The expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.
Given that,
Take into account n separate coin flips with a p percent chance of landing on heads. Say a changeover happens any time an outcome diverges from the one that came before it. For instance, there are 3 changeovers if n=5 and the result is HHTHT.
We have to determine the anticipated number of transitions.
We know that,
Independent flips,
n =12
Probability of heads =p
Probability of tails =(1-p)
Let m=1,2,...n
If mth term may be head then (m+1)th outcome could be head or vice-versa.
Probability of change overs from mth to (m+1)th outcome =2p(1-p)
So, the expected changeovers is given by
E[change overs] = (n-1) *2p(1-p)
= (12-1) × 2p(1-p)
=11 × 2p(1-p)
=22p(1-p)
Therefore, the expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.
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Please help I’m going to fail i need help please
The volume of the figure can be calculated by adding the volumes of the two rectangular prisms. The first rectangular prism has dimensions 12 in x 10 in x 2 in, so its volume is 12102 = 240 in^3. The second rectangular prism has dimensions 10 in x 7 in x 21 in, so its volume is 10721 = 1540 in^3. The total volume of the figure is 240 in^3 + 1540 in^3 = 1780 in^3.
Find the distance between (6,-2) and (1,2)
Answer: [tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]
Step-by-step explanation:
We will use the distance formula to help us solve (see attached). Let (6, -2) be point one and (1, 2) be point two.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(1-6)^2 +(2--2)^2}[/tex]
[tex]\displaystyle d=\sqrt{(-5)^2 +(4)^2}[/tex]
[tex]\displaystyle d=\sqrt{25 +16}[/tex]
[tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]
41 is a prime number, so this is the simplest radical form.
Solve for w: -3(-9w + 6) – 5w = 4(w – 6) – 8
Step-by-step explanation:
27w - 18 - 5w = 4w - 24 - 8
22w - 18 = 4w - 32
18w = -14
w = -14/18
w = -7/9
1. Gordon estimates that the ramp will be 6 inches tall when it is 60 inches
long. Explain the error that he made and correct the error.
Answer:
it's 0.25 for the first one
Diana averages 6 mph walking
to school. Averaging 35 mph on
the way back home by car, she
takes } hour less time.
How far is the school
from her home?
If Diana averages 6 mph walking to school. The distance from the school to her home is 5.4 miles.
What is distance?Distance can be defined as how far an object is from another object.
Formula for Distance
Distance = Speed × Time
Solving for t (time) to walk to school
6t = 35 (t-.75)
6t = 35t - 26.25
Collect like terms
29t= 26.25
Divide both side by 29t
t = 26.25/29
t= .9
t=54 minutes
Solving for Distance (d)
d = 6× .9
d = 5.4 miles
Therefore the distance is 5.4 miles.
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The complete question is:
Diane averages 6 mph walking to school. Averaging 35 mph on the way back home by car, she takes 3/4 hour less time. How far is the school from her home?
In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
How many were in math only?
How many were not majoring in computer science?
How many were not math or computer science?
Answer:
How many were in math only?7
How many were not majoring in computer science?9
How many were not math or computer science?2
Step-by-step explanation:
Total students 25
-math major 13
-Science major 10
_______________
2 not majoring in math or CS majors
math major 13 -6 dual majors = 7 major in math only
math major 7+ not math or CS 2 = 9 not majoring in CS
You randomly observe purchases at a candy store and record the weight of each bag of candy
with 100 different customers. You find the proportion of weights greater than 2 pounds. Is
investigating this sample proportion the same as investigating the sampling distribution of the
proportion?
Answer:
OptionB)
Step-by-step explanation:
→→When you are talking about sample proportion You are considering a Single ,set of same kind of Data,Like body weight of Students in a class, from which you are taking out samples for Observation.
For example, A colony is being studied whether each human in that colony is healthy or not by checking their body mass index.
→→When we are investigating or considering Sampling Distribution we consider two different sets or kinds of Data set Possessing Similar Characteristics because we have to compare these two sets of Data.
