Answer:
x + 3
5
Explanation:
x+3 is the equation for the first line to the left, and f(x)=5 is the second equation for the second line at the top.
Convert the equation of a line in point slope
form into slope-intercept form.
y−3 = 2 (x+9)
Answer:
y = 2x + 21 would be the slope-intercept form
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue
How to determine which statement about probability is true?Probability is the likelihood of a desired event happening.
Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.
Thus, we can write the probabilities as follow:
probability of orange = 1/8
probability of purple = 2/8 = 1/4
probability of yellow = 2/8 = 1/4
probability of blue = 3/8
Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement
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A scale measures weight to the nearest 0. 5 lb. Which measurement shows an appropriate level of precision for the scale? A. 140lbs, B. 148. 75lbs, C. 140. 5lbs, D. 141lbs
The appropriate level of precision for the scale depends on the smallest unit of measurement it can accurately determine. In this case, the scale measures weight to the nearest 0.5 lb.
A. 140 lbs. : This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision. B. 148.75 lbs.: This measurement includes decimal places that the scale cannot accurately determine. It exceeds the precision of the scale and does not show an appropriate level of precision. C. 140.5 lbs: This measurement falls within the precision of the scale. It accounts for the nearest 0.5 lb increment and shows an appropriate level of precision. D. 141 lbs: This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision.
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given: (x is number of items) demand function: d ( x ) = 3888/√x supply function: s ( x ) = 3√x find the equilibrium quantity:______. find the consumers surplus at the equilibrium quantity: ____
Calculating the integral, we find the consumer surplus at the equilibrium quantity. the equilibrium quantity is approximately 432.
Setting the demand and supply functions equal to each other, we have d(x) = s(x), which becomes 3888/√x = 3√x.
To solve for x, we can first square both sides of the equation to eliminate the square roots: (3888/√x)^2 = (3√x)^2.
Simplifying, we get (3888)^2 / x = (3^2)(x).
Cross-multiplying, we have (3888)^2 = 9x^3.
Dividing both sides by 9, we get x^3 = (3888)^2 / 9.
Taking the cube root of both sides, we find x = ∛((3888)^2 / 9).
Calculating the value, we find x ≈ 432.
Therefore, the equilibrium quantity is approximately 432.
To find the consumer surplus at the equilibrium quantity, we need to calculate the area between the demand curve and the price line at that quantity. Consumer surplus represents the difference between the maximum price a consumer is willing to pay (represented by the demand curve) and the actual price (represented by the supply curve) for the given quantity.
Since the demand function is given by d(x) = 3888/√x, we need to calculate the integral of this function from 0 to 432.
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B) Frank works as a mechanic. Joellie is having alternator problems and asks Frank to fix it. Frank
worked on the car for 2 hours and used $120 in parts. If he charged Joellie $280 in total, what
was his hourly rate?
Answer:
The hourly rate is$80.00
Step-by-step explanation:
280 - 120 = 160 This is the amount of money that was spent on labor.
160÷2 = 80
John walks from his home due east for 1 mile, due north-east for 3 miles, due west for 2 miles, and then walks straight home. Write down the Cartesian coordinates of the vector that takes him home. What was the distance that John traveled? Displacement?
The Cartesian coordinates of the vector that takes John home are (0, 1).
To determine the distance John traveled, we can calculate the sum of the distances traveled in each direction. He walks 1 mile due east, 3 miles northeast (which can be decomposed into 3 miles east and 3 miles north), and 2 miles due west. Finally, he walks straight home, which means he walks south by the same distance as the initial 1 mile east.
The total distance traveled can be calculated as follows:
Distance = 1 mile (east) + 3 miles (east) + 3 miles (north) + 2 miles (west) + 1 mile (south)
= 1 + 3 + 3 + 2 + 1
= 10 miles
Now, let's calculate the displacement, which is the straight-line distance from the starting point to the ending point.
The displacement can be determined by finding the difference in coordinates between the starting point and the ending point. John's starting point is (0, 0) and his ending point is (0, 1).
Displacement = √((change in x)^2 + (change in y)^2)
= √((0 - 0)^2 + (1 - 0)^2)
= √(0 + 1)
= 1 mile
Therefore, the distance that John traveled is 10 miles, while the displacement is 1 mile. This indicates that John traveled a longer path due to the detours he took, but the straight-line distance from the starting point to the ending point (displacement) is only 1 mile.
