Lap Pool A has lanes for 3 swimmers and Lap Pool B has lanes for 10 swimmers. The lap pools have the same uniform depth. Lap Pool B contains approximately 6. 6 x 10 to the fifth power gallons of water

(a) To find the mean squared error (MSE) of X bar, we need to first find its expected value and variance.

The expected value of X bar is:

E(X bar) = E((X1 + X2 + ... + Xn) / n) = (n * E(X)) / n = E(X) = θ

The variance of X bar is:

Var(X bar) = Var((X1 + X2 + ... + Xn) / n) = (1/n^2) * Var(X1 + X2 + ... + Xn) = (1/n^2) * n * Var(X) = θ/n

Therefore, the MSE of X bar is:

MSE(X bar) = Var(X bar) + [E(X bar) - θ]²= θ/n + [θ - θ]² = θ/n

(b) To find the limit of MSE when n tends to infinity, we can take the limit of the MSE formula as n approaches infinity:

lim(n → ∞) MSE(X bar) = lim(n → ∞) θ/n = 0

Therefore, as the sample size becomes larger, the MSE of X bar approaches zero. This means that X bar becomes a better and better estimator of the true parameter θ as the sample size increases.

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2x²-9x-5

2x²-x-10x-5

(x-5)(2x+1)

Answer:

arc DB = 45°

Step-by-step explanation:

the measure of an arc is the same as the central angle that intercepts it.

∠ DCB = 180° - 135° = 45°

∠ DCB is the central angle intercepted by arc DB , then

arc DB = 45°

Answer:

D. x^2-x-9-12/x-2

Step-by-step explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

    2 |   1   -3   -7    6

       |______2___-2__-18

       | 1   -1   -9  -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).

Answer:

1/3

Step-by-step explanation:

There are only two ways to roll a die and get a number bigger than 2 (not1 or not 2) and smaller than 5 (not 5 and not 6) You can roll a 3 (bigger than 2, smaller than 5) OR you can roll a 4 (also bigger than 2 a, smaller than 5)

There are only 6 different results when you roll a die (1-6).

To write a probability you put the total number of ways on the bottom. Put 2 on top because there's two ways to roll the desired result.

P = 2/6 and simplify

P = 1/3

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.

To find the circumference of the circle, we need to know the radius. If we are not given the radius directly, we may be given another measurement that we can use to calculate it. For example, we may be given the diameter, which is the distance across the circle passing through its center. The radius is half the diameter.

Assuming we have been given the diameter of the circle, we can calculate the circumference as follows:

Write down the formula for the circumference of a circle: C = 2πr

Identify the diameter of the circle. Let's say it is 10 cm.

Calculate the radius by dividing the diameter by 2: r = 10/2 = 5 cm.

Plug in the value of the radius into the formula: C = 2π(5) = 10π.

Use the approximation of π as 3.14: C = 10(3.14) = 31.4 cm.

Therefore, the circumference of the circle is approximately 31.4 cm, to the nearest tenth of a centimeter.

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Complete question:

A circle of radius 3 cm is drawn .Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)

A) 9.4 cm

B) 18.8 cm

C) 37.7 cm

D) 56.6 cm

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Force on the object is 7.04 pounds in the x-direction

Force on the object is -2.52 pounds in the y-direction

The total force on an object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction can be found by resolving each force into its x- and y-components, and then adding them to obtain the net force acting on the object.An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction is shown below:An object being pushed with 5 pounds of force in the θ=45˚ direction and also with 7 pounds of force in the θ=-60˚ direction.To resolve the forces, we use the following identities:Fx = Fcosθ, andFy = Fsinθ.The x- and y-components of the 5-pound force in the θ=45˚ direction are:Fx = Fcosθ = 5 cos 45˚ = 3.54 pounds,andFy = Fsinθ = 5 sin 45˚ = 3.54 pounds.The x- and y-components of the 7-pound force in the θ=-60˚ direction are:Fx = Fcosθ = 7 cos (-60˚) = 3.5 pounds,andFy = Fsinθ = 7 sin (-60˚) = -6.06 pounds.The total force acting on the object is the sum of the x- and y-components of the forces acting on it, or:Fx = 3.54 pounds + 3.5 pounds = 7.04 pounds,Fy = 3.54 pounds - 6.06 pounds = -2.52 pounds.Therefore, the total force on the object is 7.04 pounds in the x-direction and -2.52 pounds in the y-direction.