For example , Take two colonies A and B , Check their honesty by observing how many floors they have made in their Plot.Whether they care or don't care about their Surrounding or Mother Earth by looking, if number of floors exceeds than 2 i.e ground floor and first floor , it means Dishonest , if maximum number of floor =2 ,it means honest.
2. Use the product rule (and chain rule) to find the derivative of the following
(a) y = x²(3x + 4)²
(b) y = (1+x²) (2 - x²³)³
(c) y = (2+√)(x+3)²
(d) y = (2x² + 1)(x5 +3)4
The derivative of the following are:
(a) 36x³ + 72x² + 32x
(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)
(c) -1/2√x(x+3)² + 2(x+3)(2+√x)
(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³
What is a derivative?
The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Here, we have
Given
(a) y = x²(3x + 4)²
Derivative with respect to x and we get
dy/dx = 2x(3x + 4)² + x²(18x + 24)
dy/dx = 36x³ + 72x² + 32x
(b) y = (1+x²) (2 - x²³)³
Derivative with respect to x and we get
dy/dx = 2x(2 - x²³)³ + (1+x²)(-23x²²)3(2 - x²³)²
dy/dx = 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)
(c) y = (2+√x)(x+3)²
Derivative with respect to x and we get
dy/dx = -1/2√x(x+3)² + (2+√x)2(x+3)
dy/dx = -1/2√x(x+3)² + 2(x+3)(2+√x)
(d) y = (2x² + 1)(x⁵ +3)⁴
Derivative with respect to x and we get
dy/dx = 4x(x⁵ +3)⁴ + (2x² + 1)4(x⁵ +3)³(5x⁴)
dy/dx = 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³
Hence, the derivative of the following are:
(a) 36x³ + 72x² + 32x
(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)
(c) -1/2√x(x+3)² + 2(x+3)(2+√x)
(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³
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In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. Are the conditions for use of a T-model met?
1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
2. In a random sample of 50 university students (37 females and 13 males), the distribution of time spent at university recreational facilities is strongly skewed to the right for females but not strongly skewed for males. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
3. In a study of 100 brother-sister sibling pairs at the university, the distribution of time spent at university recreational facilities for the 100 males is compared to the 100 females; both distributions are fairly normal.
In the following first scenario the conditions for the t-test is not met for the difference in populations mean so the hypothesis test cannot be done.
1)The distribution of time spent at university recreational facilities is considerably skewed to the right in a random sample of 100 university students.
The variable is X, which stands for time spent at the university's leisure facilities.
Because the variable "time" is at least ordinal, this criterion is satisfied.
The sample was drawn at random, hence this requirement is met.
The data is heavily skewed to the right, the normal distribution is symmetrical, and this data set is highly unlikely to have a normal distribution.
2)The distribution of time spent at university recreational facilities is highly skewed to the right for females but not strongly skewed for males in a random sample of 50 university students (37 females and 13 males).
In this scenario, you have two groups of interest, and the variable X: Time spent at the university recreational facilities will be measured for each group.
Because the variable "time" is at least ordinal, this criterion is satisfied.
The samples "male students" and "female students" were randomly taken so this condition tests.
You have two populations of interest in this case. Male university students and female university students are divided into two groups. To use the t-test, both populations must be normal.
The distribution for the females has strongly skewed to the males have a somewhat skewed distribution.
If the distribution of females is substantially skewed, it is impossible for it to be normal.
In this case, a t-test is not appropriate.
3)Because the experimental units are dependent, this is a "paired sample" situation. (Consider the sibling pair's relationship; if they get along well, it is more likely that they will spend time together in the recreational facilities; if their relationship is not so good, it is more likely that the presence of one of the siblings in the facilities will cause the other to spend less time there.)
X will be the variable measured for each member of the "sibling pair": Time spent at university recreational facilities, and the research variable in this case, will be defined by the difference in times measured for both siblings.
The normality condition checks.
so the t-test in this scenario can be applied.
