Find the probability

For the heights, areas and perimeters of the shapes:

5. The trapezoid can be divided into a rectangle and a right triangle. Let the height of the trapezoid be h.

The area of the trapezoid is A = (1/2)(13.9 + 9.3)h = 11.6h.

We are given that A = 120.8cm², so solve for h:

11.6h = 120.8

h = 10.4 cm

Therefore, the height of the trapezoid is 10.4 cm.

6. Let s be the side length of the equilateral triangle. Then, we have:

s + s + s = 45

3s = 45

s = 15

The perimeter of the equilateral triangle is 45 inches.

The area of an equilateral triangle can be found using the formula:

Area = (√(3)/4)s²

Plugging in s = 15:

Area = (√(3)/4)(15²) = 97.31 in²

Therefore, the area of the equilateral triangle is 97.31 square inches.

7. Let a be the side length of the inscribed square and let A be the area of the inscribed square. Let b be the side length of the circumscribed square.

The area of the outer square is 169in², so b² = 169. Therefore, b = 13.

The diagonal of the inscribed square is equal to the diameter of the circle, which is equal to the side length of the outer square. Therefore, a×√(2) = 13.

Solving for a:

a = 13/√(2) = 9.19

The area of the inscribed square is A = a² = (13/√(2))² = 84.5 in².

The ratio of the area of the inscribed square to the area of the circumscribed square is:

A/(b²) = 84.5/169 = 0.5

Therefore, the area of the inscribed square is half the area of the circumscribed square.

8. Let d₁ and d₂ be the diagonals of the rhombus. Let s be the side length of the rhombus.

We know that d₁ = 6 inches and d₂ = 8 inches. We also know that the diagonals of a rhombus intersect at a right angle and bisect each other. Therefore, we can form a right triangle with legs of length s/2 and s/2 and hypotenuse of length d₁/2.

Using the Pythagorean theorem:

(s/2)² + (s/2)² = (d1/2)²

s²/4 = 9

s = 6

Therefore, the side length of the rhombus is 6 inches.

The perimeter of the rhombus is 4s = 24 inches.

The area of the rhombus can be found using the formula:

Area = (1/2)d₁d₂

Plugging in d₁ = 6 and d₂ = 8:

Area = (1/2)(6)(8) = 24 square inches

Therefore, the perimeter of the rhombus is 24 inches and the area of the rhombus is 24 square inches.

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The amount of interest that is earned on Sandra's card after 1 year if Sandra makes no payment is: $538.48.

We can obtain the right answer by using using the formula for compound interest as follows: A = P(1 + r/n)^(nt)

where:

P = $2,500

r = 0.1999 (since the APR is 19.99%)

n = 4 (since the interest compounds quarterly)

t = 1 (since we're looking at the interest earned after 1 year)

Substituting these values into the formula, we get:

A = $2,500(1 + 0.1999/4)^(4*1)

A = $2,500(1.049975)^4

A = $2,500(1.207789)

A = $3,019.47

So after 1 year, Sandra will owe $3,019.47 on her credit card. The interest earned is the difference between this amount and the initial amount charged, which is:

Interest = $3,019.47 - $2,500

Interest = $519.47

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If Lucy made "tables-of-values" to approximate the solution to "system-of-equations", then the "ordered-pair" which is the best approximation of  exact solution is (b) (1.6 , 1.3).

An "Ordered-Pair" is defined as a pair of values which are arranged in a specific order, generally denoted as (x, y), where x represents the first value and y represents the second value.

We are finding an ordered pair that satisfies the following conditions:

(i) The x-value falls within the given range of x-values between 1 and 2.

(ii) The y-value for the equation y = -3x + 6 is closest to the given y-value for the equation y = 4x - 5.

In Option (a) : (1.7, 0.9);

The "x-value" of 1.7 falls within the given range of x-values between 1 and 2.

For the equation "y = -3x + 6", the corresponding "y-value" at x = 1.7 is 0.9, which is not as close to the given y-value for the equation y = 4x - 5, which is 1.4.

So, (1.7, 0.9) is not the best approximation.

In Option (b) : (1.6, 1.3);

The "x-value" of 1.6 falls within the given range of x-values between 1 and 2.

For the equation "y = -3x + 6", the corresponding y-value at "x = 1.6" is 1.2, which is closest to the given y-value for the equation y = 4x - 5, which is 1.4.

So, the ordered pair (1.6, 1.3) is best-approximation.

In Option(c) : (1.5, 1.8);

The "x-value" of 1.5 falls within the given range of x-values between 1 and 2.

For the equation "y = -3x + 6", the corresponding "y-value" at x = 1.5 is 1.5, which is away from the y-value for equation "y = 4x - 5", which is 1.4.

