Probability of ultimate extinction: To get the probability of ultimate extinction in a branching process, we need to calculate the value of o(q) = q where q is the probability of ultimate extinction.
Now, o(s) = (1/6) + (5/6)s²
Therefore, for the probability of ultimate extinction,
o(q) = q = (1/6) + (5/6)q²=> 6q² - 5q + 1 = 0
On solving the quadratic equation,
we get q = 1 or q = 1/6.
Thus, the probability of ultimate extinction is 1/6. Mean time to extinction:
To calculate the mean time to extinction, we can use the formula, E(T) = (1/o'(1))
where o'(1) is the first derivative of the generating function o(s) evaluated at s = 1.
Now, o(s) = (5/6) + (1/6)s=> o'(s) = (1/6)
On substituting s = 1, o'(1) = (1/6).
Thus, E(T) = (1/o'(1))= (1/ (1/6))= 6
The mean time to extinction is 6.
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which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p qi)i p = 3, q = 7 p = –3, q = 7 p = 3, q = –7 p = –3, q = –7
The values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.
Let's expand the expression:
(3 - 7i)(p + qi)i = (3 - 7i)(pi - q)
Using the distributive property, we have:
= 3pi - 7pi^2 - 3qi + 7qi^2
Since i^2 is equal to -1, we can substitute -1 for i^2:
= 3pi - 7p - 3qi - 7q
Now, equating the imaginary part to 58i:
-7p - 7q = 58
Dividing both sides by -7:
p + q = -8
From the given options, only p = 3 and q = -7 satisfy this equation:
3 + (-7) = -4
Therefore, the values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.
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Which is the proper interpretation of a 95% confidence interval of a proportion of U.S. adults who own a sports car with an upper limit of 27% and a lower limit of 22%? O l am 5% confident the true proportion of U.S. adults who own a sports car is between 22% and 27%. I am 95% confident the sample proportion of U.S. adults who own a sports car is between 22% and 27%. I am 95% confident the true proportion of U.S. adults who own a sports car is between 22% and 27%. o I am 5% confident the sample proportion of U.S. adults who own a sports car is between 22% and 27%.
There is a high level of confidence that the true proportion lies within the interval of 22% to 27%
The proper interpretation of a 95% confidence interval of a proportion of U.S. adults who own a sports car with an upper limit of 27% and a lower limit of 22% is:
I am 95% confident that the true proportion of U.S. adults who own a sports car is between 22% and 27%.
This interpretation accurately conveys the meaning of a confidence interval. It means that if we were to take multiple random samples and calculate 95% confidence intervals using the same methodology, approximately 95% of those intervals would contain the true proportion of U.S. adults who own a sports car. Therefore, there is a high level of confidence that the true proportion lies within the interval of 22% to 27%.
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In the June 1986 issue of Consumer Reports, some data on the calorie content of beef hot dogs are given. Here are the numbers of calories in 20 different hot dog brands: 186, 181, 176, 149, 184, 190, 158, 139, 175, 148, 152, 111, 141, 153, 190, 157, 131, 149, 135, 132. Assume that these numbers are the observed values from a random sample of independent normal random variables with standard deviation o= 4 calories. Find a 90% confidence interval for the mean number of calories u.
The 90% confidence interval for the mean number of calories is 155.3 to 158.4
Finding a 90% confidence interval for the mean number of calories u.From the question, we have the following parameters that can be used in our computation:
The dataset
The mean is calculated as
x = sum/count
So, we have
x = (186 + 181 + 176 + 149 + 184 + 190 + 158 + 139 + 175 + 148 + 152 + 111 + 141 + 153 + 190 + 157 + 131 + 149 + 135 + 132) / 20
x = 156.85
Calculate the margin of error using
E = t * σ/√n
Where t = 1.729 i.e. the critical value
So, we have
E = 1.729 * 4/√20
Evaluate
E = 1.55
The confidence interval is then calculated as
CI = x ± E
So, we have
CI = 156.85 ± 1.55
Evaluate
CI = 155.3 to 158.4
Hence, the 90% confidence interval for the mean number of calories is 155.3 to 158.4
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Is (3,10) a solution to this system of equations?
y=2x+3
y=x+7
Answer: no
Step-by-step explanation:
plug in (3,10) to y=2x+3
10=2(3)+3
10=6+3
10[tex]\neq[/tex]9
identify the vertical asymptote(s) of each function. check all of the boxes that apply. x = -8 x = -2 x = -1 x = 1 x = 2 x = 8
The correct boxes to check are x = 1 and x = 2.
