Based on probability, we know that if you roll 6 six-sided dice, the most likely outcome is that 5 will not decay. Use this knowledge to determine the theoretical values for the decay constant, the mean life, and the half-life. i= X rolls^1
T= X rolls
T112 = rolls-1
Answers
This is how the decay of radioactive nuclei is compared in the radioactive dice experiment. When a large number of six-sided dice are thrown at once, those that show a particular number are removed as decayed, while the remaining dice are counted as undecayed.
These address the undecayed cores after a given time stretch. After a second roll, the dice with the specific number representing decayed nuclei are taken out and the ones that remain are counted. The procedure is carried out a certain number of times, and as time passes, the number of dice that have not expired decreases.
Because the dice have six sides and the probability of each number being rolled is equal, only one of the numbers on the dice is considered decayed. The probability of one die decaying is 1/6, while the probability of not decaying is 5/6. Five of the six numbers are regarded as undecayed, as stated in the question: 5 won't decay, which is the most likely outcome.
The probability of decaying per unit of time is the definition of the dacay constant. Therefore, in the analogy, each time the dice are rolled can be thought of as the time interval, and a die has a probability of decaying of one sixth each time. If the initial number of dice is N0, the expected number of dice that will decay is 1/6*N0, so = 1/6. The probability of undecayed dice multiplied by the initial number of dice after a first roll is the number of undecayed dice.
N1 = N0*(1-1/6) For a second roll, N2 = N0*(1-1/6) *(1-1/6) = N0*(1-1/6)2 If we say that n is the number of rolls, Nn = N0*(1-1/6)n Half-life is the time (rolls) required for half of the original number of dice to decay.
If probability of undecayed is 1 - 1/6, then N1 = N0*(1- As n is the number of rolls, we just need to clear it (applying logarithm properties) n = ln(0.5) / ln(1-1/6) n = 3.801 Half-life time denoted as T1/2 = 3.8 rolls The decay constant is inversely proportional to the number of faces; as more faces the dice have, the smaller the probability of decay, resulting in a smaller constant; consequently, the mean lifetime is equal to the As a result, the mean lifetime for a dice with six sides is equal to 6.
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Related Questions
Please answer these questions!
Answers
Answer:
Step-by-step explanation:
1)
She takes medicine at the moment 0
24(1/2)^0
24 · 1
24 mg
2)
24 (1/2)^1
24 (1/2)
12 mg
Which is true?
A. 0.0093>0.01
B. 0.2673>0.2562
C. 0.5330>0.533
D. 0.6409>0.641
Answers
Answer: B; B. 0.2673>0.2562
Step-by-step explanation: So, let's focus on the decimals, we already know that 0.26 IS GREATER than 0.25. All the other expressions are showing the smaller number as greater, or equal to, I hoped this helped!
For a standard normal distribution, find: P(Z > -1.56) Express the probability as a decimal rounded to 4 decimal places. For a standard normal distribution, find: P(Z < 0.26) Express the probability as a decimal rounded to 4 decimal places.
Answers
the value of P(Z>-1.56) is 0.9406
The value of P(Z<0.26) is 0.6026
For a standard normal distribution,
the standard normal distribution is also known as the Z - distribution
it is a very special type of distribution in which the value of mean is zero and the value of standard deviation is one.
the formula of standard normal distribution is
[tex]f(x)=\frac{1}{\sigma\sqrt{2\pi } } e^{\frac{-1}{2}(\frac{x-\mu}{\sigma})^2 }[/tex]
(OR)
Z=[tex]\frac{x-\mu}{\sigma}[/tex]
where
[tex]\mu[/tex] is the value of mean
[tex]\sigma[/tex] is the value of standard deviation
f(x) is the probability density function
now,
the value of P(Z>-1.56) is
P(Z> -1.56) = 1 - P(Z< -1.56)
=> 1 - 0.05938
=> 0.94062 (By rounding to 4 decimal places we get)
=> 0.9406
P(Z<0.26) = 1 - P(Z<0.26)
=> 0.60257 (By rounding to 4 decimal places we get )
=> 0.6026
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The Support Vector Classifier includes a tuning parameter C that controls the bias-variance trade-off. Which of the following statements is correct?
a) As C increases, the margin becomes smaller, which increases bias but potentially decreases variance
b) As C increases, the margin becomes smaller, which decreases bias but potentially increases variance
c) As C increases, the margin becomes larger, which increases bias but potentially decreases variance
d) As C increases, the margin becomes larger, which decreases bias but potentially increases variance
Answers
The correct answer is D) As C increases, the margin becomes larger, which decreases bias but potentially increases variance.
