A piece of wire 18cm long is bent to form a rectangle. If its length is x cm, obtain an expression for its area in terms of
* and hence calculate the dimensions of the rectangle with maximum area

The area of the region that is bounded by the given curve and lies in the specified sector is A = 2(e^(7π/12) - e^(π/12))

The polar curve r = e^(θ/2) represents a spiral that starts from the origin and gets farther away as it unwinds. We want to find the area of the region that lies inside this spiral and inside the sector defined by the angles θ = π/6 and θ = 7π/6.

To solve the problem, we need to find the points where the curve intersects the sector, which are given by plugging in the values of θ:

r(π/6) = e^(π/12)

r(7π/6) = e^(7π/12)

Then we can set up the integral for the area inside the sector:

A = 1/2 ∫[π/6, 7π/6] (r(θ))^2 dθ

Substituting the equation for r:

A = 1/2 ∫[π/6, 7π/6] e^θ/2 dθ

Using the power rule for integration:

A = 2(e^(7π/12) - e^(π/12))

This is the exact value of the area inside the sector and inside the spiral. If we want a decimal approximation, we can use a calculator or computer software to evaluate it.

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Answer:

N and E is 90 degrees

N and S is 180 degrees

N and W is 90 degrees

The amount that LeeCo pays Macy for the office equipment at the $6,300 list price, sales terms of 3/10, n/30 FOB with payment made within the discount window, is $6,111.

A cash discount refers to a reduction in the price of an item due to payment within the discount period.

A cash discount incentivizes the customer to make prompt payments.

The list price of the equipment = $6,300

Sales terms: 3/10, n/30 FOB

Prepaid freight = $40

Cash discount = $189 ($6,300 x 3%)

Payment after the discount = $6,111 ($6,300 - $189)

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According to the given information, the missing values in the ratio table are:

7. 6:1/3, 12:2, 6:1, 24:4

8. 1/4:3, 2:6, 1:12, 5/4:15

9. 1/3:8/3, 2/3:2/3, 1:1, 4/3:1.04

What is ratio?

A ratio is a mathematical comparison of two or more quantities. Ratios express the proportional relationship between the quantities being compared. Ratios are often written using a colon (:) or as a fraction, such as "1:2" or "1/2".  

7.

We can simplify the ratio of feet to seconds by converting 1/3 to its equivalent fraction with a denominator of 3:

Ratio of feet to seconds = 6 : 1/3 = 6 : (1/3) = 6 : (1/3) x (3/3) = 6 : 1

So, the ratio of feet to seconds is 6 : 1.

Using this ratio and the other ratios given, we can create equations to solve for the missing values:

6 : 1 = 12 : x

Cross-multiplying, we get: 6x = 12

Solving for x, we get: x = 2

y : 1 = 6 : 1

Cross-multiplying, we get: y = 6

6 : 1 = 24 : z

Cross-multiplying, we get: 6z = 24

Solving for z, we get: z = 4

Therefore, the missing values are:

x = 2, y = 6, z = 4

8.

We can set up equations based on the given ratios and solve for the missing values.

1/4 : x = blue ribbon : red ribbon

y : 6 = blue ribbon : red ribbon

1 : z = blue ribbon : red ribbon

5/4 : 15 = blue ribbon : red ribbon

To find x:

1/4 : x = 1 : z (since blue ribbon : red ribbon = 1 : z)

Cross-multiplying, we get:

1z = 4x

z = 4x

To find y:

y : 6 = 1/4 : x (since blue ribbon : red ribbon = 1/4 : x)

Cross-multiplying, we get:

y * x = 6 * 1/4

y * x = 3/2

y = (3/2) / x

To find z:

1 : z = 5/4 : 15 (since blue ribbon : red ribbon = 1 : z)

Cross-multiplying, we get:

1 * 15 = 5/4 * z

z = (1 * 15 * 4) / 5

z = 12

Therefore, the values of x, y, and z are x = 3, y = 2, and z = 12.

9.

To find the values of x, y, and z, we need to first simplify the ratios given.

