variance is
\(C.V=\frac{\sigma}{\mu}\)
\(\frac{\sqrt{525k}}{25k}=0.8739\)
\(\sqrt{525k}=21.8475 k\)
\(525k = 477.313256 k^2\)
\(k=\frac{525}{477.313256}\)
\(k = 1.0999066\)
\(k\approx1.1\)
Therefore, the value of k is 1.1.
Learn more about the coefficient of variation here:
https://brainly.com/question/30992240.
#SPJ12
If x2=100 then x is___
1.1
2.10
3.-50
4.-10
5.1000
6.-1000
please click all correct answers
Answers
Answer:
2x=100 2*50=100 the answer correct 50
Can someone plz help me? :(
Answers
Answer:
The answer is A
Step-by-step explanation:
Both equal 48
how do you Round 96,286 to the nearest thousand.
Answers
Answer:
The correct answer is 96,000
Step-by-step explanation:
To round you look at the thousands place and there is a 9 then you look at the number to the right of it which is 2 and it is lower than 5 since it is lower than five it rounds down so the correct answer is 96,000.
HAVE A GOOD DAY!
Answer:
96,000
Step-by-step explanation:
If the number on the right of the nearest thousand is lower than 5 the nearest thousand and the numbers to the left of it stay the same, while the numbers on the right turn into 0(zeros) but if the number in the right of the nearest thousand is 5 or grater then the nearest thousand would go up one digit while the numbers on the left of the nearest thousand stay the same, while the numbers on the right of the nearest thousand turn to zeros.
Can someone please help i can’t tell which side the base would be and i don’t understand- i will mark brainliest if correct- Thanks !!
Answers
Answer:
Base = 4 units
Height = 8 units
I think the blocks are a unit each and you have to count how much space the triangle is taking up
Answer:
6
Step-by-step explanation:
Remark
This is one of those things that when you see it, you think that really is something.
The trick is to subtract a smaller right triangle from a larger one.
The base for both triangles is 4 (going from where the right angle is to your right where the lines of the red enclosure meet.
Calculations
The height of the larger triangle is 8
The height of the smaller triangle is 5
Area_L = 1/2 8 * 4 = 1/2 * 32 = 16
Area_S = 1/2 5 * 4 = 1/2 * 20 = 10
Red area = 1/2 * 32 - 1/2*20 = 16 - 10 = 6 units
What is the measurement of AB?
I will give brainiest to whoever answers it right.
Answers
The measurement of AB is given as follows:
AB = 16.23.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For the angle of 52º, we have that:
AB is the hypotenuse.10 is the length of the adjacent side.Hence the measurement of AB is obtained as follows:
cos(52º) = 10/AB
AB = 10/cos(52º)
AB = 10/0.616
AB = 16.23.
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
Work out the volume of the cone, giving your answer
to 3 significant figures.
Answers
Answer: 1010
Step-by-step explanation:
\(V=\frac{1}{3}(\pi)(8^{2})(15) \approx \boxed{\text{ } 1010 \text{ cm}^{3}}\)
if rx y= 0.83, then we can conclude that x and y have a relatively
Answers
If rxy = 0.83, we can conclude that x and y have a relatively strong positive linear relationship or correlation.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, in this case, x and y. The value of r ranges between -1 and 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable tends to increase as well.
In this case, with rxy = 0.83, the correlation coefficient is close to 1, suggesting a strong positive linear relationship. This means that when x increases, y also tends to increase, and vice versa. The closer the value of r is to 1, the stronger the linear relationship between x and y.
It is important to note that correlation does not imply causation. While a high correlation coefficient indicates a strong linear relationship, it does not provide information about the underlying cause or direction of the relationship between the variables. Other factors and variables may influence the relationship, and further analysis may be required to understand the nature of the relationship between x and y.
To learn more about correlation click here:
brainly.com/question/16169720
#SPJ11
7 less than 6 times a number is equal to 9 more than 4 times a number. What is the number?
Answers
Answer:
Write an equation the represents the words.