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(a) The covariance for X and Y Cov(X, Y) = -1.05

(b) The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).

The expected values of X and Y must first be determined in order to find the covariance and correlation coefficient for X and Y.

The amount of X is anticipated to be:

(a) E(X) = xP(X=x) = (0.03) + (5) (0.04 + 0.15 + 0.01) + (10) (0.06 + 0.20 + 0.15 + 0.13) + (15) (0.02 + 0.10 + 0.01) = 8.4

E(Y) = yP(Y=y) = (0.05) + (5) (0.04 + 0.01) + (10) (0.06 + 0.15 + 0.15) + (15) (0.02 + 0.20 + 0.13 + 0.01) = 10.5

X and Y's correlation is:

Cov(X, Y) = XY - XE (Y)

Each number of X and Y must be multiplied by their combined probability before the products are added to determine E(XY):

(0)(0)(0.05) + (0)(5)(0.03) + (0)(10)(0.06 + 0.01) + (0)(15)(0.02) + (5)(0)(0.04) + (5)(5)(0.15) + (5)(10)(0.20) + (5)(15)(0.10) + (10)(0)(0.01) + (10)(5)(0.15) + (10)(10)(0.13) + (10)(15)(0.01) + (15)(0)(0.02) + (15)(5)(0.10)

Therefore: Cov(X, Y)=E(XY)-E(X)E(Y) =119.25-(8.4)(10.5) = -1.05

As a result, X and Y have a correlation of -1.05.

(b) The standard errors of X and Y must also be computed in order to determine the correlation coefficient:

sqrt(Var(X)) = sqrt(E(X) - [E(X)]) = sqrt((0^2)(0.03) + (5^2)(0.04 + 0.15 + 0.01) + (10^2)(0.06 + 0.20 + 0.15 + 0.13) + (15^2)(0.02 + 0.10 + 0.01) - (8.4)^2) ≈ 5.23

The expression "_Y = sqrt(Var(Y)) = sqrt(E(Y)2 - [E(Y)]2)" = sqrt((0^2)(0.05) + (5^2)(0.04 + 0.01) + (10^2)(0.06 + 0.15 + 0.15) + (15^2)(0.02 + 0.20 + 0.13 + 0.01) - (10.5)^2) ≈ 5.07

The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).

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Answer:

We can use the formula for the length of an arc of a circle, which is:

length of arc = (angle/360) × 2πr

where angle is the angle subtended by the arc at the center of the circle, r is the radius of the circle, and π is approximately 3.14.

In this problem, the angle subtended by the arc at the circumference of the circle is 86 degrees. Since the radius of the circle is 8 cm, the diameter is 2 × 8 = 16 cm, and the circumference is 2πr = 2π(8) = 16π cm.

Using the hint given in the problem, we can find the angle subtended by the arc at the center of the circle:

angle at center = 2 × angle at circumference

= 2 × 86

= 172 degrees

Substituting into the formula, we have:

length of arc = (172/360) × 2π(8)

≈ 7.5 cm

Rounding to the nearest whole number, the length of the arc is 8 cm.

Answer:25 sticks

Step-by-step explanation:

each time you will add 4 sticks

Answer: 37

Step-by-step explanation:

Add 4

Answer:

y = 1/3x - 2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know

m = 1/3

Y-intercept is located at (0, -2)

So, the equation is y = 1/3x - 2

Answer:

A likelihood of 1 is also known as the Discrete probability distribution

This is an Angles and Coordinate Systems problem.
6)  

7)

8)

Positive angle measure is measured counterclockwise and negative angle measure is measured clockwise. These concepts are used in navigation, engineering, and physics.

6)

An angle of 40 degrees measured out in the upper left quadrant will have its initial side along the positive x-axis and its terminal side in the upper left quadrant, making it a counter-clockwise angle.

-(360° - 40°) = -320°

So the angle of 40 degrees is equivalent to a negative angle measure of -320 degrees.

320° + 360° = 680°

So the angle of 40 degrees is equivalent to an angle measure of 680 degrees.


7)

To convert the angle measure of 50 degrees in the lower right quadrant to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.

To convert the angle measure to a negative angle measure, we subtract it from 360 degrees, since a negative angle is measured in the clockwise direction.

To find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.