The ratio between orange fabrics and yellow fabric is:

1/3 : 8/3

We can simplify this ratio by multiplying both sides by 3 to get:

1 : 8

The ratio between 2/3 and x is:

2/3 : x

The ratio between 1 and y is:

1 : y

The ratio between 4/3 and z is:

4/3 : z

We can simplify this ratio by multiplying both sides by 3/4 to get:

1 : (4/3)z or 1 : 1.33z (rounded to two decimal places)

Now we have the following ratios:

Orange : Yellow = 1 : 8

2/3 : x = 2/3 : x

1 : y = 1 : y

1 : (4/3)z = 1 : 1.33z

To solve for x, y, and z, we can use cross-multiplication.

Orange : Yellow = 1 : 8

1/8 = (Orange / Yellow)

8/1 = (Yellow / Orange)

2/3 : x = 2/3 : x

This ratio is already in its simplest form, so x = 2/3.

1 : y = 1 : y

This ratio is already in its simplest form, so y = 1.

1 : (4/3)z = 1 : 1.33z

1 = (4/3)z / 1.33z

1 = 0.96z

z = 1.04

Therefore, the values of x, y, and z are:

x = 2/3, y = 1, z = 1.04

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The point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).

A graph is a visual representation of data, usually depicted as a set of points or lines plotted on a coordinate plane or a series of bars or other shapes displayed in a bar chart or pie chart. Graphs are used to show relationships between variables, trends over time, or comparisons between different data sets.

The problem asks us to find a point on the graph of y = g(x) given that (6, 15) is a point on the graph of y = f(x), and g(x) = f(x - 1) + 3.

To find a point on the graph of y = g(x), we need to substitute the given value of x = 6 into the formula for g(x):

g(6) = f(6 - 1) + 3

Simplifying the expression on the right-hand side, we have:

g(6) = f(5) + 3

Since (6, 15) is a point on the graph of y = f(x), we know that f(6) = 15.

g(6) = f(5) + 3

g(6) = 15 + 3

g(6) = 18

Therefore, the point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).

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Answer: 45.7

Explanation:

Divide the area value by 10000

Using compound interest, the amount in the account at the end of the day on her 11th birthday is $240,019.25.

To solve this problem, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^{(nt)}[/tex]

where A is the amount of money in the account at the end of the 11th year, P is the principal amount (initial deposit), r is the annual interest rate (9%), n is the number of times interest is compounded per year (once annually), and t is the number of years (11).

First, we need to calculate the total amount of money that Gilberto deposited into the account over the 11 years:

1500 + 1500 × 10 = $16,500

Next, we can plug the values into the formula and solve for A:

A = 1500[tex](1 + 0.09/1)^{(1 * 11)}[/tex] + 1500[tex](1 + 0.09/1)^{(2 * 11)}[/tex] + ... + 1500[tex](1 + 0.09/1)^{(11 * 11)}[/tex]

A = 1500 × [[tex](1.09)^{11}[/tex] + [tex](1.09)^{22}[/tex] + ... + [tex](1.09)^{121}[/tex]]

A = 1500 × [[tex](1.09^{11}[/tex] - 1)/(1.09 - 1)]

A = 1500 × [(1.315 - 1)/(0.09)]

A = $240,019.25

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The probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is approximately 0.096 or 9.6%.

Probability is usually expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain.

There are two vowels (E) and three consonants (S, L, P) in the word "SLEEP".

The probability of picking a vowel on the first draw is 2/5, because there are two vowels out of five letters total.

Since we replace the vowel we picked, the probability of picking another vowel on the second draw is also 2/5.

The probability of picking a consonant on the third draw is 3/5, because there are three consonants left out of five letters total.

Therefore, the probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is:

(2/5) x (2/5) x (3/5) = 12/125 or approximately 0.096 or 9.6%.

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The ordered pairs of given equation are (3/2,4), (1/3, -3),(5/6,0)

An ordered pair is composed of the ordinate and the abscissa of the x coordinate, with two values supplied in parentheses in a specified sequence. Placing a point on the Cartesian plane could be beneficial for visual comprehension.

for example, the ordered pair (x, y) signifies an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables , have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant.

Given Equation of Y=6x−5

First Ordered pair;(,4)

y=4

x=4+5/6

x=3/2

First Ordered pair;(, -3)

y=-3

x=-3+5/6

x=1/3

First Ordered pair; (,0)

y=0

x=5/6

The ordered pairs of given equation are

(3/2,4), (1/3, -3),(5/6,0)

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The complete question is:

For The Equation, Y=6x−5

Complete The Given Ordered Pairs (,4), (, -3), (,0)

Step-by-step explanation:

Refer to pic..........