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If a water contains 29mg/l of Ca
++
and 16.4mg/l of Mg
++
, what is the hardness expressed in milligrams per liter as CaCO
3
? (Answer 140mg/l)
Therefore, the hardness of the water, expressed in milligrams per liter as CaCO3, is 280.03 mg/l.
To calculate the hardness of water expressed in milligrams per liter as CaCO3, we need to consider the calcium (Ca++) and magnesium (Mg++) concentrations given in milligrams per liter (mg/l).
Given:
- Calcium concentration (Ca++) = 29 mg/l
- Magnesium concentration (Mg++) = 16.4 mg/l
The hardness of water is determined by the combined concentration of calcium and magnesium ions. These ions contribute to the formation of mineral deposits and can affect the lathering of soaps and detergents.
To calculate the hardness as CaCO3, we need to convert the concentrations of calcium and magnesium ions into their respective equivalents in terms of CaCO3. This conversion takes into account the molar mass and valence of each ion.
The molar mass of calcium (Ca) is 40.08 g/mol, and its valence is 2+. Therefore, the equivalent weight of calcium is (40.08/2) = 20.04 g/mol.
The molar mass of magnesium (Mg) is 24.31 g/mol, and its valence is 2+. Thus, the equivalent weight of magnesium is (24.31/2) = 12.155 g/mol.
Now, let's calculate the hardness:
1. Convert the calcium concentration to the equivalent concentration of CaCO3:
Calcium concentration (Ca++) = 29 mg/l
Equivalent concentration of CaCO3 = 29 mg/l * (100.09 g/mol / 20.04 g/mol) = 145.17 mg/l as CaCO3
2. Convert the magnesium concentration to the equivalent concentration of CaCO3:
Magnesium concentration (Mg++) = 16.4 mg/l
Equivalent concentration of CaCO3 = 16.4 mg/l * (100.09 g/mol / 12.155 g/mol) = 134.86 mg/l as CaCO3
3. Add the equivalent concentrations of CaCO3 for calcium and magnesium:
Total hardness = 145.17 mg/l + 134.86 mg/l = 280.03 mg/l as CaCO3
Therefore, the hardness of the water, expressed in milligrams per liter as CaCO3, is 280.03 mg/l.
The provided answer of 140 mg/l may not be accurate based on the given concentrations of calcium and magnesium.
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hat is the probability that a random sample of 10 cars will have a mean ore weight of 70.7 tons or more? show your work.
2.28% is the probability that a random sample of 10 cars will have a mean weight of 70.7 tons or more.
To find the probability that a random sample of 10 cars will have a mean weight of 70.7 tons or more, we need to know the mean and standard deviation of the weight of the cars in the population. Let's assume that the mean weight of the cars in the population is 68 tons and the standard deviation is 4 tons.
The mean weight of a random sample of 10 cars will follow a normal distribution with a mean of 68 tons and a standard deviation of (4 tons) / sqrt(10) = 1.2 tons.
To find the probability that the mean weight of the random sample is 70.7 tons or more, we can use the standard normal distribution table or a calculator to find the area under the curve to the right of (70.7 - 68) / 1.2 = 1.95. This probability is about 0.0228, or about 2.28%.
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PLEASE HELP ME!!! I WILL GIVE YOU 15 POINTS
Answer:
gl with that
Step-by-step explanation:
Answer:
the correct answer is option B. x=2, y=0
hope it helps you
what is 2 + 2 plssssssssssssssss i need help itsso hard my brain broken and cannot do it so good so sory guys i cannot do it sory
Answer:
2+2 is 4
Step-by-step explanation:
2
+2
___
4
Answer:
4
2 is the same 1+1
1 + 1 + 1 + 1 =4
Hope this helps!
Rolf owns a package delivery business. During the current year, he purchased and placed into service $1,080,000 worth of equipment. Rolf is in the highest marginal income tax bracket this year and expects to be in that bracket for two more years. After that, he plans to semi-retire but keep the business open for another three to five years. He expects to drop into the lower marginal brackets when he semi-retires. What advice would you give Rolf regarding the use of Section 179 and cost recovery deductions
I would advise Rolf to take advantage of the Section 179 deduction for the current year to maximize his tax savings. By doing so, he can deduct the full cost of the equipment purchased and placed into service, up to the Section 179 limit.