6x - 7 = 4x + 9
To solve for x (the number), isolate it from the other variables.
Subtract 9 from both sides.
6x - 7 - 9 = 4x
Combine like terms.
6x - 16 = 4x
Subtract 6x from both sides.
-16 = 4x - 6x
Combine like terms.
-16 = -2x
Divide both sides by -2.
-16/-2 = x
x = 8
The number is 8.
Hope this helps! :)
Answer:
The number is 8.
Step-by-step explanation:
Hello there!
We're given an unknown number, let's call this number n
We know that 7 less than 6 times n is equal to 9 more than 4 times n
Let's break that statement down, starting with "7 less than 6 times n"
6 times n should be 6n, since 6 * n = 6n
"7 less" means subtraction.
So "7 less than 6n" should be 6n-7
Now with "9 more than 4 times n"
4 times n should be 4n, as 4 * n = 4n
"9 more" means addition
So "9 more than 4n" should be 4n+9
The statement says that 6n-7 is equal to 4n + 9, and so when we write it as an equation:
6n - 7 = 4n + 9
Now we can solve the equation
Subtract 4n from both sides
2n - 7 = 9
Add 7 to both sides
2n = 16
Divide both sides by n
n=8
The number is 8
PS. we can substitute 8 back into the equation as n to see if it works:
6(8)-7=4(8)+9
Multiply
48-7=32+9
41= 32 + 9
41=41
It works :))
Hope this helps!
do all square numbers have an odd number of factors
Answers
No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.
A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.
When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.
However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.
In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.
To know more about factors, refer here:
https://brainly.com/question/5468231#
#SPJ11
HELP I NEED HELP ASAP
Answers
Answer:
A
Step-by-step explanation:
Yasmine worked on HW when she got home.
She spent 20 minutes doing Math, 10 minutes
doing SS, and 40 minutes doing ELA. What is
the ratio of minutes spent doing Math to total
minutes doing HW - in lowest terms?
Answers
Answer:
Step-by-step explanation:
Yasmine spent a total of 20 + 10 + 40 = <<20+10+40=70>>70 minutes doing homework.
The ratio of minutes spent doing Math to total minutes doing HW is:
20 minutes / 70 minutes = 2/7
To express the ratio in lowest terms, we can divide the numerator and denominator by their greatest common divisor, which is 2 in this case:
2/7 ÷ 2/2 = 1/3
Therefore, the ratio of minutes spent doing Math to total minutes doing HW in lowest terms is 1/3.
know more about greatest common divisor: brainly.com/question/13257989
#SPJ11
3 equals 10% of what?
Answers
Answer:
30
Step-by-step explanation:
3 equals 10% of what?
10% = 0.1
3 = 0.1x
divide both sides by 0.1
3/0.1 = 0.1x/0.1
x = 30
Answer:
x =10
Step-by-step explanation:
10/100 = 3/x
cross multiply and you get 300 = 10x
divide by 10 on both sides 10x/10 get canceled out you want to get the varaible on one side of the equation then divide 300/10 and you get 30 so your final answer is x=30 hope this helped you sorry if incorrect
2) How many y pieces are in 6/12?
Answers
Answer:
6 out of 12
Step-by-step explanation: there was 12 before but now there are 6 because probally somebody ate them
We cannot apply the characteristic polynomial and the quadratic formula to solve the second-order linear homogeneous ODE d2y/dt2+(7t3+cost)dy/dt+3ty=0, since it does not have constant coefficients.
a. true b. false
Answers
The method of variation of parameters or the method of undetermined coefficients to find the solution.
a. True
The method of solving a second-order linear homogeneous ODE using the characteristic polynomial and the quadratic formula applies only to equations with constant coefficients. The general form of such an equation is:
a(d^2y/dt^2) + b(dy/dt) + cy = 0
where a, b, and c are constants.
However, the given ODE has a non-constant coefficient in the term (7t^3+cost)dy/dt. Therefore, we cannot use the same method to solve it as we use for equations with constant coefficients.
