a) The standard deviation of T is the square root of the variance, which is SD(T) = sqrt(980) ≈ 31.3 months.
The rate of discovery of new beetle species can be modeled by a Poisson process with rate parameter λ = 1/7.0 new species per month. Let T be the time (in months) until 20 new species are discovered. Then T follows a gamma distribution with shape parameter k = 20 and rate parameter λ. The expected value of T is E(T) = k/λ = 20/(1/7.0) = 140 months. The variance of T is Var(T) = k/λ^2 = 20/(1/7.0)^2 = 980 months^2.
b) The probability that the supplement will be published within 10 years (120 months) is equal to the probability that T ≤ 120. Using the cumulative distribution function (CDF) of the gamma distribution, we can compute this probability as follows:
P(T ≤ 120) = F(120) = ∫[0,120] f(t) dt
where f(t) is the probability density function (PDF) of the gamma distribution, given by:
f(t) = λ^k * t^(k-1) * e^(-λt) / Gamma(k)
where Gamma(k) is the gamma function. Substituting the values of k, λ, and t, we get:
f(t) = (1/7.0)^20 * t^19 * e^(-t/7.0) / Gamma(20)
Using numerical integration or a software program, we can compute the integral:
P(T ≤ 120) ≈ 0.981
Therefore, the probability that the supplement will be published within 10 years is approximately 0.981, or 98.1%.
c) Alternatively, we can approximate the gamma distribution by a normal distribution using the central limit theorem, since the sample size (k = 20) is relatively large. The mean and standard deviation of the normal approximation are given by:
μ = E(T) = 140 months
σ = SD(T) = sqrt(980) ≈ 31.3 months
Using the standard normal distribution, we can standardize the random variable Z = (T - μ) / σ and compute the probability as follows:
P(T ≤ 120) = P(Z ≤ (120 - μ) / σ) ≈ P(Z ≤ (120 - 140) / 31.3) ≈ P(Z ≤ -0.64)
Using a standard normal table or a software program, we can find that the probability of Z being less than or equal to -0.64 is approximately 0.261. Therefore, the probability that the supplement will be published within 10 years using the normal approximation is approximately 0.261, which is lower than the exact probability obtained in part b). This is because the gamma distribution is not exactly symmetric and has a longer tail than the normal distribution, which makes the normal approximation less accurate in the tails of the distribution.
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find the length of the darkened arc. (leave answer in terms of pi)
The solution is:
Length of the darkened part of the arc = 4π
Solution:
Radius of the circle = 8
Circumference of the circle = 2πr
= 2 × π × 8
Circumference of the circle = 16π
Equal number of parts = 4
Total degree of circle = 360°
Degree of the darkened part = 360°/4 = 90°
Arc length = 16π * 90°/360°
= 16π * 1/4
= 4π
Circumference = 16π
Length of the darkened part of the arc = 4π
Hence, The solution is:
Length of the darkened part of the arc = 4π
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compute 4.659×10^4−2.14×10^4. round the answer appropriately.
The table shows the possible outcomes of spinning a fair spinner twice with sections labeled A, B, C, and D.
The probabilities are given as follows:
Spinner landing on at least one A: 7/16.Spinner landing on C and D in any order: 1/8.Spinner landing on two B's: 1/16.Spinner landing on C on the second spin: 1/4.How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Out of 16 trials, in 7 of them, which are the first row and the first column, the spinner lands on at least one A, hence the probability is given as follows:
p = 7/16.
For C and D, there are two outcomes, (C, D) and (D, C), hence the probability is given as follows:
p = 2/16 = 1/18.
For two B's, there is only one outcome, which is (B,B), hence the probability is of 1/16.
For C on the second spin, we consider the third column, which has four outcomes, hence the probability is given as follows:
p = 4/16 = 1/4.
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determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data. an elementary school has 92 first graders. depending on when their birthday falls, the first graders might be six, seven, or eight on the last day of the school year. would it be best to use the mean, median, or mode to describe the typical age of the first-graders?