Rolf should consider utilizing the Section 179 deduction, which allows business owners to deduct the full cost of qualifying equipment purchased and placed into service during the year, instead of depreciating it over several years. The current Section 179 limit is $1,050,000. Since Rolf purchased equipment worth $1,080,000, he can fully deduct this amount, subject to the limit. By taking advantage of this deduction, Rolf can significantly reduce his taxable income for the current year, thereby lowering his tax liability in the highest marginal tax bracket.
Furthermore, Rolf's plan to semi-retire in the future and potentially drop into lower marginal tax brackets should be considered when deciding whether to utilize cost recovery deductions such as depreciation. If Rolf expects to be in a lower tax bracket in the coming years, it may be more advantageous to spread the deductions over the useful life of the equipment through depreciation. This would allow him to offset income in future years when his tax rate is lower. However, since Rolf plans to keep the business open for another three to five years before fully retiring, it is important to assess the potential tax implications during this period. Consulting with a tax professional would be beneficial in determining the most suitable strategy for Rolf's specific circumstances.
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Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. zero: 1, multiplicity: 2 zero: 2, multiplicity: 2 degree: 4
Polynomial expression for the given conditions is formulated in the equation
y(x)=1*(x-2)^3(x-0)^2
The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as
According to the given condition
The given conditions to write the polynomial equations are as follows
Zero 2 and Multiplicity 3
Zero 0 and Multiplicity 2
Degree of polynomial expression = 5
The leading coefficient of polynomial expression = 1
Let us consider the polynomial equation has only one variable and hence in the general form we can write the equation of polynomial as follows
From the general form of polynomial expression as shown in equation (1) we can write
Polynomial expression for the given conditions is formulated in the equation
y(x)=1*(x-2)^3(x)^2-------(2)
So the polynomial for the conditions given in the question is expressed as
y(x)=1*(x-2)^3(x)^2
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The volume of a gas held at a constant temperature varies inversely with the pressure of the gas. If the volume of a gas is 5000 cubic centimeters when the pressure is 200 millimeters of mercury, what is the volume when the pressure is 500 millimeters of mercury?
Answer:
2,000 cubic centimeters
Step-by-step explanation:
if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
the equation that represents inverse proportion :
\(v = \frac{b}{p}\)
where b = constant of proportionality
5000 = b / 200
b = 5000 x 200 = 1,000,000
v = 1,000,000 / 500
v = 2000
If you wanted to compare many different categories in a single graph, what type of visualization would you use?.
By using a bar chart or a grouped bar chart, you can visualize and compare the data across multiple categories in a single graph, making it easier to identify patterns, trends, and differences among the categories.
A bar chart is effective for comparing categorical data across different categories. It consists of rectangular bars, where the length of each bar represents the magnitude or frequency of a particular category. Each category is represented on the x-axis, and the height or length of the bars on the y-axis shows the comparison. In a grouped bar chart, multiple categories are grouped together, and each group is represented by a set of bars side by side. This type of chart is useful when you want to compare multiple categories within different groups simultaneously.
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A school bought 26 computers for a new computer lab. If each computer costs $740, how much did the school spend?
Answer:
= 19, 240 $
Step-by-step explanation:
cost of 1 computer = $ 740
cost of 26 computers = 26 × 740
= 19, 240 $
so the school spent 19, 240 $
A ski jump rises 3ft over a run of 7ft what is the length of the surface of the jump?
Answer:
7.6158 feet
Step-by-step explanation:
The rise and run form the shorter sides of a right triangle with the hypotenuse as the surface (see figure)
Hypotenuse (surface length) is given by the Pythagorean formula
\(c = \sqrt{a^2 + b^2}\) where c is the hypotenuse and a, b the shorter sides
Here
\(\sf c = \sqrt{7^2 + 3^2} = \sqrt{49 + 9} = \sqrt{58} = 7.6158\;feet\)
Read the numbers and decide what the next number should be. 1 1.25 7 7.50 2 2.25 8
calculate the length of the curve c, defined by r(t) = 〈2 cos(t),2 sin(t)〉 with domain of −π/2 ≤t ≤π/2.