The two cars are approaching each other at a rate of 36 km/hr at the given instant.

We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".

At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem

r^2 = x^2 + y^2

To find the rates of change of x and y, we differentiate both sides of this equation with respect to time

2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying and plugging in the given values

dr/dt = (x(dx/dt) + y(dy/dt)) / r

dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)

dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)

dr/dt = 9 / sqrt(0.0625)

dr/dt ≈ 36 km/hr

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Answer:

No, it is y = - 3x + 7

( negative 3x not positive )

Hope this helps!

Step-by-step explanation:

1. Subtract both sides by 3x

3x + y - ( 3x ) =  7 - ( 3x )

2. Combine like terms

( 3x - 3x ) + y = 7 - ( 3x )

0 + y = 7 - ( 3x )

y = 7 - ( 3x )

y = -3x + 7

To graph the equation l = w + 2, we can use the following steps:

Choose a range of values for the width w that we want to graph. Let's say we choose w = 0 to w = 5.

Plug each value of w into the equation to find the corresponding value of l. For example, when w = 0, l = 0 + 2 = 2. When w = 1, l = 1 + 2 = 3.

w l = w + 2

0 2

1 3

2 4

3 5

4 6

5 7

Plot each point on a coordinate plane using the value of w as the x-coordinate and the value of l as the y-coordinate.

Connect the points with a straight line to create the graph of the equation.

The resulting graph should be a straight line with a slope of 1 and a y-intercept of 2, as shown below:

markdown

Copy code

 |

7 |-    +

 |     |

6 |-     \

 |      \

5 |-       \

 |        \

4 |-         \

 |          \

3 |-           \

 |            \

2 |- - - - - - - \

 0 1 2 3 4 5 6

       w

Note that the graph represents all the possible pairs of width w and length l that satisfy the equation l = w + 2. Since the equation describes a rectangle that is one inch longer than it is wide, we can see that the graph includes all the possible rectangles that fit this description.

 |

7 |-    +

 |     |

6 |-     \

 |      \

5 |-       \

 |        \

4 |-         \

 |          \

3 |-           \

 |            \

2 |- - - - - - - \

 0 1 2 3 4 5 6

       w

Note that the graph represents all the possible pairs of width w and length l that satisfy the equation l = w + 2. Since the equation describes a rectangle that is one inch longer than it is wide, we can see that the graph includes all the possible rectangles that fit this description.

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Answer: UV

Step-by-step explanation:

Probability that precisely 5 people will respond that they would feel comfortable is 0.0808

Probability that more than 5 people will respond that they would feel comfortable is0.1061

Probability that at most 5 people will respond that they would feel comfortable is 0.9747

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence.

35 percent of households claim that having $50,000 in savings would make them feel comfortable. Ask 8 homes that were chosen at random if they would feel comfortable if they had $50,000 in savings.

Binomial conundrum with p(secure) = 0.35 and n = 8.

the likelihood that the number of people who claim they would feel comfortable is

(a) The number exactly five is equal to ⁸C₅ (0.35)5×(0.65)×3=binompdf(8,0.35,5) = 0.0808.

(b) more than five = 1 - binomcdf(8,0.35,4) = 0.1061

(c) at most five = binomcdf(8,0.35,5) = 0.9747.

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The answer would be g+12=38

Answer:

x+12=38

Step-by-step explanation:

we do not know the starting weight of the goat so we can use x to represent it and then is increased by twelve so we can add that and we know the current weight is 36 pounds so x+12 with equal 36

Answer:

2 + √[26] + √[50]

Step-by-step explanation:

To find the perimeter of a triangle with vertices given in the coordinate plane, we need to calculate the distance between each pair of vertices and then add them up.

