a) The probability that all three family members are assigned to the same station is 1/27.
b) The probability that at most two family members are assigned to the same station is 11/27.
c) The probability that every family member is assigned to a different station is 2/9.
For (a), there is only one way for all three family members to be assigned to the same station, and there are 3 stations, so the probability is 1/3^3 = 1/27.
For (b), there are three ways for two family members to be assigned to the same station, either A and B, B and C, or A and C. The probability of two family members being assigned to the same station is (1/3)^2 (2/3). There are three ways for this to occur, so the probability is (3) (1/9) (2/3) = 2/3. There is also one way for all three family members to be assigned to the same station, so the probability is (1/3)^3 = 1/27. Adding these two probabilities gives 11/27.
For (c), there are 3! = 6 permutations for the family members to be assigned to different stations. Each family member can be assigned to any of the 3 stations, so the probability is (3!) (1/3)^3 = (6) (1/27) = 2/9.
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Complete Question:
A family consisting of three persons-A, B, and C-goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that (a) All three family members are assigned to the same station? (Round your answer to three decimal places.) (Ne Responseberse ssigd tah ni sation number tor each (b) At most two family members are assigned to the same station? (Round your answer to three decimal places.) (c) Every family member is assigned to a different station? (Round your answer to three decimal places.)
question: 2.35 a contractor wishes to build 9 houses, each dif- ferent in design. in how many ways can he place these houses on a street if 6 lots are on
There is only 1 way to place the houses on the street.
If the contractor wishes to build 9 houses, each different in design, and there are 6 lots available on the street, there are 6 choose 9 (written as 6C9) ways to place these houses.
However, this number is not possible since 6C9 = 0,
which means there are no combinations of 6 elements taken 9 at a time.
A more appropriate calculation would be 6 choose 6 (written as 6C6), which represents the number of ways to place the 9 houses on the 6 available lots if each house must occupy a lot.
In this case, 6C6 = 1,
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A toy rocket is launched from a platform 39 feet above the ground at a speed of 83 feet per second. The height of the rocket in feet is given by the polynomial −16t2 + 83t + 39, where t is the time in seconds. How high will the rocket be after 3 seconds?
Answer:
144 ft
Step-by-step explanation:
Put in '3' where 't' is and compute
Height = -16(3^2) + 83(3) + 39 = 144 ft
I need help solving for both number 1 and the exemplar.
P(59) is 281 billion dollars and it agrees with the function.
What is a growth function?
A growth function is a mathematical function that describes the growth rate of some quantity over time. It can be used to model a wide range of phenomena, such as population growth, economic growth, and the growth of biological organisms.
We can see that the function can be give as;
P(t) = 567 + t(36t^0.6 - 104)
t is the number of years since 1960
At P(59) Which means 59 years after 1960;
P(59) = 567 + 59(36(59)^0.6 - 104)
P(59) = 281
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Hi can anyone help me?
The current age of Elsie is six years.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal. Equations are written with an equal sign (=) and can contain variables, numbers, and mathematical operations. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
Let Elsie's age be x;
Elsie's age five years ago = x - 5
Elsie's age in eight years time x + 8
From the statement in the question;
x - 5 = 1/2( x + 8)
2x - 10 = x + 8
2x + x = 8 + 10
3x = 18
x = 6 years
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the amount of energy required to heat water for 10 mintues shower (50 gallons0 is 2.2125kj. how many calories is that?
The 2nd option 5.2880× [tex]10^{2}[/tex] calories is the correct answer.
There are different forms of energy on earth. The sun is considered the elemental form of energy on earth. In physics, energy is considered a quantitative property that can be transferred from an object to perform work. Hence, we can define energy as the strength to do any kind of physical activity.
According to the laws of conservation of energy, “energy can neither be created nor destroyed but can only be converted from one form to another”. The SI unit of energy is Joule.
Energy =2.2125 kJ
Energy =2212.5 J (1 kJ =1000 J)
using 1 calorie = 4.184 J
Energy =2212.5 J × (1 Cal / 4.184 J)
Energy =528.800 calories =5.2880× [tex]10^{2}[/tex] calories.
Out of the available options, 2nd and 3rd have the same value. But the given energy has 4 significant figures after the decimal then answer should also have 4 significant figures.
Therefore, 2nd option 5.2880× [tex]10^{2}[/tex] calories is the correct answer.
