a vertex of a rooted tree is called a leaf if it has no children. vertices that have children are called internal vertices. if d is a vertex in a tree, the with d as its root is the subgraph of the tree containing d and its descendants and all edges incident to these descendants.

Answers

Answer 1

The root of a tree is the vertex from which all other vertices can be reached by following edges. The root of a tree is the only vertex that does not have an incoming edge.

In a rooted tree, a vertex is called a leaf if it has no children (i.e., it does not have any edges going out from it). Internal vertices are those that have children and are connected by edges to other vertices in the tree. If a vertex d is the root of a tree, the subgraph with d as its root is defined as the set of vertices that can be reached from d by traversing its edges, as well as the edges connecting them. The root is the only vertex that does not have an incoming edge, and all other vertices can be reached from the root.

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Related Questions

Write the
slope-intercept form of the equation of
the line that passes through the point (1, 2) and
has the slope of 6.

Answers

2=6x1+b this is slope intercept form

Krystal is considering job offers from two companies. Company A offered her a starting salary of $45,000 with a $2100 raise at the end of each year. Company B offered her a starting salary of $45,000 with a 4.2% raise at the end of each year. Let f(t) represent Carissa's salary at Company At years after accepting a position at Company A, and let g(t) represent Carissa's salary at Company B t years after accepting a position at Company B. a. Find a function formula for f. b. Find a function formula for g. c. If Carissa was expecting to work for 5 years before going back to school, which company do you think she should work for? Use your functions to justify your answer. I d. If Carissa was expecting to work for 10 years before going back to school, which company do you think she should work for? Use your functions to justify your answer.

Answers

The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.

Given that,

Krystal is weighing two job offers from various organizations. She received a $45,000 beginning salary from Company A, with annual raises of $2100. Company B gave her a $45,000 beginning salary with an annual rise of 4.2%. Let f(t) stand for Carissa's pay at the company. Let g(t) stand in for Carissa's pay at Company B at Years after Accepting a Position at Company B, and at Years after Accepting a Position at Company A.

We have to find the function formula for f and g.

We know that,

Company A has

f(t) = $45000+$2100t

And

Company B has

g(t) = $45000(1+0.042) to the power of t.

Therefore, The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.

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Brainly please don't delete my question it's not even breaking your guideline I even checked I just need my questions answered!

Answers

Answer:

Hey

you are correct

18x – 40

Step-by-step explanation:

2( x + 4 (2x – 5) )

= 2( x + 8x – 20)

= 2x + 16x – 40

= 18x – 40

Dont forget to rate the answer as brainliest

Have a good day

Answer: 18x-40

Step-by-step explanation: First, you have to isolate the 2, so now it would look like this:

=(2)(x+4(2x−5))

Now, You have to isolate the x, along with the 2 again, so it would look like this:

=(2)(x)+(2)(4(2x−5))

Now, you would combine the like terms of 2x & x, and all the numbers that don't have a variable, so it would look like this:

2x+16x−40

Now, finally, we can combine 2x + 16x, because they are like terms, so that is how we get 18x - 40

I hoped this helped friend!

-Shining Dream

HII EVERYONE can you help me and this problem TYSM

Answers

10) There is no solution to given the simultaneous equations

11) There is no solution to given the simultaneous equations

15) There is no solution to given the simultaneous equations

How to solve the system of simultaneous equations?

10) We are given the simultaneous equations as;

y = -6x - 8

y = -6x + 8

Plug -6x + 8 for y in eq 1 to get;

-6x + 8 = -6x - 8

Since the coefficient of the variable on both sides are equal, then there is no solution to the simultaneous equation.

11) We are given the simultaneous equations as;

3x - y = 6

-3x + y = -6

Add eq 1 to eq 2 to get;

0 = 0

Thus, there is no solution to the simultaneous linear equations.

12) We are given the simultaneous equations as;

9x - 15y = 24 ------(1)

6x - 10y = -16 ------(2)

Multiply eq 2 by 1.5 and eq 1 by 1 to get;

9x - 15y = 24 ------(3)

9x - 15y = -24 -----(4)

When we subtract eq 3 from eq 4, we get;

0 = -48

Thus, no solution exists.

