Emily recently graduated with a B.A. in economics and was offered a job with a small but growing company for $38 400 per year. About the same time, Emily inherited $60 000. She decided to pass up the job and use her inheritance to purchase a bubble tea shop rather than put the money into a bond fund (as her uncle suggested), which would have paid 5 percent per year interest. Emily works full-time at her new business, and at the end of the year she had revenues of $81 000 and total explicit costs of $42 000. a. What was Emily's accounting profit or loss for the year? b. What was her economic profit or loss for the year? 2. Table 6.5 shows the total product for a firm. Complete the average and marginal products. TABLE 6.5 Units of Total Average Marginal Labour Product Product Product 0 0 12 2 30 3 54 4 68 5 80 6 84 7 1 77 1. Emily recently graduated with a B.A. in economics and was offered a job with a small but growing company for $38 400 per year. About the same time, Emily inherited $60 000. She decided to pass up the job and use her inheritance to purchase a bubble tea shop rather than put the money into a bond fund (as her uncle suggested), which would have paid 5 percent per year interest. Emily works full-time at her new business, and at the end of the year she had revenues of $81 000 and total explicit costs of $42 000. a. What was Emily's accounting profit or loss for the year? b. What was her economic profit or loss for the year? 2. Table 6.5 shows the total product for a firm. Complete the average and marginal products. TABLE 6.5 Units of Total Average Marginal Labour Product Product Product 0 0 12 2 30 3 54 1 4 68 80 5 6 7 84 77 3. a. Complete Table 6.7 for Bannister Inc. b. How many workers are being used when the point of diminishing returns is first apparent? c. How many workers are being used when total product is at a maximum? d. What is the most productive output? TABLE 6.7 Number of Workers Average Product Total Product 2 5 Marginal Product 1 3 2 3 4 5 6 7 = ||- ||| 3 14 15

Answer:

8u - 20

Step-by-step explanation:

Answer: (3,2)

Step-by-step explanation:

(3,2) lies on the line x=3, so it is an invariant point.

Answer:

c

Step-by-step explanation:

Yes, to prove triangles to be congruent it is compulsory to have at least three congruent corresponding parts.

Explanation:

Minimum congruent corresponding parts required to prove triangles to be congruent are as follow:

Therefore, minimum three congruent corresponding parts are required to prove any two triangles to be congruent.

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A Poisson random variable represents the number of occurrences of an event in a fixed interval of time or space. It is a discrete random variable, which means that it can only take on integer values, starting from zero. Therefore, the smallest numerical value that a Poisson random variable can be is zero.

This means that there is a possibility that the event will not occur at all during the given interval. For example, if we are counting the number of customers who visit a store in an hour, it is possible that no customers show up during that hour, resulting in a Poisson random variable of zero.

However, the probability of this occurring depends on the average rate of the event occurring, which is denoted by the parameter λ in the Poisson distribution. The larger the value of λ, the smaller the probability of a Poisson random variable being zero.

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To find the intersection of a line and a plane, we need to solve for the point where the line and plane intersect.

First, let's rewrite the plane equation in standard form:

2x + 5y - 31 = 0

Next, we need to find a point on the line. We can do this by setting y = -2 in the equation of the line:

x - 3 = 7

Solving for x, we get:

x = 10

So a point on the line is (10, -2).

Now we can substitute these values into the plane equation:

2(10) + 5(-2) - 31 = 0

Simplifying, we get:

20 - 10 - 31 = -21

So the point of intersection is (10, -2, -21).

Therefore, the intersection of the line and plane is the single point (10, -2, -21).

To find the intersection of the line and plane given, we need to rewrite the equations in a more recognizable form and then solve for the point of intersection. Here are the given equations:

Line: (x - 3)/1 = (y + 2)/2 = z/7
Plane: 1/2x + 5y + 3z - 1 = 0

First, we can express the line in parametric form by introducing a parameter t:

x = 1t + 3
y = 2t - 2
z = 7t

Now, we can substitute these expressions into the plane equation:

1/2(1t + 3) + 5(2t - 2) + 3(7t) - 1 = 0

By solving for t, we can then find the point of intersection:

1/2t + 3/2 + 10t - 10 + 21t - 1 = 0
32.5t - 7.5 = 0
t = 7.5/32.5 = 3/13

Substitute the value of t back into the parametric equations to find the point of intersection:

x = 1(3/13) + 3 = 3/13 + 3 = 42/13
y = 2(3/13) - 2 = 6/13 - 2 = 6/13 - 26/13 = -20/13
z = 7(3/13) = 21/13

The intersection point of the line and plane is (42/13, -20/13, 21/13).

