Answer:
The dividend yield is the dividend next year divided by the current price, so the dividend yield is:
Dividend yield = D1 / P0
Dividend yield = $2.55 / $48.70
Dividend yield = .0524, or 5.24%
The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:
Capital gains yield = 6%
Each year an organization raises money to offer Berkeley College students scholarships. They currently have raised $14,300. This represents 58% of the money they raise. Determine the amount of money the organization will raise in total.
The amount of money the organization will raise in total is $25655.17.
What is percentage?A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. Thus, a part per hundred is what the percentage refers to. Percent signifies for every 100.
Let us suppose the total amount raised = T.
Given that, $14,300 is 58% of the total amount we have:
T (58%) = 14300
T (58/100) = 14300
T = 14300(100)/58
T = 25655.17
Hence, the amount of money the organization will raise in total is $25655.17.
Learn more about percentage here:
https://brainly.com/question/29763752
#SPJ1
write 358.41 x 10^5 in standard form
35841000 is not correct answer
give real answer
Answer:
3.5841 x 10^7
Step-by-step explanation:
358.41 / 100
and add 2 powers of 10
If X = 6 units, Y = 4 units, and Z = 13 units, then what is the volume of the triangular pyramid shown above?
A.
44 cubic units
B.
39 cubic units
C.
104 cubic units
D.
52 cubic units
The volume of the triangular pyramid shown is (c) 104 cubic units
How to determine the volume of the triangular pyramid shownFrom the question, we have the following parameters that can be used in our computation:
X = 6 units, Y = 4 units, and Z = 13 units
The volume is calculated as
Volume = xyz/3
Substitute the known values in the above equation, so, we have the following representation
Volume = 6 * 4 * 13/3
Evaluate
Volume = 104
Hence, the volume is (c) 104 cubic units
Read more about volume at
https://brainly.com/question/463363
#SPJ1
David's farm produces 12 pounds of Zuccini per acre and 3 pounds of Watermelon per acre
Morgan's farm produces 18 pounds of Zuccini per acre and 6 pounds of Watermelon per acre
David's opportunity cost of producing 1 pound of watermelon is_______
pounds of zucchini, whereas Morgan's opportunity cost of producing 1 pound of watermelon is________
pounds of zucchini. Because David has a _______ opportunity cost of producing watermelon than Morgan, _______ has a comparative advantage in the production of watermelon, and ______ has a comparative advantage in the production of zucchini.
David's opportunity cost of producing 1 pound of watermelon is 4 pounds of zucchini, whereas Morgan's opportunity cost of producing 1 pound of watermelon is 3 pounds of zucchini. Because David has a higher opportunity cost of producing watermelon than Morgan, Morgan has a comparative advantage in the production of watermelon, and David has a comparative advantage in the production of zucchini.
What is opportunity cost?
Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.
The best input combinations to achieve the highest level of output are displayed on the production potential frontier.
The individual who has a lower opportunity cost in output than another individual enjoys a comparative production advantage.
David's watermelon production -
54 units watermelon = 216 units zucchini
1 unit watermelon = 216/54 units zucchini
1 unit watermelon = 4 units zucchini
Morgan's watermelon production -
108 units watermelon = 324 units zucchini
1 unit watermelon = 324/108 units zucchini
1 unit watermelon = 3 units zucchini
Morgan has absolute advantage in production of Zucchini and Morgan has also absolute advantage in production of watermelon.
Therefore, David's opportunity cost of 1 pound of watermelon is 4 pound of Zucchini and Morgan's opportunity cost of 1 pound of watermelon is 3 pound of Zucchini.
To learn more about opportunity cost from the given link
https://brainly.com/question/481029
#SPJ1
3. If a segment of the Mid-Atlantic Ridge spreads 927 km over a span of 71 million years, what
is the rate of the spreading in one year? (Round it to the nearest hundredth.)
The rate of spreading in one year is approximately 0.00001 km/year.