Instead, we need to use other methods like the method of variation of parameters or the method of undetermined coefficients to find the solution to this ODE.
The method of variation of parameters involves assuming that the solution to the ODE can be written as a linear combination of two functions u(t) and v(t), where:
y(t) = u(t)y1(t) + v(t)y2(t)
where y1(t) and y2(t) are two linearly independent solutions to the corresponding homogeneous ODE. The functions u(t) and v(t) are found by substituting this form of the solution into the ODE and solving for the coefficients.
The method of undetermined coefficients involves assuming a particular form of the solution that depends on the form of the non-homogeneous term. For example, if the non-homogeneous term is a polynomial of degree n, then the particular solution can be assumed to be a polynomial of degree n with undetermined coefficients. The coefficients are then determined by substituting the particular solution into the ODE and solving for them.
In summary, the method of solving a second-order linear homogeneous ODE using the characteristic polynomial and the quadratic formula is only applicable to equations with constant coefficients. For ODEs with non-constant coefficients, we need to use other methods like the method of variation of parameters or the method of undetermined coefficients to find the solution.
To learn more about polynomial visit:
https://brainly.com/question/11536910
#SPJ11
NEED HELP ASSAP PLEASE!!! 30 POINTS!!
if a normal distribution has a mean of 154 and a standard deviation of 15, what is the value that has a z-score of 1.2?
A. 166
B. 196
C. 208
D. 172
Answers
Hence, The value that has a Z-Score of 1.2 is Option (D): 172
Step-by-step explanation:
Make A Plan:
Use the Z-SCORE FORMULA to find the value corresponding to the Given Z-SCORE
SOLVE THE PROBLEM: σ μ
1) - USE THE Z-SCORE FORMULA
Z = Z - μ / σ
Where Z is the Z-SCORE, X is the Value, μ is the Mean, and σ is the Standard Deviation
2) - Plug in the Given Values:
1.2 = z - 154 / 15
Solve For X:x = 1.2 * 15 + 154
We move all terms to the left:x - (1.2 * 15 + 154 ) = 0
We add all the numbers together,x - 172 = 0
x = 18 + 154
x = 172
Draw the conclusion:
Hence, The value that has a Z-Score of 1.2 is Option (D): 172
I hope this helps!
Explain in words and write mathematically how the Fundamental Theorem of Calculus is used to evaluate definite integrals. choose the correct answer below. Let f be continuous on [a,b]. To evaluate the definite integral of f using the Fundamental Theorem of Calculus, find any antiderivative of f and call it F. Then compute F(b) - F(a): the difference in the values of F between the upper and lower limits of integration. Written mathematically, f(x)dx = F(b)-F(a). Let f be continuous on [a,b].To evaluate the definite integral of f using the Fundamental Theorem of Calculus, find any antiderivative of f and call it F. Then compute F(b) - F(a): the sum of the values of F at the upper and lower limits of integration. Written mathematically f(x)dx = F(b) - F (a). Let f be continuous on [a,b].To evaluate the definite integral of f using the Fundamental Theorem of Calculus, find any derivative of f and call it f'. Then, compute f'(b) - f'(a): the difference in the values of between the upper and lower limits of integration. Written mathematically, f(x)dx = f'(b) - f'(a).
Answers
The Fundamental Theorem of Calculus is a powerful tool used to evaluate definite integrals. This theorem states that if a function f is continuous on a closed interval [a, b] then the definite integral of f from a to b can be evaluated by finding an antiderivative of f and computing the difference in values between the upper and lower limits of integration. In other words, if F is any antiderivative of f, then the definite integral of f from a to b can be written as f(x)dx = F(b) - F(a).
The fundamental theorem of calculus provides a shortcut to evaluating a definite integral, allowing us to calculate the area under a curve without having to actually compute the integral. This is done by first taking the derivative of f, which is also known as the derivative of the indefinite integral. This is referred to as the antiderivative of f, which we will call F. We then compute F(b) - F(a), which is the difference between the values of F at the upper and lower limits of integration. Written mathematically, this looks like f(x)dx = F(b) - F(a).