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Complete question: the amount of energy required to heat water for 10 minutes shower (50 gallons0 is 2.2125kj. how many calories is that? Report the answer in scientific notation.
(1) 5.2880
(2) 5.2880×[tex]10^2[/tex] calories
(3) 5.288×[tex]10^2[/tex] calories
(4) 9.2571×[tex]10^{3}[/tex]
juan starts walking at 4 miles per hour. an hour and a half later, cathy starts jogging along the same route at 5 miles per hour. how long will it take cathy to catch up with juan?juan starts walking at 4 miles per hour. an hour and a half later, cathy starts jogging along the same route at 5 miles per hour. how long will it take cathy to catch up with juan?
Answer:
6 hours
Step-by-step explanation:
They meet at distance d from their starting point.
Juan walks at 4 mph for time t.
Cathy jogs at 5 mph for time t - 1.5 since she starts 1.5 hour later.
speed = distance/time
distance = speed × time
Juan
d = 4t
Cathy
d = 5(t - 1.5)
4t = 5t - 7.5
t = 7.5
They meet 6.5 hours after Juan started walking.
Cathy jogged for 1.5 hours less than Juan walked.
7.5 hours - 1.5 hours = 6 hours
Answer: 6 hours
The difference of a number b and seven is 10. Answer: ?
The product of a number t and eight is twelve. Answer: ?
Twice the sum of a number m and five is the difference of nine and n. Answer: ?
Twenty-one is the quotient of a number y and 4. Answer: ?
Thrice the difference of number b and one is the product of a number c and then. Answer: ?
Answer:The answer to the first question is b = 3.
The answer to the second question is t = 8.
The answer to the third question is m = 2 and n = 7.
The answer to the fourth question is y = 84.
The answer to the fifth question is b = 5 and c = 3.
Step-by-step explanation:
A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal.
Each single entertainment segment is 4.5 minutes.
How to find how long is each entertainment segmentOut of the 20 minute show there are two blocks of time that are ads. The ads are each 13/4 minutes long.
13/4 = 13 ÷ 4 = 3.25
minutes.
Let's take away the time used for ads from the 20 minute total.
20 - 3.25 - 3.25
= 13.5
Without ads the show's actual runtime is 13.5 minutes.
Now we'll divide that 13.5 into three equal parts.
13.5 ÷ 3 = 4.5
Each of the three equal entertainment segments is 4.5 minutes long.
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at 0 hours, clare and her cousin are 63 miles apart. how far apart are they after 1 hour? 2 hours? 3 hours? show or explain your thinking.
The required, after 1 hour, 2 hours, or 3 hours, would still be 63 miles apart.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
If Clare and her cousin are 63 miles apart at 0 hours, their distance apart does not change with time, unless they are moving towards or away from each other. The distance between two static points cannot be affected by the passing of time.
So, after 1 hour, 2 hours, or 3 hours, they would still be 63 miles apart.
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a student bought a smartwatch that tracks the number of steps she walks throughout the day. the table shows the number of steps recorded t minutes after 3:00 p.m. on the first day she wore the watch. t (min) 0 10 20 30 40 steps 3,288 4,609 5,772 6,686 7,128 (a) find the slopes of the secant lines corresponding to the given intervals of t.
The slopes of the secant line corresponding to the given intervals of t is 132.1, 116.3, 91.4 and 44.2 steps per minute.
To find the slope of a secant line between two points, we need to divide the difference in the y-values (number of steps) by the difference in the x-values (time in minutes).
For the interval from t = 0 to t = 10 minutes:
y1 = 3,288 steps
y2 = 4,609 steps
x1 = 0 minutes
x2 = 10 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (4,609 - 3,288) / (10 - 0)
= 1,321 / 10
= 132.1 steps per minute
For the interval from t = 10 to t = 20 minutes:
y1 = 4,609 steps
y2 = 5,772 steps
x1 = 10 minutes
x2 = 20 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (5,772 - 4,609) / (20 - 10)
= 1,163 / 10
= 116.3 steps per minute
Similarly, for interval t = 20 to t = 30 minutes
Slope = (6,686 - 5,772)/ (30 - 20) = 91.4 steps per minute
for interval t = 30 to t = 40 minutes
Slope = (7,128 - 6,686)/ (40 - 30) = 44.2 steps per minute
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find the volume of the composite solid. round your answer to the nearest tenth
Answer:
2488.46 ft³
Step-by-step explanation:
the composite solid consists of;
cone and cylinder
volume of a cone=⅓πrh
volume of a cylinder=πr²h
then sum up the volume
⅓×3.142×8×9= 75.408 ft³
3.142×8×8×12=2413.056
2413.056+75.408=
2488.46 ft³
A student bought a pair of sunglasses in the USA. He paid $35.50 in the USA. In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42. How much more did he pay for them in England compared to the USA?
