Answers
1) The function f(x) is defined as follows: B. F(x) = -(x + 2)²(x - 2).
2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.
4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).
How to define the function f(x)?The function f(x) is defined according to the Factor Theorem, with the product of the linear factors of the function, which are dependent on the roots of the functions.
The zeros of the function, along with their multiplicity, are given as follows:
x = -2, with a multiplicity of 2, as the function just touches the x-axis, not crossing.x = 2, with a multiplicity of 1.Hence the function is defined as follows:
F(x) = a(x + 2)²(x - 2).
The y-intercept is positive, meaning that:
-8a > 0.
Thus the leading coefficient a is negative, and the correct option is given by option B.
A cubic function, in which the coefficients a and d are positive, is represented as follows:
A. F(x) = ax³ + bx² + cx + d.
How to solve the system of equations?The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.
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Related Questions
Kenton compared gas mileage for three cars.
Car A—450 miles for 15 gallons
Car B—651 miles for 21 gallons
Car C—598 miles for 23 gallons
Which car has the best rate of miles per gallon?
Car A has the best rate at 30 miles per gallon.
Car B has the best rate at 31 miles per gallon.
Car C has the best rate at 26 miles per gallon.
All three cars had the same rate of miles per gallon.
Answers
Answer:
Car B has the best rate
Step-by-step explanation:
A: 450 mi / 15 gal = 30 mi/gal
B: 651 mi / 21 gal = 31 mi/gal
C: 598 mi / 23 gal = 26 mi/gal
31 > 30 > 26
Answer:Car B has the best rate at 31 miles per gallon
Step-by-step explanation: i did my math
Lena and Ivan each ran every day as part of an exercise routine. Lena ran 3 miles each day for x days. Ivan ran 4 miles each day for y days.
The total number of miles that Lena ran is at least the total number of miles that Ivan ran. Write an inequality describing this relationship.
Answers
The inequality that shows the distance ran is 3x ≥ 4y
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Inequalities are used for the non equal comparison of numbers and variables.
Lena ran 3 miles each day for x days. Ivan ran 4 miles each day for y days.
Total number of miles that Lena ran = 3x
Total number of miles that Ivan ran = 4y
The total number of miles that Lena ran is at least the total number of miles that Ivan ran, hence:
3x ≥ 4y
The inequality is 3x ≥ 4y
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The prices paid for a model of a new car are approximately normally distributed with
a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $
The price that is 2 standard deviations below the mean is $
The percentage of buyers who paid between $16,500 and $17,500 is
The percentage of buyers who paid between $17,000 and $18,000 is
The percentage of buyers who paid less than $16,000 is
Answers
a) The price that is 3 standard deviations above the mean is $18500
b) The price that is 2 standard deviations below the mean is 16000
c) The percentage of buyers who paid between $16,500 and $17,500 is 68%.
d) The percentage of buyers who paid between $17,000 and $18,000 is
47.5%
e) The percentage of buyers who paid less than $16,000 is 2.5%.
What is Standard Deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Mean= 17000
standard deviation = $500.
a) The price that is 3 standard deviations above the mean is $
= 17000 + 3 x 500
= 18500
b) The price that is 2 standard deviations below the mean is $
= 17000 - 2 x 500
= 16000
c) The percentage of buyers who paid between $16,500 and $17,500 is
As, This is the bell curve numbers of 1 deviation which 68%.
d) The percentage of buyers who paid between $17,000 and $18,000 is
So, 1/2 of the 2nd deviation, or 95% x 0.5
= 47.5%
e) The percentage of buyers who paid less than $16,000 is 5% is outside of the 2nd deviation which is half of that or 2.5%.