How The answer was obtainedTo find the rate of spreading in one year, we need to divide the total distance of 927 km by the time it took to spread, which is 71 million years. However, it's important to convert the time unit from million years to years:
71 million years = 71,000,000 years
So, the rate of spreading in one year is:
927 km ÷ 71,000,000 years ≈ 0.00001307 km/year
Rounding to the nearest hundredth, we get:
0.00001307 km/year ≈ 0.00001 km/year
Therefore, the rate of spreading in one year is approximately 0.00001 km/year.
Learn more on unit conversion here https://brainly.com/question/141163
#SPJ1
3. Suppose that the supply and demand for milk are given by the following equations where Q is the quantity in units of milk and P is the price per unit of milk:
Supply of Milk: Q = 0.50P – 3
Demand for Milk: Q = 27 – 0.30P
Algebraically (mathematically) determine the equilibrium price and quantity in the milk market. Show all work. (6 pts.)
The equilibrium price and quantity in the milk market are $37.5 and $15.75
What is Market equilibrium?When you combine the supply and demand curves, there is a point where they intersect; this point is called the market equilibrium. The price at this intersection is the equilibrium price, and the quantity is the equilibrium quantity.
Given that, the equations for that the supply and demand for milk:
Supply of Milk: Q = 0.50P - 3
Demand for Milk: Q = 27 - 0.30P
We need to find the equilibrium price and quantity in the milk market.
Market equilibrium is struck when:
Market Demand = Market supply
Therefore,
Market equilibrium =
0.50P - 3 = 27 - 0.30P
0.50P + 0.30P = 30
0.80P = 30
P = 37.5
Equilibrium price = 37.5
Put P = 37.5 in equation 0.50P - 3,
0.50(37.5)-3 = 15.75
Equilibrium quantity = 15.75
Hence, the equilibrium price and quantity in the milk market are $37.5 and $15.75
Learn more about market equilibrium, click;
https://brainly.com/question/26251442
#SPJ1
[5] Which country is known as the ‘playground of Europe’?
(A) Austria
(B) Holland
(C) Switzerland
(D) Italy
ias chinadu
IAS CHINADU KUMAR KHAN
Answer:
The Playground of Europe is:
C) Switzerland.
Step-by-step explanation:
Hope it helps! =D
 Help Help Help Help Help Help
The constant of proportionality of the equation y = 1 / 3 x is 1/3.
How to find constant of proportionality?Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, proportional relationship is one in which two quantities vary directly with each other.
Therefore, proportional relationship can be represented as follows:
y ∝ x
y = kx
where
k = constant of proportionalityTherefore, the constant of proportionality of y = 1 / 3 x is 1 / 3
learn more on proportional relationship here: https://brainly.com/question/29765554
#SPJ1
What is 2 3/4 X 12 ????
Answer:
33
Step-by-step explanation:
Please brainliest, and Hope this helped you, I also answered first! :D
Answer: 33
Step-by-step explanation:
from a random sample of 185 children from school g, 108 indicated they wanted to study science in college. from a different random sample of 165 children from school h, 92 indicated they wanted to study science in college. assuming all conditions for inference are met, which of the following is closest to the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college?
The difference in population proportions of students who wish to study science in college between the two schools has a standard error for a confidence interval of about 0.0165.
What is Standard Error ?One of the mathematical methods used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It can be characterized as a projection of that standard deviation.
The standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college can be calculated as:
SE = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }
where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
For School G, p1 = 108/185 = 0.5838, and n1 = 185.
For School H, p2 = 92/165 = 0.5576, and n2 = 165.
Substituting these values into the formula, we get:
SE = sqrt{ [0.5838(1-0.5838)/185] + [0.5576(1-0.5576)/165] }
SE = sqrt{ [0.2365/185] + [0.2436/165] }
SE = sqrt{ 0.000125 + 0.000147 }
SE = sqrt{ 0.000272 }
SE = 0.0165
Therefore, the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college is approximately 0.0165.