To identify the vertical asymptotes of the function f(x) = (x - 8) / ([tex]x^{2}[/tex]- 3x + 2), we need to determine the values of x for which the denominator of the function becomes zero. These values will give us vertical asymptotes.
Breaking the denominator into the factors :
[tex]x^{2}[/tex] - 3x + 2 = (x - 1)(x - 2)
Setting the denominator equal to zero:
x - 1 = 0 --> x = 1
x - 2 = 0 --> x = 2
So, the vertical asymptotes of the function are:
x = 1 and x = 2.
Now, let's check for diffrent values of x:
x = -8 (This is not a vertical asymptote as it is not related to the function's denominator.)
x = -2 (This is not a vertical asymptote as it is not associated with the function's denominator.)
x = -1 (This is not a vertical asymptote as it is not related to the function's denominator.)
x = 1 (This is a vertical asymptote.)
x = 2 (This is a vertical asymptote.)
x = 8 (This is not a vertical asymptote as it is not related to the function's denominator.)
Therefore, the correct boxes to check are x = 1 and x = 2.
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The correct question is given below -
Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)=x-8/[tex]x^{2}[/tex]-3x+2
x = -8
x = -2
x = -1
x = 1
x = 2
x = 8
Answer:
D and E for the first one. B and D for the second one
Step-by-step explanation: edg is stinky, i hope this helped a little
which statement best explains why ben uses the width hi to create the arc at j from point k?
By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.
Which statement best explains why Ben uses the width BI to create the arc JK from point E?
A. ∠DEF ≅ ∠ABC when BH = EK, BI = JK, and HI = EJ.
B. BI = JK when ∠DEF ≅ ∠ABC.
C. BI = EJ when ∠DEF ≅ ∠ABC.
D. ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.
The statement Ben explains why Ben uses the width BI to create the arc JK from point E is ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.
The correct option is (D).
Ben ensuring that for making an arc JK,
BH = EJ
BI = EK
HI = JK
These are the three congruent corresponding sides for making an arc.
then, he will use the congruence criteria to ΔDEF ≅ ΔABC.
By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.
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Which statement best explains why Ben uses the width BI to create the arc JK from point E.
HELP ME FIND AREA I WILL MARK BRAINLEST
Answer:
472
Step-by-step explanation:
break it up into two rectangles
1) 12x18=216 in
2) 8x32=256
Hope this helped
Answer:
472 in²
Step-by-step explanation:
The figure is composed of 2 rectangles , then
area = area of lower rectangle + area of upper rectangle, that is
area = (8 × 32) + (12 × 18) = 256 + 216 = 472 in²
Which graph represents all the real numbers, , where ≥−2? THIS IS LAST QUESTION PLEASE ANSWER! I WILL GIVE BRAINLYST.
Answer:
It's the one right under the first one
A recipe for cooking rice indicates that 14 cups of boiling water are needed for 8 cups of rice.
if henri has 28 cups of boiling water how much cups of rice should he add
(WILL GIVE BRAINLIST FOR BEST ANSWER!)
Hello!
This is a question about ratios and relating them to multiples of the ratio.
We are given that a recipe for cooking rice requires 14 cups of boiling water for every 8 cups of rice.
Then we are asked how many cups of rice are needing to be added if we have 28 cups of boiling water.
Since 28 is two times 14, and assuming that this ratio is proportional, we can multiply the cups of rice by 2 to find the equal ratio.
That means that 16 cups of rice should be added if we have 28 cups of boiling water.
In terms of ratios, we can set up the following proportion.
[tex]\frac{14}{8}=\frac{28}{x}[/tex]
Then here, we can cross multiply and solve for [tex]x[/tex].
[tex]14x=224[/tex]
[tex]x=16[/tex]
Hope this helps!
19. Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left. What was the weight of each bag? Use a tape diagram and show your calculations. Focus
The weight of each bag of the mixture can be determined by using a tape diagram. Given that Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios, and after filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left.
A tape diagram is a bar model that is used to represent fractions and ratios visually. It is useful when comparing different quantities that are related to each other.Tape DiagramTo solve the problem using a tape diagram, we begin by representing the total weight of the mixture and the weight of each bag using a single length unit. For example, we can choose 1 inch to represent the weight of 1 pound.
In this case, we would represent the total weight of the mixture as 5.15 + 4.32 = 9.47 inches. Next, we divide the total length by the number of bags to find the length of each bag. If the total length of the mixture is 9.47 inches and there are 6 bags, then the length of each bag is:9.47 ÷ 6 = 1.578 inches. Finally, we convert the length of each bag back to pounds by multiplying by the weight of 1 pound, which is 1 inch in our tape diagram. Thus, the weight of each bag is:1.578 × 1 = 1.578 lb. Therefore, the weight of each bag of the mixture is 1.578 lb.