Answer:all you do is multiply 26.99*1.42
this equals 38.33 dollars
35.50 is less than 38.33
thus, USA is cheaper than England.
Step-by-step explanation:
assuming that no one is born on feb. 29 (leap day), how many people should be selected to guarantee that at least 7 were born on the same day, not considering the year?
The number of people that should be selected to guarantee that at least 6 were born on the same day are, 2190
What are the Worst Case Scenarios?The worst case scenario is one of the many possible cases where the desired outcome comes after every other probable outcome has already occurred. This case can be used to determine the number of turns with would require to make sure the desired outcome is achieved.
The number of people that will ensure at least 7 people have their birthday one single day of a non-leap year (365 days) can be determined by considering that in the number of people picked in each trial, no two people have their birthday on the same day.
According to this process, if we pick 365 people, each one is born on a different day.
We repeat this selection 6 times, and the worst-case scenario is that on each day of the year, there are 6 people who are born on that day. The total number of people selected are
365×6 = 2190.
Now, as we select one more person, the number of people born on a day for one of the days in the year will increase to 7.
Hence, the number of people that should be selected to guarantee that at least 6 were born on the same day are, 2190
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four students graphed the transformations below. Apply what you've learned to write a description of each transformation below as well as an algebraic rule.
The transformation rule descriptions are;
1) Reflection over the x-axis
(x, y) → (x, -y)
2) Reflection over the x-axis
(x, y) → (x, -y)
3) Reflection over the y-axis
(x, y) → (-x, y)
4) Reflection over the x-axis and then a reflection over the y-axis:
(x, y) → (-x, -y)
How to find the transformation rule?1) We clearly see that the transformed image is an exact mirror image of the original image which is a rhombus. Thus, the transformation is a reflection over the x-axis.
This is expressed as (x, y) → (x, -y)
2) We clearly see that the transformed image is an exact mirror image of the original image which is a triangle. Thus, the transformation is a reflection over the x-axis.
This is expressed as (x, y) → (x, -y)
3) We clearly see that the transformed image is an exact mirror image of the original image which is a rectangle. Thus, the transformation is a reflection over the y-axis.
This is expressed as (x, y) → (-x, y)
4) We clearly see that the transformed image is an exact mirror image of the original image which is a pentagon. Thus, the transformation is a reflection over the x-axis and then a reflection over the y-axis.
This is expressed as (x, y) → (-x, -y)
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so you have $9 and 12 candy bars what is your unit rate?
Answer: $0.75 per bar
Step-by-step explanation: To find the unit price for this, we need to either divide the bars by money or set up a proportion. So, 9 ÷ 12 = 0.75. The proportion would look like this:
[tex]\frac{9}{12} = \frac{x}{1}[/tex]
You'd cross multiply the 9 * 1 to get 9 then divde by 12. Either way, we should have gotten $0.75. To check if we are right, we multiply the unit price times the total amount of that item. So, 0.75 * 12 = 9, which makes this statement true. I hope this helped!
a helpful rule for converting radians to degrees is
Answer:
Degrees = Radians x 180/π
or
Degrees = 57.2958 x radians
Step-by-step explanation:
1 radian = 180/π degrees
1 radian = 57.2958 degrees
Multiply radians by this factor of 57.2958 to get the equivalent measure in degrees
π radians = 180°
2π radians = 360° which is the number of degrees in a circle
For anything greater than 2π radians you will have to subtract 360°
For example, 7 radians using the formula is 7 x (57.2958 ) ≈ 401.07°
But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°
Help! Picture below
Answer:
{a, b, c, d, e, f, g}
Step-by-step explanation:
B intersection C = (e) because that is the only variable they both share
Now A intersection (e) is just all different variables together.
So now we have 2 (e's) but they can just be written as one.
HELP? is this easy or am i ?? HELP
Answer:
6960
Step-by-step explanation:
What is 4.5pi minus pi/0.5?