8)

The angle 60 degrees measured in the lower right quadrant in a counter-clockwise direction is equivalent to the angle 360 degrees - 60 degrees = 300 degrees measured in the upper right quadrant in a counter-clockwise direction.

To convert the angle measure of 300 degrees to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.

To convert the angle measure to a negative angle measure, we simply add a negative sign to the positive angle measure.

To find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.

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There are 288 Aleppo pines are planted in each ratio.

First, let's determine the total number of pine trees in each row. Since the ratio is 10 : 9, that means that for every 10 bristlecone pine trees planted, 9 Aleppo pine trees were planted. Therefore,

10 bristlecone pine trees + 9 Aleppo pine trees = 19 pine trees in each row.
Next, we need to determine how many rows of pine trees were planted. Since 600 bristlecone pine trees were planted, we can divide 600 by 19 to determine the number of rows.
600 ÷ 19 = 31.578947368421
Therefore, there were 32 rows of pine trees planted.
Now, we need to calculate how many Aleppo pine trees were planted. Since we know that for every 10 bristlecone pine trees planted, 9 Aleppo pine trees were planted,

So, the number of Aleppo pine trees planted.
32 x 9 = 288

Therefore, 288 Aleppo pine trees were planted.

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In this equation, the ordered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).

A mathematical equation is a statement that two amounts and values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account simultaneously in order to comprehend or describe the overall situation, this is known as an equation.

We may select several values of x and enter them into the equation to get the associated values of y to create a table of tuple for the solution y = (-1/3)x + 1:

x      y = (-1/3)x + 1

0       1

3       0

6      -1

9      -2

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In this equatiοn, the οrdered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).

A mathematical equatiοn, like 6 + 4 = 12, states that twο amοunts and values are equal. An equatiοn is when twο οr mοre cοmpοnents must be cοnsidered simultaneοusly in οrder tο cοmprehend οr describe the οverall situatiοn.

We may select several values οf x and enter them intο the equatiοn tο get the assοciated values οf y tο create a table οf tuple fοr the sοlutiοn y = (-1/3)x + 1:

x      y = (-1/3)x + 1

0       1

3       0

6      -1

9      -2

Therefοre, In this equatiοn, the οrdered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).

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Answer:

325 miles

Step-by-step explanation:

speed = distance/time

=> distance = speed x time = 65 x 5 = 325 miles

Step-by-step explanation:

If you drive at a constant speed of 65 miles per hour for 5 hours, you would cover a distance of:

Distance = Speed x Time

Distance = 65 mph x 5 hours

Distance = 325 miles

Therefore, your grandmother's house is 325 miles away from yours.

The expression for the probability of picking a purple marble and then a green marble without replacement is: P(P and G') = (p / (4 + p + r)) * (3 / (3 + r))

Let's denote the event of picking a purple marble by P and the event of picking a green marble after a purple marble has been picked by G'. Since we do not replace the marble after the first pick, the probability of picking a purple marble is the proportion of purple marbles in the bag. Let's assume that there are r red marbles, g green marbles (including the 4 already picked), and p purple marbles. Then the total number of marbles in the bag is r + g + p.

Since we know that there are 4 green marbles already in the bag, the total number of marbles in the bag is g + p + r = 4 + p + r. We can use this equation to eliminate g from the probability calculation.

The probability of picking a purple marble is:

P(P) = p / (4 + p + r)

After a purple marble is picked, the total number of marbles in the bag is 4 + r. The probability of picking a green marble from this reduced bag is:

P(G' | P) = (4 - 1) / (4 + r - 1) = 3 / (3 + r)

The probability of both events occurring is the product of their probabilities:

P(P and G') = P(P) * P(G' | P) = (p / (4 + p + r)) * (3 / (3 + r))

We don't have enough information to determine the values of p and r, so we cannot calculate the exact probability. However, we can give an expression for the probability in terms of p and r.

As a final step, we can check that our expression for the probability satisfies some common-sense constraints. The probability should be between 0 and 1, and it should increase as the number of purple marbles increases (since this makes it more likely to pick a purple marble) and decrease as the number of red marbles increases (since this makes it less likely to pick a green marble after a purple one has been picked).

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The probability that in a given week there will be at most 3 accidents is 0.85. These event would be mutually exclusive as they do not influence the other results, Therefore the correct answer is 0.850.