Learn more about Standard Error , visit:
https://brainly.com/question/13179711
#SPJ1
10 + 2x - 3x = - ( x + 2 )
Answer:
No solutionStep-by-step explanation:
[tex]\mathrm{10+2x-3x=-\left(x+2\right)}[/tex]
*2x-3x=-x*
[tex]\mathrm{10-x=-\left(x+2\right)}[/tex]
Expand:-
[tex]\mathrm{10-x=-x-2}[/tex]
Cancel the x from both sides:-
[tex]\mathrm{10=-2}[/tex]
and since 10=-2 is false, there is no solution.
__________________
Hope this helps!
Triangle XYZ is mapped onto triangle X′Y′Z′ by a dilation with a scale factor of 3 and center (2,1). What are the coordinates of triangle X′Y′Z′ when X(-3,2), Y(0,0), Z(2,1).
Don't forget that your ordered pairs need to be in parentheses and the coordinates separated by a comma!
X'=
Y'=
Z'=
30 points
Answer:
Step-by-step explanation:
To find the image of each point under the dilation, we need to apply the scale factor of 3 to the distances between the point and the center, and then add the coordinates of the center to get the new coordinates.
The center of dilation is (2,1), so we subtract 2 from the x-coordinates and 1 from the y-coordinates to get the distances from the center to each point:
X: (-3 - 2, 2 - 1) = (-5, 1)
Y: (0 - 2, 0 - 1) = (-2, -1)
Z: (2 - 2, 1 - 1) = (0, 0)
Next, we apply the scale factor of 3 to each distance:
X': (-5 × 3, 1 × 3) = (-15, 3)
Y': (-2 × 3, -1 × 3) = (-6, -3)
Z': (0 × 3, 0 × 3) = (0, 0)
Finally, we add the coordinates of the center (2,1) to each image:
X': (-15 + 2, 3 + 1) = (-13, 4)
Y': (-6 + 2, -3 + 1) = (-4, -2)
Z': (0 + 2, 0 + 1) = (2, 1)
Therefore, the coordinates of the image triangle X'Y'Z' are:
X' = (-13, 4)
Y' = (-4, -2)
Z' = (2, 1)
A circle is inscribed in a square
as shown. The area of the circle
is 153.94 square inches. What is
the area of the square?
The area of the square is 196.1019 square inches
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
area of the circle = 3.14r² , r =radius
=> 153.94 = 3.14r²
=> r² = 153.94/3.14 = 49.0254
=> r= ± √ 49.0254 =± 7.0018
=> r= + 7.0018, r= - 7.0018
Consider positive value
r= + 7.0018
Diameter, d= 2r = 2*7.0018 = 14.0036 inches
Side (a) of square = Diameter = 14.0036 inches
The area of the square
= a²
= 14.0036² square inches
= 196.1019 square inches
The area of the square is 196.1019 square inches
To learn more about the area from the given link
https://brainly.com/question/25292087
#SPJ1
The moon is about 382500 km away from earth. The distance actually varies by about 22500 km. What are the maximum and minimum distances to the moon
Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $240.00. The number of cards is at least 22 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $2.00 and for a package the cost is $6.00.
Write a system of 2 inequalities to model this situation. Use "
x
" for the number of packages and "
y
" for the number of cards.
First Inequality:
Select an answer
240.00
Second Inequality:
y
Select an answer
His postal expenses total 6.5x + 2.5y $357.50 and 13x + 5y 715, respectively, according to two systems of inequality.
what is inequality ?A relationship among two expressions or concepts that is not equal in mathematics is referred by the term inequality. Hence, inequalities results from imbalance. In mathematics, an equality establishes the connection between two quel numbers. Egality and inequality aren't the same thing. Use the not equal symbol most frequently when two quantities are not equal (). Values of any size can also be contrasted using a variety of inequalities. By changing the two sides until only components are left, many straightforward disparities can be solved. All the same, a host of mechanisms support inequality: Both sides' lowest values are split or added. Switch the left and the right.
given
It costs $2.50 to ship a card.