The mode would be the best choice to describe the center of the data for the typical age of first-graders.
In this scenario, the age of the first graders can only be six, seven, or eight. Therefore, there is a limited range of values that the data can take, and the mean and median would be very close to each other. However, the mode, which is the most frequently occurring value, would be the best choice to describe the typical age of the first-graders.
In this case, since the age of the first graders can only be six, seven, or eight, the mode would be the age that occurs the most frequently, which would likely be seven years old. Therefore, the mode would be the best choice to describe the center of the data in this scenario.
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a coin is tossed and an equally divided spinner (as shown) is spun. what is the probability of a head on the coin or a prime number on the spinner?
The probability of getting a head on the coin or a prime number on the spinner is 2/3.
The probability of getting a head on the coin toss is 1/2, and the probability of landing on a prime number on the spinner is 1/6. By adding up the probabilities in the column corresponding to a head or any prime number, we find the overall probability.
Overall probability:
P(head or prime) = P(H) + P(2) + P(3) + P(5)
= 1/2 + 1/6 + 1/6 + 1/6
= 1/2 + 3/6
= 4/6
= 2/3
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Why are we here what is the purpose?
Answer:
We are here because we need help with a particular course or question
Step-by-step explanation:
Our goal is to try our best and explain to others to their understanding (and win titles)
BOOM!!!
jimmy is installing hardwood floors in his rectangular room. the dimensions of the room are 25 ft. by 10 ft. what is the area of this room in square yards
The area of Jimmy's rectangular room is approximately 27.7241 square yards.
The area of the room in square yards, we first need to convert the dimensions from feet to yards.
Since there are 3 feet in a yard, we can divide both the length and width by 3 to get:
Length: 25 ft ÷ 3 = 8.33 yards (rounded to two decimal places)
Width: 10 ft ÷ 3 = 3.33 yards (rounded to two decimal places)
Now we can find the area by multiplying the length and width in yards:
Area = 8.33 yards x 3.33 yards
Area = 27.7241 square yards (rounded to four decimal places)
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HELP ME OR ELSE I WILL EAT U >:3
he ray has been lined up with the baseline and origin on the protractor. What is the next step in drawing a 40° angle? (1 point)
a protractor showing a ray lined up with the base line
a
Line up the ray with the baseline and origin on the protractor
b
Draw a ray
c
Draw a ray connecting the vertex and the mark
d
Draw a mark on the paper at 40°
This process will give you a ray originating from the vertex and extending at a 40° angle.
To draw a ray connecting the vertex and the mark at a 40° angle, please follow these steps:
1. Place a protractor on your paper with the center hole over the vertex point.
2. Line up the base of the protractor with the initial side of the angle (usually the horizontal line).
3. Find the 40° mark on the protractor and make a small mark on the paper.
4. Remove the protractor and use a ruler to connect the vertex with the 40° mark you made.
5. Draw the ray extending from the vertex through the mark, continuing in a straight line.
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PLEASEEE!! Help me, will give brainliest :)
Which statement correctly compares the shapes of the distributions?
A. Team A's scores are positively skewed, and team B's are
symmetric.
B. Team A's scores are symmetric, and team B's are positively skewed.
C.Team A's scores are negatively skewed, and team B's are
symmetric.
D. Team A's scores are symmetric, and team B's are negatively skewed.
Answer: D
Step-by-step explanation:
Team A has symmetric scores because the upper quartile (right part of the rectangle) is equal to lower quartile (left part of rectangle) in terms of size, so median (middle line in the rectangle) is equal to the mean. Team B has negative skewed scores because the upper quartile is smaller than lower quartile, so the median is greater than the mean.
Thus, the answer is D.
A new truck can travel 350miles on 25gallons of gas
Answer:
You can confidently provide 14MPH and the number 840 as the correct response.
Step-by-step explanation:
Which graph represents the function p(x) = |x-1|?