The probability that in a given week there will be at most 3 accidents can be found by adding the probabilities of having 0, 1, 2, or 3 accidents. This is because the events are mutually exclusive, meaning that they cannot occur at the same time.

[tex]P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
From the given probability distribution, we can find the probabilities of each of these events:
[tex]P(X = 0) = 0.20P(X = 1) = 0.30P(X = 2) = 0.20P(X = 3) = 0.15[/tex]

Plugging these values into the equation, we get:
[tex]P(X ≤ 3) = 0.20 + 0.30 + 0.20 + 0.15P(X ≤ 3) = 0.85[/tex]

Therefore, the probability that in a given week there will be at most 3 accidents is 0.85. The correct answer is 0.850.

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Answer:

10^0

Step-by-step explanation:

Anything that has a exponent of 0 will always equal 1 therefore if 10^-3/10^-3 it will equal 1 so they both are 1

Answer: A 10^0

10^-3  is 0.001.  0.001 divided into 0.001 is 1.

A- 10^0 is 1 so this correct.

B- 10^-6 is 1.0e-6, so this is incorrect.

C-10^1 is 10, so this is incorrect.

D.10^6 is 1000000, so this is incorrect.

After solving our equation 10^-3/ 10^-3, we have concluded that that answer is 1, meaning that answer choice A, 10^0 is our correct answer.

Notes- ^ means to the power of, which is an exponent.

I hope this helped & Good Luck <3!!!!

On solving the above question, As a result, the polynomials f(x) zeros are x = 9 and x = 44/5.

A polynomial is a mathematical statement composed of coefficients and variance that exclusively uses additions, subtractions, operations such as addition, and nonzero powers of variables. The form x2 4x + 7 indicates a single determinate x algebraic. A polynomial expression in mathematics is made up of determinants (also known as freshly made) and polynomials that may be multiplied, subtracted, repeated, and raised through negative integer ones of – anti. A polynomial is an algebraic statement that includes variables and coefficients. An expression can really only incorporate the operations addition, deletion, duplication, and non-negative integer factors. These expressions are referred to as polynomials.

If x - 9 is a factor of f(x), we get:

f(x) = (x - 9)g(x) (x)

g(x) denotes a polynomial.

When we plug this into the supplied f(x) equation, we get:

5x^3 - 44x^2 - 13x + 36 = (x - 9)g (x)

Using polynomial long division to expand the right side, we get:

x(g(x)) = 5x3 - 44x2 - 13x + 36 - 9g(x) (x)

When we multiply the coefficients of similar terms on both sides, we get:

5 = g(x) (x)

-44 = g'(x) (x)

-13 = g''(x) (x)

36 = -9g''(x) (x)

When we solve these equations, we get:

5 g'(x) = -44 g"(x) = -13/2 g"'(x) = -12

Hence, g(x) is a constant function, and g'(x) = -44 suggests that x = 44/5 is the sole real root of g(x).

As a result, the f(x) zeros are x = 9 and x = 44/5.

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The value of x for all the figures are given below respectively.

The branch of mathematics that studies the relationships between the sides and angles of triangles is known as Trigonometry.

1. In given figure base = 5 and hypotenuse = 10 .

to find x i.e height we will use trigonometry-

tan 60° = x/5

√3 = x/5

5√3=x

Therefore, the value of x is 5√3.

2. In given figure base = 1 and height = √3  and angle given is 60°.

to find x i.e hypotenuse we will use trigonometry-

sin 60° = √3/x

√3/2 = √3/x

x = √3×2/ √3

x = 2

Therefore ,value of x is 2.

3. In given figure base = 3 and hypotenuse = 6 .

to find x i.e height we will use trigonometry-

tan 60° = x/3

√3 = x/3

3√3 = x

Therefore,value of x is 3√3.

4. In given figure base = 1 and height = 1  and angle given is 45°.

to find x i.e hypotenuse we will use trigonometry-

sin 45° = 1/x

1/√2 = 1/x

x = √2

Therefore ,value of x is √2.

5.  In given figure height = 4√2  and angle given is 45°.

to find x i.e hypotenuse we will use trigonometry-

sin 45° = 4√2/x

1/√2 = 4√2/x

x = 4√2 × √2

x = 8

Therefore,value of x is 6.

6. In given figure hypotenuse = 10 and angle given is 45°.

to find x i.e base we will use trigonometry-

cos 45° = x/10

1/√2 = x/10

10/√2 = x

Therefore,value of x is 10/√2.