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Determine whether the rule represents an exponential function. Explain why or why not.
Y=-2•x^7 WILL MARK BRAINLIEST
A. Since the independent variable X is not the exponent, y=-2•x^7 does not represent an exponential function.
B. Since the independent variable X is not the base, y=-2•x^7 does not represent an exponential function.
C. Since the independent variable x is the base, y=-2•x^7 does represent an exponential function.
D. Since the independent variable X is the exponent, y=-2•x^7 represents an exponential function.
The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)
Does a given expression represent an exponential function?
In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:
y = b · aˣ
Where:
a, b - Real coefficients. (b - Value when x = 0, a - Base)x - Independent variable.y - Dependent variable.By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.
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Find the average rate of change for the function over the given interval y=x^2+9x between x=3 and x=7.
Answer:
average rate of change = 19
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 3, 7 ] and y = f(x) , then
f(b) = f(7) = 7² + 9(7) = 49 + 63 = 112
f(a) = f(3) = 3² + 9(3) = 9 + 27 = 36
then
average rate of change = [tex]\frac{112-36}{7-3}[/tex] = [tex]\frac{76}{4}[/tex] = 19
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
Answer:
2268π ft³ ≈ 7125 ft³
Step-by-step explanation:
You want the volume of a 22 ft long cylinder capped by a hemisphere 9 ft in radius.
CylinderThe formula for the volume of a cylinder of radius r and height h is ...
V = πr²h
HemisphereThe formula for the volume of a hemisphere of radius r is ...
V = 2/3πr³
Total volumeThe sum of the volumes of the two figures is ...
Vtotal = πr²h +2/3πr³ = πr²(h +2/3r)
Using the given values for height and radius, we find the volume to be ...
Vtotal = π(9 ft)²(22 ft + 2/3(9 ft)) = π(9 ft)²(28 ft)
Vtotal = 2268π ft³ ≈ 7125 ft³
The volume of the composite is about 7125 cubic feet.
An organization needs to reach out to a specific target audience, and has decided that it wants to use social media advertising to do so. It wants to buy specific keywords to accurately target the audience who would want to see these ads. The aim is to get a high effective exposure rate and engagement rate without invading consumer privacy. Which of the following advertising revenue models would best suit the organizations' needs? a. Bidding for ad words b. Pay-per-click c. I-Traffic Index d. Pop-under ads e. Bidding for ad space
The advertising revenue model that would best suit the organization needs is Bidding for ad words.
Given that,
A company has made the decision to employ social media advertising to connect with a certain target population in order to accomplish this. To precisely target the demographic that would be interested in seeing these ads, it wants to purchase a set of keywords. The objective is to increase consumer involvement and exposure rates without violating their privacy.
The Organization investing to buy specific keywords for advertising, when someone searches for some words in a social media search engine, the search engine queries it's users looking for the keyword matches in it's ad group thus displaying the most relevant ad aiming for more exposure.
Therefore, bidding for ad words is the advertising income strategy that would best meet the organization's needs.
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Arianys invested $61,000 in an account paying an interest rate of 7% compounded
continuously. Yusuf invested $61,000 in an account paying an interest rate of 7%
compounded monthly. After 14 years, how much more money would Yusuf have in
his account than Arianys, to the nearest dollar?
Given the above information the amount Yusuf would have more in his account than Arianys is $9,929,539.57
How to calculate compound interest?You should be aware that compound interest is sum of money that accrues on the capital over a stated period of time.
The given parameters are:
Arianys investment = $61,000, interest rate 7% compounded continuously
Yusufs investment = $61,000, rate 7% compounded monthly
number of years each 14 years
Arianys investment
Compound interest = [tex]P(1+r)^{t}[/tex] - 1
Applying the figures we have
CI= 61000(1+0.07)¹⁴ - 1
=61000(1.07)¹⁴ -1
CI=$96,290.58
For Yusuf investment
CI=[tex]P(1+\frac{r}{n})^{nt} - 1[/tex]
Applying the figures we have
Ci=61000(1+0.0121)²⁹⁶⁸ -1
Compound Interest = 61000(1.0058)¹⁶⁸ - 1
Simplifying this we have
61000(164.36)
CI=$10,025,830.12
Therefore the amount in Yusufs account more than Arianys account is $(10,025,830.12-96,290.58)
Amount = $9,929,539.57
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Q3. (b)
The length of human pregnancies from conception to birth approximate a normal
distribution with a mean of 266 days and a standard deviation of 16 days.
