Answer:
slope = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 5x - 2 ← is in slope- intercept form
with slope m = - 5
A standard deck of cards contains 52 cards. There are four suits (spades, clubs, hearts, and diamonds) and thirteen of each suit (2-10, jack, queen, king, ace). One card is selected at random from the deck. What is the probability the card selected is an Ace or a heart?
The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.
Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.
We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.
Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:
Probability=Number of items/total number of items.
Number of hearts=13
Number of ace=4
Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)
=13/52 * 4/52
=52/(52*52)
=1/52
Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.
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Identify the equation that describes the line in slope-intercept form slope = 3/4 point (2, 2) is on the line
Answer:
y = (3/4)x + 1/2
Step-by-step explanation:
the slope-intercept form is in general
y = ax + b
with a being the slope, and b the y-intercept (the y-value when x = 0).
because we got the slope and a point we can start with the point-slope form and then transform the equation.
the point-slope form is in general
y - y1 = a(x - x1)
a is again the slope (the same value), and (x1, y1) is a point on the line.
so,
y - 2 = 3/4 × (x - 2) = (3/4)x - 3/2
y = (3/4)x - 3/2 + 2 = (3/4)x - 3/2 + 4/2 = (3/4)x + 1/2
Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:
A. 19 p
B. 20 p
C. 21 p
D. 18 p
Based on the fact that the number of points scored are consecutive numbers, the number of points scored by Lewis is D. 18 points.
How many points did Lewis score?Lewis is the player who scored the least amount of points as they are first in the order.
To find the total number of points scored in the game therefore, you need to assume Lewis's points based on the options, and then sum up the three numbers above it to see if they add up to 78 points.
If Lewis scored 19 points as the lowest then the total points would be:
= 19 + 20 + 21 + 22
= 82 points
If Lewis scored 20 points, the total points would be:
= 20 + 21 + 22 + 23
= 86 points
Lewis therefore scored less than 19 points.
If Lewis scored 18 points, the total is:
= 18 + 19 + 20 + 21
= 78 points
Lewis therefore scored 18 points.
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Which values represent solutions to cosine (startfraction pi over 4 endfraction minus x) = startfraction startroot 2 endroot over 2 endfraction sine x, where x is an element of [0, 2pi)?
The given trigonometric function consists of trigonometric values of common angles.
The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
What are trigonometric functions?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.The given function is: [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]
Where; x ∈ [0, 2·π).
We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).
[tex]cos(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}, sin(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}[/tex]Which gives:
[tex]cos(\frac{\pi }{4}-x )=\frac{\sqrt{2} }{2}. cosx+\frac{\sqrt{2} }{2}.sinx[/tex]So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]
Therefore, the possible solutions (x-values) to cos x = 0 are:
[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]
Where, n = 1, 3, 5, .., x ∈ [0, 2·π)
We get: [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
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Halfway through the season, the USF Bulls football team had the highest average final score. What was the USF Bulls' average score if their final
scores were 31, 36, 28, 52, and 27
Answer:
D 34.8
Step-by-step explanation:
[tex]\frac{31+36+28+52+27}{5}[/tex]
Given f(x) = 3 and g(x) = cos(x). what is limit of left-bracket f (x) minus g (x) right-bracket as x approaches negative pi? 2 3 4 dne
Answer:
3
Step-by-step explanation:
f(x)-g(x)=3-cos(x)
when u limit it
u have
3-cos180
which is 3-0
3
MN =7. Find AB.
3.5
10.5
14
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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n January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?
Answer: The gas would not have remained liquid
Step-by-step explanation:
Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid
HELP PLEASE
if a function representing distance (feet) as a function of time (minutes), what does f(30) represent in terms of the situation?
We know
In a function
y=f(x)x represents the input and y represents output
So
f(30)x is time
So
f(30) represents distance traveled in 30mins
Given: the equation of a parabola is x2 = 8y. step 4: where does the focus for the given parabola lie?
The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
What is the vertex of a parabola?The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.
Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].
[tex]$\mathrm{y}=x^{2} / 8[/tex]
General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]
where (a, b) exists the coordinates of the vertex.
For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]
The vertex of the given parabola exists at (0, 0).
Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
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HELP! A city pays a manufacturing company to produce more stop signs for the city due to an increase in traffic incidents at intersections. After doing some research, the company manager reads that a standard stop sign is a regular octagon that is 30 inches wide and 30 inches tall.