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PLS PLS HELP WILL MARK BRAINLIEST
Answer:
d: 83
e: 97
f: 83
Step-by-step explanation:
d: We first have to find out f, so f and d can be alternate interior angles, which means they can be congruent to each other.
e: e is a vertical angle to the given angle, which means they are congruent, making it also 97 degrees.
f: f is a supplementary angle to the given angle, which means we can subtract 97 from 180 to give us 83.
Going back to angle d, now that we know f is 83 degrees, then d is an alternate interior angle, so d=f, meaning d is also 83 degrees.
Hope this helps! :)
a converging lens with a focal length of 6.70 cmcm forms an image of a 4.80 mmmm -tall real object that is to the left of the lens. the image is 1.50 cmcm tall and erect.
A converging lens with a focal length of 6.70 cm forms an erect image of a 4.80 mm tall real object positioned to the left of the lens. The resulting image is 1.50 cm tall.
A converging lens is a lens that bulges in the middle and causes light rays to converge. In this case, the lens has a focal length of 6.70 cm, which means that parallel rays of light incident on the lens will converge to a point 6.70 cm away from the lens. The object, positioned to the left of the lens, has a height of 4.80 mm. When the light rays from the object pass through the lens, they refract and intersect at a point to form the image. The image formed is erect, meaning it is in the same orientation as the object. The height of the image is 1.50 cm.
The magnification of the image can be calculated using the formula: magnification = height of image / height of object. In this case, the magnification is 1.50 cm / 4.80 mm. To convert the height of the object to centimeters, we divide 4.80 mm by 10, which gives us 0.48 cm. Therefore, the magnification is 1.50 cm / 0.48 cm, which equals approximately 3.125.
Since the image is erect and the magnification is greater than 1, we can determine that the image is larger than the object. The positive magnification indicates that the image is virtual, which means it cannot be projected onto a screen. The image is formed on the same side of the lens as the object, which is the left side in this case. The image distance can be calculated using the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. Since the image is formed on the same side as the object, the object distance is negative (-u). By plugging in the values, we can solve for the image distance. However, additional information, such as the object distance, would be needed to calculate the exact position of the image.
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use the information provided to write the equation of each circle
Answer:
1.
centre(h,k)=(-13,9)
radius (r)=6
we have
equation of the circle is
(x-h)²+(y-k)²=r²
(x+13)²+(y-9)²=6²
x²+26x+169+y²-18y+81=36
x²+y²+26x-18y+169+81-36=0
x²+y²+26x-18y +214=0
is a required equation of the circle.
2.
centre(h,k)=(1,-1)
radius (r)=11
we have
equation of the circle is
(x-h)²+(y-k)²=r²
(x-1)²+(y+1)²=11²
x²-2x+1+y²+2y+1=121
x²+y²-2x+2y=121-2
x²+y²-2x+2y=119
is a required equation of the circle.
Write an equation in terms of x and y for the function that is described by the given characteristics. a cosine curve with a period of , an amplitude of 1, a left phase shift of , and a vertical translation down by 9/2 of a unit.
The equation for the described function can be written as:
y = cos(x - π) - 9/2
Let's break down the components of the equation:
The cosine function, cos(x), produces a periodic wave with an amplitude of 1.
The period of the cosine curve is determined by the coefficient in front of the angle, which is 1 in this case. A period of 1 corresponds to one complete cycle of the cosine curve.
The left phase shift of π shifts the entire curve to the right by π units.
The vertical translation down by 9/2 units shifts the entire curve downwards by 9/2 units.
Therefore, the equation y = -cos(x - π) - 9/2 represents a cosine curve with the given characteristics.
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Find the unit rate.
2 2/5 to 3 3/4
Answer:
2 2/5=5/5+5/5+2/5=12/5
3 3/4= [(3•4)+3]/4=15/4
(12/5) / (15/4)= 12/5 • 4/15=12•4/5•15=
48/75 kilometers in 1 minute
Step-by-step explanation:
How that this helps! :)
Have a great rest of your day/night!
please help me ......
Answer:
no solution
Step-by-step explanation:
Help please with number 1. Writw the orderd pair that coresponds to Point H.
Answer: yeah you got it
Step-by-step explanation:
2
Select the correct answer from each drop-down menu.
Consider polynomial function f.
f(x) = (1 - 1)?(1 + 3)3 (+ 1)
Use the equation to complete each statement about this function.