By using the Fundamental Theorem of Calculus, we can calculate the area under the curve of a continuous function, as well as other definite integrals. This theorem provides a shortcut to computing a definite integral, saving us time and effort. It is an invaluable tool in calculus and one that is often used by mathematicians and scientists.
To know more about Theorem of Calculus refer here:
https://brainly.com/question/30761130
#SPJ11
Find the solutions to the following system by substitution. y=2x+5
y=2x^2 −7
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There is no solution.
Answers
A system of equations: y = 2x + 5 and y = 2x^2 - 7.Therefore, the solution to the system of equations is (3, 11) and (-2, 1). So, the correct choice is A.
To solve the system of equations by substitution, we can start by solving one equation for one variable and then substituting that expression into the other equation. Let's solve the first equation for y:
y = 2x + 5
Now we can substitute this expression for y in the second equation:
2x + 5 = 2x^2 - 7
By rearranging the equation, we get:
2x^2 - 2x - 12 = 0
Next, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. After solving, we find that x = 3 or x = -2.
Substituting these values back into the first equation, we can find the corresponding values of y. For x = 3, y = 2(3) + 5 = 11. For x = -2, y = 2(-2) + 5 = 1.
Therefore, the solution to the system of equations is (3, 11) and (-2, 1). So, the correct choice is A.
Learn more about system of equations here:
https://brainly.com/question/32645146
#SPJ11
would the sample size be large enough if the population is school-aged children and young adults in the united states? explain in 2-3 sentences.
Answers
Yes, the sample size would be large enough if the population is school-aged children and young adults in the United States as this is a simple random sampling.
Simple random sampling is used for randomly selecting the sample size for research. No member in the population has a higher chance in comparison to others for selection in sampling. Every individual has an equal chance to be a part of the sample for the study. This is a type of probability sampling method.
The probability sampling method states that every individual has a fair and equal chance to be selected as a research sample. It includes simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Here the researchers have picked around 150 students and young adults which is an appropriate amount of simple random sample for the study.
Learn more about sampling methods here https://brainly.com/question/17743025
#SPJ4
Consider the control of Y(s) 10 (a) Let y = x1 and x1 = x2, and write state equations for the system. (b) Find K1 and K2 so that u = --K1x1 -K2x2 yields closed-loop poles with a natural frequency wn = 3 and a damping ratio = 0.5. (c) Design a state estimator that yields estimator error poles with wn1 = 15 and 21 = 0.5
Answers
The answer of the control of Y(s)= 10 are:
(a)The state equations for the system are:
\(\frac{dx_1}{dt} = x_2\\ \frac{dx_2}{dt} = Y(s) = 10\)
(b)The value of \(K_1\) = \(K_2 = \frac{3}{2}\)
(c)The desired pole locations α\(_1\)≈ -22.023 and α\(_2\) ≈ 7.523.
What is the quadratic formula?
The quadratic formula is a formula used to find the solutions (roots) of a quadratic equation of the form \(ax^2 + bx + c = 0\), where the coefficients are a, b, and c and x represents the variable.
(a) To write state equations for the system, we need to define the state variables and derive their dynamics based on the given control of Y(s) = 10.
Let y =\(x_1\)and \(x_1\)= \(x_2\). Therefore, our state variables are \(x_1\) and\(x_2\).