The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59
How to solve for the octagonThe side of the octagon is given by x inches
the interior side of the angles can be gotten by:
8-2 * 180 / 8 sides
= 135
We have to find the value of the angles
<abc = 180 - 135 = 45 degree
<acb = 180 - 135 = 45 degrees
x² = 2AB²
AB = x/√2
30 = x/√2 + x + x/√2
x = 30 / 1 + √2
The apothem = 30 / 2
= 15
perimeter = 8x
= 8(30 / 1 + √2)
= 99.4 inches
area = 0.5 x 15 x 99.4
= 745.59
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Please give me a correct answer and the step by step explanation.
keeping in mind that the points are A(-8 , 6) and C(2 , 5), so
[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{2}{5}\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \stackrel{x_1}{-8}~~+~~\frac{2}{5}(10)~~,~~\stackrel{y_1}{6}~~+~~\frac{2}{5}(-1) \right)\implies \left(-8+4~~,~~6-\frac{2}{5} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5\frac{3}{5} \right)~\hfill[/tex]
Find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] (−1)n xn 2n n = 0
For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
For given question,
We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]
We need to find the radius of convergence of the power series.
We use ratio test to find the radius of convergence of the power series.
Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]
[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]
Consider,
[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]
By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]
⇒ |x| < 2
So, the radius of convergence is 2.
Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
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When calculating a nation’s digital power, what term is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense?
When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.
What is Cyberwarfare?Cyberwarfare can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.
It should be noted that Cyber Warfare is set of actions which is been carried out by nation or organization so as to be able to launch an attack on institutions' computer network systems.
The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;
To weaken the system of another country.To disrupt or destroy the sytem of another nation.In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.
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PLEASE ASAP - Drag each tile to the correct box. Arrange the figures from least to greatest according to their volumes. Assume the variable h has the same value for each figure.
Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:
Cone with radius of 3 units Cylinder with radius of 3 units Cone with radius of 6 units Cylinder with radius of 6 unitsWhat are the volumes of these shapes?The value of h is the same for all the shape so assume the value of h is 2 units.
The volume of a cylinder is:
= πr²h
First cylinder area:
= 22/7 x 3 x 2
= 56.54867 units
The second cylinder area:
= 22/7 x 6 x 2
= 226.19467 units
The volume of a cone is:
= πr²h/3
First cone volume:
= 22/7 x 3 x 2/3
= 18.84956 units
Second cone volume:
= 22/7 x 6 x 2/3
= 75.39822 units
The order is therefore:
Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units
In conclusion, the shapes with the larger radius of 6 units will have more volume.
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Can someone please help me with this?
Answer:
-2
Step-by-step explanation:
See attachment
The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth. (PLEASE ANSWER)
Answer:
29.9 cm³
Step-by-step explanation:
You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.
ConeThe volume of a cone is given by ...
V = 1/3πr²h
The volume of the cone of interest is ...
V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³
Slosh1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...
1/3(89.797 cm³) ≈ 29.9 cm³
They sloshed out about 29.9 cm³ before they drank the water.
<95141404393>
#6 pls quick answer!!!
Answer:
ANSWER: mix 120 ml of 35% acid solution with 60 ml of 65% acid solution to obtain 180 ml 0f 45% acid solution
Step-by-step explanation:
If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.
Acid content of first ingredient + acid content of second ingredient = acid content of the mixture
So, 0.35x + 0.65(60) = 0.45(x + 60)
0.35x + 39 = 0.45x + 27
12 = 0.10x
120 = x
If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]
▪ [tex] \sf{Area = 72 yd^2}[/tex]
▪ [tex] \sf{BD = 6yd}[/tex]
[tex]\leadsto[/tex] Substitute the values:
[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]
[tex]\leadsto[/tex] Solve for AC:
[tex]\longrightarrow \sf{72=8\times AC}[/tex]
[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]
[tex]\longrightarrow \sf{AC=9}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large \bm{AC= \: 9 yd}[/tex]
BD = 16 yd
Area of ABCD = 72 yd²
AC = ?
Area of rhombus, using diagonal:
[tex] \frac{1}{2} \times d1 \times d2[/tex]
Therefore:
[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]
Then:
[tex] \frac{16ac}{2} = 72[/tex]
Cross multiply the above into:
[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]
Divide by the coefficient of AC:
[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]
Final answer is 9 yd
Match the key features of functions terms to their corresponding definitions.
The key features of the above given functions are correctly matched to their corresponding definition.
