The differential of the function is dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
How to find the differential of the function.From the question, we have the following parameters that can be used in our computation:
y= 4x^(3/2)+x^(1/2)
Using the first principle of differentiation, we have
dy/dy = 3/2 * 4x^(3/2 - 1) + 1/2 * x^(1/2 - 2)
Evaluate the expressions
dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
Hence, the solution is dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
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a package of 8 count AA batteries costs $6.16, a package of 20 count AA batteries costs $15.20
Answer:
What is the unit price of each battery in each package?
To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.
For the package of 8 count AA batteries:
Total cost: $6.16
Number of batteries: 8
Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery
For the package of 20 count AA batteries:
Total cost: $15.20
Number of batteries: 20
Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery
Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.
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Step-by-step explanation:
To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.
For the package of 8 count AA batteries:
Total cost: $6.16
Number of batteries: 8
Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery
For the package of 20 count AA batteries:
Total cost: $15.20
Number of batteries: 20
Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery
Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.
Using arithmetic operation, the statement that is true is -
A: The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.
D: The 8-count pack of AA batteries has a lower unit price of S0.77 per battery
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
To find the unit price per battery, we divide the cost of each package by the number of batteries in the package.
For the 8-count pack -
Use the arithmetic operation of division.
Unit price per battery = $6.16 / 8 batteries = $0.77 per battery
For the 20-count pack -
Use the arithmetic operation of division.
Unit price per battery = $15.60 / 20 batteries = $0.78 per battery
Therefore, the statements A and D are correct.
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Use implicit differentiation to find an equation of the tangent line to the curve
sin(x+y)=4x−4y at the point (π,π)
Answer:
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Step-by-step explanation:
o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:
Differentiate both sides of the equation with respect to x:
cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx
Simplify by grouping the terms with dy/dx on one side and the rest on the other side:
cos(x+y) * (1 + dy/dx) + 4dy/dx = 4
Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):
cos(2π) * (1 + dy/dx) + 4dy/dx = 4
Simplify:
-5dy/dx = 4 - cos(2π)
dy/dx = -4/5
Use the point-slope form of the equation of a line to write the equation of the tangent line:
y - π = (-4/5)(x - π)
Simplify:
y = (-4/5)x + (8/5) + π
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Refer to the parallelogram at the right for Exercises 13 and 14
Justify your answers.
13. Suppose the base and height are each
multiplied by . What effect would this
have on the area? (3pts.)
10 ft
14 ft
12 ft
14. Suppose the side lengths are multiplied by 2. Describe the change in the
perimeter. (3pts.)
The area of the resulting figure is 4 times smaller than the area of the original figure.
And, When the side lengths are multiplied by 2, the perimeter is 2 times the original perimeter.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. And, Opposite sides of the rectangle are equal and parallel to each other.
We know that;
When two figures are similar, then ratio of its areas is also equal to the scale factor squared.
Hence, We can assume that the figure is a rectangle or a triangle;
Let
z = the scale factor
x = Area of the resulting figure
y = Area of the original figure
So, We get;
z² = x/y
Since, we have;
z = 1/2
Hence, We can substitute;
⇒ (1/2)² = x/y
⇒ x/y = 1/4
⇒ x = y/4
Therefore, The area of the resulting figure is 4 times smaller than the area of the original figure.
And, If the side lengths are multiplied by 2.
We get;
Perimeter = 2 (L + W)
= 2 (2L + 2W)
= 2 (2L + 2W)
Thus, When the side lengths are multiplied by 2, the perimeter is 2 times the original perimeter.
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Multiple choice: The distance between the bases on a softball field is 60 ft
By answering the above question, we may infer that The equation's answer is B) 60 ft.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
What is the distance between the bases on a softball field
A) 50 ft
B) 60 ft
C) 70 ft
D) 80 ft
The answer is B) 60 ft.
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On a standardized science test, the seniors at a high school have a mean score of 425 with a standard deviation of 80. What is the probability that a random sample of 50 seniors has a mean score of at most 415?
