BRAINLIEST. Can someone please answer all the question in the picture below. BRAINLIEST.

The number of trials (n) represents the group's size, and the probability of success (p) represents the population's proportion of extroverts or introverts.

(a) Assume that X is the proportion of extroverts among a team of 15 marketing employees. X exhibits a binomial distribution with n = 15 and p = 0.8 as its parameters.

The following formula can be used to determine the likelihood of having at least 10 extroverts:

Binom.cdf(9, 15, 0.8) = 0.836; P(X 10) = 1 - P(X 10) = 1 - P(X 9) = 1

The likelihood of having five or more extroverts can be determined using the formula below:

Binom.cdf(4, 15, 0.8) 0.999, P(X 5) = 1 - P(X 5) = 1 - P(X 4) = 1.

The following formula can be used to determine the likelihood that all 15 employees are extroverts:

The formula P(X = 15) = binom.pmf(15, 15, 0.8) 0.035

(b) Assume that there are Y introverts among the four computer programmers in the group. Y has a binomial distribution with n = 4 and p = 0.35 (because 65% of respondents identify as introverts, 35% must identify as extroverts).

The following formula can be used to determine the likelihood that none of the programmers are introverts:

P(Y = 0) is equal to binom.pmf(0, 4, 0.35) 0.150.

The following formula can be used to determine the likelihood that two or more programmers are introverts:

Binom.cdf(1, 4, 0.35) = 0.586 when P(Y 2) = 1 - P(Y 2) = 1 - P(Y 1) = 1.

The following formula can be used to determine the likelihood that all four programmers are introverts:

P(Y = 4) is equal to binom.pmf(4, 4, 0.35) 0.015.

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Answer:

d=69, e=32, f=79

Step-by-step explanation:

e=32

d=69

f=180-69-32=79

The measure of each of the missing angles include the following:

d = 69.

e = 32.

f = 79.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to the geometric figure, we have the following:

m∠e = 32°

m∠d = 69°

From the linear postulate theorem, we have:

m∠e + m∠d + m∠f = 180°

32° + 69° + m∠f = 180°

m∠f = 180° - (32° + 69°)

m∠f = 79°

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To find a general solution to the equation ax^(2) + bx + 1 = 0 using the completion of the square, we need to follow these steps:

1. Divide the entire equation by a to get x^(2) + (b/a)x + 1/a = 0.

2. Move the constant term to the right side of the equation: x^(2) + (b/a)x = -1/a.

3. Complete the square by adding (b/2a)^(2) to both sides of the equation: x^(2) + (b/a)x + (b/2a)^(2) = -1/a + (b/2a)^(2).

4. Factor the left side of the equation: (x + b/2a)^(2) = -1/a + (b/2a)^(2).

5. Take the square root of both sides of the equation: x + b/2a = ±√(-1/a + (b/2a)^(2)).

6. Solve for x: x = -b/2a ± √(-1/a + (b/2a)^(2)).

This is the general solution to the equation.

The conditions for both solutions to be real are that the discriminant, -1/a + (b/2a)^(2), is greater than or equal to 0. This means that b^(2) - 4a >= 0.

The conditions for both solutions to be complex numbers are that the discriminant, -1/a + (b/2a)^(2), is less than 0. This means that b^(2) - 4a < 0.

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Answer:

the ans is f(x)=1.7x+21,472

The equation of the function is exponential and the function is f(x) = 21472(1.017)ˣ.

The population of a small town in Connecticut is 21,472 and the expected population growth is 1.7% each year.

Let's use a function to represent the town's population x years from now.

Hence,

1.7% = 1.7  / 100 = 0.017

Therefore,

f(x) = 21472(1 + 0.017)ˣ

Hence,

f(x) = 21472(1.017)ˣ

Therefore, the function is exponential.

The equation of the function is f(x) = 21472(1.017)ˣ

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A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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The value of −tanx is 1−secx, which is option c) in the given choices.

The correct answer is option c) 1−secx.

To find the value of −tanx, we can use the identity tanx = sinx/cosx. Multiplying both sides of the equation by −1 gives us −tanx = −sinx/cosx.

