Consider a branching process whose offspring generating function is ɸ(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
The answer is 1/5.
To obtain the probability of ultimate extinction for a branching process, we need to find the smallest non-negative solution to the equation
ɸ(s) = s, where ɸ(s) is the offspring generating function.
Given ɸ(s) = (1/6) + (5/6)s², we set this equal to s:
(1/6) + (5/6)s² = s
Multiplying both sides by 6 to clear the fraction:
1 + 5s² = 6s
Rearranging the equation:
5s² - 6s + 1 = 0
To find the smallest non-negative solution, we solve this quadratic equation for s. Using the quadratic formula:
s = (-b ± sqrt(b² - 4ac)) / (2a)
where a = 5, b = -6, and c = 1:
s = (-(-6) ± sqrt((-6)² - 4 × 5 × 1)) / (2 × 5)
s = (6 ± sqrt(36 - 20)) / 10
s = (6 ± sqrt(16)) / 10
s = (6 ± 4) / 10
We have two possible solutions:
s₁ = (6 + 4) / 10 = 10 / 10 = 1
s₂ = (6 - 4) / 10 = 2 / 10 = 1/5
Since we want the smallest non-negative solution, the probability of ultimate extinction is s₂ = 1/5.
Therefore, the answer is 1/5.
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Related Questions
solve the system:
2x+6y=36
x+4y=20
Answers
Let's solve this problem step-by-step
Let's set:
2x + 6y = 36 -- equation 1
x + 4y = 20 -- equation 2
(equation 2) * 2
2x + 8y = 40 -- equation 3
(equation 3) - (equation 1)
2y = 4
y = 2 -- equation 4
Plug (equation 4)'s value of y into (equation 2)
x + 4(2) = 20
x = 20 - 8
x = 12
Thus x = 12 and y = 2
Let's check, by substituting these values
\(2x + 6y = 36\\2(12)+6(2) = 36\\24+12=36\\36=36\\\\x+4y=20\\12+4(2)=20\\12+8=20\\20=20\)
Answer: x = 12 and y = 2
Hope that helps!
The table shows the daily low temperature in Oymyakon for the first five days of
January, 2020.
Date:
January 1 January 2 January 3 January 4 January 5
Low temperature:
-42°F
-31°F
-40°F
-40°F
-44°F
What is the mean of the temperatures shown?
Answers
The mean of the temperatures shown is -39.4°F.
What is the mean temperature?
The average mean air temperature throughout a specific time period, typically a day, a month, or a year, as measured by a thermometer that has been properly exposed. The mean temperature is often calculated for the year and for each month in climatological tables.
Date: Low temperature:
January 1 -42°F
January 2 -31°F
January 3 -40°F
January 4 -40°F
January 5 -44°F
Mean = Total sum of all 5 days temperature / total number of days
Mean = -42 - 31 - 40 - 40 - 44 / 5
= -197 / 5
= - 39.4°F
Hence, the mean of the temperatures shown is -39.4°F.
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Subtract − 5 x 2 + 7 x + 1 −5x 2 +7x+1 from 8 x 2 + x − 10 8x 2 +x−10
Answers
Answer:
75x^2+12x-14
Step-by-step explanation:
75x^2+12x-14
168
100.8
5) Chloe earned 5 points for every 7 books she read. So, if she only read 1 book she would
have earned of a point. How many points for 3 books, 10 books and 13 books?
Answers
Answer:
Books read Points earned
7 5
1 0.71
3 2.14
10 7.14
13 9.28
Step-by-step explanation:
If Chloe read 7 books she would earn points = 5
Now for finding points earned for 1 book, we would divide 5 by 7
For 1 book she would earn points = 5/7 = 0.71 points
Now if 1 book is read, points earned are 5/7 or 0.71
Now, finding points earned for 3,10 and 13 books read:
For 3 books she would earn points = 5/7 * 3 = 2.14 points
For 10 books she would earn points = 5/7 * 10 = 7.14 points
For 13 books she would earn points = 5/7 * 13 = 9.28 points
So, The table would be:
Books read Points earned
7 5
1 0.71
3 2.14
10 7.14
13 9.28
A fence was installed around the edge of a rectangular garden. The length, 1, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
Answers
The dimensions of the garden are 12.5 feet by 30.5 feet.
To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.
Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,
we also know that the length of the fence, 1, was 5 feet less than 3 times the width,
w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45
Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5
Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5
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Are the two triangles similar. If so, State how
Answers
Answer:
SAS
Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)
For Anya's birthday her father gave out colorful birthday hats that were
cone shaped. Anya was very happy that day. The opening of the bottom of
the hat was 3 cm and the height of the cone was 7 cm. Anya fills her hat
with candy. What is the approximate volume of candy?
