Nolan has some nickels and some dimes. He has no more than 19 coins worth no less than $1.30 combined. If Nolan has 5 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values.

Answer:C, B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you are looking for a missing angle measure, you use the 2nd button and the cos button.  Make sure, first off, that your calculator is in "degree" mode by hitting the "mode" button and making sure that the "degree" is highlighed and not the "radian".  Then hit "clear".  Once you know that you are in the correct mode, hit "2nd" then "cos" and you will see this on your screen:

[tex]cos^{-1}([/tex]

Inside the parenthesis you will enter your decimal, so it looks like this now:

[tex]cos^{-1}(.7431[/tex]

You do NOT have to close the parenthesis, but you can if you want to.  Then hit "enter" to get that the angle that has a cosine of .7431 is 42.0038314 or, to the nearest degree, 42

The inverse cosine function is used to find the angle from the cosine value. In this case, angle A is approximately 42 degrees.

To find the angle measure when given the cosine value, you use the inverse cosine function, sometimes written as cos-1 or arccos. The inverse cosine of a given number tells you what angle has that given cosine value.

So for cos A = 0.7431, we need to find the inverse of cosine of 0.7431. Use your calculator's inverse cosine function (often labeled as cos-1 or arccos) with the input 0.7431. Ensure your calculator is in degree mode if the answer needs to be in degrees, which seems to be your case.

Using this process, you should find that angle A is approximately 42 degrees (42.006 to be exact).

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Answer:

Therefore,

A quadrilateral that has no pairs of parallel sides is

KITE.

Step-by-step explanation:

A quadrilateral that has no pairs of parallel sides is

KITE.

In Kite there are no pairs of Parallel sides.

The Figure for Kite ABCD is below (not to the scale).

Rectangle and Parallelogram:

Opposite sides are Parallel .

Hence they have pairs of parallel sides,

Trapezoid:

Trapezoid has one pair of parallel side.

Hence it has a pair of parallel sides,

Therefore,

A quadrilateral that has no pairs of parallel sides is

KITE.

Answer:

Kite

Step-by-step explanation:

Answer:

The percent increase between getting a high school scholarship and bachelor's degree is 59.14%.

Step-by-step explanation:

Given:

High school scholarship is $421.

Bachelor's degree is $670.

Now, to find the percent increase between a high school scholarship and bachelor's degree.

So, we get the amount of increase between a high school scholarship and bachelor's degree.

[tex]670-421=249.[/tex]

Thus, the amount of increase = $249.

Now, to get the percent increase between a high school scholarship and bachelor's degree:

[tex]\frac{249}{421}\times 100[/tex]

[tex]=\frac{24900}{421}[/tex]

[tex]=59.14\%.[/tex]

Therefore, the percent increase between getting a high school scholarship and bachelor's degree is 59.14%.

The percent increase from a high school scholarship ($421) to a bachelor's degree ($670) is calculated to be roughly 59.1%. The overall value of a bachelor's degree over a lifetime typically exceeds this amount, with degree holders potentially earning millions more than their counterparts with only a high school diploma.

The subject of this question is a mathematical one, dealing with percentage increase. To find the percent increase between getting a high school scholarship and a bachelor's degree, we first subtract the smaller value (high school scholarship) from the larger value (bachelor's degree). We then divide the result by the starting value (high school scholarship). Thus, the formula is: [(670 - 421)/421] * 100%.

A simplified calculation gives us: [(249)/421] * 100% = 59.1%.

Therefore, there is a 59.1% increase in the value from a high school scholarship to a bachelor's degree based on the given figures.

It's also worth noting that over the course of a career, according to a 2021 report from the Georgetown University Center on Education and the Workforce, adults with a bachelor's degree earn an average of $2.8 million during their careers, $1.2 million more than the median for workers with a high school diploma.

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Answer:

  (x -5)² +(y -1)² = 25

Step-by-step explanation:

The equation for a circle centered at (h, k) with radius r is ...

  (x -h)² +(y -k)² = r²

Here, the radius is equal to the x-coordinate of the center, since you want the circle tangent to the y-axis. That means (h, k) = (5, 1) and r = 5. The equation you want is ...

  (x -5)² +(y -1)² = 25

The equation of the circle with center at (5,1) and tangent to the y-axis is (x - 5)² + (y - 1)² = 25.

