The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 14 days. In what range would you expect to find the middle 98% of most pregnancies
Answers
We would expect to find the middle 98% of most pregnancies in the small rural village in the range of approximately 237 to 303 days.
We can use the properties of the normal distribution to determine the range in which we would expect to find the middle 98% of most pregnancies in the small rural village.
First, we need to find the z-scores associated with the upper and lower tails of the distribution that exclude the middle 2%. We can use a standard normal distribution table or calculator to find these values:
For the upper tail, the z-score is 2.33 (corresponding to a probability of 0.01 or 1%).
For the lower tail, the z-score is -2.33 (corresponding to a probability of 0.01 or 1%).
Next, we can use the formula for transforming a z-score into an actual value:
z = (x - μ) / σ
where z is the z-score, x is the actual value, μ is the mean, and σ is the standard deviation.
Substituting the values we know, we can solve for the upper and lower limits of the range:
For the upper limit:
2.33 = (x - 270) / 14
x - 270 = 32.62
x = 302.62
For the lower limit:
-2.33 = (x - 270) / 14
x - 270 = -32.62
x = 237.38
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Related Questions
paige just finished a road trip where she visited the following square pyramids: the bent pyramid and the red pyramid. the table below shows the approximate dimensions of the two pyramids. dimensions of pyramids base side length height bent pyramid 619 feet 332 feet red pyramid 722 feet 341 feet paige has to write a paper on volume for school and needs some help. what is the difference in volume of the two pyramids, rounded to the nearest cubic foot?
Answers
The difference in volume between the two pyramids is 12,371,740 cubic feet.
To find the volume of a square pyramid, you use the formula :
V = (1/3)Bh, where B is the area of the base and h is the height.
Using the dimensions given in the table, we can calculate the volumes of the two pyramids:
- Volume of Bent Pyramid = (1/3)(619 feet * 619 feet)(332 feet) = 26,384,053.33 cubic feet
- Volume of Red Pyramid = (1/3)(722 feet * 722 feet)(341 feet) = 38,755,793.33 cubic feet
To find the difference in volume between the two pyramids, we subtract the smaller volume from the larger volume:
38,755,793.33 - 26,384,053.33 = 12,371,740 cubic feet.
Rounding to the nearest cubic foot, the difference in volume between the two pyramids is 12,371,740 cubic feet.
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I need showing work for this question for finding the volume of it
Answers
Volume of rectangular prism:
V=l•w•h
V=6•1 2/3•3 1/3
V=4
V = l * w * h
Where l is length = 6yd
w is width = 1 2/3
( 1 2/3 can be rewritten as 5/3)
h is height = 3 1/3
( 3 2/3 can be rewritten as 11/3)
we then want to plug them into our formula
V = 6 * 5/3 * 11/3
We then multiply our fractions so we can just multiply across to get
V = 30/3 * 11/3
V = 330/9
Which we can simplify and get
V = 110/3 yd^3
Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,[infinity]). Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.
Answers
The required answer is sec θ = -√2.
Explanation:-
Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).
To determine three possible angles θ, the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.
Therefore, sec θ = 1/cos θ.To find cos 11π/4, the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.
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A quilt design is made up of right triangles that have a base of 6 inches and a height of 2 2/3 inches. If the quilt is rectangular with dimensions of 90 inches by 72 inches, how many triangles are needed to complete the quilt?
Answers
Answer:
810
Step-by-step explanation:
number of triangles needed = area of rectangle / area of triangle
area of triangle = 1/2 x base x height
1/2 x 6 x 8/3 = 8
area of rectangle = length x width = 90 x 72
90 x 72/ 8 = 810
the scholarship for hoosiers organization hosted its annual fundraiser and receivedb$500k in contributions. historically, they've collected 85% of whatnisbpromised
Answers
The Scholarship for Hoosiers organization received $500k in contributions during its annual fundraiser. Historically, they have collected 85% of what was promised.
The statement implies that the organization has a history of collecting 85% of the promised contributions. This suggests that there might be cases where contributors commit to donating a certain amount but do not fulfill their commitment entirely.
In the context of the fundraiser, if individuals or organizations pledged a total amount of, let's say, $X, the Scholarship for Hoosiers organization can expect to collect approximately 85% of that total amount. In this case, the total amount pledged could be higher than the $500k received.
The 85% collection rate indicates that there may be various reasons why contributors do not fulfill their full commitment. It could be due to changing financial circumstances, budget constraints, or other unforeseen factors. Nonetheless, the organization has historically experienced this 85% collection rate.