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Read the following prompt and type your response in the space provided.
Kim's teacher has marked this problem as one to recheck, but Kim cannot determine what she has done incorrectly. Identify Kim's error and write a correct solution.

Six less than 2 times a number is 50. What is the number?

2x – 6 = 50 (line 1)

2x – 6 – 6 = 50 – 6 (line 2)

2x = 44 (line 3)

2x ÷ 2 = 44 ÷ 2 (line 4)

x = 22 (line 5)

Answers

Kim’s error was in line 2 when she subtracted 6 instead of adding it. To cancel out -6, you would have to ADD 6, not subtract. So doing what Kim did would actually just make the problem 2x - 12 = 44, not have gotten rid of the -6.
If Kim had added 6 instead, she would’ve gotten
2x - 6 + 6 = 50 + 6 in line 2
2x = 56 in line 3
2x / 2 = 56 / 2 in line 4
x = 28 in line 5

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

Answers

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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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.

Answers

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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An evergreen nursery usually sells certain shrub after 6 years of growth and shaping: The growth rate during those 6 years is approximated by dh/dt = 1.2t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t = 0). (a) Find the height after years h(t) (b) How tall are the shrubs when they are sold? cm

Answers

(a) After t years, the height is 18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

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collect at least 50 observations from a data source of your choice. the observations you collect may be discrete data or continuous data but cannot be categorical in nature. you can generate or collect the observations yourselves, but you may not use mass emailing to the class to do so. you can obtain the data from internet sites, but you must include where you collected the data from as a reference

Answers

The discrete data can be number of legs, number of teeth.

The continuous data can be the length of tail, and the height of dog.

Consider the provided information.

The discrete data is a data whose value is obtained by counting and they can be described by an integer value.

So, the discrete data can be number of legs, number of teeth.

A continuous data is a variable whose value is obtained by measuring.

The continuous data can be the length of tail, and the height of dog.

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What number is 0.1 less than 15.2?

Answers

Answer:

15.1

Step-by-step explanation:

Hey WRLD... 999

Match each polynomial with its factorization. Type the number of the corresponding polynomial on the line of it’s factorization on the right.

1.
x2 – 2x – 48
_____ (x + 2)(9 – x)

2.
-3x2 + 14x - 8
____ (2 – 3x)(x – 4)

3.
X2 – 10x – 25
_____ (x + 6) (x – 8)

4.
-x2+7x+18
____ 3(x – 7) (x + 7)

5.
X4 – 16
_____ (x – 5)2

6.
3x2 – 147
_____ ( x – 2)( x + 2)( x2 + 4)

Answers

Each equation is expressed and mentioned in its factorized form are given above.

What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given are the polynomials along with their factorized forms.

The polynomials along with their correct factorized forms are as follows -

x² - 2x - 48 → (x + 6) (x – 8)-3x² + 14x - 8 → (2 – 3x)(x – 4)x² – 10x + 25 → (x - 5)²- x² + 7x + 18 → (x + 2)(9 – x)x⁴ - 16 → (x – 2)(x + 2)(x² + 4)3x² – 147 → 3(x – 7) (x + 7)

Therefore, each equation is expressed and mentioned in its factorized form are given above.

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elementary surveying two ridges b and c forms a valley having a at the bottom part in between the ridges. elevation difference between b nad c is 111..356 m. observing at point a, the angle of elevation is

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the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m

We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.

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Please Help

Have a close look at the diagram below. What is the probability of selecting the following marbles in order: red - blue - blue - blue ? Show your work and explain your thinking.

Answers

The probability of selecting the following marbles in order: red - blue - blue - blue will be 3 / 40.

How to calculate the probability?

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

From the diagram Illustrated, it should be noted that that there are 2 blue balls and 3 red balls. The total number of balls will be 5.

The probability of selecting the following marbles in order: red - blue - blue - blue will be:

= 3/5 × 2/4 × 1/4 × 0/3

= 6 / 80

= 3 / 40

The probability is 3 / 40.

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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?

Answers

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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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?

Answers

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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Researchers in the Hopkins Forest (see Problem 7-16 from) also count the number of maple trees (genus
acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots
sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard
deviation of 23.65 trees.
a). If we took the mean of a sample of eight plots, what would be the standard error of the
mean?
b). Using the central limit theorem, what is the probability that the mean of the eight would be
within 1 standard error of the mean?
c). Why might you think that the probability that you calculated in (b) might not be very
accurate?