To find this equation, we can use the general form of a circle's equation, which is:

(x - A)² + (y - B)² = C

Where A and B are the x and y coordinates of the center of the circle, respectively, and C is the square of the radius of the circle. Since the circle is tangent to the y-axis and its center is at (5,1), the radius of the circle must be 5 units because this is the horizontal distance from the center to the y-axis. Therefore, C will be 5², which is 25. The complete equation of the circle is:

(x - 5)² + (y - 1)² = 25

Answer:

[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]

So then the we have perfect linear association.  Because the heights and weights of the men are similar.

Step-by-step explanation:

Let X represent the Height and Y the weigth

We have the follwoing dataset:

X: 70, 69

Y: 169, 164

n=2

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

And in order to calculate the correlation coefficient we can use this formula:  

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

For our case we have this:  

n=2 [tex] \sum x = 139, \sum y = 333, \sum xy = 23146, \sum x^2 =9661, \sum y^2 =55457[/tex]  

And if we replace in the formula we got:

[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]

So then the we have perfect linear association.  Because the heights and weights of the men are similar.

The question is asking to create a new mathematical identity by combining binomials and trinomials from two different columns. An example of such identity could be 2x2 + 2y2. We also used the appendix to solve a quadratic equation by completing the square.

This question is asking you to combine binomials and trinomials from column A and column B to create a new mathematical identity. An example of creating such an identity could be squaring the binomial (x - y) from column A and adding it to the trinomial (x2 + 2xy + y2) from column B.

So, if we square (x - y), we get x2 - 2xy + y2. Adding that to x2 + 2xy + y2 from column B, we get 2x2 + 2y2, which is the new identity.

Also, using the appendix to solve an equation of the form ax² + bx + c = 0, we rearrange terms and complete the square to find x. Using the example of x² +0.0211x -0.0211 = 0, the factors of 0.0211 are easy to determine. After rearranging terms, the equation becomes (x +0.01055)² - 0.0211 = 0. Finally, to solve for x, you would add 0.0211 to both sides and then take a square root.

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Answer:$920

Step-by-step explanation:

Since the variation is joint, I=KPr where k is the constant of proportionality.

Plugging in the values of I=$375, P=$1500 and r=5% in the equation I=KPr, the value of k can be calculated. Hence, the formula connecting the three quantities (I,P and r) can be generated.

375 = K (1500×5)

Making k the subject of change,

K = 375/(1500×5)

K=1/20

Formula connecting the three quantities :I =Pr/20

when P=$2300, r=8%,

I = (2300×8)/20

I = $920

Answer:

A.

Step-by-step explanation:

Probability sampling means that each unit in population has an equal chance or probability of selection in a sample.

Cluster sampling is a probability sampling method because population is divided into clusters at random and no personal judgement is involved. Thus, each cluster has equal probability of selecting and sampling is done as random. Hence, cluster sampling is a probability sampling method.

Cluster sampling is a probability sampling method. Here option A is correct.

It involves dividing the population into clusters or groups based on certain characteristics, such as geographical location or other relevant attributes. Then, a random sample of clusters is chosen, and all individuals within those selected clusters become part of the sample.

This method is considered probabilistic because each cluster has a known probability of being selected, and thus each individual within the chosen clusters has a chance of being included in the sample. This makes it possible to estimate population parameters and make statistical inferences.

Cluster sampling differs from other probability sampling methods, such as simple random sampling, in that it involves a multi-stage process.

It is particularly useful when it's impractical or too costly to gather a complete list of all individuals in the population, making it a valuable tool in various fields of research, including public health, sociology, and economics. Here option A is correct.

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Answer:

The answer to your question is B. (1.5, -6)

Step-by-step explanation:

Data

A (8, -3)

B (-5, -9)

Formula

Xm = [tex]\frac{x1 + x2}{2}[/tex]

Ym = [tex]\frac{y1 + y2}{2}[/tex]

Substitution

x1 = 8    x2 = -5

                     Xm = [tex]\frac{8 - 5}{2} = \frac{3}{2}[/tex]

y1 = -3   y2 = -9

                     Ym = [tex]\frac{-3 - 9}{2} = \frac{-12}{2} = -6[/tex]

Midpoint = (3/2, -6) = (1.5, -6)

Answer: C. 115 pieces of candies divided equally between 5 friends is not equal to 21 each

Step-by-step explanation: 115 divided by 5 is 23 each and not 21.

Answer:

1 meter farther

Step-by-step explanation:

The difference in time from 4 seconds to 10 seconds is 6 seconds.

The speed is half of the difference of time.

That is why the speed is 3 m/s.

The difference in time from 10 to 18 is 8 seconds.

Take the time and divide it by 2 to get the speed.

The speed is 4 m/s.

The object's position is 1 more meter.