We can then substitute the value of cosx from the given equation into the equation for −tanx:

−tanx = −sinx/(1−sinx)

Multiplying both sides of the equation by (1−sinx) gives us:

−tanx(1−sinx) = −sinx

Distributing the −tanx on the left side of the equation gives us:

−tanx + tanx*sinx = −sinx

Rearranging the equation and factoring out sinx gives us:

tanx*sinx + sinx = tanx

sinx(tanx + 1) = tanx

Dividing both sides of the equation by (tanx + 1) gives us:

sinx = tanx/(tanx + 1)

Using the identity 1/cosx = secx, we can substitute secx for 1/cosx in the equation:

sinx = (sinx/cosx)/(sinx/cosx + 1/cosx)

Simplifying the equation gives us:

sinx = sinx/(sinx + secx)

Cross multiplying and rearranging the equation gives us:

sinx*(sinx + secx) = sinx

sinx^2 + sinx*secx = sinx

Subtracting sinx from both sides of the equation gives us:

sinx^2 + sinx*secx - sinx = 0

Factoring out sinx gives us:

sinx(sinx + secx - 1) = 0

Setting each factor equal to 0 gives us:

sinx = 0 or sinx + secx - 1 = 0

Solving for secx in the second equation gives us:

secx = 1 - sinx

Therefore, the value of −tanx is 1−secx, which is option c) in the given choices.

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Answer:

To approximate the monthly interest rate, we need to use the formula for the annual percentage rate (APR) that takes into account the effect of compounding:

APR = (1 + r/m)^m - 1

where r is the annual interest rate, m is the number of compounding periods per year, and APR is the annual percentage rate.

In this case, r = 11.1% and m = 12 (since there are 12 months in a year). We want to solve for the monthly interest rate, which we can call r_m:

r_m = (1 + r/12)^12 - 1

r_m = (1 + 0.111/12)^12 - 1

r_m = 0.009141

To convert this to a percentage, we multiply by 100:

r_m = 0.9141%

Therefore, the approximate monthly interest rate is 0.9141%, rounded to two decimal places.

To make the remainder 0, the final value of k must be -1.

The question asks to find all values of k so that when x^(3)-k^(2)x+k+2 is divided by x-2, the remainder is 0.

To find the values of k, we need to use synthetic division.

First, we can write the equation as follows:

Now we can continue with the synthetic division:

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The given sequence is A(n) = 6.3 + (n-1)(5), where n is the term number. To find the 5th term of the sixth term of the sequence, we need to first find the value of the sixth term and then find its fifth term.

To find the sixth term of the sequence, we substitute n = 6 in the given formula:

A(6) = 6.3 + (6-1)(5)

A(6) = 6.3 + 25

A(6) = 31.3

Now, to find the fifth term of this sequence, we need to go back one term from the sixth term, which means we need to substitute n = 5 in the original formula:

A(5) = 6.3 + (5-1)(5)

A(5) = 6.3 + 20

A(5) = 26.3

Therefore, the fifth term of the sixth term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.

The equation for the line that passes through the point (4, -4) and is parallel to the line with the equation -6x - 2y = 14 is y = -3x + 8.

To find the equation for the line that passes through the point (4, -4) and is parallel to the line with the equation -6x - 2y = 14, we first need to find the slope of the given line. We can do this by rearranging the equation to solve for y and putting it in slope-intercept form, y = mx + b.

-6x - 2y = 14

-2y = 6x + 14

y = -3x - 7

The slope of the given line is -3. Since the line we are trying to find is parallel to the given line, it will have the same slope. Therefore, the slope of the line we are trying to find is also -3.

Now, we can use the point-slope form of a linear equation, y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line, to find the equation of the line. Plugging in the slope and the point (4, -4), we get:

y - (-4) = -3(x - 4)

y + 4 = -3x + 12

y = -3x + 8

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Given line: y = -2x + 6 and Perpendicular line: y = 2x - 6: The slope of the given line is -2 and the slope of the perpendicular line is 2. Both slopes are in simplest form.

Slope is a measure of the steepness or inclination of a line, or a rate of change. It is usually represented by the letter m, and is calculated by finding the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. Slope can also be used to describe the angle of a line or surface, which is usually expressed as a percentage or in degrees. In mathematics, slope is used to describe the behavior of a line or curve, as well as to compare lines or curves with different slopes.

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If the ratio is less than 1, then the series converges, and if the ratio is greater than 1, then the series diverges.

To find the properties that two units are sold in a given day, the formula P(2) is used.

The Ratio Test can be used to determine the convergence or divergence of the series given by the expression n=1∑[infinity]2nn2→.

To use the Ratio Test, you must calculate the ratio of the values of the  successive terms that occurs in the series.

The ratio is calculated by dividing the n+1th term by the nth term.