To calculate the length of the curve defined by r(t) = 〈2 cos(t), 2 sin(t)〉 with the domain -π/2 ≤ t ≤ π/2, we need to find the arc length using the following formula:
Arc length = ∫(from a to b) ||r'(t)|| dt
First, let's find the derivative r'(t) of the given vector function r(t):
r(t) = 〈2 cos(t), 2 sin(t)〉
r'(t) = 〈-2 sin(t), 2 cos(t)〉
Next, find the magnitude ||r'(t)|| of the derivative vector:
||r'(t)|| = √((-2 sin(t))^2 + (2 cos(t))^2)
||r'(t)|| = √(4 sin^2(t) + 4 cos^2(t))
Factor out 4:
||r'(t)|| = √(4(sin^2(t) + cos^2(t)))
Since sin^2(t) + cos^2(t) = 1:
||r'(t)|| = √(4) = 2
Now, we can find the arc length by integrating ||r'(t)|| over the given domain:
Arc length = ∫(from -π/2 to π/2) 2 dt
To integrate, simply multiply the constant by the difference in t:
Arc length = 2(π/2 - (-π/2)) = 2(π) = 2π
So, the length of the curve is 2π.
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IN ONE REGION 40% OF ALL RESIDENTIAL TELEPHONE NUMBERS ARE UNLISTED. IF 5 RESIDENTIAL HOUSING UNITS ARE RANDOMLY SELECTED FIND THE PROBABILITY THAT ALL OF THEM HAVE UNLISTED NUMBERS
Given:
Percentage of numbers unlisted = 40% = 0.40
Sample size, n = 5
Let's find the probability that all 5 of the selected houses have unlisted numbers.
To find the probability, we have:
p(numbers unlisted) = 0.40
Hence, we have:
q = 1 - p = 1 - 0.40 = 0.60
For the probability, apply the binomial probability:
0 .
\(P(x=5)=(^5C_5)(0.40)^5(0.60)^{5-5}\)Solving further:
\(\begin{gathered} P(x=5)=(\frac{5!}{5!(5-5)!})(0.01024)(0.60)^0 \\ \\ P(x=5)=(\frac{5!}{5!(0)!})(0.01024)(1) \\ \\ p(x=5)=1*0.01024*1 \\ \\ p(x=5)=0.01024 \end{gathered}\)Therefore, the probability that all 5 numbers have unlisted numbers is 0.01024
• ANSWER:
0.01024
We want to build 10 letter "words" using only the first n=11 letters of the alphabet. For example, if n=5 we can use the first 5 letters, {a,b,c,d,e} (Recall, words are just strings of letters, not necessarily actual English words.) a. How many of these words are there total? b. How many of these words contain no repeated letters? c. How many of these words start with the sub-word "ade"? d. How many of these words either start with "ade" or end with "be" or both? e. How many of the words containing no repeats also do not contain the sub-word "bed"?
In order to determine the total number of 10-letter words, the number of words with no repeated letters
a. Total number of 10-letter words using the first 11 letters of the alphabet: 11^10
b. Number of 10-letter words with no repeated letters using the first 11 letters of the alphabet: 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 = 11!
c. Number of 10-letter words starting with "ade" using the first 11 letters of the alphabet: 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 = 1
d. Number of 10-letter words either starting with "ade" or ending with "be" or both using the first 11 letters of the alphabet: (Number of words starting with "ade") + (Number of words ending with "be") - (Number of words starting with "ade" and ending with "be")
e. Number of 10-letter words with no repeated letters and not containing the sub-word "bed" using the first 11 letters of the alphabet: (Number of words with no repeated letters) - (Number of words containing "bed").
a. To calculate the total number of 10-letter words using the first 11 letters of the alphabet, we have 11 choices for each position, giving us 11^10 possibilities.
b. To determine the number of 10-letter words with no repeated letters, we start with 11 choices for the first letter, then 10 choices for the second letter (as we can't repeat the first letter), 9 choices for the third letter, and so on, down to 2 choices for the tenth letter. This can be represented as 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2, which is equal to 11!.
c. Since we want the words to start with "ade," there is only one choice for each of the three positions: "ade." Therefore, there is only one 10-letter word starting with "ade."
d. To calculate the number of words that either start with "ade" or end with "be" or both, we need to add the number of words starting with "ade" to the number of words ending with "be" and then subtract the overlap, which is the number of words starting with "ade" and ending with "be."
e. To find the number of 10-letter words with no repeated letters and not containing the sub-word "bed," we can subtract the number of words containing "bed" from the total number of words with no repeated letters (from part b).