The response to the given question would be that As a result, there is a probability 1.3% chance (or about 0.013) that a random sample of 50 seniors will have a mean score of no higher than 415.
What is probability?Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.
The sample mean's sampling distribution may be approximated using the central limit theorem as having a mean of 425 and a standard deviation of[tex]80\sqrt(50) = 11.31.[/tex]
z is equal to (x - mu) / (sigma / sqrt(n))
where n is the sample size, x is the sample mean, mu is the population mean, sigma is the population standard deviation.
When we enter the values, we obtain:
[tex]z = (415 - 425) / (80\sqrt(50)) = -2.23[/tex]
As a result, there is a 1.3% chance (or about 0.013) that a random sample of 50 seniors will have a mean score of no higher than 415.
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What is the area of this complex figure?
178 m²
128 m²
30 m²
20 m²
Answer: 164
Step-by-step explanation: (16 X 8) + (6 X 5)+ (^^triang)+ 164
pleeeeeeeeeeeeeeese helpFind the percent equivalent to 16 over 25.
Answer:
64%
Step-by-step explanation:
Convert a fraction to a decimal and move the decimal point to make a percent
Consider the sequence: 7, 13, 19, 25, 31,…
Which expression describes this sequence, using n
to represent the position of a term in the sequence, where n=1
for the first term?
The full expression is 6n+1. We can find the solution of the given sequence in the following manner.
First take the differences: 13–7 = 19–13 = 25–19 = 31–25 = 6. So, we know there is a 6n in the expression. Then subtract 6n from each term: 7–6 = 13–12 = 19–18 = 25–24 = 31–30 = 1.
Reduce the size, number, or amount of something else by taking (something) away from it is called subtraction. Subtraction is the activity or procedure of determining the difference between two amounts or numbers. The phrase "taking away one number from another" is also used to describe the act of subtracting one number from another. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process since it is the number from which we subtract another integer in a subtraction phrase.
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Image! (URGENT)
(Please give answer to combine like terms part too if its not correct)
Answer:
3y²+6y-2y²+3y
collect like terms
3y²-2y²+6y+3y
5y²+9y
Patrick bought 4 bags of beans. There are b beans in each bag. Write an expression that shows how many beans Patrick bought.
how do you figure this out????????????
Patrick bought 4 times the number of beans in each bag.
What is expressions ?
An expression is a combination of one or more numbers, variables, and operations. It can contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be evaluated to obtain a numerical result or simplified by combining like terms or using mathematical rules.
To find an expression that shows how many beans Patrick bought, you can multiply the number of bags by the number of beans in each bag.
So, if Patrick bought 4 bags of beans, and there are b beans in each bag, then the expression would be:
4b
This means that Patrick bought 4 times the number of beans in each bag.
Therefore, Patrick bought 4 times the number of beans in each bag.
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A pack of gray wolves was reintroduced to a forest. The table gives the size
of this population of wolves over time.
If the trend in the table continues, which value is closest to the predicted
population size during year 12?
A. 42
B. 49
C. 46
D. 53
Answer:42
Step-by-step explanation: 42x0=42
Please help on this fast
Answer:
21 miles per gallon
Step-by-step explanation:
find the gradient of the line:
change in y = 105 - 21 = 84
change in x = 5 - 1 = 4
gradient is change in y/ change in x
= 84/4 = 21
Oil change at Citi auto is regular $30 Mr. Allen has a coupon for 15% off he wants to know the sale price of the service which equation can be used to find the cell price S of an oil change
S = 30 - 0.15(30) or S = 0.85 can be used to calculate the sale price S of an oil change (30).
What are an example and an equation?By resolving this equation, we find that the value of the variable x is 7. An equation is a mathematical formula that states that two quantities or values are equal, as in the example 6 x 4 = 12 x 2.
S will serve as a stand-in for the sale price of the oil change.