Buying a package will cost you $6.50.
Suppose x is the number of packages
Moreover, if y represents the number of cards
The situation is described by a system of inequalities that is
At least 16 more cards than packages make up the total number of cards.
⇒y ≥ 2x +16
Reiko wants to keep his postal expenses to a maximum of $357.50.
⇒6.5x +2.5y ≤ 357.5
⇒13x +5y ≤ 715
His postal expenses total 6.5x + 2.5y $357.50 and 13x + 5y 715, respectively, according to two systems of inequality.
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
You have $500,000 saved for retirement. Your account earns 6% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?
The answer comes to $43,592.00. 28 can be wiped from the account after 20 years, leaving nothing behind.
What is a fascinating illustration?Think about taking out a $1,000 loan with a seven-year, 10% interest rate. The first year's interest would cost you $100. You would pay $1,100 in interest the next year, which is the sum of the initial amount plus interest. Because of this, your salary for the upcoming year will be $110 (1,100 times 0.10).
Calculate the Yearly Amount (A) given the Prepaid Value (P), at interest rate I over n periods using the equation (A/P, I n).
The equation is:
[tex]A=P \frac{i(1+i)^n}{(1+i)^n-1}[/tex]
Where:
P is the Present value = $500,000
A is the monthly Amount
i is the interest rate = 0.06
20 years are the number of periods (n).
Substituting values:
[tex]A=\$ 500,000 \frac{0.06(1.06)^{20}}{(1.06)^{20}-1}=\$ 43,592.28[/tex]
To know more about Interest visit:
https://brainly.com/question/2294792
#SPJ1
Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 2.2 month. 33 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
F) Find the IQR for the average first time walking age for groups of 33 people.
Q1=
Q3=
IQR=
The values are Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and range IQR ≈ 0.5250 months.
What is IQR?The IQR for the average first-time walking age for groups of 33 people can be found as follows:
The standard deviation of the sample mean is given by:
σM = σ/√n = 2.2/√33 ≈ 0.3839
Using the standard normal distribution, the z-scores for the first and third quartiles are:
zQ1 = invNorm(0.25) ≈ -0.6745
zQ3 = invNorm(0.75) ≈ 0.6745
The corresponding sample means can be found using:
M = μ ± z(σM)
Where μ = 12, the population mean.
M1 = 12 - 0.6745(0.3839) ≈ 11.7375
M3 = 12 + 0.6745(0.3839) ≈ 12.2625
Therefore, the first quartile Q1 is approximately equal to 11.7375 months and the third quartile Q3 is approximately equal to 12.2625 months.
The IQR is given by:
IQR = Q3 - Q1 = 12.2625 - 11.7375 ≈ 0.5250 months.
Rounding to 4 decimal places gives Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and IQR ≈ 0.5250 months.
To know more about IQR and standard deviation follow
https://brainly.com/question/16782066
#SPJ1
Use this table to answer the question. Round to 2 decimal places.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total are made up of Yellow?
Yellow makes up approximately 17.32% of the total number of trips.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.
To find the percentage of the total that Yellow makes up, divide the total number of Yellow trips by the overall total number of trips, and then multiply by 100 to convert to a percentage -
Yellow total = 820
Overall total = 4730
Yellow percentage = (820/4730) x 100%
Yellow percentage = 0.1734
Yellow percentage = 17.34%
Therefore, Yellow makes up approximately 17.32% of the total number of trips.
To learn more about percentage from the given link
https://brainly.com/question/317717
#SPJ1
A car’s MPG went from 29 mpg to 34 mpg after a tune up. What was the percent change?