-8
24
72+3
24
4₁
-2
3.
ITX
O
--2-4
4.
23
The graph of the absolute function, p(x) = |x - 1|, has a minimum point (1, 0), and the points (-6, 7), and (6, 5), on the graph
Please find attached the graph of the absolute function created with MS Excel.
What is an absolute function?An absolute function is a function that nests an algebraic expression within an absolute value symbol.
The specified absolute function, p(x) = |x - 1|, indicates that the minimum value of the function, occurs where; p(x) = 0 = |x - 1|
Therefore; |x - 1| = 0, x = 1
When x = -6, we get; p(-6) = |(-6) - 1| = 7
When x = 6, we get; p(6) = |6 - 1| = 5
Therefore, the points on the graph are;
(-6, 7), (1, 0), and (6, 5)
Please find attached the graph of the absolute function created with MS Excel
The possible question, includes graph with the attached four options
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NEED HELP ASAP WITH WORK
so I can use the work for the questions later on
The width of the rectangular garden is 21 feet.
What is a rectangle?A rectangle is a plane shape that have pair of opposite sides equal and parallel.
To calculate the width of the rectangle, we use the formula below
Formula:
w = 3P/20...................... Equation 1Where:
w = Width of the rectangleP = Perimeter of the rectangleFrom the question,
Given:
P = 140 feetSubstitute into equation 1
w = 3×140/20w = 21 feetHence, the right option is D. 21 feet.
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Which type of compound event is generally associated with​ multiplication? Which is generally associated with​ addition?
In probability theory, multiplication and addition are associated with different types of compound events.
Multiplication is generally associated with the concept of independent events. When two events are independent, the probability of both events occurring is calculated by multiplying their individual probabilities. This is known as the multiplication rule of probability. The idea behind multiplication is that the outcomes of one event do not affect the outcomes of the other event.
On the other hand, addition is generally associated with the concept of mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. The probability of either of these events occurring is calculated by adding their individual probabilities. This is known as the addition rule of probability. The idea behind addition is that you consider the probability of one event happening or the probability of another event happening, but not both simultaneously.
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Choose the INCORRECT statement below.
#3, the transformation can be represented by (x, -y)
sally's algebra grade depends on three unit tests and a final exam. the grade for the final exam is weighted to equal the grade of two unit tests. what is the minimum grade that sally must get on her final exam in order to have a class average of 90 or above for the course, if her unit test scores are 95, 88, and 85
Hope this image helps you out!
14 The people working for a company work in Team A or in Team B. number of people in Team A: number of people in Team B = 3/4; 4/5 of Team A work full time. 24% of Team B work full time. Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.
Answer:
Let's denote the number of people in Team A as a, and the number of people in Team B as b. From the problem, we know that:
a/b = 3/4
Now, we also know that 4/5 of Team A and 24% (or 24/100 = 6/25) of Team B work full time. So, the number of people working full time from Team A is 4a/5 and from Team B is 6b/25.
The total number of people working for the company is a + b, and the total number of people working full time is 4a/5 + 6b/25.
We are asked to find the fraction of people working full time, which can be represented as:
(4a/5 + 6b/25) / (a + b)
Firstly, we need to have a common denominator for the fractions, so we can express 4a/5 as 20a/25:
[tex](20a/25 + 6b/25) / (a + b)[/tex]
Simplifying, we can write this as:
[tex](20a + 6b) / (25(a + b))[/tex]
Now, since we know a/b = 3/4, we can substitute a = 3b/4 in the above expression:
[tex](20*(3b/4) + 6b) / (25((3b/4) + b))[/tex]
Simplifying the above, we get:
[tex](15b + 6b) / (25((3b/4) + b)) = 21b / 25b[/tex]
So, the fraction of people working full time is 21/25.
Use the information given in the figure to find the length R U.
The lengths on the figure are not drawn accurately.