(i). What percentage of all pregnancies will last less than 240 days?.
Soln.
Answer:
5.2%
Step-by-step explanation:
determine the number of n digit numbers with all digits even, such that 2 and 4 each occur a nonzero, odd number of times.
According to the question asked the number of digits with all digits even can be found as:
aₙ = 6ⁿ + 2.3ⁿ + 1(n≥0)
Given:
let the number be aₙ.
The number aₙ equals the number of n permutations at the multiset S
where S = { ∞ 2, ∞ 4, ∞ 6, ∞, 8, ∞ 10} on which 2 and 4 occurs
a non zero even number at times.
The exponential generating function have a₀, a₁, a₂,....aₙ
f'(x) = (1+x²/2! + x⁴/4!+...)ⁿ
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Diana
averages 6 mph walking
to school. Averaging 35 mph on
the way back home by car, she
takes 3/4 hour less time.
How far is the school
from her home?
The school is 5.43 miles from Diana's house. This is evaluated by using the speed-distance-time relationship.
What is the relation between the speed-distance-time?The ratio of distance to time gives speed to an object.
I.e., S = D/T or D = ST ot T = D/S
Calculation:It is given that,
Diana walks to her school at a speed of 6 mph.
So, the time taken for her to walk is t1 = d/6 hours
Diana returns home by car at a speed of 35 mph.
So, the time taken for her to return by car is t2 = d/35 hours
But it is given that, she takes 3/4 hours less time for returning by car.
Thus, we can write t2 = t1 - 3/4
⇒ d/35 = d/6 - 3/4
⇒ 3/4 = d/6 - d/35 = d(1/6 - 1/35)
⇒ 3/4 = d(29/210)
⇒ d = (3 × 210)/(4 × 29) = 5.431 miles
On rounding the obtained value to the nearest hundredths is 5.43 miles.
Thus, the distance between Diana's home and her school is 5.43 miles.
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Royal Co. receives a dividend of $4.88 per share. Today the closing price of the stock is $59.95. The current stock yield to the nearest tenth of a percent is: 8.1% 8.0% 8.2% 8.3% None of these
Receiving $4.88 dividend out of the closing stock price of $59.95, means that the stock yield is 8.1%
Dividend is defined as a distribution of payment by a company to its shareholders that is originated from the company's profit and is payable to the shareholders every quarter in a given year, while stock yield is defined as an income generated by the stock being held by the shareholders.
To determine the percentage of stock yield, we will need to divide the closing price of the stock which is $59.95 with the amount of dividend distributed for each stock held which is $4.88, and the calculation is as follows:
59.95/4.88×100%=8.1%
Therefore the stock yield is 8.1%
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use a proof by contraposition to show that for integers m and n if m n is even then m is even or n is even
The contrapositive is true
Proving a contraposition involves proving that the contrapositive of a statement is true. The opposite of "if m n is even then m is even or n is even" is "if m is not even and n is not even then m n is not even".
To prove this statement by a proof by contrast, first assume that m is not even and neither is n. This means that both m and n are odd.
Since m and n are odd, m n is also odd. This can be expressed as:
If m and n are odd, we can write m as;
2k + 1 and n as 2l + 1 for integers k and l.
Then mn = (2k + 1)(2l + 1) = 4kl + 2k + 2l + 1 = 2(2kl + k + l) + 1,
which is odd. Therefore, m n is not even if m is not even and n is not even.