Answer:
17.24
Step-by-step explanation:
find the difference between 29 and 34. Then divide by 29 and multiply by 100. 34-29=5/29=0.1724 multiply by 100 =17.24%
True or False? Justify your answers (a) A linear transformation T:R" → R™ is completely determined by the effect on the columns of the n x n identity matrix. (b) Every linear transformation from R" to R" is a matrix transformation. (c) The range of the matrix transformation H Ax is the set of all linear combi- nations of the columns of A. (d) A linear transformation T:R" →Ris one-to-one if each vector in R" maps onto a unique vector in R". (e) The matrix transformation x H Ax is one-to-one if and only if the equation Ax = 0 has a unique solution. (f) The matrix transformation x Ax is one-to-one if and only if the columns of A are linearly independent.
True, false, true, true, false and true are the answers of statements a to f respectively.
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
(a) A linear transformation [tex]T:R^n\rightarrow R^m[/tex] is completely determined by the effect on the columns of the n x n identity matrix is true from the fact that the columns of any n x n matrix A completely determine the linear transformation T defined by T(x) = Ax for any vector x in Rⁿ.
(b) False. There exist linear transformations from Rⁿ to Rⁿ that are not matrix transformations.
(c) True. The range of the matrix transformation H Ax is the set of all possible linear combinations of the columns of A.
(d) True. A linear transformation [tex]T:R^n\rightarrow R^m[/tex] is one-to-one if and only if T(x) = T(y) implies x = y for any vectors x and y in Rⁿ.
(e) False. The matrix transformation x → Ax is one-to-one if and only if the equation Ax = 0 has only the trivial solution (i.e., x = 0).
(f) True. The matrix transformation x → Ax is one-to-one if and only if the kernel of the linear transformation T(x) = Ax is trivial, which is equivalent to the columns of A being linearly independent.
Hence, true, false, true, true, false and true are the answers of statements a to f respectively.
To learn more on Matrices click:
https://brainly.com/question/28180105
#SPJ1
. Corey has a piece of teak wood that is three times as long as his piece of oak wood. He
says that he can use two different equations to find out how long his piece of teak wood is
compared to his piece of oak wood. Is he correct? Explain your reasoning.
Corey's piece of oak wood is 8 inches long. Write and solve an equation to find the length of
mis teak wood piece.
The equation and solution to find the length of mis teak wood piece is x=3*8 and 24.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The length of oak wood=8inches
Teak wood= 3* oak wood
Now,
Let the length of teak wood be x
Then,
x=3*8
x=24
Therefore, by algebra the answer will be 24.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ1
You are testing the claim that smiling, rather than remaining neutral, during a court proceding will lead to a different punishment from the judge.
A sample of 34 people who smiled during their hearing and 34 people who kept neutral facial expressions during their hearing is taken and each judgment was rated for leniency. Those who smiled (population 1) had a mean leniency rating of 4.9 with a standard deviation of 1.7, while those who did not smile (population 2) had an average leniency rating of 4.1 and standard deviation 1.5. Test the claim using a 10% level of significance.
What are the correct hypotheses?
Based on the hypotheses, find the following:
Test Statistic =
p-value =
Therefore , the solution of the given problem of test statistic comes out to be Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.
Which test statistic is this?The Z-statistic has been the test statistics for anything resembling a Z-test and it confirms that the ordinary standard neutral hypothesis is true. Consider doing two separate X-y tests with a 0.05 level of significance and getting a 2.5 R-t value from your data (also referred as a Z-value). The p-value associated with this Z-value is 0.0124.
Here,
The hypotheses are:
Null hypothesis: There is no significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.
Alternative hypothesis: There is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.
To test this claim, we can use a two-sample t-test since we are comparing the means of two independent samples.
The formula for the test statistic is:
t = (x1 - x2) / sqrt((s1² / n1) + (s2² / n2))
where:
x1 = sample mean of those who smiled
x2= sample mean of those who remained neutral
s1 = sample standard deviation of those who smiled
s2 = sample standard deviation of those who remained neutral
n1 = sample size of those who smiled
n2 = sample size of those who remained neutral
Substituting the given values, we get:
t = (4.9 - 4.1) / sqrt((1.7² / 34) + (1.5² / 34))
t ≈ 2.116
Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.