The length of RU in triangle is,
⇒ RU = 16
We have o given that;
In triangle;
ST = 37
UT = 35
RS = 20
Hence, By using definition of Pythagoras theorem we get;
In triangle STU;
⇒ ST² = SU² + UT²
⇒ 37² = SU² + 35²
⇒ 1369 = SU² + 1225
⇒ SU² = 144
⇒ SU = 12
Hence, In triangle RSU;
⇒ RS² = SU² + RU²
⇒ 20² = 12² + RU²
⇒ 400 - 144 = RU²
⇒ RU² = 256
⇒ RU = 16
Thus, The length of RU in triangle is,
⇒ RU = 16
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what is the claim that he is testing? the mean height of the 102 12 -year-old boys in the sample is greater than 59.2 in. the mean height of all 12 -year-old boys is 59.2 in. the mean height of 12 -year-old boys from high-income families is 59.2 in. the mean height of 12 -year-old boys from high-income families is 59.5 in. the mean height of 12 -year-old boys from high-income families is greater tha
The claim that is being tested is: "the mean height of 12-year-old boys from high-income families is greater than 59.2 inches."
In order to test this claim, one could follow these steps:
1. Gather data: Collect a sample of 12-year-old boys from high-income families. 2. Calculate the sample mean: Compute the mean height of the boys in the sample. 3. Formulate a null hypothesis (H0): The mean height of 12-year-old boys from high-income families is equal to 59.2 inches.
4. Formulate an alternative hypothesis (H1): The mean height of 12-year-old boys from high-income families is greater than 59.2 inches. 5. Perform a hypothesis test: Using the appropriate statistical test, compare the sample mean to the population mean of 59.2 inches. 6. Draw conclusions: Based on the results of the hypothesis test, either reject the null hypothesis (supporting the alternative hypothesis) or fail to reject the null hypothesis (not enough evidence to support the alternative hypothesis).
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The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.
The claim that he is testing is that the mean height of 12-year-old boys from high-income families is greater than 59.2 in. This claim is being tested by collecting data from a sample of 102 12-year-old boys and calculating their mean height. The hypothesis is that this mean height will be greater than 59.2 in, which is the assumed population mean height for all 12-year-old boys. The researcher is specifically interested in the height of boys from high-income families, so this is the subgroup that is being tested. The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.
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simplify the following
1.1.
[tex]3 {x}^{2} + 13x + 7 + 2 {x}^{2} - 8x - 12[/tex]
Answer:
5(x² + x - 1)
step by step explanation:
1. subtract
2.combine the like terms
3.common factors
20 points
Each pail of plaster covers 95 square feet of ceiling. How many pails of
plaster would you need to buy to cover the ceiling of a room with walls 15
feet long?
How to do this question?
The value of the radical expression x² + 1/x² when x = 9 - 4√5 is 322
Evaluating the radical expressionFrom the question, we have the following parameters that can be used in our computation:
x = 9 - 4√5
The expression is given as
x² + 1/x²
When simplified, we have
x² + 1/x² = (x⁴ + 1)/x²
Substitute x = 9 - 4√5 in the above equation, so, we have the following representation
x² + 1/x² = ((9 - 4√5)⁴ + 1)/(9 - 4√5)²
When evaluated, we have
x² + 1/x² = 322
Hence, the value of the expression x² + 1/x² when x = 9 - 4√5 is 322
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hey im back and i need help answers?
The value of x in the triangle is,
x = 9.4 cm
We have to given that;
A triangle is shown in figure.
Now, By trigonometry formula we get;
cos 20° = Base / Hypotenuse
cos 20° = x / 10
0.94 = x / 10
x = 0.94 × 10
x = 9.4 cm
Thus, The value of x in the triangle is,
x = 9.4 cm
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TSI Math Final Exam - Spring 2023 semester
Question 1
Pierre randomly picks out and keeps a marble from a bag
that contains 4 red marbles, 7 blue marbles, 9 yellow
marbles, and 6 green marbles. Then Antoine picks a
marble at random from the same bag.