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ASHPREET buys two packages of plates and three packages of forks for the class party she gives the clerk $50 how much was the total. And how much did the clerk give back
Answers
The total that Ashpreet bought, given the price of the plates and the forks, is $ 16. 95
The amount that the clerk should give back, given the amount Ashpreet gave the clerk, is $ 33. 05
How to find the total amount ?The total amount that Ashpreet will pay for the two packages of plates and the packages of forks, given the price of the plates and the price of the forks is:
= ( Cost of plates x Number of packages of plates ) + ( Cost of forks x Number of plate packages )
= ( 5. 79 x 2 ) + ( 1. 79 x 3 )
= 11. 58 + $ 5. 37
= $ 16. 95
The amount that the clerk would therefore give back to Ashpreet is:
= Amount Ashpreet paid with - Cost
= 50 - 16. 95
= $ 33. 05
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The rest of the question is:
The price of the packages of napkins and forks is: napkins $ 5.79 and forks $1.79
How do you write an interval notation on quadratic inequality?
Answers
Solve for x values that satisfy a quadratic inequality to write interval notation. This usually involves factoring the quadratic and putting it equal to zero, then utilizing the inequality sign to select viable solutions. After finding the answers, write (a,b) to indicate the interval of x-values that make the inequality true. The interval notation for -3 and 5 is (-3,5).
What is interval notation?In general, you must first solve for the values of x that are consistent with the inequality being met before you can build an interval notation for a quadratic inequality. The quadratic equation will often need to be factored in order to be fixed to zero.
The relevant answers will then be determined using the inequality sign. After you have identified the solutions, you may use the notation (a,b), where a and b stand for the solutions, respectively, to show the range of x-values that cause the inequality to hold.
The interval notation, for instance, might appear as follows if the responses were -3 and 5. (-3,5).
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Go math lesson 4-2 constant rate of change. Pg 29
Answers
The equation to represent the given table is y=27x.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the table:
a) Proportional
2/54 = 3/81
1/27 =1/27
Yes, the number of tickets and total cost are Proportional
b) Using coordinates (2, 54) and (3, 81)
m=(81-54)/(3-2)
m=27
Substitute m=27 and (x, y)=(2, 54) in y=mx+c, we get
54=27(2)+c
c=0
Substitute m=27 and c=0 in y=mx+c, we get
y=27x
So, the equation is y=27x
c) Number of tickets are 14
d) Total cost = $378
Therefore, the equation to represent the given table is y=27x.
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I added a picture below
Answers
If the final statement when solving a system of linear equations is "5 = 0", it means that: E. none of these statements are true.
What is the Solution to a System of Linear Equations?A solution to a system of linear equations is a set of values for the variables that satisfy all the equations in the system simultaneously. In other words, it is a collection of values for the variables that make all the equations in the system true at the same time.
The solution can be represented graphically as the intersection of the lines or planes defined by the equations in the system, or it can be represented algebraically as a set of values for the variables.
The equation "5 = 0" is false. It means that 5 cannot be equal to 0. This could indicate that the system of linear equations has no solution or that there is an error in the method being used to solve it.
Therefore, the answer is: "none of these statements are true".
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the largest number that divides two or more numbers evenly
Answers
The largest number that divides two or more numbers evenly is greatest common divisor (GCD).
What is GCD, or the greatest common divisor?The biggest positive number that divides any non-zero integer by two or more is known as the greatest common divisor.
The greatest common divisor is the biggest number that divides two or more numbers proportionally (GCD).
How do you calculate a GCD's largest common divisor?Using the LCM method, the steps to calculate the GCD of (a, b) are as follows:
Find the result of a and b in step 1.
Find a and b's least common multiple (LCM) in step two.
Step 3: Dividing the results of Steps 1 and 2.
Step 4: The value that results from division is the most significant common divisor of (a, b).
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Consider the parent function f (x) below.
1. Graph f(2x) in the color green below.
2. Graph -3f(x) in the color blue below.
3. Graph 2f (2x) in the color red below.
Answers
The graph of all the functions are given below.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
From the graph:
The parent function f(x) = eˣ.
The graph of the parent function is given the attached image in purple line.
So,
1). f(2x) = e²ˣ
Graph f(2x) in the color green below.
2). -3f(x) = -3 eˣ.
Graph -3f(x) in the color blue below.
3). 2f(2x) = 2e²ˣ
Graph 2f (2x) in the color red below.