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Answer:

97.5

Step-by-step explanation:

Supplementary means the angles add up to 180°

So,

m∠A = 180 - m∠B

m∠A = 180 - 82.5

m∠A = 97.5

the vector x determined by the given coordinate vector [x]g and the given basis B is x = (-9, 16, -3).

Given coordinate vector is [x]g = [1 5 6 -3] and the basis B is as follows. B = {-4, [xls], II, 0, 3, -3}The basis vector in a matrix is given by B = [b1 b2 b3 b4 b5 b6] So, the matrix will be B = {-4 [xls] II 0 3 -3} Therefore, the vector x determined by the given coordinate vector [x]g and the given basis B can be found as follows.[x]g = a1b1 + a2b2 + a3b3 + a4b4 + a5b5 + a6b6 where a1, a2, a3, a4, a5, a6 are scalar coefficients. Here, we need to find the vector x. Therefore, substituting the given values, we get [x]g = a1(-4) + a2[xls] + a3(II) + a4(0) + a5(3) + a6(-3) [1 5 6 -3] = -4a1 + [xls]a2 + IIa3 + 3a5 - 3a6 So, we can write this equation in matrix form as A[X] = B where A = {-4 [xls] II 0 3 -3}, [X] = {a1 a2 a3 a4 a5 a6}, B = [1 5 6 -3] Now, we need to find the matrix [X]. To find this, we need to multiply both sides of the above equation by the inverse of A, which gives[X] = A-1B where A-1 is the inverse of matrix A. So, to find [X], we need to find A-1. A-1 can be found as follows.A-1 = 1/40[13 -6 3 -12 -1 -26][3 -3 3 0 1 -4][-4 -4 -4 -4 -4 -4][-2 -1 0 2 1 4][1 2 1 1 2 1][-2 -1 0 2 -1 -4] Therefore, substituting the values, we get [X] = A-1B = 1/40[13 -6 3 -12 -1 -26][3 -3 3 0 1 -4][-4 -4 -4 -4 -4 -4][-2 -1 0 2 1 4][1 2 1 1 2 1][-2 -1 0 2 -1 -4][1 5 6 -3] = [2 0 -1 -2 1 1]So, the vector x determined by the given coordinate vector [x]g and the given basis B is [2 0 -1 -2 1 1].Hence, the correct answer is x = [2 0 -1 -2 1 1].
To find the vector x determined by the given coordinate vector [x]g and the given basis B, you should perform a linear combination of the basis vectors with the coordinates in [x]g.

Given the coordinate vector [x]g = (-1, 5, 6) and basis B = (-4, 2, 0), (1, 0, 3), (-3, 3, -3), we can find the vector x as follows:

x = (-1) * (-4, 2, 0) + (5) * (1, 0, 3) + (6) * (-3, 3, -3)

x = (4, -2, 0) + (5, 0, 15) + (-18, 18, -18)

x = (-9, 16, -3)

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Option B is the correct answer: It shows that H is closed under scalar multiplication, which is all that is required for a subset to be a vector space.

To elaborate, a subspace of a vector space R must meet three conditions:
1. The zero vector is included in the subspace.
2. The subspace is closed under vector addition.
3. The subspace is closed under scalar multiplication.

In this case, H consists of vectors of the form tv, where v = (0, -5) and t is any scalar. The zero vector is included when t = 0, which gives (0, 0). For scalar multiplication, any vector in H multiplied by a scalar will still be in H. For example, if t1 and t2 are scalars, then (t1 * t2)v = t1(t2v), and since t1(t2v) is still a scalar multiple of v, it remains in H. This shows that H is a subspace of R³ as it meets the necessary conditions.

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9% of the volume of the original volume is removed.

Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.

So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter

The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter

For each corner one cube so the number of cube is 4

So total volume removed = 4*27 = 108 cubic centimeters

The percent of volume is removed = (108/1200)*100% = 9%

Hence the percentage of volume removed is 9%.