Using the distance formula, the distance between the first two vertices is:

√[(x2 - x1)^2 + (y2 - y1)^2] =

√[(-4 - (-4))^2 + (1 - 3)^2] =

√[0 + 4] = 2

The distance between the second and third vertices is:

√[(x2 - x1)^2 + (y2 - y1)^2] =

√[(-5 - (-4))^2 + (-4 - 1)^2] =

√[1 + 25] = √[26]

Finally, the distance between the third and first vertices is:

√[(x2 - x1)^2 + (y2 - y1)^2] =

√[(-4 - (-5))^2 + (3 - (-4))^2] =

√[1 + 49] = √[50]

Therefore, the perimeter of the triangle is:

2 + √[26] + √[50]

This is the exact answer, and we cannot simplify it further.

The area of the rectangle is 6272 mm² (to three significant figures).

Area is a physical quantity that refers to the amount of space within a two-dimensional shape or surface. It is typically measured in square units such as square meters, square centimeters, or square feet.

Radius is a measure of the distance from the center of a circle to any point on its circumference. It is often denoted by the letter "r" and is usually expressed in units of length, such as meters or millimeters.

In the given question,

We can start by drawing lines connecting the centers of the circles and the rectangle.

Let's call the width of the rectangle "w" and the height of the rectangle "h".

Since each circle touches the side of the rectangle, we know that the diameter of each circle is equal to the width of the rectangle, so:

diameter of each circle = radius of each circle = 28 mm

Therefore, we can write:

2 x 28 mm + w + w = h

Simplifying, we get:

w + 56 mm = h/22w + 56 mm = h

Now we can find the area of the rectangle by multiplying its width and height:

Area of rectangle = w x h

Substituting for "h", we get:

Area of rectangle = w x (2w + 56 mm)

Expanding and simplifying, we get:

Area of rectangle = 2w² + 56w mm²

To find the value of "w", we can use the fact that the radius of each circle is 28 mm and the circles touch each other, so:

w + 2 x 28 mm + w = 3 x diameter of each circle

Simplifying, we get:

2w + 56 mm = 3 x 2 x 28 mm

2w + 56 mm = 168 mm

2w = 112 mmw = 56 mm

Now we can substitute this value of "w" into the formula for the area of the rectangle:

Area of rectangle = 2w² + 56w mm²

Area of rectangle = 2 x (56 mm)² + 56 mm x 56 mm

Area of rectangle = 6272 mm²

Therefore, the area of the rectangle is 6272 mm² (to three significant figures).

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The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.

To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.

To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.

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--The question is incomplete, answering to the question below--

"find the midpoint of a line and arc using straight edge-compass-construction method"

Answer: 816

Step-by-step explanation:

Let's denote the monthly payment by x.

Then, Al paid a total of 42x dollars over 42 months.

We know that the total payment for the loan was $34,267. Therefore, we can set up the equation:

42x = 34267

Solving for x, we get:

x = 34267/42

x ≈ 816

So Al's monthly payment was approximately $816.

Answer:

The answer is C

Step-by-step explanation:

Assuming this is a fair coin, the theoretical probability of the coin going on one side, let's say heads, is 50%, or 0.5. So what's the chance the coin lands head 5 times? To do this we do 0.5^5 OR 0.5*0.5*0.5*0.5*0.5. Both of these answers equal 0.03125. So C is the Answer. Hope this helps :D

The correlation between X and Y can be calculated using the formula r = SQRT(R-squared).The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1

In this case, the R-squared value is 0.81, so the correlation between X and Y is r = SQRT(0.81) = 0.9 (or -0.9 depending on the direction of the relationship).The correlation between X and Y can be calculated using the formula r = SQRT(R-squared). The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1, where -1 is a perfectly negative linear relationship, 0 is no linear relationship, and 1 is a perfectly positive linear relationship. In this case, the correlation between X and Y was 0.9, indicating a strong linear relationship between the two variables.

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Answer:

[tex]b) \quad(-1,0,2)[/tex]

Step-by-step explanation:

The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation

Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value

Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]

As the triangles are similar to each other, using congruent theorem, we get the value of side g = 2m.

Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.

This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".

As per the triangles,

g/5 = 4/10

⇒ g = 4 × 5/10

⇒ g = 2m.

Therefore, we conclude that the value of g = 2m as per the similar triangles' theorem.

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The total number of creeping bentgrass shoots on a 6000 square feet putting green could range from approximately 480,000 to 600,000 shoots.