Definition of termsNegative sections of the graph: They are the parts where the graph is below the x-axis. That is option C.End behaviour: This is what happens to the graph on the far left or far right. That is option E.Positive sections of the graph: This is the parts where the graph is above the x-axis. That is option D.Intercepts: This is the points where the graph crosses an axis. That is option BRelative extrema: This is the points of relative minimum or maximum in a graph. That is option A.Learn more about graphs here:
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Choose the expression that represents a cubic expression. 2x 11 −3x2 − 2x 11 4x3 − 3x2 − 2x 11 5x4 4x3 − 3x2 − 2x 11
(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
What is a cubic expression?A cubic polynomial has the generic form [tex]p(x): ax^{3} +bx^{2} +cx+d[/tex], a 0, where a, b, and c are coefficients and d is the constant, all of which are real integers. A cubic equation is one that involves a cubic polynomial.To determine which expression represents a cubic expression:
[tex]8x^{3} -7x^{2} -6x+5[/tex] is a cubic expression.The variable is x. [tex]8x^{3} -7x^{2} -6x+5[/tex] : The variable x has the highest power as 3. [tex]8x^{3} -7x^{2} -6x+5[/tex] is a polynomial.[tex]-7x+4[/tex] is a linear expression because the highest power of the variable x is 1.[tex]7x^{2} -5x+6[/tex] is a quadratic expression because the highest power of the variable x is 2.[tex]9x^{4} +8x^{3} -6x^{2} -2x+11[/tex] is a polynomial with the highest power of the variable being 4.Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
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The complete question is given below:
Choose the expression that represents a cubic expression.
(A) −7x + 14
(B) 7x2 − 5x + 6
(C) 8x3 − 7x2 − 6x + 5
(D) 9x4 + 8x3 − 6x2 − 2x + 11
Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x
Answer:
x= 5/2
Step-by-step explanation:
Answer:
-4 =x
Step-by-step explanation:
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Veronica's trail-mix package says there are 7 peanuts for every 3 cashews. Casey's trail-
mix package says there are 63 peanuts and 27 cashews. Are these ratios proportional?
If not, how many peanuts should there have been to make it proportional?
Answer:
Yes, they are proportional.
Step-by-step explanation:
The ratio for Veronica's trail mix is 3:7
The ratio for Casey's trail mix is 27:63 <--- Simplify this number
27:63 simplified is 3:7, which means these ratios are proportional.
hope this helps :)
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. if a marble is randomly selected from the bag, what is the probability that it is blue?
3/12, or 1/4 is the probability that it is blue.
What is probability?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .Probability = number of successes / total number of outcomes
Total marbels in bag = 4+ 3 + 5 = 12
A total of 12 marbles are in the bag.
3 blue marbles are in the bag.
Therefore, the probability of picking a blue is 3/12, or 1/4.
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Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Cos C
C
21
B
35
28
A
Write the algebraic expression that represents the following: Forty more than a number
Answer:
x+40
Step-by-step explanation:
Let's say the the "number" is x.
"Forty more than a number" would be x+40
[tex]\Large\texttt{Answer}[/tex]
[tex]\bold{40+n}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Letting n be the number
[tex]\bold n[/tex]
⇨ Add 40 to n (40 more)
[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)
Hope that helped
QUICK!!!HELP!!!!!!!!!!!!!!!!!!
Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:
Z = (X - mu)/sigma
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
mu = 400, sigma = 50
The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:
X = 550:
Z = (X - mu)/sigma
Z = (550 - 400)/50
Z = 3
Z = 3 has a p-value of 0.9987.
X = 500:
Z = (X - mu)/sigma
Z = (500 - 400)/50
Z = 2
Z = 2 has a p-value of 0.9772.
0.9987 - 0.9772 = 0.0215 = 2.15% probability.
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Bob needs to send out a mailing for his company. Working alone, it will take him 10 hours to get the job done. Ellen can do the job in 8 hours by herself. They work together for 2 hours, and then Ellen finishes the job by herself. Which choice is the best estimate for how long the job will take in all?
Answer:
6 2/5 hrs or 6.4 hours total
Step-by-step explanation:
In two hours, Bob completes 2/10 = 1/5 of the job
Ellen completes 2/ 8 = 1/4
Find amount left
1 - 1/5 -1/4 = 1 - 4/20 - 5/20 = 11/20 left
Ellen will need 8hrs * 11/20 = 88/20 = 4 2/5 hours to finish the job
2 hours to start + 4 2/5 hours to finish = 6 2/5 hours total
Oscar corporation is planning to construct an elliptical gate at its headquarters. the width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. the company wants to place two bright spots at the foci of the ellipse. how far from the center of the ellipse will the spots be located?
The distance from the center of the ellipse to where the spots are located will be 2 feet.
What is Distance?
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.The distance from the center of the ellipse to where the spots are located will be -
= 5 - 3
= 2 feet.
Therefore, the distance from the center of the ellipse is 2 feet.
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Find the Area Of each circle.
The area of the circle A and B is 86.54 inches and 124.62 mm
According to the statement
we have given that the radius of the circle A and b and we have to find the area of the given circle.
So, we know that the
The area enclosed by a circle of radius r is πr².
So, For area of the circle
For condition A :
diameter = 10.5 inches
then radius = 5.25
Area = πr²
Area = 3.14*27.56
Area = 86.54 inches
Now, For condition B :
radius = 6.3 mm
Area = πr²
Area = 3.14*39.69
Area = 124.62mm
So, The area of the circle A and B is 86.54 inches and 124.62 mm
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