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Suppose a dog is carrying a virus returns to a isolated doggy day care of 40 dogs. Determine the differential equation for the number of dogs D(t) who have contracted the virus if the rate at which it spreads is proportional to the number of interactions between the dogs with the virus and the dogs that have not yet come in contact with the virus.A.dD/dt=kD(40−D)B. dD/dt=k40−D2C. dD/dt=kPD. dD/dt=k(40−D)E. dD/dt=kD
Answers
The differential equation for the number of dogs D(t) who have contracted the virus is A. dD/dt=kD(40−D), where k is the constant of proportionality.
This equation describes the rate of change of the number of infected dogs with respect to time. The term kD represents the rate at which the virus spreads due to interactions between infected dogs and healthy dogs. The term (40-D) represents the number of healthy dogs that could potentially become infected.
The product of these two terms, kD(40-D), represents the rate of change of the number of infected dogs, dD/dt. This differential equation is a classic example of a logistic growth model, which describes how populations grow and eventually level off due to limiting factors such as limited resources or the spread of disease.
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Ashton says that the zeros of the equation y=6x^2−5x−25 are at x=52 and x=−53. Which statement correctly describes Ashton's claim?
Answers
Answer:
Ashton is correct. The quadratic expression has the factors (2x−5) and (3x+5), so the zeros are at x=5/2 and x=−5/3.
Step-by-step explanation:
The answer itself has the step-by-step explanation.
Step-by-step explanation:
Andre, Lin, and Noah each designed and built a paper airplane. They launched each plane several times and recorded the distance of each flight in yards. Write the five-number summary for the data for each airplane. Then, calculate the interquartile range for each data set.
Answers
Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35
Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33
Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25
To find the five-number summary for each data set, we need to find the minimum, maximum, median, and quartiles. We can start by ordering the data sets from smallest to largest:
Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35
Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33
Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25
Minimum:
Andre's: 18
Lin's: 15
Noah's: 10
Maximum:
Andre's: 35
Lin's: 33
Noah's: 25
Median:
Andre's: (28 + 29) / 2 = 28.5
Lin's: (21 + 22) / 2 = 21.5
Noah's: (18 + 20) / 2 = 19
First Quartile (Q1):
Andre's: (22 + 25) / 2 = 23.5
Lin's: (18 + 20) / 2 = 19
Noah's: (12 + 13) / 2 = 12.5
Third Quartile (Q3):
Andre's: (31 + 32) / 2 = 31.5
Lin's: (23 + 25) / 2 = 24
Noah's: (22 + 23) / 2 = 22.5
Interquartile Range (IQR):
IQR = Q3 - Q1
Andre's: 31.5 - 23.5 = 8
Lin's: 24 - 19 = 5
Noah's: 22.5 - 12.5 = 10
So the five-number summary and interquartile range for each data set are:
Andre's: Min = 18, Q1 = 23.5, Median = 28.5, Q3 = 31.5, Max = 35, IQR = 8
Lin's: Min = 15, Q1 = 19, Median = 21.5, Q3 = 24, Max = 33, IQR = 5
Noah's: Min = 10, Q1 = 12.5, Median = 19, Q3 = 22.5, Max = 25, IQR = 10
Answer:
Andre's: Min = 18, Q1 = 23.5, Median = 28.5, Q3 = 31.5, Max = 35, IQR = 8
Lin's: Min = 15, Q1 = 19, Median = 21.5, Q3 = 24, Max = 33, IQR = 5
Noah's: Min = 10, Q1 = 12.5, Median = 19, Q3 = 22.5, Max = 25, IQR = 10
Step-by-step explanation:
The m<1=9y-2 and m<3=7y+16.Find the measure of both angles
Answers
The measure of the angles are 91.375°and 88.625°. Both the angles are obtained by the supplementary angle principal.
What exactly are supplementary angles?Supplementary angles are two angels whose total is 180 degrees. When a straight line is crossed by a line, two angles develop on each of the examined straight line's sides.
Two sets of additional angles make up those two-two angles. That is, if supplementary angles are placed next to each other, the exterior sides of their exterior sides will form a straight line.
The given data in the problem is;
∠1 = 9y-2
∠2 = 7y+16
The sum of the supplementary angle is 180
⇒9y-2 +7y+16 = 180
⇒16y +14 =180
⇒16y= 166
⇒ y=10.375
The measure of the angle 1 is;
∠1 = 9y-2
∠ 1 = 9 ×10.375 -2
∠ 1 = 91.375°
The measure of the angle 2 is;
∠2 = 7 × 10.75 +16
∠2 = 88.625°
Hence, the measure of the angles are 91.375°and 88.625°.