Mr. Allen has a 15% off voucher, and the oil change normally costs $30. The reduction can be shown as 15% of the standard price, or:
0.15 * $30 = $4.50
We can deduct the discount from the list price to determine the oil change's selling price:
S = $30 - $4.50
S = $25.50
As a result, S = 30 - 0.15 can be used to calculate the sale price S of an oil change (30)
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Answer:
The answer is s=0.85*30=22.50(final sale price) which will be 15 % of the 30 dollars
Step-by-step explanation:
Effect of Price on Supply of Eggs Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation.
625p2 − x2 =100
If 37000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? (Round your answer to the nearest whole number.) (Hint: To find the value of p when x = 37, solve the supply equation for p when x = 37.)
The supply of the supply of eggs is changing at 10.7¢ per carton per week
How to determine the rate at which the supply changing?The equation of the function is given as
625p^2 - x^2 = 100
When the supply is 37000, we have
x = 37
So, the equation becomes
625p^2 - 37^2 = 100
Evaluate
625p^2 - 1369 = 100
This gives
625p^2 = 1469
Divide by 625
p^2 = 2.3504
Take the square roots of both sides
x = 1.53
The supply rate is then calculated as
Rate = 7¢ * 1.53
Evaluate
Rate = 10.7¢
Hence, the supply is changing at 10.7¢ per carton per week
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Is this line proportional or non-proportional
In a daycare with 125 children, there are 43 babies, 15 one-year olds, 20 two-year olds, 13
three-year olds, and 9 four-year olds. What is the probability that a randomly selected child is a
two-year old?
Answer:
20/125 is the answer
Step-by-step explanation:
Given CB is 7 and angle A is 25, find the value of triangle ABC.
The value of area of triangle ABC is found as 11.42 sq. unit.
Explain about the area of triangle?A triangle is really a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides with three angles in every triangle, and some of them could be the same.A triangle's surface area is equal to the product of its base and height.Area of a triangle = ½ × base × height.
From the given data:
Using trigonometric function.
tan 25 = 7 / AC
AC = 7*tan 25
AC = 3.26
Area of triangle ABC = ½ × 7× 3.26
Area of triangle ABC = 11.42
Thus, the value of area of triangle ABC is found as 11.42 sq. unit.
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Question 10
8 pts
At Dunkin Donuts, you can get 12 donuts for $10 or you can get 6
donuts for $6.99.
Which is the better deal, 12 or 6? Explain your answer.
The better deal is 12 donuts for $10 because the unit rate is $0.83.
How to determine the unit price?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the unit price, we would determine the unit price for number of donuts by using the following mathematical expression;
Unit price = Cost of donuts/Number of donuts
Substituting the given parameters into the unit price formula, we have the following;
Unit price = $10/12
Unit price = $0.83.
For the second deal, we have:
Unit price = $6/6.99
Unit price = $0.86.
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Which function has the same zeros as h(x) = (x² - 4)(x² - 9)?
The function which has the same zeros as h(x) = (x² - 4)(x² - 9) is f(x) = (x - 2)(x + 2)(x - 3)(x + 3).
To determine which function has the same zeros as h(x) = (x² - 4)(x² - 9), we need to first find the zeros of h(x).
The zeros of h(x) are the values of x that make h(x) equal to zero.
h(x) = (x² - 4)(x² - 9)
h(x) = 0 if and only if (x² - 4) = 0 or (x² - 9) = 0
Solving for x, we get -
x² - 4 = 0 -> x = ±2
x² - 9 = 0 -> x = ±3
So, the zeros of h(x) are x = ±2 and x = ±3.
Now, we need to find the function that has the same zeros.
A function that has the same zeros will have the same factors of (x - 2), (x + 2), (x - 3), and (x + 3).
One such function is -
f(x) = (x - 2)(x + 2)(x - 3)(x + 3)
Therefore, this function has the same zeros as h(x) = (x² - 4)(x² - 9).
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Answer:
Step-by-step explanation:
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Aaron sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
38 visitors purchased no costume.
239 visitors purchased exactly one costume.
12 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase no costume as a decimal to the nearest hundredth.