The zero located at x = 1 has a multiplicity of , and the zero located at x = -3 has a multiplicity of
The graph of the function will touch, but not cross, the x-axis at an x-value of
Reset
Next
Answer:
2 of the 3 answers in picture
Step-by-step explanation:
Answer:
The answers are 2, 3, and 1 only
Step-by-step explanation:
This is the correct answer for plato users
An angle measures 52° more than the measure of its complementary angle. What is the measure of each angle?
Please help.
Is algebra.
I need help with this ( see image). Please show workings.
Answer:
32. (E)stopped at 2pm
33. (A)
Step-by-step explanation:
32. on the graph you go across the x axis and find where the straight line starts and look for the time
33. look at the y-axis and see what line and the number it is on
Similar to the univariate t-test, the bivariate t-test
a. requires ratio or interval data.
b. assumes that samples are drawn from populations with normal distributions.
c. is especially helpful when the sample size is large (n>80).
d. is useful when the population standard deviation is known.
e. All of the above
Similar to the univariate t-test, the bivariate t-test has all of the mentioned characteristics, so, E. All of the above.
What are the similarities?The univariate and bivariate t-tests are different in the fact that while one measures only one variable, the other measures two variables.
The similarities between these tests include the fact that they both require ratio or interval data, they are both drawn from populations with normal distributions and they are useful for analyzing large sample sizes. Also, the two tests ate useful when the population's standard deviation is known.
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pls solve this
(-21) x [(-4) + (-6)] = [(-21) (-4)] +[(-21)×(-6)]
Answer:
ree kid it is 3409,3567
Step-by-step explanation:
Ben rolls a number cube 50 times. He records the result of each roll in the table below.
RESULTS OF ROLLING NUMBER CUBE
Outcome 1 2 3 4 5 6
Frequency 7
6
5
11
10
11
Based on the data, which statement is true?
Ben will roll an even number about 250 times if the number cube is rolled 500 times.
Ben will roll an even number about 220 times if the number cube is rolled 500 times.
Ben will roll an even number about 700 times if the number cube is rolled 1,000 times.
Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.
Answer:
picture ?
Step-by-step explanation:
PLZZZ HELP!! BRAINLIEST FOR WHOEVER GETS RIGHT ANSWER
The graphs below have the same shape. What is the equation of the red graph.
Answer:
2 - x^2
Step-by-step explanation:
The ages of student volunteers at an event are: 13, 11, 12, 15, 16, 11, 12, 14, 15,
and 11. Find the median *
Answer:
12.5
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest . Need answer and work/explanation. Thank you.
Answer:
Hope it helps...
Step-by-step explanation:
which point is on the line that passes through point h and is perpendicular to line fg?
The point on the line that passes through point H and is perpendicular to line FG is (–6, 10).
First, we need to find the slope of line FG. The slope of a line can be calculated by dividing the change in the y-coordinate by the change in the x-coordinate. In this case, the change in the y-coordinate is 10 and the change in the x-coordinate is 3, so the slope of line FG is 10/3.
Since the lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of 10/3 is -3/10.
Now, we need to find the equation of the line that passes through point H and has a slope of -3/10. The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, we know that m = -3/10 and the y-coordinate of point H is 10. Plugging these values into the equation, we get y = -3/10*x + 10.
To find the x-coordinate of the point we are looking for, we can substitute in the y-coordinate of point H. 10 = -3/10*x + 10, so x = –6.
Therefore, the point on the line that passes through point H and is perpendicular to line FG is (–6, 10).
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WHAT IS THE SLOPE IF I HAVE (-3,5) AND (4,-5)
Answer:
-10/7
Step-by-step explanation:
Use slope formula
[tex]\frac{y2-y1} {x2-x1}[/tex]
x1= -3
y1 = 5
x2 = 4
y2 = -5
[tex]\frac{-5-5}{4--3}[/tex]
[tex]\frac{-5 + -5}{4 +3}[/tex][tex]\frac{-10}{7}[/tex]
MATH
NATION
The data from a survey of ages of people taking an exercise class was skewed to the left.
Part C: The box plot represents the data. Calculate the appropriate measure of spread.
Answer choices:
A. IQR= 45
B. IQR= 13
C. Standard deviation = 8
D. Standard deviation=55
Answer:
IQR=13 im pretty sure
Step-by-step explanation:
The measure interquartile range is 13 option (B) IQR= 13 is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have a box plot, and the data from a survey of ages of people taking an exercise class was skewed to the left.
We know on the left side skewed has more data on the right and on the left side, there are fewer data.
From the dot plot, the end point is not given, so we are assuming the end point is 58.
IQR = 58 - 45 = 13
Thus, the measure interquartile range is 13 option (B) IQR= 13 is correct.
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