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The solution to the system of equations is (4/3, 6, -2).

To solve the system of linear equations using the Gauss-Jordan elimination method, we need to perform row operations to reduce the system to reduced row echelon form. This will allow us to easily solve for the variables. Here are the steps:

1. Start with the given system of equations:

{ 6x - 2y + 2z = 4
{ 3x - y + 2z = 2
{ -12x + 4y - 8z = 8

2. Write the system as an augmented matrix:

[ 6 -2 2 | 4 ]
[ 3 -1 2 | 2 ]
[ -12 4 -8 | 8 ]

3. Divide the first row by 6 to get a leading 1:

[ 1 -1/3 1/3 | 2/3 ]
[ 3 -1 2 | 2 ]
[ -12 4 -8 | 8 ]

4. Use the first row to eliminate the x terms in the second and third rows:

[ 1 -1/3 1/3 | 2/3 ]
[ 0 2/3 5/3 | 2/3 ]
[ 0 0 -4 | 8 ]

5. Divide the second row by 2/3 to get a leading 1:

[ 1 -1/3 1/3 | 2/3 ]
[ 0 1 5/2 | 1 ]
[ 0 0 -4 | 8 ]

6. Use the second row to eliminate the y terms in the first and third rows:

[ 1 0 7/6 | 5/6 ]
[ 0 1 5/2 | 1 ]
[ 0 0 -4 | 8 ]

7. Divide the third row by -4 to get a leading 1:

[ 1 0 7/6 | 5/6 ]
[ 0 1 5/2 | 1 ]
[ 0 0 1 | -2 ]

8. Use the third row to eliminate the z terms in the first and second rows:

[ 1 0 0 | 4/3 ]
[ 0 1 0 | 6 ]
[ 0 0 1 | -2 ]

9. The system is now in reduced row echelon form, and we can easily solve for the variables:

x = 4/3
y = 6
z = -2

So the solution to the system of equations is (4/3, 6, -2).

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a) At the time the article was published, the federal minimum wage was $5.85 per hour.

b) According to the US Department of Labor website, the federal minimum wage in 2008 was $6.55 per hour.  

c) To earn the current federal minimum wage of $7.25 per hour, a person must pick up a penny in 4.97 seconds.

d) The phrase "penny dreadful" is a British expression referring to cheaply printed stories of sensational and sometimes gruesome content that were sold for a penny in the 19th century.

A) The minimum wage when Owen wrote his article can be calculated by using the equation:

Minimum wage = (Amount of money earned)/(Amount of time taken to earn it)

In this case, the amount of money earned is $0.01 (the value of a penny) and the amount of time taken to earn it is 6.15 seconds. Therefore:

Minimum wage = ($0.01)/(6.15 seconds) = $0.00162601626 per second

To convert this to an hourly wage, we can multiply by the number of seconds in an hour (3600):

Minimum wage = ($0.00162601626 per second) x (3600 seconds per hour) = $5.85365854 per hour

Minimum wage =  $5.85

B) According to the U.S. Department of Labor, the federal minimum wage in 2008 was $6.55 per hour.

Therefore, Owen's arithmetic was slightly off, as his calculated minimum wage is lower than the actual minimum wage at that time.

C) To calculate how much time you would need to spend picking up a penny in order to earn the current minimum wage, we can use the same equation as before, but rearrange it to solve for the amount of time:

Amount of time = (Amount of money earned)/(Minimum wage)

The current federal minimum wage is $7.25 per hour, or $0.00201388889 per second. Therefore:

Amount of time = ($0.01)/($0.00201388889 per second) = 4.97 seconds

So you would need to spend 4.97 seconds picking up a penny in order to earn the current minimum wage.

D) The phrase "penny dreadful" refers to a type of cheap, sensationalist fiction that was popular in the 19th century. These stories were typically published in weekly installments and sold for a penny each, hence the name "penny dreadful."

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a) maximum profit 20.5.

b) maximum profit 20,025.

c)  price 10.35

The given function, f(p)=-50p+2050p-20,700, is not a degree 3 polynomial. It is a degree 1 polynomial or a linear function. Therefore, the given conditions of degree 3 polynomial with integer coefficients and zeros 8i and 6/5 do not apply to this function.

Instead, we can use the given function to answer the questions about the company's monthly profit.

(a) To find the price that generates the maximum profit, we can use the formula for the vertex of a parabola, which is (-b/2a, f(-b/2a)). In this case, a = -50 and b = 2050.
The price that generates the maximum profit is -b/2a = -2050/(2*-50) = 20.5.