The state equations are for the system:
\(\frac{dx_1}{dt} = x_2\\ \frac{dx_2}{dt} = Y(s) = 10\)
(b) To find \(K_1\) and\(K_2\) for closed-loop poles with a natural frequency =3 and a damping ratio = 0.5, we can use the desired characteristic equation:
\(s^2 + 2\zeta w_ns + w_n^2 = 0\)
Substituting the given values, we have:
\(s^2 + 2(0.5)(3)s + (3)^2 = 0\\ s^2 + 3s + 9 = 0\)
Comparing this to the characteristic equation of the closed-loop system:
\(s^2\)+ (\(K_1\)+ \(K_2\))s + \(K_1\)\(K_2\)= 0
We can equate the coefficients to find \(K_1\) and \(K_2\):
\(K_1\) + \(K_2\) = 3 (coefficient of s term)
\(K_1\)\(K_2\)= 9 (constant term)
Here, we can see that \(K_1\) and \(K_2\) are the roots of the equation:
\(s^2 - 3s + 9 = 0\)
Using the quadratic formula, we find:
\(s = \frac{3 \pm\sqrt{(-3)^2 - 4(1)(9)}}{2(1)}\\ s =\frac{3 \pm\sqrt{-27}}{ 2}\\ s =\frac{3 \pm 3i\sqrt{3}}{ 2}\)
The values of \(K_1\) and \(K_2\) are the real parts of these complex conjugate roots, which are both equal to\(\frac{3}{2}\):
\(K_1\) = \(K_2 = \frac{3}{2}\)
Therefore, u = -\(K_1\)x1 - \(K_2\)x2 yields closed-loop poles with a natural frequency \(w_n\) = 3 and a damping ratio \(\zeta\) = 0.5.
(c) To design a state estimator that yields estimator error poles with \(w_n_1\) = 15 and \(\zeta_1\) = 0.5, we can use the desired characteristic equation:
\((s - \alpha)^2 = 0\)
where α is the desired pole location.
For \(w_n_1\) = 15 and\(\zeta_1\)= 0.5, we can calculate α as:
α = -\(\zeta_1\)\(w_n_1\pm w_n_1\sqrt{1 - \zeta_1^2}\)
α =\(-(0.5)(15) \pm (15)\sqrt{1 - 0.5^2}\)
α = -7.5 ± 15\(\sqrt{1 - 0.25}\)
α = -7.5 ± 15\(\sqrt{0.75}\)
α ≈ -7.5 ± 15(0.8660)
α ≈ -7.5 ± 12.99
The two desired poles for the estimator error dynamics are approximately:
α\(_1\) ≈ -20.49
α\(_2\) ≈ 5.49
Therefore, the state estimator should be designed such that the estimator error poles have \(w_n_1 = 15\) and \(\zeta_1\) = 0.5, which correspond to the desired pole locations α\(_1\)≈ -22.023 and α\(_2\) ≈ 7.523.
To learn more about the quadratic formula refer here
brainly.com/question/1214333
#SPJ4
How to calculate a rate or unit rate?
Answers
To calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.
What is rate ?
In mathematics, a rate is a ratio that compares two quantities with different units. It is typically expressed as the amount of change of one quantity with respect to another quantity. Rates are often used in the context of describing how quickly or slowly something changes over time or space.
To calculate a rate, we need to divide two quantities that have different units. For example, if we want to find the rate of a car's speed, we divide the distance traveled (in miles) by the time taken to travel that distance (in hours).
The formula for rate is:
rate = quantity / time
To calculate a unit rate, we need to divide a rate by the quantity being measured. For example, if the rate is the number of miles traveled per hour, the unit rate would be the number of miles traveled in one hour. To find the unit rate, we divide the rate by 1 hour.
The formula for unit rate is:
unit rate = rate / 1
When calculating rates or unit rates, it is important to make sure that the units of the quantities being divided are consistent. If the units are not the same, we need to convert them to the same unit before performing the division.
Therefore, to calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.
To know more about rate visit :
https://brainly.com/question/119866
#SPJ1
Pls Help me!A,B,C OR D
Answers
Answer:
D. y = - 2/3x - 3Step-by-step explanation:
The slope is - 2/3 and the point on the line is (-3, -1).
Find the y-intercept:
-1 = (-3)(-2/3) + bb = -1 - 2b = -3The line is:
y = - 2/3x - 3Correct choice is D
Equation in point slope form
y+1=-2/3(x+3)y+1=-2/3x-2y=-2/3x-3Option D