In the Support Vector Classifier (SVC), the parameter C controls the trade-off between the model's complexity and the amount of training error that it is allowed to have. A larger value of C means that the model will be more complex, and therefore will have a larger margin.
This will decrease the bias of the model but may increase the variance.
On the other hand, a smaller value of C means that the model will be less complex and will have a smaller margin, which will increase the bias of the model but potentially decrease the variance.
So, in summary, as C increases, the margin becomes larger, which decreases bias but potentially increases variance.
Hence, the correct answer would be an option (D).
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apply dijkstra's algorithm to find the shortest path from vertex a to vertex g in h. for full credit you must show your work, follow dijkstra's algorithm approach explicitly, and indicate both the shortest path and cumulative weight at the end
Answers
On solving the provided question, Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.
What is Dijkstra's algorithm?In a graph that may, for instance, represent a network of roads, Dijkstra's Method is an algorithm for determining the shortest routes between nodes. Computer scientist Edsger W. Dijkstra created it in 1956, and it was published three years later. Algorithms come in a wide variety.
Here is how the algorithm is described:
Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.Make current node C the non-visited node with the shortest current distance. You should double the distance between your current node C and each of its neighbors, N, by the weight of the edge that connects C and N. Make it the new current distance of N if it is less than the current distance of N. C is the current node; mark it as visited.
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4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D
Answers
The required equation that following the pattern is n = 4s+1. So the option c is correct.
In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.
The given options are:
a) n = s+4
b) n = 4s
c) n = 4s+1
d) s = 4n
We find the pattern we firstly observe the given diagram closely.
As we can see that in first diagram have 5 blocks.
In second diagram have 9 blocks.
In third diagram have 13 blocks.
So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.
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1. A survey of local car dealers revealed that 64% of all cars sold last month had CD players,
28% had alarm systems, and 22% had both CD players and alarm systems.
a.
What is the probability one of these cars selected at random had neither a CD player nor
an alarm system?
b. What is the probability that a car had a CD player unprotected by an alarm system?
C.
What is the probability a car with an alarm system had a CD player?
D.
Are having a CD player and an alarm system disjoint events? Explain.
Answers
64% of all cars sold last month had CD players
28% of all cars sold last month had alarm systems
22% of all cars sold last month had both CD players and alarm systems
a. To find the probability that one of these cars selected at random had neither a CD player nor an alarm system, we need to subtract the probability that it had either a CD player, an alarm system, or both from 1. The probability that a car has either a CD player, an alarm system, or both is the sum of the probabilities of each of these events, which is 64% + 28% - 22% = 70%. Therefore, the probability that a car has neither a CD player nor an alarm system is 1 - 70% = 30%.
b. To find the probability that a car had a CD player but no alarm system, we can subtract the probability that it had both a CD player and an alarm system from the probability that it had a CD player. The probability that a car had both a CD player and an alarm system is 22%, so the probability that a car had a CD player but no alarm system is 64% - 22% = 42%.
c. To find the probability that a car with an alarm system had a CD player, we can use the formula for conditional probability: P(CD player | alarm system) = P(CD player and alarm system) / P(alarm system). The probability that a car had both a CD player and an alarm system is 22%, and the probability that it had an alarm system is 28%, so the probability that a car with an alarm system had a CD player is 22% / 28% = 78.6%.
8x + 9y = 3 and x + y = 0
Answers
Answer:
x is 3 and y is -3
Step-by-step explanation:
[tex]x + y = 0 \\ x + y - y = 0 - y \\ x = - y \\ \\ 8x + 9y = 3 \\ (8 \times - y) + 9y = 3 \\ - 8y + 9y = 3 \\ y = 3[/tex]
X = -3
find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 1 + 10. Vt, y+t^5 -t, and z + t^5 + t; (11, 0, 2)?
Answers
Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.
What is the formula for parametric equations?The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.
The given x=1+12+ dx=dt 0+12(1) =12
Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12
(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).