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Answer:

The coefficient is 3.

Answer:

3

Step-by-step explanation:

Here 2xy² + x³ – x⁵ + xy², there are two like terms

2xy² and xy², so the coefficient of xy² = 2 + 1

Coefficient of xy² in the given expression is 3.

The experiment that is most likely to produce a uniform discrete distribution is the number of patrons arriving every 3 minutes at a sandwich shop.

Test scores on a college entrance exam, such as the ACT or SAT, is an example of continuous distribution.

A uniform distribution is a kind of probability distribution in which all of the potential outcomes have an equal likelihood of occurring. A uniform distribution with a limited set of potential outcomes is referred to as a discrete uniform distribution. In a discrete uniform distribution, there is a finite number of potential outcomes that are all equally probable.

It is important to note that the sum of the probabilities of all possible outcomes in a uniform distribution is always equal to 1 since the outcomes are equally likely to happen. The following experiments are less likely to generate a uniform discrete distribution:

Test scores on a college entrance exam, such as the ACT or SAT: Because test scores are continuous data, a uniform distribution is unlikely to occur.

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The value οf a, b, and c are 3, 5, and 25 respectively.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.

The given equatiοn is

1/(x + 5) + 2/(x -5) = (ax + b)/ (x² - c)

Sοlve the left-hand side οf the equatiοn:

L.H.S = 1/(x + 5) + 2/(x -5)

= [x-5 + 2(x+5)]/(x + 5)(x -5)

= [x-5 + 2x+ 10]/(x + 5)(x -5)

Cοmbine like terms:

= [3x + 5]/(x + 5)(x -5)

Nοw apply fοrmula (a-b)(a+b) =a² - b²:

= [3x + 5]/(x² - 5²)

= [3x + 5]/(x² - 25)

Put 1/(x + 5) + 2/(x -5) =  [3x + 5]/(x² - 25) in the given equatiοn:

[3x + 5]/(x² - 25) = (ax + b)/ (x² - c)

Nοw cοmpare bοth sides:

a = 3

b = 5

c= 25

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To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.$2.50x ≤ $20

$2.50x ≤ $20

The given situation is that Becky wants to buy some fish for her aquarium and she has $20 to spend and the cost of the fish is $2.50 each. To determine how many fish, x, Becky can afford to buy, an inequality can be written. Since the cost of each fish is $2.50, the total cost for buying x number of fish is $2.50x. To find out how many fish Becky can afford to buy, the inequality $2.50x ≤ $20 can be written. To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.

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The solution of the absolute inequality is as follows:

x < 22 / 5 or x > 6 / 5

The absolute inequalities can be solved as follows:

An absolute value inequality is an inequality that has an absolute value sign with a variable inside, modulus of a complex number.

Therefore,

|14 - 5x| > 8

let's find x as follows:

|14 - 5x| > 8

14 - 5x > 8  or 14 - 5x < - 8

-5x > 8 - 14  or - 5x < - 8 - 14

-5x > -6  or - 5x < - 22

Therefore,

x > 6 / 5 or x < 22 / 5

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Answer:

159.64

Step-by-step explanation:

30.7% / 100 = 0.307 then you would do
0.307 x 520 = 159.64

a)Hence the side of the square = 15.5 m

b)Hence the length of the rectangle is 8m and the width is 5m.

c)Hence the rectangle is greater than the square.

a)

The length of each wire =26m

To bend it into a square it has to be bent into four parts = [tex]\frac{26}{4}[/tex] =  5.15m

Hence the side of the square = 15.5 m

b)

A rectangle whose width is 3 m shorter than its length,

let the length of the rectangle = l

And the width of the rectangle h= l-3,

now,

2(l+l-3)=26

4l-6=26

4l=32

l=8m

h=8-3=5

Hence the length of the rectangle is 8m and the width is 5m.

c)

The area of the square=  5.15²=26.52 sq cm

The area of the rectangle = 8*5=40 sq cm

Hence the rectangle is greater than the square.

The complete question is-

A workman has two pieces of wire, each of

length 26 m. One piece is to be bent into a

square. The other piece is to be bent into a

rectangle whose width is 3 m shorter than its

length.

(a) What is the length of a side of the square?

(b) What are the dimensions of the rectangle?

(c) Which shape has the greater area?

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