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Given matrices: A₁ = [1 -1 4; 4 2 3]B = [3; 5; 7; -3; 2]We have to check whether the matrix B lies in span(A1, A2) or not. Now, we need to find A₂ such that the matrix B lies in span(A1, A2) i.e.

it can be represented as a/ of A₁ and A₂.We can find A₂ as follows:Let A₂ = [a b c; d e f]We want B to be a linear combination of A₁ and A₂i.e. there exist constants x and y such that:B = xA₁ + yA₂= x[1 -1 4; 4 2 3] + y[a b c; d e f]Now, the above equation can be written in the form:[1 -1 4; 4 2 3 | 3; 5; 7] [a b c; d e f | -3; 2]

This can be written in the form of an augmented matrix as:[1 -1 4 3; 4 2 3 5] [a b c -3; d e f 2]Now, we perform row operations to put the matrix in echelon form:[1 -1 4 3; 0 6 -13 -7] [a b c -3; 0 -2 5 5]Now, we perform back-substitution to find the values of a, b, c, d, e and f:Since the above matrix is not in echelon form, we cannot perform back-substitution, thus, we can say that the matrix B does not lie in span(A1, A2).Hence, the matrix B = [3; 5; 7; -3; 2] does not lie in span(A₁, A₂).

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7250×(60+6) and 7250×66 are equivalent to the  66×7250

An expression is combination of variables, numbers and operators.

The given expression is 66×7250

We need to find the equivalent expressions.

The given expressions are

725×10²×66

725×10×60×6

7250×(60+6)

7250×66

66×(7000+200)

In the above expressions 7250×(60+6) and 7250×66 are equivalent to the  66×7250

Hence 7250×(60+6) and 7250×66 are equivalent to the  66×7250

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Answer:

1. It is easier to find the area of a trapezoid than it is to find the area of a triangle all she would need to do is add the two bases which are both four to get eight then divide that by two and than multiply that by the height which is 5

so the answer to her problem would be 20

2 Since the parallelogram is just double the triangle all she would need to do is find the area of the trapezoid and divide that by two to find the area of the triangle.

3.

Triangle A=30

Triangle B=22.5

The Triangle area formula is A=1/2 base times height

This restricted portion of the fundamental niche that Chthamalus can effectively utilize in the presence of competition is referred to as its realized niche.

The weaker competitor is forced to retreat to a more restricted niche (its realized niche) than it would inhabit in the absence of the competition when interspecific interactions result in competitive exclusion.

For Chthamalus, a typical intertidal barnacle animal categories, its key specialty alludes to the full scope of ecological circumstances and assets it is hypothetically fit for taking advantage of without rivalry. Chthamalus would occupy its entire fundamental niche in the absence of competition.

However, Chthamalus is outcompeted and forced to withdraw from a portion of its fundamental niche when competing with a stronger competitor, such as Balanus, the dominant barnacle species. This limited part of the essential specialty that Chthamalus can actually use within the sight of contest is alluded to as its acknowledged specialty.

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By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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Answer:

A) The Jenga game is appropriate for the middle childhood age group, typically ranging from around 6 to 12 years old.

B) Jenga promotes cognitive, physical, and socioemotional development in middle childhood through enhancing spatial reasoning and problem-solving skills, improving fine motor skills and proprioceptive input, and fostering social interaction, cooperation, and risk assessment.

Step-by-step explanation:

Jenga, a game played with rectangular blocks, can promote cognitive, physical, and socioemotional development through various concepts.

Cognitive Development: Jenga enhances spatial reasoning as players analyze the tower's structure, evaluate block stability, and strategize their moves. They mentally manipulate objects in space, building an understanding of spatial relationships and balance. Problem-solving skills are fostered as players make decisions about which block to remove, considering the consequences of their actions. They must anticipate the tower's reaction to their moves, think critically, and adjust their strategies accordingly.

Physical Development: Jenga improves fine motor skills as players carefully remove and stack blocks using only one hand. Precise finger movements, hand-eye coordination, and grip strength are required for successful manipulation of the blocks. The game also provides proprioceptive input as players gauge the weight and balance of each block, refining their sense of touch and motor control.

Socioemotional Development: Jenga promotes social interaction and cooperation when played with multiple players. Taking turns, discussing strategies, and supporting each other's successes and challenges enhance communication, collaboration, and empathy skills. Players learn to respect and consider others' perspectives, negotiate and compromise, and work together towards a common goal. Sportsmanship is nurtured as players accept both victory and defeat gracefully, fostering resilience and emotional regulation.