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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)
x(t), y(t), z(t) =
in a certain quadrilateral, the three shortest sides are congruent and both diagonals are as long as the longest side. what is the degree measure of the largest angle of tihs quadrilateral
Answers
The measurement of the largest angle of the quadrilateral is 108°
Given,
Quadrilateral;
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Here,
Three shortest sides of the quadrilateral are congruent.
Both diagonals are as long as the longest side.
That is,
Side 1 ≅ Side 2 ≅ Side 3
Side 4 = Diagonal 1 = Diagonal 2
Then,
The largest angles of the quadrilateral will be 108°
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PLS HELP QUICK! 20 POINTS
Can a triangle be formed with side lengths 5, 6, 12? Explain.
No, because 5 + 6 < 12
Yes, because 5 + 6 > 12
No, because 12 − 6 < 6
Yes, because 12 − 6 < 5
Answers
Answer:
No, because [tex]5+6<12[/tex]
Step-by-step explanation:
The side lengths do not satisfy the triangle inequality.
the following are midterm scores of an algebra class of 20 students in a high school: 69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77 find the interquartile range using r.
Answers
13.3 is the interquartile range of the data set.
Given,
The midterm scores of an algebra class of 20 students;
69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77
We have to find the interquartile range using r.
Interquartile Range;-
The second and third quartiles, or the centre half of your data set, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data set.
Interquartile range = Q3 - Q1
Q1 is the lower quarter
Q3 is the upper quarter
Q2 is the median
Here,
Q2 = 63 + 87 / 2 = 150 / 2 = 75
Q1 = 81 + 74 / 2 = 77.5
Q3 = 74 + 55 / 2 = 64.5
Then,
Interquartile range = Q3 - Q1 = - (64 . 5 - 77.5) = 13.3
That is,
The interquartile range for the given data set is 13.3
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a child is riding in a boat in a 12-m-deep pond. while in the boat he plays with a stone sphere of radius 2.0 cm. a). if the sphere has a mass of 89 g. what is its density?b). if the child holds the sphere under water, what is the difference in pressure between the top and bottom of the sphere?c). as you kne would happen, the child drops the stone sphere in the pond. what is the total pressure exerted on the sphere when it is at the bottom of the pond?
Answers
the total pressure exerted on the sphere when it is at the bottom of the pond is 8∛2 ≈ 10.08
The volume of a hemisphere is given by the formula ...
V = (2/3)πr³
Then the radius is ...
r = ∛(3V/(2π))
r = ∛(3·1071.79/(2·3.14)) ≈ ∛512.00 ≈ 8.00
The radius of Sarah's pond is 8 inches.
We can see from the above that the radius is proportional to the cube root of the volume. If Sarah wants to double the volume, she needs to multiply the radius by ∛2 ≈ 1.260.
The pressure will be 8∛2 ≈ 10.08
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Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
Answers
The area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
Given that,
The vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
We have to find the area of parallelogram with the vertices.
We know that,
PQ=Q-P=(3,3,3) -(1,0,2)=(2,3,1)
PR=R-P=(7,5,8) -(1,0,2)=(6,5,6)
Find area using cross product as
Area= |PQ x PR|
=|i (3(6)-1(5)) - j (2(6)-1(6)) + k (2(5)-3(6)) |
= |i (18 - 5) - j (12 -6) + k (10 -18) |
= |{13; 6; -8}|
=√(13²+6²+(-8)²)
=√269
Therefore, the area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
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Use the marginal tax rate chart to answer the question.
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the effective tax rate for a taxable income of $192,700. Round the final answer to the nearest hundredth.
32.00%
21.77%
24.00%
18.57%
PLEASE HELP
Answers
Answer: B. 21.77%
Step-by-step explanation: See picture. I'm currently taking the test right now
Answer:
(b) 21.77%
Step-by-step explanation:
Using the given tax rate table, you want to know the effective tax rate on a taxable income of $192,700.
TaxThe tax will be the sum of the taxes due in each of the brackets. This sum can be simplified to make the tax computation a little less work.
tax = 0.10(10275) +0.12(41175 -10275) +0.22(89075 -41175) +0.24(17050 -89075) +0.32(192700 -170050)
= 10275(0.10 -0.12) +41175(0.12 -0.22) +89075(0.22 -0.24) +170050(0.24 -0.32) +192700(0.32)
= 192700(0.32) -(10275(0.02) +41175(0.10) +89075(0.02) +170050(0.08))
= 192,700(0.32) -19708.50
tax = 41955.50
Effective rateThe tax as a percentage of the taxable income is ...
tax/income × 100% = 41955.50/192700 × 100% ≈ 21.77%
The effective tax rate is about 21.77%.