Answers

a) The standard error of the mean is equal to the standard deviation divided by the square root of the sample size. In this case, the standard error of the mean would be equal to 23.65/sqrt(8) = 6.61.

b) Using the central limit theorem, we can say that the probability that the mean of the eight plots would be within 1 standard error of the mean is approximately equal to 68%. This is because, under the central limit theorem, the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, in this case, we would expect that 68% of the sample means would be within 1 standard deviation of the population mean.

c) The probability that we calculated in (b) might not be very accurate because the central limit theorem assumes that the underlying population is normally distributed. However, it is not clear from the histogram whether the number of live maples per plot is normally distributed. If the distribution of the number of live maples per plot is not normal, then the central limit theorem would not be applicable and the probability we calculated might not be accurate.

when max and evie were counting their items of candy after trik or treating. the total humber of items was at least 90 and at most 115. If Evie had 42 items of candy, which of the following inequalities represents all possible number of items, m, that Max could have had?

Answers

Answer:

48 ≤ m ≤ 73

Step-by-step explanation:

Evie has 42, Max has x.

Total candy = x + 42

90 ≤ x+42 ≤ 115

48 ≤ m ≤ 73

Max can have 48 or more, but no more than 73

The function g(x) is graphed below. According to the graph, what is the
value of g(4)?

Answers

Answer:

Step-by-step explanation:

g(4) tells us that we need to look for the y coordinate when g(x) reaches 4 on the x axis.

6 is the answer

Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting. Unfortunately, it only took him 1 12
hours to melt.

Percent error is a way to describe error, expressed as a percentage of the actual amount. What is the percentage error in this situation?

Answers

The percentage error in this situation will be 33%.

How to calculate the percentage?

It's important to note that Percent error is a way to describe error, expressed as a percentage of the actual amount.

Since Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting but it only took him 1 1/2 hours to melt. The percentage error in this situation will be:

= (2 - 1 1/2) / 1 1/2 × 100

= 1/2 ÷ 1 1/2 × 100

= 1/3 × 100

= 33.33%

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Indicate whether a binomial distribution is a reasonable probability model for the random variable X. give your reasons in each case.
joey buys a virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

Answers

The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.

How to identify binomial distribution model?

The conditions for binomial distribution are;

1: The number of observations n must be fixed.

2: Each observation must be independent.

3: Each observation must represent one of two outcomes ("success" or "failure").

4: The probability of "success" p must be the same for each outcome.

Now, we are given the statement;

Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.

Secondly, we can say that there could be success by winning a price or failure by not winning the price.

Each weekly observation is independent.

The probability is the same for each outcome.

Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.

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The given point is reflected across the line indicated. Find the coordinates of the image.
R across y = -2
If the given point R is reflected across the line y = -2, the image is
(Type an ordered pair.)

Answers

When a point is reflected across a line, the resulting image is always the same distance from the line as the original point, but on the opposite side. Since the original point R is above the line y = -2, the image will be below the line.

To find the coordinates of the image, we can use the fact that the y-coordinate of the image will be 2 units below the y-coordinate of the original point R. If the original point R has coordinates (x,y), then the image will have coordinates (x, y-2).

Therefore, the coordinates of the image of point R reflected across the line y = -2 are (x, y-2).

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 = ______

Answers

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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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?

Answers

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

The least expensive
buttons cost
$0.28 each. Yellow bought all of
the buttons she could for $1.40 and
wore them proudly.

Answers

The number of buttons that she can wear proudly will be 5.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another.

As per the given,

Cost of one button = $0.28

The cost of buttons that she can wear = $1.40

A number of buttons = $1.40/$0.28 = 5

Hence "She will be able to wear five buttons with pride.".

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A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33

Answers

The 95% confidence interval for this situation is (0.95, 9.71).

What is the Standard deviation?

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The formula for Confidence Interval for Population Mean When Population Standard deviation is known

[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]

α for 95% confidence level = (100-95)/100 =0.05

[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025

[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96

σ = 20

95% Confidence Interval for Population Mean When Population Standard deviation is known