Therefore, all the graphs are given in the attached image.
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How much must a carpenter cut off a 48-inch board if the length must
be 40 ± 0.25 inches?
Answers
Answer:
Step-by-step explanation:
let 'x' represent the amount removed, then we require:
40-0.25 <= 48-x <= 40+0.25
which solves to:
7.75 <= x <= 8.25
the carpenter must saw off between 7.75 and 8.25 inches
If the width of the quilt is 4 feet less than its length and the area of the quilt is 96 square feet what is the quilts length
Answers
The length of the quilt is 12 feet.
We can start solving this problem by using algebra. Let x be the quilt's length in feet. Then, the width of the quilt can be represented as (x - 4) feet. The area of the quilt is the product of its length and width, which is x(x - 4) = 96.
Expanding the left side of the equation:
x^2 - 4x = 96
Now we have a quadratic equation that we can solve by factoring or using the quadratic formula.
x^2 - 4x - 96 = 0
(x-12)(x+8) = 0
x=12 or x=-8 (length cannot be negative)
So the length of the quilt is 12 feet.
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which compact sets does there exist a number m such taht every open cover contains a finite subcover of m elemens
Answers
The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.
A compact set is a set that satisfies the finite subcover property, which means that every open cover of the set contains a finite subcover. This means that for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set.
Examples of compact sets that satisfy this property include closed and bounded sets in a metric space, such as closed intervals in real numbers, and closed and bounded subsets of Euclidean space.
The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.
Other examples of compact sets are the closed unit ball in a Euclidean space, and any finite set, where the number m would be equal to the number of elements in the set.
In summary, compact sets are sets that have the property of finite subcover, and for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set. Some examples of compact sets are closed and bounded sets in a metric space, closed intervals in real numbers, closed and bounded subsets of Euclidean space, closed unit balls in Euclidean space, and any finite set.
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El primo de la señora Martha fue a pedir un préstamo de $1800 bajo las mismas condiciones que la señora Martha ¿cuánto pagara de interés en primo de la señora Martha?
Answers
Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
What is interest in a simple definition?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.Interest is the money you owe when borrowing or receive when lending. Lenders calculate interest as a percentage of the loan amount. Consumers can earn interest by lending money (such as through a bond or certificate of deposit) or depositing funds into an interest-bearing bank account.The three types of interest include simple (regular) interest, accrued interest, and compounding interest.Since Mrs. Martha is paying an interest rate of 6% per year, her cousin will also pay 6% per year.
To calculate the amount of interest paid, we can use the formula:
Interest = Principal * Rate * Time
Where:
Principal = $1800Rate = 6% (or 0.06 as a decimal)Time = 1 yearSo:
Interest = $1800 * 0.06 * 1 = $108
Therefore, Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
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Alan wants to earn at least $73 trimming trees. He charges $7 per hour and pays $4 in equipment fees. What are the possible numbers of hours Alan could trim
trees?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answers
The number of hours Alan could trim to earn at least $73 is 11.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Charges per hour = $7
Equipment fees = $4
The number of hours to earn at least $73.
7t - 4 ≤ 73
Where t is the number of hours.
Now,
7t - 4 ≤ 73
7t ≤ 73 + 4
7t ≤ 77
t ≤ 11
Thus,
The number of hours is 11.
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there are $20$ cars in my building's parking lot. all of the cars are red or white. also, all the cars are either $2$-door or $4$-door. $12$ of them are red, $15$ of them are $4$-door, and $4$ of them are $2$-door and white. how many of the cars are $4$-door and red?there are $20$ cars in my building's parking lot. all of the cars are red or white. also, all the cars are either $2$-door or $4$-door. $12$ of them are red, $15$ of them are $4$-door, and $4$ of them are $2$-door and white. how many of the cars are $4$-door and red?
Answers
There are a total of 20 cars average in the parking lot, all of which are either red or white and either 2-door or 4-door. 12 of the cars are red, 15 of them are 4-door, and 4 of them are 2-door and white. Out of the 12 red cars, 12 of them are 4-door, so the answer is 12 cars are 4-door and red.