Answer:
≈ 7.8598
Step-by-step explanation:
Let's round pi to 3.14159. First, we multiply 3.14159 by 4.5, which is around 14.13716. Then, we divide 3.14159 by 0.5, which is around 6.28318. So, 14.13716 - 6.28318 = 7.8598
which of the following variables are categorical and which are numerical? if the variable is numerical, then specify whether the variable is discrete or continuous. a. colors of cars in a mall parking lot.
The variable "colors of cars in a mall parking lot" is a categorical variable because it is a qualitative variable.
Categorical variables are variables that describe the characteristics of a group of entities and are usually described by words or labels. They are used to classify data into categories or groups and do not have a numerical or quantifiable meaning.
Examples of categorical variables include gender, religion, nationality, etc. In contrast, numerical variables are quantitative variables that have numerical or quantifiable meaning. They can be either discrete or continuous.
Discrete variables are countable, meaning that they have a finite number of possible values. Examples of discrete variables include age, number of siblings, etc. Continuous variables are variables that can take on any value within a given range. Examples of continuous variables include height, weight, etc.
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5200 is invested into an account that pay’s simple Interest annually after 8 years there is £6,240 in the account at what rate dose the account pay simple interest?
On solving the provided question, we can say that we have been provided with, by Simple Interest SI = PRT/100 =>rate = 15% per yr
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
we have been provided with,
Interest = 6240
principal = 5200
time = 8 yrs
so, by SI = PRT/100
R = SI * 100/PT = 15%
rate = 15% per yr
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Do the following lengths satisfy the Pythagorean Theorem? Lengths= 15 10 5
Which text structure does Scott Westerfeld use in this excerpt from Leviathan?
A descriptive
B problem solution
C cause and effect
D sequencing
The different text structures are discussed below.
What is text structure?Text structures refer to the way authors organize information in text.Recognizing the underlying structure of texts can help students focus attention on key concepts and relationships, anticipate what is to come, and monitor their comprehension as they read.Given is the excerpt from Leviathan by Scott Westerfeld.
Since the excerpt is not given, we will have a brief idea about the given text structures.
Description-Explanation
A description text structure shows mental images of the details of an event, person, place, or object. An explanation text structure shows a set of facts, which clarify the context, causes, and consequences of those facts.
Problem-Solution
A problem-solution text structure presents a problem, including why there is a problem, followed by one or more possible solutions.
Cause-Effect
A cause and effect text structure shows the connection between what has happened and its impact or result. Cause is what happened. Effect is the resulting action or consequence.
Sequence-Time
A sequence-time text structure describes or explains how things happen or work in chronological order.
Therefore, the different text structures are discussed above.
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models that are based on mathematic formula are called _____ models.
Symbolic models are those that are based on mathematical formulas.
By symbolic model, what do you mean?The goal of symbolic modelling is to help clients become more aware of their own "symbolic domain of experience," allowing them to create their own "metaphor landscape" and explore internal metaphors, which are believed by conceptual metaphor theory to influence behaviour.
What benefits do symbolic models offer?
One of the most significant and defining technologies of next-generation modelling methodologies is swiftly emerging as symbolic computation. It allows the freedom to easily create model equations, manage models more effectively, and reach the best outcomes more quickly.
Describe domain through an example.
the domain name example.com might be connected to the address 198.102. 434.8.
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cynthia jones recently surveyed 200 of her classmates to get a sense of the demand for a new software product she is working on. collecting data via a survey you administer yourself is referred to as research. question 6 options: a) secondary b) derivative c) primary d) initial e) direct
The survey conducted by Cynthia jones is an example of primary research
Primary research is a process used by researchers to acquire data directly rather than relying on data gathered from earlier study. They technically "own" the data. Primary research is conducted primarily to solve a specific problem that necessitates in-depth investigation.
There are two types of research:
Primary Research
Secondary Research
Businesses or organisations can do primary research themselves or hire a third party to do it on their behalf. One significant advantage of primary research is that it is "targeted," meaning that it is centered on a single topic or problem and all efforts are geared at obtaining relevant answers.
In Cynthia Jones's case, collecting data via a survey she administered herself is an example of primary research as she is collecting data directly from her classmates.
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a hole of radius unit is bored through the center of a sphere of radius unit. find the exact value of the volume of the remaining portion of the sphere.
The volume of the remaining portion of the sphere is 2.096 cubic units.