It turns out that the opposite of the original statement is true, so the original statement must also be true. Therefore, if m n is even, then we can say that that m is even or n is even using a proof by contrast.
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A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
(a)
State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let p1 = population proportion saying financial security more than fair in 2012 and p2 = population proportion saying financial security more than fair in 2010.)
H0: p1 − p2 = 0
Ha: p1 − p2 ≠ 0
H0: p1 − p2 > 0
Ha: p1 − p2 ≤ 0
H0: p1 − p2 ≠ 0
Ha: p1 − p2 = 0
H0: p1 − p2 ≥ 0
Ha: p1 − p2 < 0
H0: p1 − p2 ≤ 0
Ha: p1 − p2 > 0
The hypotheses that can be used to test for a significant difference between the population proportions for the two years is H0 :- P1 = P2
How to calculate the hypotheses?
In math, the process of calculating the hypotheses is to select a statistic based on a sample of fixed size, calculate the value of the statistic for the sample and then reject the null hypothesis if and only if the statistic falls in the critical region.
Here we know that certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
And we need to find the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
Here let us consider P1 refers population proportion saying financial security more than fair in 2012 and P2 refers population proportion saying financial security more than fair in 2010.
As per the definition of the hypotheses, the resulting hypotheses is written as,
=> H0 :- P1 = P2
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Travis, Jessica , and robin are collecting donations for the school band. Travis wants to collect 20% more than jessica and robin wants to collect 35% more than travis. If the students meet there goals and Travis collects $43 how much money did they collect in all
They collected $134.45 and we can find this using percentage.
Travis = $43
Jessica = 43 - (43 × 20%) = $34.4
Robin = 43 + (43 × 35%) = $58.05
Percentage (%):
In maths percentage is the value of ratio that shows the fraction of 100.percent means per 100.It does not have any units.Percentage is denoted by %It is also known as per cent.In order to find percent, we use the formula (original number/ another number) multiply by 100.It has a variety of uses in mathematics.Percentage increase and decrease can be calculated by computing the difference between the two values and comparing to the initial value.To know more about Percentage:
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two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .
Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.
Given that,
If and only if, two events, a and b, are independent. Remember that rearranging the multiplication rule will result in. Consider some events a and b.
We have to find which of the following claims about a and b is true.
We know that,
We have if the occurrence of event A has no bearing on the probability that event B will also occur, then the two events A and B are said to be independent.
P(A and B) = P(A) P(B) can be used to numerically describe the probability of two separate events.
As a result, we can draw the conclusion that two events, a and b, are independent if and only if they are.
Therefore, Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.
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You can spend at most $8 on potatoes and carrots for a stew. Potatoes cost $2 per pound,
and carrots cost $1 per pound. Write an inequality that represents the amounts of potatoes
and carrots you can buy. Let x = pounds of potatoes and let y = pounds of carrots.
Answer:
[tex]2x + y \leq 8[/tex]
Step-by-step explanation:
since potatoes cost $2 they are represented as 2x
Carrots cost $1 and are simply y
Does y = x2 + 1 represent a linear or nonlinear function? Explain.
Answer: the function is nonlinear
Step-by-step explanation:
y = x2 + 1 is a nonlinear equation because for it to be an linear question it must be the following
Linear:
2x-1=y
y=2x-1
nonlinear
y = x2 + 1
Linear equations are a constant slope ( straight line ) and nonlinear equations has a slope that varies between points so y = x2 + 1 is an non-linear equation because it has an slope that varies between points.An article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. Ethnicity: African, American, Asian, Caucasian, Hispanic Frequency: 69, 11, 330, 8, In a recent census, the proportions for these four ethnic groups are 0.177.0.020, 0.734, and 0.069, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out a test of appropriate hypotheses using a significance level of 0.01. (Let P, PPs, and be the population proportions of the four ethnic groups (African American, Asian, Caucasian, and Hispanic respectively) appearing in commercials on Philadelphia television stations.) State the appropriate hypotheses. o H0: P1 = 0.165, P2 = 0.026, P3 = 0.789, P4 = 0.019 Ha: at least one P1 ≠ P10o H0: P1 = 0.069, P2 = 0.011, P3 = 0.330, P4 = 0. 008Ha: at least one P1 ≠ P10o H0: P1 = 0. 177, P2 = 0.020, P3 = 0.734, P4 = 0.069Ha: at least one P1 ≠ P10o H0: P1 = P2 = P3 = P4 = 0.250Ha at least one p1 ≠ 0.25 Calculate the test statistic (Round your answer to two decimal places.)x^2 = ______
When comparing the proportions of ethnic groups represented in television commercials on Philadelphia stations to census data, we can use a chi-squared test to see if there is a difference.