4 m/s - 3 m/s = 1 m/s

The object's position after 8 seconds is 24 m to have elapsed.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Over the interval from 4 seconds to 10 seconds, the object's speed was calculated to be 3 m/s.

Now,

Since, Over the interval from 4 seconds to 10 seconds, the object's speed was calculated to be 3 m/s.

That is,

The speed = 3 m/s

Time = 10 - 4 = 6 seconds

So, The distance cover by object's in 6 seconds = 3 x 6

                                                                         = 18 m

Hence, The object cover the distance in 8 seconds = 18 x 8 / 6

                                                                                = 24 m

So, The object's position after 8 seconds is 24 m to have elapsed.

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Answer:

b. 20%

Step-by-step explanation:

2014

Car price = 20000

2015

Car price = 16000

Depreciation = 20000 - 16000 = 4000

Depreciation % = (4000/20000)*100 = 20%

2016

Car price = 12800

Depreciation = 16000 -12800 = 3200

Depreciation % = (3200/16000)*100 = 20%

Final answer:

To find the union of sets C and D, you combine the elements of both sets without repeating any elements. The union, C ∪ D, is therefore {2, 3, 4, 5, 9, 10, 11, 12}.

Explanation:

The question asks to list the elements of the set that is the union of two sets C and D. The union of two sets contains all the elements that are in either set. Therefore, C ∪ D is the set that includes all the elements from both sets C and D without duplication.

Set C contains the integers {2, 3, 4, 5} and set D contains the integers {9, 10, 11, 12}. Hence, the union of sets C and D, denoted C ∪ D, would be {2, 3, 4, 5, 9, 10, 11, 12}. This combines all the unique elements from both sets.

Answer:

a) [tex] \mu_{\bar x} =\mu = 276.1[/tex]

[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]

b) From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]

c) [tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]

[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

[tex] \mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4[/tex]

And we select a sample size of 64.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

For this case the mean and standard error for the sample mean would be given by:

[tex] \mu_{\bar x} =\mu = 276.1[/tex]

[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]

Part b

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]

Part c

For this case we want this probability:

[tex] P(\bar X \geq 285)[/tex]

And we can use the z score defined as:

[tex] z=\frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]

And using this we got:

[tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]

And using a calculator, excel or the normal standard table we have that:

[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]

Answer: dr/dt = 0.042 cm/minute

Step-by-step explanation:

Given;

dV/dt = 4cm^3/minute

t = 2.25minutes

Volume of a sphere is given as;

V = (4/3)πr^3

Change in Volume ∆V can be derived by differentiating the function.

dV/dt= 4πr^2 . dr/dt

dV/dt = 4πr^2dr/dt ....1

dV/dt is given as 4 cm^3/min

radius after 2.25 minutes can be gotten from the the volume.

Volume after 2.25mins = 4×2.25 = 9cm^3

9cm^3 = V = 4/3πr^3

r^3 = 27/4π

r = (27/4π)^1/3

From equation 1.

dr/dt = (dV/dt)/4πr^2 = 4/(4πr^2) = 1/(πr^2)

dr/dt = 1/(π(27/4π)^2/3)

dr/dt = 0.042cm/minute.

Answer: 35 granola bars and 45 pies were sold.

Step-by-step explanation:

Let x represent the number of granola bar that was sold.

Let y represent the number of pie that was sold.

A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies.

This means that

x + 5y = 260 - - - - - - - - - -1

Since they sold a total of 80 bars and pies, it means that

x + y = 80

Substituting x = 80 - y into equation 1, it becomes

80 - y + 5y = 260

- y + 5y = 260 - 80

4y = 180

y = 180/4 = 45

x = 80 - y = 80 - 45

x = 35

Answer:

The broker's commission was rupees 8,250

Step-by-step explanation:

Selling price of property = rupees 450,000

The sale price is higher than rupees 300,000

Commission for rupees 300,000 = 2% × rupees 300,000 = rupees 6,000

Remaining amount = rupees 450,000 - rupees 300,000 = rupees 150,000

Commission for the remaining amount = 1.5% × rupees 150,000 = 0.015 × rupees 150,000 = rupees 2,250

Total commission = rupees 6,000 + rupees 2,250 = rupees 8,250

Answer:

6 rolls

Step-by-step explanation:

Data provided in the question:

Height of wall = 9'

Width of walls = 13', 13', 18' and 18'

Dimension of roll = 3' x 2' x 50'

Now,

Total area of the walls = 9' × 13' + 9' × 13' + 9' × 18' + 9' × 18'

= 117 + 117 + 162 + 162

= 558 ft²

Area of each roll = 2' × 50'

= 100 ft²

Thus,

Number of rolls required = [ Total area of the walls  ] ÷ [ Area of each roll ]

= 558 ft² ÷ 100 ft²

= 5.58 ≈ 6 rolls

Final answer:

To insulate the recreation room, the homeowner needs to calculate the total area of the walls and then divide it by the area covered by one roll of insulation. After calculating the areas and factoring in the size of the rolls, it is determined that the homeowner needs to purchase 4 rolls of insulation.