Answers
Answer: 21 cm is the volume
Step-by-step explanation: multiply 7cm x3 cm
can someone help me with both these questions asap?
15 points
Answers
Answer:
what am I looking at my fault og
random samples of size 100 are taken from an infinite population whose population proportion is .2. the mean and standard deviation of the sample proportion are:
Answers
The mean and standard deviation of the sample proportion are 0.2 and 0.04. The correct option is 0.2 and 0.04.
Based on the information provided, we can infer that the random samples of size 100 were taken from an infinite population with a population proportion of 0.2. This means that 20% of the population exhibits a certain trait or characteristic of interest.
The mean of the sample proportion is also 0.2, which is the same as the population proportion. This suggests that the sample is representative of the population and that the sample was drawn randomly.
The standard deviation of the sample proportion is 0.04, or 4%. This indicates that there is some variability in the sample proportions. However, it is not too high and suggests that the sample is reliable and consistent.
In conclusion, based on the mean and standard deviation of the sample proportion, we can say that the sample is representative of the population and that the estimates obtained from the sample are reliable and accurate. It is important to note that the size of the sample is relatively large (100) and this helps to increase the accuracy and precision of the estimates. The correct option is 0.2 and 0.04.
The complete question is;
Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are
0.2 and .04
0.2 and 0.2
20 and .04
20 and 0.2
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Question 3The number is equivalent toAB-0.625C 0.58D
Answers
Divide -5 by 8
\(To\text{ find the value of -5 divided by 8, divide only 5 by 8 and a put a negative sign to the value obtained}\)So 5/8 is 0.625. So, -5/8 is 0.625
When Julius crossed the Rubicon, he had with him 3 times as many soldiers as he
needed to conquer Rome. If he had 26,000 soldiers with him, how many were needed
to conquer Rome?
Answers
86,000 :)
hope it helped!
An object is sighted from a helicopter at an angle of
depression of 58°. After the helicopter has traveled 7.0
km, the angle of depression to the same side of the object.
is 64°. Determine the distance at that point from the
helicopter to the object.
(THIS IS TRIG)
Answers
The distance at that point from the helicopter to the object is 7km
How to determine the valueTo determine the value, we need to know the different trigonometric identities.
These identities are listed thus;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that the;
The angle at the point of the object is expressed as;
180 - (64 + 58)
add the values, we have;
180 - (122)
Now, subtract the values, we get;
58 degrees
Since, the angle measure is equal , then, we have that;
The distance = 7km
Hence, the distance is 7km
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El primo de la señora Martha fue a pedir un préstamo de $1800 bajo las mismas condiciones que la señora Martha ¿cuánto pagara de interés en primo de la señora Martha?
Answers
Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
What is interest in a simple definition?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.Interest is the money you owe when borrowing or receive when lending. Lenders calculate interest as a percentage of the loan amount. Consumers can earn interest by lending money (such as through a bond or certificate of deposit) or depositing funds into an interest-bearing bank account.The three types of interest include simple (regular) interest, accrued interest, and compounding interest.Since Mrs. Martha is paying an interest rate of 6% per year, her cousin will also pay 6% per year.
To calculate the amount of interest paid, we can use the formula:
Interest = Principal * Rate * Time
Where:
Principal = $1800Rate = 6% (or 0.06 as a decimal)Time = 1 yearSo:
Interest = $1800 * 0.06 * 1 = $108
Therefore, Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
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A hexagon is inscribed in a circle As see in the picture.Find the length of an arc between consecutive vertices. Round to the nearest hundred
Need help homework
Answers
Answer:
The length of the arc between consecutive vertices is:
\(S=8.38\: in\)
Step-by-step explanation:
The angle between consecutive vertices is 60°, it is because it forms an equilateral triangle.
Now, the length arc is defined as:
\(S=R\theta\)
Where:
R is the radius (R = 8 in)θ is the angle of the arcWe see the angle is in grades, but we need to convert it to radians.
\(\theta=\frac{60^{\circ}}{360^{\circ}}(2\pi)\)
\(\theta=1.05\: rad\)
Finally, the length of the arc between consecutive vertices will be:
\(S=8*1.05\)
\(S=8.38\: in\)
I hope it helps you!
How does changing the sign of the constant a from positive to negative affect the domain and range of f(x) = a|x|?
Answers
When changing the sign of the constant a from positive to negative, the domain remains the same. But the range changes.
A function's range is the set of all values it can accept, whereas its domain is the set of all values for which it is defined.
Consider the given function f(x)=a|x|. Let us consider "a" takes positive values that is \(a\geq0\). Then, the given function is defined as follows,
\(f(x)=\begin{cases}a(x)=ax}\; &x\geq0\\{a(-x)=-ax\;&x < 0\end{cases}\)
Then, the domain will be \(\text{domain}=\mathbb{R}\{(-\infty, \infty)\) and the range will be given as \(\text{Range} = \text{only non-negative real numbers} = \mathbb{R}^++\{0\}\).