1. Determine the total number of cars in the parking lot: 20
2. Subtract the number of 2-door cars from the total number of cars to get the number of 4-door cars:
20 - 4 = 15
3. Subtract the number of 2-door and white cars from the number of red cars to get the number of 4-door and red cars:
12 - 4 = 8
4. Add the number of 4-door and red cars to the number of 4-door cars to get the answer:
8 + 15 = 12
To find the answer, we first determined the total number of cars in the parking lot, which was 20. We then subtracted the number of 2-door cars from the total number to get the number of 4-door cars, which was 15. We then subtracted the number of 2-door and white cars from the number of red cars to get the number of 4-door and red cars, which was 8. Finally, we added the number of 4-door and red cars to the number of 4-door cars to get the answer, which was 12.
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What is the length of AB?
Answers
Answer:4
Step-by-step explanation:
because it is a right triangle so if cb is 2 that makes ac 2 then if you just look at the ab line it’s actually longer so it’s 4 ;)
a swimming pool had 2.5 million liters some of the water evaporated and now the pool had 2 million liters of water what percent of water evaporated.
show all work
Answers
Answer:
4/5 = .8. 20% evaporated
Step-by-step explanation:
2.5 million divded into fifth. you have 5/5
take away half a million and that is 1/5th
at the end you have 4/5th left
4/5 = .8 = 80% left over meaning 20% evaporated
Which table represents a linear function example?
Answers
On solving the provided question, we can say that Graph Onerepresents a linear equation.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
Graph One
The graph is linear, commonly known as being in a straight line. Other graphs are not, though. Additionally, the range (y) of the tables is rising linearly every time, by a factor of.5 (1/2).
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Given the diagram below solve for side b
Answers
The length of the hypotenuse of the right triangle is:
B = 24.4
How to find the length of side B?Side B is the side opposite to the angle B, so it will be the hypotenuse of the right triangle.
We know the other two sides of the right triangle, so we can use the Pythagorean theorem to get:
C^2 + A^2 = B^2
Replacing the values that we know:
A = 20
C = 14
We will get:
20^2 + 14^2 = B^2
√(20^2 + 14^2) = B
24.4 = B
That is the length of the hypotenuse
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Help!
Explain how to employ the Pythagorean theorem in calculating the volume of a right cylinder if you know the distance from the edge of the base to the center of the top along with either its radius or its height.
Answers
To use the Pythagorean theorem to calculate the volume of a right cylinder, you would first need to know the radius of the base and the height of the cylinder. Once you have those two measurements, you can use the Pythagorean theorem to calculate the distance from the edge of the base to the center of the top.
The formula for the volume of a cylinder is V = πr^2h where r is the radius of the base and h is the height of the cylinder.
So if you know the distance from the edge of the base to the center of the top along with either its radius or its height, you can use the Pythagorean theorem to calculate the missing measurement and then use the formula for the volume of a cylinder to calculate the volume.
If you know the distance from the edge of the base to the center of the top, together with either its radius or its height, we can compute the volume of a right cylinder.
What is the Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.
Note that h refers to half of the total height of the cylinder. I chose to use
h instead of h/2 to simplify things later on.
To find the volume of our cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;
V = pi * (radius of cylinder)² (height of cylinder)
V = pi(r² - h²) 2h
V = 2pi h(r² - h²)
This is our volume function. Next, we take the derivative of the volume function and set it equal to zero. If we move the h inside the parenthesis, we only need to use the power rule to get the derivative.
d/dxV(h) = 2pi(r² -3 h²) = 0
The 2π divides out and we are left with;
r² − 3h²=0
After some rearranging;
h² = r²/3
Take the square root of both sides.
h = r/√3
That is how we can calculate the volume of a right cylinder, if you know the distance from the edge of the base to the center of the top along with either its radius or its height.
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What index of x will equal to 1/x^x
Answers
Answer:
The index of x should be 0 so that its value will be equal to 1.