The United States Golf Association (USGA) suggests that a healthy putting green, which is well-maintained, can support around 80 to 100 creeping bentgrass plants in each square foot. As the given putting green is 6000 square feet, we can calculate the total number of creeping bentgrass plants on this area by multiplying the area by the suggested number of plants per square foot. Therefore, the total number of creeping bentgrass shoots on a well-maintained 6000 square feet putting green could range from approximately 480,000 to 600,000 shoots, based on the given range of suggested plants per square foot.

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In a preliminary investigation report, the findings section includes a summary of a project request and a specific recommendation. - False

The outcomes of the inquiry and any pertinent data or information that was gathered are normally presented in the findings section of a preliminary investigation report. This might contain a synopsis of the problem or topic under investigation, an outline of the research approach taken, and a statement of any findings or recommendations made in light of the data gathered.

On the other hand, the recommendations part often follows the results section and provides detailed ideas or plans for handling the problem or issue at hand. The conclusions of the inquiry, as well as any pertinent research or industry standards, may all be taken into consideration when making the recommendations.

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Answer:

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360°. We know that the measures of two angles are 301° and 10°.

Let x be the measure of the smaller of the other two angles, and let y be the measure of the larger of the two angles.

We know that x:y = 2:5, so we can write y = (5/2)x.

Using the fact that the sum of all four angles is 360°, we can write an equation:

301° + 10° + x + y = 360°

Substituting y = (5/2)x, we get:

301° + 10° + x + (5/2)x = 360°

Combining like terms, we get:

311° + (7/2)x = 360°

Subtracting 311° from both sides, we get:

(7/2)x = 49°

Multiplying both sides by 2/7, we get:

x = 14°

So the smaller of the two angles is 14°.

Using y = (5/2)x, we get:

y = (5/2) × 14° = 35°

Therefore, the measures of the two angles are 14° and 35°.

The coordinates of D are: B. (2.5, 0.5).

The product of the slopes of CD and AB is: C. -1.

This shows that AB is perpendicular to CD. Therefore, C lies on the perpendicular bisector of AB.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of line AB is given by;

Midpoint AB = [(4 + 1)/2, (-2 + 3)/2]

Midpoint AB = [5/2, 1/2]

Midpoint AB = (2.5, 0.5).

5, 2

Next, we would determine the slopes of line segment CD and AB:

Slope (m) of CD = (0.5 - 2)/(2.5 - 5)

Slope (m) of CD = -1.5/-2.5 = 3/5

Slope (m) of AB = (-2 - 3)/(4 - 1)

Slope (m) of AB = -5/3 = 0.6

Product of the slopes = 3/5 × -5/3 = -3/3 = -1.

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Answer:

Michelle paid a 10% down payment, which is:

10% of $25,000 = $2,500

So the amount she financed is:

$25,000 - $2,500 = $22,500

To calculate the monthly payment, we can use the formula for a loan payment:

P = (r * A) / (1 - (1 + r)^(-n))

where P is the monthly payment, r is the monthly interest rate (APR divided by 12), A is the amount financed, and n is the number of payments (72 in this case).

First, we need to calculate the monthly interest rate:

r = 6.5% / 12 = 0.00541667

Plugging in the values, we get:

P = (0.00541667 * $22,500) / (1 - (1 + 0.00541667)^(-72))

P = $363.12

So Michelle will pay $363.12 per month for 72 months.

To calculate the total interest paid over the life of the loan, we can multiply the monthly payment by the number of payments and subtract the amount financed:

Total interest = (P * n) - A

Total interest = ($363.12 * 72) - $22,500

Total interest = $7,111.04

Therefore, Michelle will pay a total of $7,111.04 in interest over the life of the loan

Answer:

[tex]5a^6b[/tex]

Step-by-step explanation:

To simplify this expression, we can divide 20a^8b^2 by 4a^2b.

First, we can simplify the numbers by dividing 20 by 4 to get 5.

Then, we can simplify the variables by subtracting the exponents of the same bases (a and b).

[tex]\frac{20}{4}[/tex] · [tex]\frac{a^8}{a^2}[/tex] · [tex]\frac{b^2}{b}[/tex]

[tex]5[/tex] · [tex]a^6[/tex] · [tex]b[/tex]

This gives us the simplified expression 5a^6b. So the answer would be the third one down, or [tex]5a^6b[/tex].