Since the p-value (0.039) is less than the significance level (0.10), we reject the null hypothesis. Therefore, we have sufficient evidence to conclude that there is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.
To know more about test statistic , visit
brainly.com/question/14128303
#SPJ1
CAN SOMEONE HELP WITH THIS QUESTION?✨
The marginal revenue at 8 units is given as follows:
MR(8) = 288 dollars per unit.
How to obtain the marginal revenue?The revenue function is defined as follows:
R(q) = -7q² + 400q.
The marginal revenue function is the derivative of the revenue function, hence it is obtained as follows:
MR(q) = -14q + 400.
At 8 units, the marginal revenue is found with the numeric value of MR(q) at q = 8, hence:
MR(8) = -14(8) + 400 = 288 dollars per unit.
More can be learned about marginal revenue at https://brainly.com/question/13444663
#SPJ1
What is 1/2 divided by 1/10
Answer: 2
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{10}{1} = \frac{10}{2} = 5[/tex]
please help ASAP! Show ur work
The linear equations represented by graph are y=6-2.5x and y=0.8x.
What is a linear equation, exactly?
When the greatest power of a variable is 1, the equation is said to be linear. Other term used for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There is three more constants added to the constant C: the variables x and y, the coefficients A and B, and the variables.
Now,
In given graph for y=6-2.5x
when x y
1 3.5
2 1
and for y=0.8x
when x y
1 0.8
2 1.6
hence,
The linear equations represented by graph are y=6-2.5x and y=0.8x as shown in the image.
To know about linear equations visit the link
https://brainly.com/question/29739212
#SPJ1
coupon-collecting problem. there are c different types of coupon, and each coupon obtained is equally likely to be any one of the c types. find the probability that the first n coupons which you collect do not form a complete set, and deduce an expression for the mean number of coupons you will need to collect before you have a complete set
This expression gives the mean number of coupons you will need to collect before you have a complete set, given that each coupon obtained is equally likely to be any one of the c types.
What is probability?In general, probability is a measure of the likelihood that a certain event or outcome will occur. It is a branch of mathematics concerned with analyzing and quantifying uncertainty. In formal terms, the probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probabilities between 0 and 1 represent the degree of uncertainty associated with the event.
Here,
The probability that the first n coupons collected do not form a complete set can be found as follows:
Let S be the event that the first n coupons do not form a complete set, and let Ci be the event that the i-th coupon collected is a new type (i.e., a coupon of a type that has not been collected before).
Then, the event S can be expressed as the intersection of the events C1, C2, ..., Cn, where each Ci is independent of the others and has probability (c-i+1)/c of occurring. This is because there are c-i+1 types of coupons remaining after i-1 types have been collected, and each of these types is equally likely to be the next coupon collected.
So, the probability of S can be calculated as:
P(S) = P(C1 ∩ C2 ∩ ... ∩ Cn) = P(C1) × P(C2) × ... × P(Cn)
= (c-1)/c × (c-2)/c × ... × (c-n+1)/c
= Π(i=1 to n) (c-i+1)/c
To deduce an expression for the mean number of coupons you will need to collect before you have a complete set, let X be the random variable representing the number of coupons collected until a complete set is obtained. Then, the expected value of X can be calculated using the formula:
E(X) = Σ(k=1 to c) P(X ≥ k)
This formula sums the probabilities of all possible numbers of coupons collected until a complete set is obtained, weighted by their respective probabilities.