Explanation:

The homeowner needs to calculate the amount of insulation needed for a new recreation room. To determine the number of rolls required, we first need to calculate the total area to cover by adding the areas of all four walls. The walls are 9’ high with two of them measuring 13’ in length and the other two are 18’ in length.

The total area These areas can be calculated using the formula Area = Height × Length for each wall. For the 13’ walls: Area = 9’ × 13’ = 117 sq ft (per wall). So, for both, it would be 117 sq ft × 2 = 234 sq ft. And for the 18’ walls: Area = 9’ × 18’ = 162 sq ft (per wall), which is 162 sq ft × 2 = 324 sq ft in total. Now, let's add these together to get the total area of all walls that need insulation: 234 sq ft + 324 sq ft = 558 sq ft.

Next, we calculate how many square feet are in each roll. Since each roll measures 3’ x 50’, the area per roll is 3’ x 50’ = 150 sq ft.

Finally, by dividing the total area needed by the area one roll covers, we can determine the number of rolls:
Number of rolls needed = Total area ÷ Area per roll = 558 sq ft ÷ 150 sq ft/roll ≈ 3.72 rolls.

Since we cannot purchase a fraction of a roll, the homeowner will need to purchase 4 rolls of insulation.

Answer:

Joe baked a high ratio. Hope this helps :)

Answer:

  Joe

Step-by-step explanation:

Joe baked more than twice as many apple pies as blueberry. (16 > 12)

Whitney baked less than twice as many apple pies as blueberry. (19 < 24)

Joe baked a higher proportion of apple pies.

Answer:

24.2(to the nearest tenth)

Step-by-step explanation:

The question is ungrouped data type

standard deviation =√ [∑ (x-μ)² / n]

mean (μ)=∑x/n

           = [tex]\frac{5+5+6+12+13+26+37+49+51+56+56+84}{12}[/tex]

          =33.3

x-μ   for data 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84 will be

                   -28.3, -28.3, -27.3, -21.3, -7.3, 3.7, 15.7,17.7, 22.7,22.7,50.7

(x-μ)² will be 800.89, 800.89,745.29,453.69,53.29,13.69,246.49,313.29,515.29,515.29,2570.49

∑ (x-μ)² will be = 7028.59

standard deviation = √(7028.59 / 12)

                      =24.2

Answer:

That the government did not defend the rights of the Indians.

Step-by-step explanation:

Sand Creek, Colorado was the place where hundreds of Cheyenes and Arapahoes were massacred by the Colorado Territory militia, which terrorized indigenous peoples to abandon their lands.

Answer:

The 13 students on floor

Step-by-step explanation:

The sample is a portion of population selected to view the aspects of population as whole population is difficult to follow. Here, the sample is 13 students on the floor because it is selected from 22 students on the floor.

The population consists of 22 students on floor and 13 out of 20 is the sample because it is a portion of population.

Answer: h = 12mm

Step-by-step explanation:

The volume of a pyramid is given as :

V = [tex]\frac{1}{3}[/tex] lwh

Therefore:

324 = [tex]\frac{1}{3}[/tex] lwh

324 x 3 = 9 x 9 x h

Therefore:

h = 972/81

h = 12mm

Answer:

a) The number of correct answers

b) Discrete

c) Ratio        

Step-by-step explanation:

We are given the following in the question:

Experiment:

Evaluate the effectiveness of different study strategies. All students were then given a test on the passage material and the researchers recorded the number of correct answers.

a) The dependent Variable

The number of correct answers given is the dependent variable because it depends on the number of times the passage is read.

b) Nature of dependent variable.

c) Scale of measurement

The correct answers are as follows: a: number of correct answers on the test, b: discrete, and c: ratio scale.

a. The dependent variable for this study is the number of correct answers on the test.

b. The dependent variable is discrete because it consists of countable values, specifically the number of questions answered correctly, which can only be whole numbers.

c. The scale of measurement used to measure the dependent variable is the ratio scale. This is because the number of correct answers has a true zero point (it is possible to have zero correct answers), and the differences between the numbers of correct answers are meaningful and consistent. Additionally, the ratio scale allows for the comparison of ratios, such as one student answering twice as many questions correctly as another.