During the first three hours of a recent storm the rain fell at a constant rate of 10 mm per hour. The storm stopped for the next 2 hours and then it started raining again at a constant rate of 20 mm per hour for the next 5 hours. Match the pieces of the piecewise function that describes the total rainfall in this situation with the appropriate domain.
f(h)=10h
f(h)=30
f(h)=30+20(h-5)
Answers
The total rainfall in this situation with the appropriate domain is f(h)=10h is 1-3 hours, f(h)=30 is 4 to 6 hours and f(h)=30+20(h-5) is 7 to 12 hours.
What is domain?The range of input values where a function can be defined, or the set of possible inputs, is known as the domain of the function. The domain is the collection of objects that the function machine will accept as inputs.
During the 1 to 3 hours, rain fell at a constant rate of 10 mm per hour, expressed as
f(h)=10h
During the 4 to 6 hours, rainfall is same, expressed as
f(h)=30
During the 7 to 12 hours, raining again at a constant rate of 20mm, expressed as
f(h)=30+20(h-5)
Thus, the total rainfall in this situation with the appropriate domain is f(h)=10h is 1-3 hours, f(h)=30 is 4 to 6 hours and f(h)=30+20(h-5) is 7 to 12 hours.
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Find the measure of each acute angle.
Answers
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180
So, (19x-1)+(13x-5)+90(right angle) =180
32x+84=180
32x=96
x=3
19x3-1=56
13x3-5=34
answer : 56, 34
What is the slope of a function called?
Answers
The term “slope of a function” is short for “slope of the graph of a function” for some particular value of the independent variable.
The linear function's slope. A slope is a measure of how steep a hill is. The same is true of a line's steepness. The ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two points, is known as the slope.
The derivative of a function is if it has one, the slope at any point. The slope of the line that is tangent to the curve there is another definition for it. In calculus class, you learn how to discover derivatives starting with limit theorems and moving on to numerous other "shortcut" theorems that make finding many derivatives easier.
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what do you think about the proposed new york city ban on sugary soft drinks larger than 16 ounces? think about both sides of the argument, and give pros and cons.
Answers
The proposed ban on sugary soft drinks larger than 16 ounces in New York City has both pros and cons. Pros include reducing obesity and diabetes, while cons include potential infringement on personal freedom and potential negative impact on small businesses.
The proposed ban on sugary soft drinks larger than 16 ounces in New York City aims to reduce obesity and diabetes by limiting the consumption of high-calorie beverages. This can also help to lower the healthcare costs associated with these conditions. However, some argue that this is an infringement on personal freedom and that people should have the right to make their own choices about what they eat and drink. Additionally, there are concerns that small businesses, such as convenience stores and vending machine operators, could be negatively impacted by the ban. This is because they may lose sales as a result of the ban, which could lead to job losses and financial hardship.
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the three angles in a traingle are 5x, 6x and 7x. work out the size of the largest angle in the triangle
Answers
Answer:
the largest angle is 70
Step-by-step explanation:
180 degrees in a triangle
180=5x+6x+7x
simplify
180=18x
x=10
7x=70
the largest angle is 70 degrees.
Is Ace or Alfonzo correct
Answers
Answer:
Ace
Step-by-step explanation:
The range has only one value 100
Elsa will spend more than $25 on gifts. So far, she has spent $17. What are the possible additional amounts she will spend?
Answers
The required possible amount that she spends additionally is more than $8.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Elsa will spend more than $25 on gifts. So far, she has spent $17.
Let the possible additional amounts she will spend be x,
According to the quesiton,
x + 17 > 25
x > 25 - 17
x > 8
Thus, the required possible amount that she spends additionally is more than $8, as of the given condition.
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2 pound into ounces
Answers
Answer: 32 oz
Step-by-step explanation:
Answer: 32
Step-by-step explanation: a pound is 16 ounces
approximately what percentage of children will score within the average range of iq testing? group of answer choices 20% 37% 68% 85%
Answers
The required interval of the given normal distribution using the empirical rule is [100, 140].
The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.
In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.
N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.
By the empirical formula, 68% of the data lies within one standard deviation from the mean.
Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].
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