__
Additional comment
We can use this same idea to simplify the tax table all around. The various tax computations are shown in the second attachment. Interestingly, the tax due is the maximum of the computations for the different brackets. The graph shows the effective tax rate (%) as a function of income. The effective rate for $192,700 is marked.
Because the tax tables are written with discontinuities, there can be some confusion about the amount that fits in each bracket. For example, the tax on 10276 is not 10% of 10275 plus 12% of zero. Rather it is 10% of 10275 plus 12% of (10276 -10275), for a total of $1027.62.
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find the critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom
Answers
The critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom are roughly 21.02 and 32.36.
The critical value for the 95% confidence interval using the 15 degrees of freedom chi-square distribution is the value that divides the distribution into two;
lower tail and upper tail. These values are calculated such that the area under the curve of the chi-square distribution between the critical values represents 95% of the total area under the curve.
To find critical values, you can use a chi-square table or a computer program that calculates critical values for a given confidence level and degree of freedom.
In this case, the critical value for the 95% confidence interval with 15 degrees of freedom can be determined as follows:
Lower critical value:
The lower critical value is the value corresponding to the area under the chi-square distribution curve to the left of the value, equal to 2.5% (half of 5% not included in the confidence interval). Using a chi-square table or computer program, we can find that the lower critical value for the 95% confidence interval with 15 degrees of freedom is approximately 21.02. Upper critical value:
The upper critical value is the value corresponding to the area under the chi-square distribution curve to the right of the value, equal to 2.5% (half of 5% is not included in the confidence interval).
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Determine the number and type of solutions for the equation x^2+8x+15=0
Two different irrational-number solutions
One repeated irrational-number solution
One repeated rational-number solution
Two different rational-number solutions
Two imaginary-number solutions
Answers
And those are two different rational numbers.
Answer:
Step-by-step explanation:
disc=8²-4×1×15=64-60=4=2²>0
it is a perfect square and >0
so it has one repeated rational number solution.
a. Bared an the information in the figure, which of the two cities have nearest to each other?
Select choice
b. Based on the information in the figure, which of the two cities are farthest apart from each other?
Select Choice
c. If you were going to use the information from 5 Sate's sketch to plan a road trip between these cities, what is an assumption that you would have to make?
Select Choice
Answers
The City A and Abilene are nearest to each other
The Austin and Abilene are farthest apart from each other
Here the two angles of the triangle = 59 degrees and 64 degrees
The sum of the angles in a triangle is 180 degrees
Then the third angle will be
59 + 64 + x = 180
123 + x = 180
x = 180 - 123
x = 57 degrees
The third city name is not visible so consider it as city A
Part a
Here the smallest angle is 57 degrees
Opposite side of the angle will be the smallest distance
That is the distance between city A and Abilene
Part b
Here the largest angle is 64 degrees
The opposite side of the angle will be largest distance
That is the distance between Austin and Abilene
Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other
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Professor Bowdidge taught four business statistics classes during the fall semester with the following grade averages for each class: 74%, 82%, 86%, and 91%. Calculate the mean (round to the nearest hundredth). A. 83.00% B. 83.12% C. 85.00% D. 83.25%
Answers
By using the mean formula, the mean grade across all four classes was 83.25%.
What is mean?The mean is a measure of central tendency that represents the average value of a set of data
What is formula to calculate mean?The formula for calculating the mean:
Mean = (x1 + x2 + x3 + ... + xn) / n
Where:
x1, x2, x3, ..., xn are the individual values in the set
n is the total number of values in the set
Mean = (74 + 82 + 86 + 91) / 4
Mean = 333 / 4
Mean = 83.25
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5 + 2a = a - 9 what does a equal
Answers
Add the negative nine to the five and subtract the 2a from a. Should leave you with 14=-a. Multiply both sides by -1. -14=a
a= -14.