Suitable hypotheses for this test include the following: H0: P1 = 0.165, P2 = 0.026, P3 = 0.789, and P4 = 0.019 Ha: at least one P1 to P10, where P1, P2, P3, and P4 represent the proportions of the four main ethnic groups—African, Asian, Caucasian, and Hispanic—in the population.
The test statistic cannot be calculated until we get the predicted frequencies for each group under the null hypothesis. Given that N is the total number of observations and E I is the expected frequency for group I, E I = N * P I provides the expected frequency for each group.
the population percentage for group I is P i.
These equations allow us to determine the anticipated frequencies in the following ways:
E 1 = 69 * 0.165 = 11.485
E 2 = 11 * 0.026 = 0.286
E 3 = 330 * 0.789 = 261.67
E 4 = 8 * 0.019 = 0.152
After that, the chi-squared test statistic is calculated as follows: x2 = ∑_(i=1)4 [(O i - E i)2 / E i], where O i is the observed frequency for group I and E i is the anticipated frequency for group i.
The numbers for the observed and anticipated frequencies are substituted to produce the following equation: x2 = (69 - 11.485)2 / 11.485 + (11 - 0.286)2 / 0.286 + (330 - 261.67)2 / 261.67 + (8 - 0.152)2 / 0.152
= 57.015^2
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nikki williams wishes to evaluate the risk and return behaviors associated with various combinations of assets x and y
Nikki can use modern portfolio theory to assess the risk and return behaviors associated with different combinations of assets X and Y.
Modern portfolio theory involves calculating the expected return and risk of a portfolio of assets by analyzing the correlations between the assets. It also looks at the diversification benefits of combining different assets and the impact of adding riskier assets to a portfolio. By quantifying the risk and return behaviors of different portfolios, Nikki can make informed decisions about which portfolios are most suitable for her.Modern portfolio theory is used to assess the risk and return behaviors of different combinations of assets X and Y. It considers correlations between the assets, the diversification benefits of combining them, and the impact of adding riskier assets. By quantifying the risk and return behaviors, Nikki can make informed decisions about which portfolios are most suitable for her.
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assume that the heights of of adult males in a certain region are normally distributed. the heights (in inches) of 20 randomly selected adult males from this region are listed below: 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 use this sample data and a .05 significance level to test the claim that the variance of all heights in this region is less than 6.25.
The sample variance is 2.976 , which means it's lesser than 6.25. We calculate this using the standard method.
Given:
Sample data is 0.05
The sample size is 20.
And ,
The hypotheses are:
H0: sigma^2 = 6.25 (>=)
Ha: sigma^2 < 6.25
The critical value is 10.117. If the test statistic is less than this value, we'll reject the null hypothesis. We Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go.
The test statistic is:
2.976 * 19 / 6.25 = 9.047.
So we reject the null hypothesis. The variance is not 6.25, which means it is lesser then 6.25
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. If $6000 is invested at 4% interest, compounded annually, then after n years the investment is worth an = 6000(1.04) dollars. Exercise (a) Find the first five terms of the sequence {an}. Step 1 For an = 6000(1.04)", we have a = 6000(1.04) 6240 6240.00 and a2 = 6000(1.04) = 6489.6 6489.60 Step 2 Rounding answers to two decimal places, we similarly have a3 = 6749.184 ,24 = 7019.151 ,ag = 7299.197 X Submit Skip_(you cannot come back) Exercise (b) Is the sequence convergent or divergent? Step 1 Since 1.04 is greater than 1, we have the following. (If an answer does not exist, enter DNE.) lim (1.04)" = 6000n + 1 6000n n00 x Submit Skip (you cannot come back)
As per question and the information provided we can compute the solution for both exercises as follows:
Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate additional revenue or to make money on the investment over a certain amount of time.