Furthermore, Jenga offers opportunities for developing patience and perseverance. As the tower becomes increasingly unstable, players must exercise self-control, focus, and delayed gratification. They learn to take their time, plan their moves carefully, and tolerate the suspense of potential collapse. The game also presents a low-risk environment for risk assessment, allowing children to assess the consequences of their decisions and make calculated judgments.

By engaging in Jenga, children actively participate in a multi-dimensional activity that combines physical manipulation, cognitive analysis, and social interaction. Through the concepts of spatial reasoning, problem-solving, fine motor skills, proprioceptive input, social interaction, cooperation, sportsmanship, patience, perseverance, and risk assessment, Jenga supports holistic development in cognitive, physical, and socioemotional domains.

The length of KP is given as follows:

23 ft.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

The parameters for this problem are given as follows:

a = 15, b = 14, C = 105º.

Hence the length of KP is obtained as follows:

c² = 15² + 14² - 2 x 15 x 14 x cosine of 105 degrees

c² = 529.7

c = sqrt(529.7)

c = 23 ft.

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Answer:

3

Step-by-step explanation:

Answer:

x = 6 cm

Step-by-step explanation:

Given ratio of sides of similar figures = a : b , then

ratio of areas = a² : b²

Here ratio of areas = 5 : 45 = 1 : 9 , so

ratio of sides = \(\sqrt{1}\) : \(\sqrt{9}\) = 1 : 3

Thus side of B is 3 times side of A

x = 3 × 2 = 6 cm

Standard trigonometry texts typically do not include formulas for the cotangent, secant, and cosecant of the sum and difference of two numbers or angles due to several reasons.

Firstly, these functions can be easily derived from the well-known trigonometric identities involving sine, cosine, and tangent. Including separate formulas for the cotangent, secant, and cosecant would result in redundancy and unnecessary complexity.

Secondly, the cotangent, secant, and cosecant are not as commonly used as sine, cosine, and tangent in practical applications, so their inclusion may not be prioritized.

Moreover, space limitations in textbooks also play a role, as providing comprehensive formulas for all trigonometric functions could make the texts excessively lengthy.

Therefore, students are encouraged to understand the relationships between trigonometric functions and employ the existing identities to derive the values they need.

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Answer:

\(\huge\boxed{\sf V = 4778.4\ cm\³}\)

Step-by-step explanation:

Given:

Height = 27 cm

Radius = 13 cm

Formula:

\(Volume \ of \ cone \ V = \frac{1}{3} \pi r^2h\)

Solution:

V = 1/3 (3.14)(13)²(27)

V = (3.14)(169)(9)

V = 4778.4 cm³

\(\rule[225]{225}{2}\)

Hope this helped!

Answer: 24

Step-by-step explanation: 6*4=24

4+4+4+4+4+4=24

Answer:

she paid $1.50 / 1lb

Step-by-step explanation:

6lbs divided by $4 = 1.50 or $1.50 / 1lb

The area of the circle is 452.16 square inches

Area is the the total surface that is occupied by a two dimensional shape

The radius of the circle = 12 inch

The radius of a circle is the distance between the center and any point on the circumference of the circle

The area of the circle A = π×\(r^2\)

Where A is the area of the circle

r is the radius of the circle

π = 3.14

substitute the values in the equation

The area of the circle = 3.14 × \(12^2\)

= 3.14 × 144

= 452.16 square inches

Hence, the area of the circle is 452.16 square inches

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The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

Given that

In a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal. Calculate a 90% confidence interval for the percentage of all U.S. adults who support the proposal based on the results of this poll (at the time of the poll). Complete the table below after that. Carry your calculations to a minimum of three decimal places.

We have to find the lower limit of 90%.

We know that

In a poll of 200 randomly selected U.S. Among adults, 104 expressed support for the novel idea.

p-hat = 104/200 = 0.52

ME = z×√[pq/n] = 2.5758×√[0.52*0.48/200] = 0.091

Now, the lower limit of the 90% confidence interval well be

p-hat-ME = 0.52-0.091 = 0.429

Therefore, The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

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The equation to describe this will be y = 8x. It is assumed that Pass holders pay $8 each movie for the first five films. After five films, up to fifteen films, additional films are free. This will be represented by the function y = 40.

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Using the formula for the area and circumference of a circle, we have the following answers:

1. radius = 2 in. (given)

Diameter = 4 in.

Circumference = 12.56 in.

Area = 12.56 in.²

2. radius = 10 in.

Diameter = 20 in. (given)

Circumference = 62.8 in.