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2.) let x represent the number of correct guesses out of all the attempts for members in your group. what kind of distribution does x have? justify your response, indicating values for any of the variables that describe the distribution.
Answers
X, the number of correct guesses out of all the attempts for members in the group, follows a binomial distribution
The theoretical probability of one correct guess is the total number of correct guesses divided by the total number of guesses, which in this case is 11/15 or 0.73.
X represents the number of correct guesses out of all the attempts for members in the group. Since each member's guess is independent of the others, and each guess has the same probability of being correct, X follows a binomial distribution.
The binomial distribution is characterized by two parameters: the number of trials (n) and the probability of success on each trial (p). In this case, n is the total number of guesses, which is 15, and p is the theoretical probability of one correct guess, which is 0.73.
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The given question is incomplete, the complete question is:
Theoretical Probability of one correct guess # of Correct Total # of Group Member Guesses Guesses Jay 3 Amanda 4 Nicholas 4 Overall 11 5 5 15 2.) Let X represent the number of correct guesses out of all the attempts for members in your group. What kind of distribution does X have? Justify your response, indicating values for any of the variables that describe the distribution.
if p > 5 is prime and p is divided by 10, show that the remainder is 1, 3, 7, or 9
Answers
If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9
The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.
However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).
Therefore, p must end in 5. This means that p can be written in the form:
p = 10n + 5
where n is some integer. Now, let's consider what happens when we divide p by 10:
p/10 = (10n + 5)/10 = n + 0.5
Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.
To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).
Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.
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Find the product of (x + 7)(x - 7).
x2 - 14x + 49
x2 - 49
x2 + 14x + 49
x2 + 49
Answers
Answer:
x² - 49
Step-by-step explanation:
Identity: (a + b)(a - b) = a² - b²Here a = x and b = 7
(x +7) (a -7) = x² - 7²
= x² - 49
Answer:\(x^{2} -49\)
Step-by-step explanation:
Factor the quadratic trinomial x^2-7x+12
Answers
Answer:
(x-4)(x-3) hope this helps
Step-by-step explanation:
What set of reflections and rotations would carry rectangle ABCD onto itself?
Reflect over the y-axis, reflect over the x-axis, rotate 180°
Rotate 180°, reflect over the x-axis, reflect over the line y = x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y = x
Answers
Answer:
2 line is the answer to the questions
What is the value of z?
Answers
Answer:
33
Step-by-step explanation:
The diameter of a circle is 7 m. Find the circumference to the nearest tenth
Answers
Answer:
22 m
Step-by-step explanation:
Diameter d = 7 m
Circumference of the circle C =?
\(C = \pi d = 3.14 \times 7 \\ \\ C= 21.98 \: m\\ \\ C \approx 22.0 \: m\)
Incredible Skating has a family special this weekend: You rent skates for $5
and pay $1 an hour for skating per person. Write an equation, where h
represents the number of hours and C represents the total cost.
Answers
Answer:
c=5+1h
Step-by-step explanation:
The equation for where h represents the number of hours and C represents the total cost is C = 5 + nh.
Given that the skates were rented for $5 and pay $1 an hour for skating per person.
We need to write an equation, where h represents the number of hours and C represents the total cost.
To calculate the total cost (C) for a family with h hours of skating, you would need to consider the cost of renting skates ($5) and the cost of skating per person per hour ($1 per person per hour).
Let n be the number of people in the family.
The equation for the total cost (C) can be expressed as follows:
C = 5 + nh
The $5 is added to the equation as a one-time cost for renting skates, which is the same for any number of people.
nh represents the cost for the number of people (n) skating for h hours, at the rate of $1 per person per hour.
The cost per person is multiplied by the number of hours they skate.
Hence the required equation is C = 5 + nh.