Let's take the volume of the remaining portion of the sphere = V
The volume of the sphere = [tex]\frac{4}{3}[/tex] * π * [tex]r^3[/tex]
The volume of the sphere with radius 1 = 4/3 * π
The volume of the cylinder = π * [tex]r^2[/tex] * h
The volume of the cylinder with height 2 and radius 1 = π * [tex]r^2[/tex] * h = 2 * π.
The difference between the volume of the sphere and the cylinder is
V = 4/3 * π - 2 * π = 4/3 * π - 2 * π = 2/3 * π.
By taking π = 3.14
V = [tex]\frac{2}{3}[/tex] * 3.14
V= 2.096.
So, the volume of the remaining portion of the sphere is 2.096 cubic units.
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scrabble in the game of scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. th describe the sampling distribution
The sampling distribution of the A tile in this population is 0.04.
The sampling distribution is a probability distribution of an observed result from a sample that is used to draw inferences about a population. In the game of Scrabble, the sampling distribution is used to draw inferences about the population of 100 tiles. Specifically, the sampling distribution explains the likelihood of a certain tile being drawn. For example, if the population contains 4 A tiles and 96 other tiles, then the probability of drawing an A tile is 4/100 or 0.04. This probability is the sampling distribution of the A tile in the population of 100 tiles. The sampling distribution can also be represented by the formula P(X=x)=nx/n, where n is the total number of tiles and x is the number of tiles of a certain type. Therefore, in the example above, P(X=A)=4/100=0.04. Thus, the sampling distribution of the A tile in this population is 0.04.
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candace just accepted her first job paying a $48,000 salary and is planning to take a $5,000 vacation cruise throughout europe for 2 weeks. she is debating whether to take the trip now and finance it with a promotion from the travel company offering no payments for a year at a monthly periodic rate of 1%, or wait the year and save to pay for the trip. if she takes the trip now she will start her career 2 weeks late. approximately how much would she save by waiting a year and not taking her unpaid time from work to travel?
Candace would save approximately $2,480 by waiting a year and not taking her unpaid time from work to travel. Thus, Option A holds the truth.
By waiting a year, Candace would be able to save her 2 weeks of salary, which would amount to:
$48,000 / 52 weeks * 2 weeks = $1,615.And since she would not have to pay the 1% interest for a year on the loan for her trip, she would save:
$5,000 * 1% = $50.So in total, Candace would save:
$1,615 + $50 = $2,480Candace would save $2,480 by waiting a year to take her trip and paying for it with her own money.
This question should be provided with answer choices, which are:
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if you find you are on a wait and have a party of 8 to accommodate, how many tables should you bring in and push together to fit the party of 8? (all your tables are 4 tops and square.)
If you are trying to accommodate a party of 8 and you have square tables that seat 4 people each, you would need to bring in 2 tables and push them together to fit the party of 8.
The reason for this is that 4 people can be seated at each table, and 2 tables together would provide enough seating for 8 people. Pushing the tables together will create a larger table that can accommodate the party of 8. It's important to ensure that the tables are pushed together securely so that they don't move or separate during the meal.
It's also important to consider the layout of the tables and how they will fit in the space where they will be used. It's a good idea to measure the space and the tables to ensure that they will fit comfortably and provide enough room for people to sit and move around. If the tables need to be rearranged or moved, it's important to do so carefully to avoid damaging the tables or injuring yourself or others.
When setting the tables, it's also important to consider the comfort of the diners. Make sure that there is enough room for people to sit comfortably and move their arms and legs, and that the tables are positioned so that everyone has a clear view of their surroundings and is not blocked by other diners or objects.
In conclusion, to accommodate a party of 8, you would need to bring in 2 square tables that seat 4 people each and push them together. It's important to consider the layout and comfort of the diners, as well as the safety of the tables and those who are setting them up.
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high school students who take the sat math exam a second time generally score higher than on their first try. past data suggest that the score increase has a standard deviation of about 50 points. how large a sample of high school students would be needed to estimate the mean change in sat score to within 2 points with 95% confidence? show your work.
A sample size of 384 high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence.
To calculate the sample size needed to estimate the mean change in SAT score to within 2 points with 95% confidence, we need to use the formula for sample size calculation:
n = (z^2 * σ^2) / (E^2)
where n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin of error.
In this case, our confidence level is 95%, so z = 1.96. The standard deviation of the score increase is 50 points and the margin of error is 2 points. So, plugging these values into the equation, we get:
n = (1.96^2 * 50^2) / (2^2)
Solving, we get n = 384. Therefore, a sample size of 384 high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence.
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