We have determined the total number of 10-letter words, the number of words with no repeated letters, the number of words starting with "ade," and provided a general approach for calculating the number of words that satisfy certain conditions.
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There are four candidates for homecoming queen and three for king. How many different king-queen combinatons are there
There will be 12 combination of different king-queen.
When grouping objects or figuring out how many subgroups can be created from a given collection of objects, combinations are employed. We also employ permutations to calculate the number of possible combinations of unrelated things.
To determine the number of different king-queen combinations, we need to multiply the number of candidates for king by the number of candidates for queen. In this case, there are four candidates for homecoming queen and three candidates for king.
There are 4 candidates for queen and 3 candidates for king, so:
4 x 3 = 12
Therefore, the total number of different king-queen combinations is 4 multiplied by 3, which equals 12. So, there are 12 different king-queen combinations.
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Is the number 102
a prime number?
No
Yes
Answer:
No, its divisible by 2
Step-by-step explanation:
Kevin needs to buy shrubs for his yard. He can buy 6 shrubs for $72.00 at a nursery and 7 shrubs for $77.00 at a garden store.
Answer:
He would pay less at the garden store.
Step-by-step explanation:
We have to find the unit prices of both shrubs.
The unit price is the cost per unit, and to find the unit price, divide the price by the number of units.
72/6 = 12
77/7 = 11
He would pay less at the garden store because the unit price is lower than the nursery.
$14.40 for 4.5 pounds of beef
Answer:
One pound of beef is $3.2
Step-by-step explanation:
14.40 / 4.5
= 3.2
CHECK:
3.2 * 4.5
=14.40
Answer:
Step-by-step explanation:
The unit rate for this beef is:
$14.40
---------- = $3.20/lb
4.5 lb
A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = \(\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h\)
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = \(\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)\)
⇒ \(\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)\)
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = \(\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)\)
⇒ \(\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)\)
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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What’s the mean,median,mode, and range of 5,28,16,32,5,16,48,29,5,35
Answer:
Step-by-step explanation:
5, 5, 5, 16, 16, 28, 29, 32, 35, 48
Mode: 5, 16
Median: 44/2 = 22
range: 48 - 5 = 43
mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9
Every day The burger buns restaurant serves 1/5 of a bottle of cherry soda to the customers for how many days will 1 4/5 bottles of soda last? Please say the answer correctly and explain the equation well
Write an equation in standard form of the line that passes through the given point and the given slope. (-9, -4); m = -1/3
First, we must determine b using slope-intercept form*, the given point, and the given slope.
\(-4 = -\frac{1}{3}(-9) + b\\\\-4 = -3 + b\\\\-1 = b\)
Second, we need to set up the equation of the line in slope-intercept form.
\(y = -\frac{1}{3}x - 1\)
Third, we convert the above equation to STANDARD FORM**.
\(y = -\frac{1}{3}x - 1\\\\\frac{1}{3}x + y = -1\)
We now have our equation: \(\frac{1}{3}x - y = -1\)
*Slope-intercept form: y = mx + b
**Standard form: ax + by = c
If p and q are all positive integers and the maximum integer not greater than
31p/8q is 5, find the
minimum value of p +q .
Answer:
71Step-by-step explanation:
As per question we have:
p > 0, q > 031p/8q ≤ 5 ⇒ 31p ≤ 40qSince 31 and 40 have no common factors, the minimum values of p and q are 40 and 31 respectively.
So the minimum value of p + q is:
40 + 31 = 71Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.
A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.
What is a circle?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 centre.
The arc length of radius 6 inches is equal to,
Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches
The area of the circular paper = πr² = π×6×6 = 113.097²
The area of the square with a side of 6 inches = 36 in²
Therefore, the area of the circular paper is more than the area of the square.
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