So, (1.5, 1.8) is not the best approximation.

In Option (d) : (1.9, 1.5);

The "x-value" of 1.9 falls within the given range of x-values between 1 and 2.

For the equation "y = -3x + 6", the corresponding y-value at x = 1.9 is "0.3", which is not as close to the given y-value for the equation "y = 4x - 5", which is 1.4.

So, (1.9, 1.5) is not the best approximation.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Lucy made tables of values to approximate the solution to a system of equations. First she found that the x-value of the solution was between 1 and 2. And then she found that it was between 1. 5 and 2. Next, she made this table,

 x           y = -3x + 6          y = 4x - 5

1.5               1.5                         1

1.6               1.2                        1.4

1.7               0.9                       1.8

1.8               0.6                       2.2

1.9               0.3                       2.6

2.0                0                          3

Which ordered pair is the best approximation of the exact solution?

(a) (1.7 , 0.9)

(b) (1.6 , 1.3)

(c) (1.5 , 1.8)

(d) (1.9 , 1.5)

The true statement regarding the hypothesis will be:

The correct option is D II and III only.

A two-sample t-test of the hypotheses Hoμ1-2 = 0 versus H 41-μ2> 0 produces a p-value of 0.03.

In this case, a 95 percent confidence interval for the difference in means will contain the value 0.

Also, a 99 percent confidence interval for the difference in means will contain the value 0.

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Answer:

Step-by-step explanation:

-109f

The amount of fabric that should be used to build a kite with the above given dimensions would be = 2,285.125cm²

To calculate the area of a kite the formula that should be used would be = 1/2 d1d2

where d1 = 50½cm

d2 = 90½cm

The area of the kite;

= 1/2 × 50.5×90.5b

= 4570.25/2

= 2,285.125cm²

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Answer:

840 feet

Step-by-step explanation:

1 yard = 3 feet

280 yards = x

x = 280 × 3

x = 840 feet

Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975% in the compound interest.

When interest is earned on a loan or investment, it is earned on both the principal and any accumulated interest, which is known as compound interest. In other words, interest is added to the principal, and the resulting sum is then used to determine future interest. Compounding causes an investment or loan to increase more quickly than it would with simple interest, where just the principal is charged interest. Compounding may occur daily, monthly, quarterly, annually, or at any other interval.

To compare the plans of the two accounts we have:

Rate = ( 1 + rate / n)ⁿ - 1

where, n is the compounded period.

For plan A:

Effective annual interest rate = (1 + (0.5%/4))⁴ - 1 ≈ 0.5025%

For Plan B, we have:

Effective annual interest rate = (1 + 3.5%)¹- 1 = 3.5%

Comparing the two we see that Plan B offers higher rates by:

3.5% - 0.5025% ≈ 2.9975%.

Hence, Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975%.

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Using mathematical operations of division and multiplication, the total weight of the order in pounds is 3 pounds.

The total weight is firstly computed in ounces before being converted into pounds.

The computation follows the mathematical operations of multiplication and division, respectively.

The number of Orange You Fresh soap bars ordered by a customer = 12

The weight of each bar of soap = 4 ounces

The total weight of 12 bars in ounces = 48 ounces (4 x 12)

1 pound = 16 ounces

3 pounds = 48 ounces (48 ÷ 16)

Thus, based on mathematical operations, the number of pounds this order will weigh is 3 pounds.

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A) The coefficient of determination can be computed using the SSE and SST values in regression and correlation analysis.

SSE (Sum of Squared Errors) is the sum of the squared differences between the actual and predicted values of the dependent variable. SST (Total Sum of Squares) is the sum of the squared differences between the actual values of the dependent variable and their mean.
The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model.

It is calculated as follows:
R² = 1 - (SSE/SST)
Since both SSE and SST are given, you can compute the coefficient of determination.

However, the information provided is not sufficient to calculate the slope, Y-intercept, or X-intercept of the regression line.

Based on the given information, the correct answer is:
A) Coefficient of determination can be computed.

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This coefficient of determination (R²) gives you a measure of how well the regression line fits the data in your correlation analysis.

A) The coefficient of determination can be computed with the known values of SSE (sum of squared errors) and SST (total sum of squares) in regression and correlation analysis. The coefficient of determination is a measure of how well the regression line fits the data and is expressed as a percentage. It represents the proportion of variability in the dependent variable (Y) that can be explained by the independent variable (X).

Based on the information provided, with the known SSE (Sum of Squares Error) and SST (Sum of Squares Total), you can compute the coefficient of determination. So, the correct answer is:

A) Coefficient of determination can be computed

To calculate the coefficient of determination (R²), follow these steps:

1. Calculate the Sum of Squares Regression (SSR) by subtracting SSE from SST:
  SSR = SST - SSE

2. Compute the coefficient of determination (R²) by dividing SSR by SST:
  R² = SSR / SST

This coefficient of determination (R²) gives you a measure of how well the regression line fits the data in your correlation analysis.