The probability that the next person will purchase no costume is 0.13.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The total number of visitors to the website in a single day is:
38 + 239 + 12 = 289
Of these visitors, we know that 38 purchased no costume.
Therefore, the probability that the next person to visit the website will also purchase no costume is:
38/289 = 0.13
Hence, the probability that the next person will purchase no costume is approximately 0.13, or 13% to the nearest hundredth.
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which part of diagram shows the quantity x?
The diagram shows the quantity x is 13.
What is tape diagram?A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.
The full completed question is related to an equation as shown in the below diagram (Check it).
Given equation is x+4 = 17
Draw a tape diagram to represent the equation.Which part of the diagram shows the quantity of x ?If we select part 'a' the diagram is shown in the below diagram, see it.
For part 'b' the quantity x can be represent by:
x+4 = 17
x = 17 - 4
x = 13
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Work out 15:
6
Give your answer as an integer or as a
fraction in its lowest terms.
PLEASE HELP
Answer:
[tex] \frac{25}{2} [/tex]
Step-by-step explanation:
Given 15 ÷6/5
[tex]15 \div \frac{6}{5} \\ = > 15 \times \frac{5}{6} \\ = > 5 \times \frac{5}{2} \\ = > \frac{25}{2} \\ therefore \: the \: answer \: is \: \frac{25}{2} \\ this \: is \: because \: it \: cannot \: be \: broken \: down \: into \: lowest \: term \: again[/tex]
Find
Domain:
Range:
x-intercept:
Y-intercept:
Horizontal Asymptote:
Vertical Asymptote:
For =1/x
Pic attach below
Answer:
Ignore my handwriting loll
Step-by-step explanation:
Hope this helps! :)
to find the sum of two fractions with the same denominator you just have to add the
A. numerators
B. medians
C. differences
D. denominators
hi
im pretty sure the answer is
a. numerators
hope this helps
good luck;)
Answer:
A
Step-by-step explanation:
You have to add the numerator and keep the denominators the same! :)
explain what we mean by marginal cost
Answer: Marginal cost is the added cost to produce an additional good or the increase in production costs generated by the production of additional product units
Step-by-step explanation: It is calculated by taking the total change in the cost of producing more goods and dividing that by the change in the number of goods produced.
Answer:
So it's basically the cost added by producing one extra unit of a product or service. I hoped this helped and if you need a better explanation let me know!
Kurt uses 3 cups of flour for every 2 cups of sugar in a recipe. How many cups of sugar will he need if he uses 6, 9, or 12 cups of flour?
Answer: 6 cups of flour = 4 cups of sugar
9 cups of flour = 6 cups of sugar
12 cups of flour = 9 cups of sugar
Step-by-step explanation:
Well, if Kurt uses 3 cups of flour for every 2 cups of sugar, than for every 6 cups of flour, he would need 4 cups of sugar. With 9 cups of flour, he would need 6 cups of sugar. For 12 cups of flour, he would need 9 cups of sugar.
Write the set using the roster method.
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
.
Set D ∈ {76, 90, 92, 94, 96}
What is a Set?Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
As per the given data:
Set D consists of positive two-digit even numbers greater than 74 without the digit 8 in them.
For writing set D in the roster form:
For greater than 74:
{76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}
Without the digit 8:
{76, 90, 92, 94, 96}
Hence, Set D ∈ {76, 90, 92, 94, 96}
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Help me please I need help i dont know the answer!
The value of x that makes the equation true is 2.25.
What are model representations of equation?A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modelling is the process of creating a mathematical model. Both applied mathematics and the natural sciences employ mathematical models. The area of operations research is largely concerned with using mathematical models to resolve issues in commercial or military operations.
Using the figure we see that, for the left model we have:
3 (-x) = -3x.
Also, we have 10(1) = 10
Thus the left model has the equation:
-3x + 10
For the right model we have:
5x - 8
Equate the two models:
-3x + 10 = 5x - 8
18 = 8x
x = 2.25
Hence, the value of x that makes the equation true is 2.25.