Area = 314 in.²

3. radius = 5 in.

Diameter = 10 in. (given)

Circumference = 31.4 in.

Area = 78.5 in.²

4. radius = 20 in.

Diameter = 40 in. (given)

Circumference = 125.6 in.

Area = 1,256 in.²

5. radius = 18 in. (given)

Diameter = 36 in.

Circumference = 113.04 in.

Area = 1,017.36 in.²

6. radius = 8 in. (given)

Diameter = 16 in.

Circumference = 50.24 in.

Area = 200.96 in.²

7. radius = 12 in. (given)

Diameter = 24 in.

Circumference = 75.36 in.

Area = 452.16 in.²

8. radius = 16 in.

Diameter = 32 in. (given)

Circumference = 100.48 in.

Area = 803.84 in.²

9. radius = 15 in. (given)

Diameter = 30 in.

Circumference = 94.2 in.

Area = 706.5 in.²

1. radius = 2 in. (given)

Diameter = 2(2) = 4 in.

Circumference = πd = π(4) = 12.56 in.

Area = πr² = π(2²) = 12.56 in.²

2. radius = 1/2(20) = 10 in.

Diameter = 20 in. (given)

Circumference = πd = π(20) = 62.8 in.

Area = πr² = π(10²) = 314 in.²

3. radius = 1/2(10) = 5 in.

Diameter = 10 in. (given)

Circumference = πd = π(10) = 31.4 in.

Area = πr² = π(5²) = 78.5 in.²

4. radius = 1/2(40) = 20 in.

Diameter = 40 in. (given)

Circumference = πd = π(40) = 125.6 in.

Area = πr² = π(20²) = 1,256 in.²

5. radius = 18 in. (given)

Diameter = 2(18) = 36 in.

Circumference = πd = π(36) = 113.04 in.

Area = πr² = π(18²) = 1,017.36 in.²

6. radius = 8 in. (given)

Diameter = 2(8) = 16 in.

Circumference = πd = π(16) = 50.24 in.

Area = πr² = π(8²) = 200.96 in.²

7. radius = 12 in. (given)

Diameter = 2(12) = 24 in.

Circumference = πd = π(24) = 75.36 in.

Area = πr² = π(12²) = 452.16 in.²

8. radius = 1/2(32) = 16 in.

Diameter = 32 in. (given)

Circumference = πd = π(32) = 100.48 in.

Area = πr² = π(16²) = 803.84 in.²

9. radius = 15 in. (given)

Diameter = 2(15) = 30 in.

Circumference = πd = π(30) = 94.2 in.

Area = πr² = π(15²) = 706.5 in.²

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Answer:

Graphs shown below.

4.) x-intercept: (3,0)  y-intercept: (0,-2)  slope: 2/3

5.) x-intercept: none  y-intercept: (0,4.5)  slope:0

6.) x-intercept: (3,0) and (-1,0)  y-intercept: (0,-1)   slope: none

#4 is blue graph, #5 is green graph, #6 is red graph

Step-by-step explanation:

** #4 is blue graph, #5 is green graph, #6 is red graph **

The inequality for the statement:-2/7 is at most the product of a number and -4/5. is --4x/5 ≤ -2/7

Information from the question

the statement: -2/7 is at most the product of a number and -4/5

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using equal to

at most means the highest value hence the answer is either the number or less.

let the number be x

x * -4/5 ≤ -2/7

--4x/5 ≤ -2/7

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Answer:

N^2-3

Step-by-step explanation:

N (squared) minus three

Answer:

n*2-3

good luck :\

Answer:

line EF

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals. Their product is -1. The given line has slope -1/3, so the line we are looking for has slope 3.

Slope AB (-3, 2), (3, 0)

m = (2 - 0)/(-3 - 3) = 2/(-6) = -1/3

Slope EF (0, -3), (2, 3)

m = (-3 - 3)/(0 - 2) = -6/(-2) = 3

Slope JK (-3, -4), (3, -2)

m = (-4 - (-2))/(-3 - 3) = -2/(-6) = 1/3

Slope MN (-1, 4), (2, -5)

m = (-5 - 4)/(2 - (-1)) = -9/3 = -3

The only line with slope = 3 is line EF.

Answer: line EF

Answer:

8

Step-by-step explanation:

If I am doing this correctly you count all the dots the triangles lines are on. Which is 8 to find the area. Hope it helped have a wonderful day!