Exercise (a)
The sequence "an "'s" first five terms are:
[tex]a1 = 6000(1.04) = 6240 [/tex]
[tex]a2 = 6000(1.04) ^2 = 6489.6 [/tex]
[tex]a3 = 6000(1.04)^3 = 6749.184 [/tex]
[tex]a4 = 6000(1.04) ^4 = 7019.151 [/tex]
[tex]a5 = 6000(1.04)^5 = 7299.197[/tex]
Exercise (b)
Because infinity, which is not a finite number, serves as the series's limit as n approaches infinity, the sequence is divergent.
[tex]an = 6000(1.04)^n [/tex]
that is the formula for the nth term of the sequence. As n rises, the value of
[tex](1.04)^n[/tex]
it grows steadily larger, which causes a to grow steadily larger until it approaches infinity. The sequence "an" diverges as a result.
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Question 2
What is the length of DE? (number only)
The length of DE is 6.3
Similar triangles are triangles that have a similar appearance but differ in size.
Two triangles are similar if their angles are the same (corresponding angles) and their sides have the same ratio or proportion (corresponding sides)
If two triangles are similar, it means that their corresponding angle pairs are all equal.All triangle corresponding sides are proportional.The " ~ " symbol is used to represent similarity.
According to the question,
In ΔABC and ΔDBE,
(1) ∠B = ∠B (common)
(2) ∠ACB = ∠DEB (opposite sides are equal)
(2) ∠CAB = ∠ECB
Therefore , ΔABC ~ ΔDBE
By using similar triangle property
The ratio of correspond sides are equal ,
AB/BD = BC/BE = AC/DE
=> 2/1 = AC/DE
=> 12.6 / DE = 2/1
=> DE = 12.6/2
=> DE = 6.3
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A manufacturer of floor mops would like her product to last 700 hours, on the average. She hopes the mean number of hours is not a lot less than 700 (people will not continue to buy her product) or a lot more than 700 (people would seldom have to buy the product). However, the manufacturer has reason to believe the mean may have changed. A random sample of 48 items shows that sample mean = 675 and sample standard deviation = 77 hours. Use the significance level α=.05. What is the appropriate test to perform? Regarding the hypothesis testing in question 1, what is the rejection region? Regarding the hypothesis testing in question 1, what is the p-value of the test? Round your answer to four decimal places Regarding the hypothesis testing in question 1, what is your conlusion?
The appropriate test to perform is one sample t test
The rejection reason is t statistic less than -2.012 or t statistic more than -2.012
The p value of the test is 0.0292
Firstly,
As the population standard deviation is unknown and the sample size is more than 30, it is appropriate to use one sample t test for this hypothesis testing
Testing if the mean is changed from 700 levels or not
Null and alternate hypothesis are 700
Degree of freedom,
n-1
= 48-1
= 47
Using alpha level 0.05 and t critical table, we found the following two critical values
t critical values= -2.012 and 2.012
So, the rejection reason is t statistic less than -2.012 or t statistic more than -2.012
Now,
Population means = 700 hours
Sample mean = 675 hours
n = 48
So,
Test statistic= (mean-alternate hypothesis)/(s/√n)
= (675-700)/ (77/√48)
=-25/11.1140
= -2.249
Degree of freedom = n-1
= 48-1
= 47
With t distribution table for -2.249 and 47 degrees of freedom obtain p value of 0.0292
So, pvalue= 0.0292
Reject null hypothesis since the p value is less than alpha level
So, we conclude that the mean has changed from 700 hours
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