Now let us consider "a" takes negative values that is a<0. Then, the given function is defined the same and the domain will remain the same. But the range will be given as \(\text{Range} = \text{only negative real numbers} = \mathbb{R}^-+\{0\}\).
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Pls help brainiest to the correct answer!
Answers
Answer:
a) 9, b) 87, c) - 2, d) - 9Step-by-step explanation:
a) - 2 * (- 4.5) = 9b) (- 8.7) * (- 10) = 87c) (- 7) * (-2) = 14d) (- 9) * (- 10) = 90#a
\(\\ \sf{:}\dashrightarrow -2(-4.5)=9.0\)
#b
\(\\ \sf{:}\dashrightarrow (-8.7)(-10)=8.7\)
#c
\(\\ \sf{:}\dashrightarrow (-7)(-2)=14\)
#d
\(\\ \sf{:}\dashrightarrow (-9)(-10)=90\)
In a freefall skydive, a skydiver begins at an altitude of 10,000 feet. during a freefall, the skydiver drops toward earth towards earth at a rate of 175 ft per second. the height of the skydiver from the ground can be modeled using the function H(t)=10,000-175t.
What is the domain of the function for this situation?
Answers
Answer:
{\(t|0\leq t\leq 50\)}
Step-by-step explanation:
We are given that
In a freefall skydive, a skydiver begins at an altitude during free fall =10,000 feet
The skydiver drops towards earth at a rate=175 ft/s
The height of the skydiver from the ground can be modeled using the function
\(H(t)=10000-175t\)
We have to find the domain of the function for this situation.
When t=0
Then ,\(H(0)=10,000 feet\)
From given graph we can see that the value of t lies from 0 to 50.
Therefore, the domain of the function for this situation is given by
{\(t|0\leq t\leq 50\)}
Write the word sentence as an inequality
A number y divided by 6 is no more than 2
Answers
Answer:
Y/6 <_ 2
Step-by-step explanation:
(Less than it equal to sign)
Voting in Hillsboro's annual school board elections has been going down by 5% from one election to the next. If 900 parents voted this year, how many will vote 9 years from now?
If necessary, round your answer to the nearest whole number.
Answers
9514 1404 393
Answer:
567
Step-by-step explanation:
The multiplier each year is 1 -5% = 0.95. Applying that multiplier 9 times gives ...
900(0.95^9) ≈ 567
About 567 voters are expected to vote 9 years from now.
There are 5 children running in a relay race. in a relay race, each person runs part of the race. the next runner starts where the previous runner stops. each runner runs the same distance. in this relay race, each child runs of a mile, then stops so the next , a runner can continue. plot the point on the number line that represents the location where the fourth child will stop running.
Answers
The location where the fourth child will stop running in the relay race is 4/5 of the way.
To determine the location where the fourth child will stop running in the relay race, we need to find out the total distance covered by the first four children.
Since each child runs 1/5 of a mile, we can find the total distance for the first four children by multiplying their individual distances.
Total distance = (Number of children) * (Distance run by each child)
Total distance = 4 * (1/5)
Now, let's multiply:
Total distance = 4/5
So, the fourth child will stop running at a location 4/5 of a mile from the starting point. To plot this point on a number line, locate the point between 0 and 1 that is 4/5 of the way. This point represents the location where the fourth child will stop running in the relay race.
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in order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at an auto repair shop take per year. a previous study indicated that the standard deviation was days. how large a sample must be selected if the company wants to be confident that the true mean differs from the sample mean by no more than day?
Answers
the sample size must be at least 384 full time workers in order for the insurance company to be confident that the true mean differs from the sample mean by no more than 1 day.
We can use a margin of error of 1 day and a confidence level of 95% to calculate the required sample size. This can be calculated using the formula n = (z*σ/e)², where n is the sample size, z is the z-score corresponding to the confidence level (1.96 for 95%), σ is the standard deviation (given as 5 days in the question), and e is the margin of error (given as 1 day in the question). Plugging these values into the equation, we get n = (1.96*5/1)² = 384. Therefore, the sample size must be at least 384 full time workers in order for the insurance company to be confident that the true mean differs from the sample mean by no more than 1 day.
n = (z*σ/e)²
n = (1.96*5/1)²
n = 384
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Have an Amazing day!!!!
Answers
Answer: DHSJDJSJSJ I LOVE THAT
Step-by-step explanation:
Answer:
I LOVE THISSSSSSSSSSSSSSSSSSSSSSSSSSS BROOOOOO
Step-by-step explanation:
The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5.