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Solve for x: 3x − 5 = 2x + 6. need answer plz :(
Answers
Answer:
x = 11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
3x -5 = 2x +6
add 5
3x -5 +5 = 2x +6 +5 =
3x = 2x +11
subtract 2x
3x - 2x = 2x - 2x +11 =
1x = 11
divide by 1
1x/1 = 11/1 =
x = 11
a cube shaped dog kennel is replaced by a larger kennel the volume of the original kennel was 27 cubic feet the volume of the new kennel is 64 cubic feet how many feet were added to eat Edge length of the kennel 1 foot 2 ft 3 ft 4 ft
Answers
The volume V of a cube is given by
\(V=L^3\)where L is the lenght of one side. Hence, the side L measures
\(L=\sqrt[3]{V}\)In the first case, the dog kennel has 27 ft^3 of volume, hence
\(\begin{gathered} L=\sqrt[3]{27} \\ L=3\text{ } \end{gathered}\)that is, L is 3 feets of lenght.
In the same way, for the second case we have that,
\(\begin{gathered} L=\sqrt[3]{64} \\ L=4 \end{gathered}\)that is, in the second case, L is 4 feet of lenght. This means that, 1 foot was added to each edge of the dog kennel.
Nic borrowed $350 to buy a bow. The finance charge on the loan was $25 and the
term on the loan was 45 days. What was the APR for Nic's loan?
1 pts
Answers
In answering the question, we discovered that a sample size of 20 was required in order to reach this conclusion.
How big a sample is it?The sample size is the number of observations used to estimate a certain population. The population was used to determine the sample size.
The act of promoting a product to increase sales is known as advertising. Based on the scenario given, the advertisement is misleading for the following reasons:
For this finding to be reliable, a sample size of 20 samples is rather small. Although the company was aware that the fertilizer treatment might get rid of weeds in approximately 2 weeks, customers said it would take 4 weeks for all of the weeds to die.
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What are the four conditions necessary for X to have a Binomial Distribution? Mark all that apply.
a. There are n set trials.
b. The trials must be independent.
c. Continue sampling until you get a success.
d. There can only be two outcomes, a success and a failure
e. You must have at least 10 successes and 10 failures
f. The population must be at least 10x larger than the sample. T
g. he probability of success, p, is constant from trial to trial
Answers
Options a, b, d, and g are the correct conditions for a Binomial Distribution.
The four conditions necessary for X to have a Binomial Distribution are:
a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.
b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.
d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.
g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.
The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.
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can someone please help me with this
Answers
For the square,
Area would be 289ft2 since 17x17 is 289
Perimeter would be 68ft since 17x4 is 68!!
So basically area of a rectangle= L*W
And perimeter of a rectangle = 2 (w + h)
Then area of a square= s2
And perimeter of a square= 4 • s
How many solutions does this equation have?
4b – 4b = 0
no solution
one solution
infinitely many solutions
Answers
The answer is infinitely many solutions because 0 = 0.
If you don't seem to see where I got 0 = 0, look at the equation,
4b – 4b = 0
first lets do the math on the left side.
4b - 4b is equal to 0.
so lets put 0 on the left side, now lets look at the equation all together,
0 = 0,
and this means that it has infinitely many solutions.
The reason why it is not no solution because no solution means when there are no answers to the equation. For example, the solution is not true, such as the equation 24 ≠ 29. This is a no solution equation. One solution can be 4x = 20, as x = 5, concluding it being one solutions.
A sample of 1400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Refer to Exhibit 8-6. Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year. [0.3074, 0.3726] [0.3105, 0.3695] [0.3140, 0.3660] [0.3392, 0.3408]
Answers
The question asks you to create a confidence interval for the percentage of American households that plan to buy a new automobile next year. A survey of 1400 American homes revealed that 34% expected to purchase a new automobile in the coming year. The aim is to create a 98% confidence interval for the population share of households planning to purchase a new automobile in the coming year. The solution will be one of the offered possibilities, which are all a range of numbers that may or may not include the population proportion.
We can use the following formula to construct the confidence interval:
CI = (proportion ± z*(√(proportion*(1-proportion)/n)))
Where z is the critical value for the given confidence level, the proportion is the proportion of those who indicated they plan to buy a new car next year, and n is the sample size.
For a 98% confidence level, the critical value, z, is 2.326. Therefore, the confidence interval is (0.3074, 0.3726).
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In an alternating treatments design, the baseline is implemented for a long period of time and then the treatment is implemented for a long period of time True False
Answers
According to the question, the statement "In an alternating treatments design, the baseline is implemented for a long period of time and then the treatment is implemented for a long period of time" is false.
In an alternating treatments design, the baseline and treatment conditions are alternated in a systematic manner. This design is used to compare the effects of different treatments or interventions on a target behavior. The key characteristic of the alternating treatments design is that the baseline and treatment conditions are implemented in a rapid and alternating fashion, rather than for long periods of time.