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3. If triangle ABC was reflected across the y-axis, what would be the coordinates of C'?
(4,1)
(-4,-4)
(1,1)
(-4,-1)
Answer:
(4,1)
Step-by-step explanation:
(4,1) is the answer
Age, f
15, 1
14, 1
13, 1
12, 1
11, 1
10, 1
9, 0
8, 2
7, 2
1. Which measure of central tendency would be the most appropriate to describe the variable Gender? Age?
2. Calculate Mode, Median and Mean for Age. 3. Calculate the range, variance and standard deviation (use the formula for population variance and SD) for Age.
4. What are the ages of participants that reflect 68% of your sample?
Answer:
It seems like there is a mistake in the variable provided. The variable mentioned is "Gender" but the data provided is about "Age" and "f" (frequency). Assuming that "f" is the frequency of participants at each age, here are the answers to your questions:
For the variable "f", the most appropriate measure of central tendency would be the mode, which represents the most frequently occurring value. For the variable "Age", the most appropriate measure of central tendency would be the median, as it is less affected by outliers than the mean.
Mode = 8; Median = 11; Mean = 10.11 (rounded to two decimal places)
Range = 15 - 7 = 8; Variance = 8.99 (rounded to two decimal places); Standard deviation = 2.99 (rounded to two decimal places)
To calculate the age range that reflects 68% of the sample, we need to find the mean age and the standard deviation. The mean age is 10.11, and the standard deviation is 2.99. 68% of the data falls within one standard deviation of the mean. Using the empirical rule, we can say that the ages of participants that reflect 68% of the sample are between (10.11 - 2.99) and (10.11 + 2.99), which is between 7.12 and 13.10.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since the variable Gender is not given in the data, we cannot compute any measure of central tendency for it. For the variable Age, the most appropriate measure of central tendency would be the mode, since all the observations have the same value for this variable.
To calculate the mode, median and mean for Age, we can first arrange the data in ascending order of age:
7, 2
8, 2
9, 0
10, 1
11, 1
12, 1
13, 1
14, 1
15, 1
The mode is the most frequently occurring value, which is 1 for all ages. The median is the middle value when the data is arranged in ascending order. Since there are 9 observations, the median is the average of the 5th and 6th values, which are 12 and 13. So, the median is (12+13)/2 = 12.5. The mean is the sum of all the values divided by the number of observations, which is:
(72 + 82 + 90 + 101 + 111 + 121 + 131 + 141 + 15*1) / 9 = 11.44 (rounded to two decimal places)
Therefore, the mode is 1, the median is 12.5 and the mean is 11.44.
To calculate the range, variance and standard deviation for Age, we can use the following formulas (assuming the data is a population):
Range = maximum value - minimum value = 15 - 7 = 8
Mean = 11.44 (computed in step 2)
Variance = Σ(x - μ)^2 / N, where μ is the mean, x is each value, and N is the number of observations. Plugging in the values, we get:
Variance = [(7-11.44)^2 + (8-11.44)^2 + (9-11.44)^2 + (10-11.44)^2 + (11-11.44)^2 + (12-11.44)^2 + (13-11.44)^2 + (14-11.44)^2 + (15-11.44)^2] / 9 = 5.72 (rounded to two decimal places)
Standard deviation = square root of variance = √5.72 = 2.39 (rounded to two decimal places)
Therefore, the range is 8, the variance is 5.72, and the standard deviation is 2.39.
Since the data is approximately normally distributed, we can use the empirical rule to estimate the ages that reflect 68% of the sample. According to the empirical rule, 68% of the data falls within one standard deviation of the mean. So, we can compute the lower and upper limits of this range by subtracting and adding one standard deviation from the mean, respectively:
Lower limit = mean - standard deviation = 11.44 - 2.39 = 9.05 (rounded to two decimal places)
Upper limit = mean + standard deviation = 11.44 + 2.39 = 13.83 (rounded to two decimal places)
Therefore, the ages of participants that reflect 68% of the sample are between 9.05 and 13.83 years old.