Step-by-step explanation:1. Write the expression.[tex]5 + 2a = a - 9[/tex]
2. Subtract 5 from both sides of the equation.[tex]5 + 2a -5= a - 9-5\\ \\2a=a-14[/tex]
3. Subtract "a" from both sides of the equation.[tex]2a-a=a-14-a\\\\a=-14[/tex]
4. Verify.[tex]5 + 2(-14) = (-14) - 9\\ \\5-28=-23\\ \\-23=-23[/tex]
Both sides are equal to each other, hence a= -14 is the correct solution.
5. Conclude.a= -14.
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X is the midpoint of UV. Y is the midpoint of UW. If mZUYX= 46, find mZW.
mZW=
U
Y
W
Answers
Answer:
46°
Step-by-step explanation:
As m<UYX and m<W is corresponding angle because X is the midpoint of UV and Y is the midpoint of UW, therefore
m<W = 46°
I hope my answer helps you.
Answer:
m<W = 46 degrees
Step-by-step explanation:
UX = UV/2 ==> This is because X is the mid-point of UV, dividing UV by 2
to make UX
UY = UW/2 ==> Y is the mid-point of UW, dividing UW by 2 to make UY
XY = VW/2 ==> Since X is the midpoint of UV and Y is the midpoint of UW,
segment XY is exactly in the middle of point U and
segment VW, so segment XY is half of segment VW.
Since all sides of the small triangle(ΔUXY) are exactly half of all sides in the big triangle(ΔUVW), The corresponding angles in each triangle are equal to each other:
Hence, m<UYX = m<UWV
m<UWV ==> m<W = 46 degrees ==> since m<UYX=46, m<W = 46 as well
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07, The present age of Queens University College is three times that of GAGE University College. After 5 years, the difference of their ages will be 30 years. Find the present ages of Queens and GAGE University College?
Answers
Answer: Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.
Step-by-step explanation: Let Q be the present age of Queens University College and G be the present age of GAGE University College.
Since the present age of Queens University College is three times that of GAGE University College, we can write the equation Q = 3G.
After 5 years, the difference of their ages will be 30 years, so we can write the equation Q + 5 = G + 30.
Substituting the first equation into the second equation, we get 3G + 5 = G + 30.
Solving for G, we find that G = 15.
Substituting this value into the equation Q = 3G, we find that Q = 3 * 15 = 45.
Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.
Which angle is an adjacent interior angle to
Answers
The required adjacent interior angle is the angle angles that lie later or former to the given angle.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
Consider a triangle,
In triangle, there are three angles in triangle
Each of the angle is adjacent with the other two lying former and later in the sequence.
Thus, the required adjacent interior angle is the angle angles that lie later or former to the given angle.
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Read the following prompt and type your response in the space provided.
Give an example of a problem involving multiplication of fractions that can be made easier using the associative property. Explain how it makes the problem easier.
Answers
One example of a problem involving multiplication of fractions that can be made easier using the associative property is as follows:
Given the expression (2/3) * (4/5) * (6/7), we can use the associative property to rearrange the terms and simplify the expression. Specifically, the associative property states that the order in which we perform operations does not change the result. In this case, we can rearrange the terms as follows:
(2/3) * (4/5) * (6/7) = (4/5) * (2/3) * (6/7)
Then, we can simplify the expression using the commutative property of multiplication (which states that the order of the terms does not affect the result of the multiplication):
(4/5) * (2/3) * (6/7) = (2/3) * (4/5) * (6/7)
Finally, we can simplify the expression by multiplying the fractions:(2/3) * (4/5) * (6/7) = (12/21).
Using the associative property allows us to rearrange the terms and simplify the expression, making the problem easier to solve.
The pattern in this table continues. Which equation below relates the number of squares to the figure number?
a) s=4 f+1
b) s=2 f+3
c) s=f+2
d) f=2 s+3
A
B
C
D
Answers
The final equation that represent the given table is s=f+2. So the option c is correct.
In the given question, the pattern in this table continues.
We have to check which equation below relates the number of squares to the figure number.
a) s=4f+1
b) s=2f+3
c) s=f+2
d) f=2s+3
From the given table;
f(1) = 5, f(2) = 7, f(3) = 9, f(4) = 11, f(5) = 13
If we check closely the value of f(x), we can see that the difference between each number is of 2.
So if we want to write the function as
f(1) = 5,
f(2) = f(1)+2 = 7,
f(3) = f(2)+2 = 9,
f(4) = f(3)+2 = 11,
f(5) = f(4)+2 = 13
So the final equation that represent the given table is;
s=f+2
So the option c is correct.