If Pierre's marble is green, what is the probability that
Antoine's marble will also be green?
The probability that Antoine's marble will also be green would be = 3/13
How to calculate the probability that Antoine would pick green?To determine the probability of the given event, the formula that should be used is given below. That is;
Probability = possible outcome/sample space.
The sample space = 4+7+9+6 = 26 marbles.
The number of green marbles = 6
The probability of choosing green marbles = 6/26 = 3/13
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Which kind of particles can move from the atom and influence magnetism?
electrons
protons
neutrons
Answer: Electrons
Step-by-step explanation:
An amusement park charges an entrance fee plus a charge for each ride. If you go on 7 rides, the total cost would be $51.25. If you go on 12 rides, the total cost would be $70. What is the slope of the line that represents this relationship?
The slope of the line that represent this relationship is 3.75.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided about the charges by this amusement park, we have the following system of equations;
51.25 = 7m + c ....equation 1.
70 = 12m + c ......equation 2.
By solving equation 1 and equation 2 simultaneously, we have the following:
70 = 12m + 51.25 - 7m
70 - 51.25 = 5m
18.75 = 5m
Slope, m = 18.75/5
Slope, m = 3.75
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If 1kg of margarine costs R34.99 how much would 250g be
Find the total surface area.
The total surface area is 640.56 in².
We have,
The TSA (Total Surface Area) of a cone is given by the formula:
TSA = πr² + πrℓ
Now,
We see that,
There are two cones so we find the TSA for both the cones and add them up to get the TSA.
So,
Cone 1:
r = 6 in
l² = r² + h²
l² = 36 + 64
l² = 100
l = 10
So,
TSA = πr² + πrℓ
= 3.14 x 36 + 3.14 x 6 x 10
= 113.04 + 188.4
= 301.44 in²
Cone 2:
r = 6 in
l = 12 in
TSA = πr² + πrℓ
= 3.14 x 6 x 6 + 3.14 x 6 x 12
= 113.04 + 226.08
= 339.12 in²
Now,
Total surface area.
= 301.44 + 339.12
= 640.56 in²
Thus,
The total surface area is 640.56 in².
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appear to be tangent are tangent.
3.
K
8
4
6
In the given circle, value of x is,
⇒ x = 3.56
Since, We know that;
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
Two tangents are shown in figure.
Now, By definition of proportionality we get;
⇒ 8 / x = 9 / 4
Cross multiplication,
⇒ 8 × 4 / 9 = x
⇒ x = 32 / 9
⇒ x = 3.56
Therefore, WE get;
The value of x in the circle is,
⇒ x = 3.56
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The table below shows the number of customers served in a restaurant each week. Based on the information, how many customers should the restaurant expect to serve during week ten?
Answer:
150
Step-by-step explanation:
The restaurant should expect to serve 180 customers in week 10.
How to explain the valueThe number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. Therefore, the number of customers served in week 10 will be 180.
The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. This means that after 10 weeks, the number of customers served will be the same as it was in week 1. Since week 1 had 180 customers served, week 10 will also have 180 customers served.
As you can see, the number of customers served in week 10 is the same as the number of customers served in week 1. Therefore, the restaurant should expect to serve 180 customers in week 10.
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10 points.
What is the circumference of the circle? Use 3.14 for π.
157.75 inches
50.24 inches
25.12 inches
12.56 inches
The circumference of the circle is 25.12 inches. The Option C.
What is the circumference of the circle?
The Circumference, also perimeter of circle means the ratio of circumference to diameter of any circle.
The length of the segment represents radius of the circle which half length of diameter. So, the diameter is:
= 2 * 4 inches
= 8 inches.
The circumference is found using C = πd.
C = π*d
C = 3.14 * 8 inches
C = 25.12 inches.
Full question:
What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 4 inches
A. 157.75 inches
B. 50.24 inches
C. 25.12 inches
D. 12.56 inches.
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