Note that P(X ≥ k) is the probability that a complete set has not been obtained after k-1 coupons have been collected, which is equal to the probability of the event S above. So, we can substitute the expression for P(S) into the formula for E(X) to get:
E(X) = Σ(k=1 to c) P(X ≥ k)
= Σ(k=1 to c) Π(i=1 to k-1) (c-i+1)/c
= Σ(k=1 to c) Π(i=0 to k-2) (c-i)/c
= Σ(k=0 to c-1) Π(i=0 to k-1) (c-i)/c (by changing the index of summation)
= Σ(k=0 to c-1) (c-k)/cˣ
= c Σ(k=0 to c-1) (1/c)ˣ - Σ(k=0 to c-1) (k/c)ˣ
= c (1 - (1/c)ˣ)/(1 - 1/c) - B(c, 1/c)
where B(c, 1/c) is the sum of the first c terms of the series (k/c)ˣ.
To know more about probability,
https://brainly.com/question/30034780
#SPJ1
Please Answer Quick!!
Therefore , the solution of the given problem of graph comes out to be
option c is correct it shows an association of the distribution of different mode of transportation among the same age of group.
What is graph ?Academics use graphs to visually represent or chart happenings or quantities in a logical manner. The interaction between a number of objects is frequently represented by a graph point. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The vertices, sometimes referred to as nodes, should be joined together with glue. Vertex numbers in this graph are 1, 2, 3, or 5, while edge numbers are 1, 2, 1, 3, 2, 4, etc. (2.5). (3.5). (4.5). (4.5). (4.5).
Here,
Given : A graph having choices of adult , child , teen and senior mode of transportation ,
In different age the mode of transportation preferred by among the same ages .
Thus ,
it shows an association of the distribution of different mode of transportation among the same age of group.
So , option c is the correct answer.
To know more about graphs visit:
https://brainly.com/question/11950136
#SPJ1
I am unsure how to do this, please help!
The original number in the given question solved by algebra is 39/7.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The number is divided 5 times by 7 more than that number.
Let the number be x
Then,
x+7/5x = 8
x+7=40x
7=39x
x=39/7
Therefore, by algebra the answer will be 39/7.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ1
On the Navajo Reservation, a random sample of 210 permanent dwellings in the Fort Defiance region showed that 70 were traditional Navajo hogans. In the Indian Wells region, a random sample of 141 permanent dwellings showed that 20 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defiance region, and let p2 be the population proportion of all traditional hogans in the Indian Wells region.
(a) Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
Using the Confidence-interval formula, we get that the confidence interval for p1-p2 = 1.962.
Define Confidence-interval formula.The term "confidence interval" is used to define the degree of uncertainty surrounding a sampling technique. The probability that the parameter's true value will fall inside a given range is provided by a confidence interval.
A confidence interval estimate of a population mean is often presented as follows: = Sample mean × Standard error of Mean
Given, n1 = 210 and n2 = 141
Sample proportions that have been given are p1 = 70 and p2 = 20
difference of the estimate, p1 - p2 = 50
Confidence interval for p1-p2:
(p1 - p2)-E ≤ (p1-p2) ≤ (p1-p2) + E
Where E = z × √ (p1q1/n1 + p2q2/n2)
Z is the critical value for confidence level.
Putting the values of n1, n2, p1 and p2 we get:
Critical z value, z = 1.962
Standard Error, [tex]SE_{p1 - p2}[/tex] = NaN
Therefore, ≈95% Confidence Interval:(NaN, NaN).
To know more about Confidence-interval formula, visit:
https://brainly.com/question/14121106
#SPJ1
Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation
The key features of this rational function include the following:
Domain: (-∞, -2) ∪ (-2, ∞)
Range: (-∞, -1) ∪ (-1, ∞)
Y-intercept: -5/2.
X-intercept: -5.
Vertical asymptote: x = -2.
Horizontal asymptote: y = -1.
What is a rational function?In Mathematics, a rational function simply refers to a type of function which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:
NumeratorDenominatorAdditionally, the vertical extent of any graph of a rational function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Read more on asymptote here: brainly.com/question/28003042
#SPJ1