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A population of squirrels lives in a forest with a carrying capacity of 1800 Assume logistic growth with growth constant k = 0.8 yr-1 . (a) Find a formula for the squirrel population P(t) , assuming an initial population of 450 squirrels_ P(t) 1800/(1+3e^(-0.8t)) (b) How long will it take for the squirrel population to double? doubling time ~ 83 years
Answers
By applying formulas of logistic growth we can find the answers as part (a) P(t) = 1800 / (1+3e^(-0.8t)) and part(b) 1.37 years
What is logistic growth?In a logistic growth the growth rate decreases with the passage of time until the growth reaches the maximum capacity at infinite time.
What is formula for logistic growth?The formula is f(t) = L / (1+ ye^(-kt))
where L is the maximum value, k is the growth rate, y is a constant and t is time.
Part(a)
In this case, L = 1800, k = 0.8 yr-1
f(t) = 1800 / (1 + ye^(-0.8)t)
at t = 0 , f = 450,
450 = 1800/ (1+y)
solving this gives, y = 3
Thus the final answer is f(t) = 1800/ (1+ 3e^(-0.8t))
Part(b)
we need to find the time when f(t) = 900
900 = 1800/(1+3e^(-0.8t))
t = 1.37 years
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5, Brittney is conducting an experiment in class to determine the probability of getting four heads when flip-
four coins. What is the sample space of her experiment?
Answers
Answer:
16 possible outcomes
Step-by-step explanation:
The sample space of Brittney's experiment is the set of all possible outcomes of flipping four coins. Since each coin can either land on heads or tails, there are two possible outcomes for each coin. Therefore, there are a total of 2^4 = 16 possible outcomes for the experiment. These outcomes can be represented as a list, with each outcome represented by a string of four "H"s and "T"s, where "H" represents a heads and "T" represents a tails. For example, one possible outcome of the experiment could be "HHHT" (two heads, one tails, one heads), and another could be "TTTT" (four tails). The complete sample space of Brittney's experiment would include all 16 possible outcomes.
Someone please help me! Find the cotangent! Thank you!
Answers
The value for cotangent of ∠V is 55.6°.
What is pythagora's theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.Cotangent = adjacent / opposite
Pythagoras theorem,
WV² = XW² + VW²
9² = x² + (√57)²
x² = 81 - 57
= 24
x = √24
= 4.89
cot (v) = √24 / √57
v = cot⁻¹ (0.6488)
v = 55.6°
Hence, the value for cotangent of ∠V is 55.6°.
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refer to the work hrs.rds dataset. in this problem, we want to examine the effect of an hourly wage (wage), education (educ), and the number of children (nchild) on the hours worked per week by married women (hrswork).
Answers
The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).
To examine this, we would use a regression analysis to look at the relationship between each of these variables and the hours worked per week. We would create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable. We can then analyze the coefficient of each of these variables to measure the effect they have on the hours worked per week. The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).
1. Load the work hrs.rds dataset.
2. Examine the data to identify the independent and dependent variables. In this case, the independent variables are wage, educ, and nchild, and the dependent variable is hrswork.
3. Use a regression analysis to examine the relationship between the independent and dependent variables.
4. Create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable.
5. Analyze the coefficient of each of the independent variables to measure the effect they have on the dependent variable (hrswork).
6. Interpret the results to determine the effect of the independent variables on the dependent variable.
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henry flips 10 coins then lays them on a desk. he then chooses one of the coins at random, and if it is tails, he flips it to heads.
Answers
As per the concept of probability, the probability of getting head is 99.5%.
The term probability in statistics is known as the possible way of getting the particular event.
Here we have given that
And we need to find the probability of getting head.
Here we know that the number of coins is 10.
So, the sample space for the 10 coins is calculated as,
Here we already know that for each of the 10 coin tosses, we have either a head (H) or a tail (T).
so, the total number of probability of 10 coins is 210 strings in the sample space.
Here we know that the only option of all tails doesn't have head in it.
So, the number tosses that have head in it is calculated as,
=> 210 - 1
=> 209
Therefore, the probability is calculated as,
=> P = 209/210
=> P = 0.995
Therefore, the probability in percentage is 99.5%
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