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The probability of exactly 17 successes in a binomial distribution with p=0.20 and n=60, using normal approximation to the binomial, is approximately 0.0129.

To use the normal approximation to the binomial, we need to check if the conditions for the approximation are met

np = 60 x 0.20 = 12 ≥ 10

n(1-p) = 60 x 0.80 = 48 ≥ 10

Both conditions are met, so we can use the normal approximation to the binomial.

The mean of the binomial distribution is μ = np = 12, and the standard deviation is σ = √(np(1-p)) = √(60 x 0.20 x 0.80) ≈ 2.19.

To find the probability of exactly 17 successes, we can use the normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19, and approximate the discrete binomial distribution with a continuous normal distribution

P(X = 17) ≈ P(16.5 < X < 17.5)

where X is a continuous random variable that follows a normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19.

Using the standard normal distribution, we can calculate the z-scores for 16.5 and 17.5

z1 = (16.5 - 12) / 2.19 ≈ 1.83

z2 = (17.5 - 12) / 2.19 ≈ 2.28

Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores

P(1.83 < Z < 2.28) ≈ P(Z < 2.28) - P(Z < 1.83) ≈ 0.0129

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Answer:

y = (-5/9)x + 30/9

Step-by-step explanation:

To rewrite the equation 5x + 9y = 30 in slope-intercept form, we need to isolate y on one side of the equation.

5x + 9y = 30

Subtract 5x from both sides of the equation to isolate 9y:

5x - 5x + 9y = -5x + 30

9y = -5x + 30

Divide both sides of the equation by 9 to solve for y:

9y/9 = (-5x + 30)/9

y = (-5/9)x + 30/9

The probability of selecting a J or an A on the second draw, given that an E was selected on the first draw is 0.101.

The number of tiles which have an E on them are shown to be 12 which means that if an E was selected on the first draw, there are now 99 tiles left.

The probability that an A or J will be selected in this second draw would be :

= ( Number of A tiles and J tiles ) / 99

Number of A tiles = 9

Number of J tiles = 1

The probability is then :

= ( 9 + 1 ) / 99

= 10 / 99

= 10.1%

= 0.101

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The area of the composite figure is 343.62 square inches.

What is a 3D composite shape's area?

Composite things that are three dimensional (3D) are created by joining two or more objects. Finding each object's outside surface area and adding the surface areas together will yield the surface area of a 3D composite object.

Area of rectangle = length x width = 12 x 18 = 216 sq in

As a result, the radius is equal to 9 inches, or half the diameter.

[tex]Area \ of\ semicircle = (1/2) * \pi * r^{2} \\\\Area \ of \ semicircle = (1/2) * 3.14 * 9^{2} \\\\Area \ of \ semicircle = 127.62\ sq\ in[/tex]

The combined area of the rectangle and the semicircle is therefore equal to the area of the composite figure as a whole:

Total area = 216 sq in + 127.62 sq in = 343.62 sq in

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The volume of the ball is 904.78 cubic cm

We know that the formula for the volume of sphere is:

V = (4/3) × π × r³

where r is the radius of the sphere

Here, Michael fills a plastic ball with air until it is a sphere with a radius of 6 cm.

So, the radius of spherical ball r = 6 cm

Using above formula of volume of sphere, the volume of the ball would be,

V = (4/3) × π × r³

V = (4/3) × π × (6)³

V = (4/3) × π × 216

V = 904.78 cubic cm

Therefore, the required volume = 904.78 cubic cm

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Step-by-step explanation:

Tan 20 = 50 / d

d =  50 / tan 20   = 137 m

As per the fraction, the lowest score in the examination is 44.

Let's consider the given information. We are told that the highest score and the lowest score in an examination differ by 55 marks. We can represent the highest score as x and the lowest score as y. Therefore, we have:

x - y = 55 ----- equation 1

We are also given that the higher score, which is x, is 9/4 times the lower score, which is y. This can be represented as:

x = (9/4)y

We can use this equation to substitute x in equation 1 and solve for y.

Substituting x in equation 1, we get:

(9/4)y - y = 55

Simplifying the above equation, we get:

(5/4)y = 55

Multiplying both sides by 4/5, we get:

y = 44

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Complete Question:

In an examination, the highest score and the lowest score are different by 55 and the higher one was 9/4 times the lower one. Find the lowest score.