During an alternating treatments design, multiple conditions (baseline and treatment) are applied interchangeably across different time periods, often within the same session or day. This allows for the comparison of the effects of the different conditions on the target behavior within a relatively short timeframe.
The purpose of this design is to determine the differential effects of the treatments by directly comparing their effects in a more controlled manner. By rapidly alternating between conditions, it becomes possible to evaluate the immediate impact of the treatment and establish a causal relationship between the treatment and the observed changes in behavior.
Therefore, the statement "In an alternating treatments design, the baseline is implemented for a long period of time and then the treatment is implemented for a long period of time" is false.
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i) Multiply: (3.1x10°) x ( 1.5 x 10) = j) Divide: (3.1x10) / ( 1.5 x 10') = Small angle formula is a very useful approximation for angles smaller than about 0.25 radian (~15°). It allows calculation
Answers
i) The multiplication of (3.1x\(10^0\)) and (1.5x10) results in 4.65x\(10^1\).
j) The division of (3.1x10) by (1.5x\(10^{-1\)) equals 2.07x\(10^1\).
i) To multiply numbers in scientific notation, we multiply the coefficients (3.1 and 1.5) and add the exponents (0 and 1) together. In this case, 3.1 multiplied by 1.5 gives us 4.65. Adding the exponents, \(10^0\) multiplied by \(10^1\) results in \(10^1\). Therefore, the final result is 4.65x\(10^1\).
j) When dividing numbers in scientific notation, we divide the coefficients (3.1 and 1.5) and subtract the exponents (1 and -1) from each other. Dividing 3.1 by 1.5 gives us approximately 2.07. Subtracting the exponents, \(10^1\)divided by \(10^{-1\) is equivalent to \(10^{(1-(-1))}\) which simplifies to 10^2. Hence, the result is 2.07x\(10^1\).
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.Which is larger? ½ of 280or⅜ of 400
Answers
Answer:
3/8 of 400
Step-by-step explanation:
3/8 of 400 is 150 while 1/2 of 280 is 140
square root method 5x+9=134
Answers
Answer:
Step-by-step explanation:
What are you trying to find? If you want to find x then:
5x = 134 - 9
5x = 125
x = 25
if you want square root then,
x = √625 or
x = 5^2
Can a function of the form p(x)={
c(
3
2
)
x
0
x=1,2,3
elsewhere
be a probability mass function?
Answers
No, a function of the form p(x) = { c (32) x0 x = 1,2,3 elsewhere} cannot be a probability mass function(PMF).
A probability mass function is defined as a function that gives the probability that a discrete random variable X is exactly equal to some value x. In a probability mass function, for any given x, the value of the function p(x) must be between 0 and 1 inclusive, and the sum of the probabilities for all possible values of x must be equal to 1.
Let us now consider the given function p(x) = { c (32) x0 x = 1,2,3 elsewhere}. If x takes any value other than 1, 2, or 3, p(x) = 0. But if x takes any of the values 1, 2, or 3, then p(x) = c (32) x0 = c.
The function p(x) takes a value of c for three possible values of x, and it takes a value of 0 for all other possible values of x.
Thus, if c is such that 3c > 1, then the sum of probabilities for all possible values of x will be greater than 1.
So, the given function cannot be a probability mass function.
Therefore, we can conclude that the given function p(x) = { c (32) x0 x = 1,2,3 elsewhere} cannot be a probability mass function.
Thus, no, a function of the form p(x) = { c (32) x0 x = 1,2,3 elsewhere} cannot be a probability mass function.
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An ice cream cone has a diameter of 4.2 cm and a height of 11.5 cm. What is the volume of the cone? A. 18.6 cm³ B. 53.1 cm³ C. 212.3 cm³ D. 25.3 cm³
Answers
Answer:
B. 53.1 cm³
Explanation:
\(\sf volume \ of \ cone: \dfrac{1}{3} \pi r^2h \ \ \ \ (r \ is \ radius, \ h \ is \ height)\)
Here Given:
height: 11.5 cm
diameter: 4.2 cm
radius: d/2 = 4.2/2 = 2.1
Volume:
\(\sf \cdot \ \dfrac{1}{3} \pi r^2h\)
\(\sf \cdot \ \dfrac{1}{3} (3.14) (2.1)^2(11.5)\)
\(\sf \cdot \ 53.11 \ cm^3\) ≈ \(\sf 53.1 \ (rounded \ to \ nearest \ tenth)\)