To elaborate, in experimental design, the dependent variable is the variable that is measured to assess the effect of the independent variable (in this case, the study strategy). The dependent variable is what changes as a result of manipulating the independent variable. In this study, the researchers are interested in how different study strategies affect test performance, so they measure test performance by counting the number of correct answers each student provides.

The nature of the dependent variable as discrete or continuous depends on whether the data can take on any value within a range (continuous) or only specific values (discrete). Since the number of correct answers can only be whole numbers (e.g., 5 correct answers, not 5.5), it is discrete.

Finally, the scale of measurement indicates the level of precision with which the variable is measured. The nominal scale is used for categorical data without any order (e.g., gender, race). The ordinal scale is used for data that can be ranked but without equal intervals between ranks (e.g., socioeconomic status). The interval scale is used for data with equal intervals between values but no true zero (e.g., temperature in Celsius or Fahrenheit). The ratio scale is used for data with a true zero and equal intervals between values, allowing for the comparison of ratios (e.g., height, weight, and in this case, the number of correct answers). Since the number of correct answers can be zero (indicating no correct answers) and the differences between scores are meaningful, the dependent variable in this study is measured on a ratio scale.

Answer:

It would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.          

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution is a bell shaped distribution that is a normal distribution.

Empirical rule

Thus, approximately 68% of data will lie within one standard deviation of mean.

[tex]\mu - \sigma = 100-15 = 85\\\mu + \sigma = 100 + 15 = 115[/tex]

Thus, it would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.

68 percent of the scores would fall between 85 and 115.

Empirical rule states that for a normal distribution, about 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.

Given that mean(μ) = 100 and standard deviation (σ) = 15

68 percent of the scores would fall between μ ± σ = 100 ± 15 = 85, 115

68 percent of the scores would fall between 85 and 115.

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Answer: you need to have in total sales of $16667 to earn the same amount in each job

Step-by-step explanation:

Let x represent the amount that you need to have in total sales in order to earn the same amount in each job.

Company A offers a $35,000 annual salary plus a 6% commission of his total sales. This means that the total amount earned with company A when x sales is made yearly would be

35000 + 0.06x

Company B offers a flat annual salary of $36,000. This means that the total amount earned with company B yearly would be

36000

To earn the same amount with both jobs,

35000 + 0.06x = 36000

0.06x = 36000 - 35000

0.06x = 1000

x = 1000/0.06 = $16667

Answer: 26

Step-by-step explanation: From the remainder theorem ,

If P (x) = 2x⁴ ⁻ x³ + 2x² ⁻ 6. is divided by ( x - 2 ).

It means that if P(x) is divided by (x - 2 ) and leaves a Remainder, it implies that x - 2 is not a factor of P(x) , but if it leaves no remainder, it means x-2 is a factor of P(x).

Therefore , to find the remainder, find the zero of x - 2, and substitutes for the value in P(x)  to know the remainder

x - 2 = 0

x = 2

Now put this in P(x)

P(x) = 2(2)⁴ - (2)³ + 2(2)² - 6

= 2(16) -8 + 2(4) -6

= 32 -8 +8 -6

=26

Therefore the remainder when P(x) is divided by x -2

=26

Note: Since the division of P(x) by x - 2 leaves a remainder, it means that

x - 2 ≠ a factor of P(x)

Answer:

A) Yes , the triangles are similar as indicated and shown from the analysis of the diagram.

B) Yes, the canyon width AE can be found and it is calculated and gotten as 109.09ft

Step-by-step explanation:

Attached below is the step by step calculations and explanation of both answers.

Answer:

d. 32 π

Step-by-step explanation:

As given

Area of circle = 64 π

Area of circumference = 1/2*(Area of circle)

Area of circumference = 1/2*(64π)

Area of circumference = 0.5*64π

Area of circumference = 32π

A circle is a curve sketched out by a point moving in a plane. The correct option is A, 12π unit.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that the area of the circle is less than 64π. Therefor, the area of the circle can be written as,

Area of the circle < 64π units²

πR² < 64π

R < 8 units

Now, the circumference of the circle should be less than the circumference of the circle having radius of 8 units. Therefore, we can write,

Circumference of the circle with radius R < Circumference of the circle with radius of 8 units

2πR < 2 × π × 8 units

2πR < 16π units

Therefore, from the above inequality the circumference of the circle should be less than 16π unit. Since the only feasible option is 12π.

Hence, the correct option is A, 12π unit.

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