Answer:

c and a

Step-by-step explanation:

1. AABBCCDD: The probability of this happening is [tex]1/16[/tex], since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is [tex](1/2)^4 = 1/16[/tex] , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128[/tex]

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is[tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32[/tex]

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is [tex](1/2)^8 = 1/256.[/tex]

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128.[/tex]

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is [tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.[/tex]

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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In the given equation which is 3 + 2n = 7, the value of n = 2.

For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.

Given equation = 2n + 3 =7

In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:

2n + 3 = 7

2n = 7 - 3

2n = 4

n = [tex]\frac{4}{2}[/tex]

n = 2.

So, from the above solution the value of 'n' is 2.

Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"

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Answer: D

Step-by-step explanation:

The amount of gasoline used in the lawn mowers is 2/5 of the total amount of gasoline used. Therefore:

Gasoline used in lawn mowers = (2/5) x 81.5 gallons

Gasoline used in lawn mowers = 32.6 gallons

Therefore, the answer is D. 32.6 gal.

Each person will get 17 pencils.

Division is the opposite of multiplication. For example, If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.

The main goal of dividing is to see how many equal groups are formed or how many are in each group when sharing fairly.

In the problem given above, to divide 68 colored pencils to 4 students each, you will have to put 68 colored pencils for each student. So, 68 divided by 4 will give the result 17.

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The equation of the circle with center (3, -4) and a radius of 6 units is (x - 3)^2 + (y + 4)^2 = 36.

The equation of a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values given, we get:

(x - 3)^2 + (y + 4)^2 = 6^2

Expanding and simplifying, we get the final equation of the circle:

(x - 3)^2 + (y + 4)^2 = 36

Therefore, the equation of the circle with center (3, -4) and a radius of 6 units is (x - 3)^2 + (y + 4)^2 = 36.

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The quadratic formula x = (-b ± √ ( [tex]b^2[/tex] - 4ac)  / (2a) is used to find the solutions (or roots) of a quadratic equation of the form [tex]ax^2[/tex] + bx + c = 0.

In this formula, "a", "b", and "c" are coefficients of the quadratic equation, and the ± symbol indicates that there are two possible solutions, one with a positive square root and one with a negative square root. By plugging in the values of "a", "b", and "c" from the given quadratic equation, one can use the quadratic formula to calculate the solutions for x that satisfy the equation.

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x = (-b ± √(b² - 4ac)) / (2a) is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.

The formula x = (-b ± √(b² - 4ac)) / (2a) is known as the Quadratic Formula, used to find the solutions to a quadratic equation of the form ax² + bx + c = 0.

The formula x=-b± b2 -4ac2a, is called the quadratic formula, which is used to find the solutions (or roots) to a quadratic equation of the form ax2+bx+c=0,

where a, b, and c are coefficients of the equation.

The term under the square root sign (b2-4ac) is called the discriminant and can tell you whether the quadratic equation has two real solutions (if the discriminant is positive), one real solution (if the discriminant is zero), or two complex conjugate solutions (if the discriminant is negative).

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If we rewrite 4.86 x 104 in decimal notation, we will have 48,600. The Option A.

In decimal notation, 4.86 x 104 is equivalent to 48600. To convert scientific notation to decimal notation, you simply move the decimal point to the right by the number of places indicated by the exponent.

In this case, since the exponent is 4, you move the decimal point four places to the right of the digit 4, resulting in 48600. Therefore, 4.86 x 104 in decimal notation is 48600.

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Answer:

The mathematical property demonstrated by the statement 3 + (-6) = -6 + 3 is the commutative property of addition.

This states that: A + B = B + A

The commutative property of addition is the property that is demonstrated by the formula "3 + (-6) = -6 + 3".

This characteristic states that the sum is unaffected by the sequence in which two numbers are added. In other words, a + b = b + a for any two numbers a and b.

In this instance, the left side has 3 + (-6) which equals -3. We have -6 + 3 on the right side, which also equals -3. This indicates that the result is unaffected by the sequence in which the numbers are added.

We can thus write:

3 + (-6) = -6 + 3

-3 = -3

This demonstrates the truth of the assertion and serves as an illustration of the commutative property of addition.

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You can take a look at this, the image that I attached might help.

For example, the first one shifts left because the h value is positive 3. -(3) = -3.

The prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.

A three-dimensional object's surface area is the sum of all its faces.

The formula for the surface area of a right rectangular prism is:

surface area = 2lw + 2lh + 2wh

where l, w, and h are the prism's length, breadth, and height, respectively.

When we substitute the provided values, we get:

Surface Area = 2(4.5)(6) + 2(4.5)(4) + 2(6)(4)

Surface Area = 54 + 36 + 48

surface area = 138 [tex]cm^{2}[/tex]

As a result, the prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.

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