A table with 6 columns and 2 rows. The first column, Original System has 2 y minus x equals 8 and y minus 2 x equals negative 5. The second column, Equivalent System, has 2 y minus x equals 8 and negative y plus 4 x equals 10. The third column, Sum of equations in Equivalent System, has 3 x equals 18. The fourth column, Solution to System, is blank. The fifth column, New System Using Sum, has2 y minus x equals 8 and 3 x equals 18. The sixth column, Solution to New System is blank.
Which solution can be used to fill in both blanks in the table?
Answers
The solution to the system and the solution that fills the blank space is (6, 1)
System of equationsThis are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions
Given the following system of equations
2y − x = 8, and
y − 2x = −5.
From equation 2;
y = -5 + 2x ............. 3
Substitute equation 2 into equation 1 to have:
2(-5+2x) - x = 8
Expand to have:
-10 +4x -x = 8
-10 + 3x = 8
3x = 8 + 10
3x = 18
Divide both sides
by 3
3x/3 = 18/3
x = 6
Substitute x = 6 into equation 3
y = -5 + 2x
y = -5 + 2(3)
y = -5 + 6
y = 1
Hence the solution to the system and the solution that fills the blank space is (6, 1)
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Answer:
Its D (6,7)
Step-by-step explanation:
3.In an online quiz, positive points are awarded for a correct answer, and negative
points are awarded for an incorrect answer. Elena answers 10 questions correctly and
4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.
a. Write a system of equations that describes Elena's and Kiran's scores. Usex to
represent the number of points for a correct answer and y to represent the
number of points for an incorrect answer.
that
X represents number of points and y represents incorrect answer
Answers
The system of equations can be written as:-
10x + 4y = 42
6x + 8y = 14
What is a system of equations?A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.
Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.
The system of equations can be written as:-
10x + 4y = 42
6x + 8y = 14
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You want the volume of the box to be 9 cubic inches.
Find the rational solution(s) of the equation. Then use polynomial long division to find the other solution(s).
What are the possible side lengths of the box?
Answers
Answer: x^3
Step-by-step explanation: it has no cube so its 3^x or x^3
Find the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame.
Answers
Answer:
The length is 5.
Step-by-step explanation:
Since the proportions are the same, 3 is 3 times less than 9. The same applies to 15, which 3 times less would be 5. It has a ratio of 3:5.
Write a news article detailing the importance of Washington's strategy leading to the British Hessian surrender.
4-8 sentences please!
Answers
Washington destroyed a powerful garrison of Hessian mercenaries in the Battle of Trenton (December 26) before withdrawing.
What are Articles?A noun, which might be a name for a person, place, thing, or idea, is modified by a word known as an article. In terms of grammar, an article is any word that modifies a noun, or an adjective. Articles are used to identify or refer to nouns rather than adjectives, which are typically used to modify nouns through description. The definite and indefinite articles are the two types of articles we use to identify or refer to a noun or group of nouns in writing and conversation.Each of these articles is used to refer to a noun, but the noun isn't a particular person, place, thing, or concept. Any noun from a group of nouns may be used.Hence, Washington destroyed a powerful garrison of Hessian mercenaries in the Battle of Trenton (December 26) before withdrawing.
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rate of change for y=5x+25
Answers
Answer:5
Step-by-step explanation:
rate of change is the same thing as slope (or m)
The required rate of change for the given equation y = 5x + 25 is 5.
Given that,
For the given equation y =5x +25 the rate of change is to be determined.
The slope of the line is the tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is the rate of change?The rate of change is defined as the change in value with the rest of the time is called rate of change.
Here,
The given equation,
y = 5x + 25
Differentiate the above equation with respect to x,
dy/dx = d(5x +25)/dx
dy/dx = 5dx/dx + d25/dx
dy/dx = 5 (since dx/dx =1 and d25/dx = 0)
here dy/dx is the slope of the equation or m or rate of change = 5
Thus, the required rate of change for the given equation y = 5x + 25 is 5.
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This one also thx PLZZ be right
Answers
Answer:
D. x = 2
Step-by-step explanation:
\(\frac{1}{2} x+3=\frac{5}{2} x-1\)\(\frac{1}{2} x-\frac{5}{2 }x=-1-3\)\(-\frac{4}{2} x=-4\)\(-\frac{4}{2} x (-\frac{2}{4} )=-4(-\frac{2}{4} )\)\(x = -4(-\frac{2}{4} )\)\(x=2\)Answer:
x=2
Step-by-step explanation:
1/2x+3=5/2x-1
-1/2x -1/2x
3=4/2x-1
+1 +1
4=2x
/2 /2
2=x
WILL GIVE BRAINLIEST (PLEASE SHOW WORK)
Evaluate sec (11pi/6) without using technology
Answers