(b) To find the maximum profit, we can plug the price that generates the maximum profit into the function.
f(20.5) = -50(20.5) + 2050(20.5) - 20,700 = 20,025.

(c) To find the price(s) that would enable the company to break even, we can set the function equal to 0 and solve for p.
0 = -50p + 2050p - 20,700
20,700 = 2000p
p = 10.35

Therefore, the price that would enable the company to break even is 10.35. There is only one price that would enable the company to break even.

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The inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:

[0  -2  4/3]
[4/3  -1  -4/3]
[-4/3  4/3  2/3]

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. To find the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3], we need to use the following steps:

Step 1: Find the determinant of the matrix. The determinant of a 3x3 matrix is given by:

|A| = a(ei - fh) - b(di - fg) + c(dh - eg)

where a, b, c, d, e, f, g, h, and i are the elements of the matrix. Plugging in the values from the given matrix, we get:

|A| = (1)(2*3 - (-1)*3) - (-1)(-4*3 - 0*4) + (0)(-4*(-1) - 2*4)

|A| = (1)(6 + 3) - (-1)(-12) + (0)(4 - 8)

|A| = 9 - 12 + 0

|A| = -3

Step 2: Find the matrix of minors. The matrix of minors is found by taking the determinant of each 2x2 matrix that can be formed by removing one row and one column from the original matrix. The matrix of minors for the given matrix is:

[(-1)(3) - (-1)(3)  (0)(3) - (-1)(4)  (0)(3) - (-1)(-4)]
[(-4)(3) - (2)(3)   (1)(3) - (0)(4)   (1)(-4) - (0)(2) ]
[(-4)(-1) - (2)(0)  (1)(0) - (-1)(-4) (1)(2) - (-1)(-4)]

= [0  4  4]
 [-6 3 -4]
 [4 -4 -2]

Step 3: Find the matrix of cofactors. The matrix of cofactors is found by multiplying each element of the matrix of minors by -1 raised to the power of the sum of its row and column indices. The matrix of cofactors for the given matrix is:

[0  -4  4]
[6  3  -4]
[-4 4  -2]

Step 4: Find the adjugate matrix. The adjugate matrix is found by taking the transpose of the matrix of cofactors. The adjugate matrix for the given matrix is:

[0  6  -4]
[-4 3  4]
[4  -4  -2]

Step 5: Find the inverse matrix. The inverse matrix is found by dividing each element of the adjugate matrix by the determinant of the original matrix. The inverse matrix for the given matrix is:

[0/(-3)  6/(-3)  -4/(-3)]
[-4/(-3) 3/(-3)  4/(-3)]
[4/(-3)  -4/(-3)  -2/(-3)]

= [0  -2  4/3]
 [4/3  -1  -4/3]
 [-4/3  4/3  2/3]

Therefore, the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:

[0  -2  4/3]
[4/3  -1  -4/3]
[-4/3  4/3  2/3]

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After building 18 shelves and 24 tables, the carpenter will have 9 boxes of screws, 80 2x4s, and 39 sheets of plywood leftover.

To find the leftover materials, we need to calculate the total materials used to build 18 shelves and 24 tables, and then subtract that from the total materials the carpenter had on hand.

For 18 shelves, the carpenter used 18 boxes of screws, 36 2x4s, and 72 sheets of plywood. For 24 tables, the carpenter used 48 boxes of screws, 48 2x4s, and 72 sheets of plywood.

So, the carpenter used 66 boxes of screws, 84 2x4s, and 144 sheets of plywood in total.

Subtracting this from the materials on hand, we get 9 boxes of screws, 80 2x4s, and 39 sheets of plywood leftover.

Therefore, the carpenter can potentially use these leftover materials for future projects or sell them to recoup some of their costs.

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The functions involved in g(x) are multiply by 2 and subtract the value of 5.

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted on the line y = x. This graph's line traverses the origin and has a slope value of 1.

Given that, f(x) involves the following functions:

Divide by 2

Add 5

Also, g(x) is the inverse of the function of f(x) hence, the function involved are inverse of the original function.

Hence, the functions involved in g(x) are multiply by 2 and subtract the value of 5.

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The equation of the circle that has center (-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.

The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (-1,2) so h = -1 and k = 2. We can use the given point (-6,6) to find the radius of the circle.

The distance between the center and the given point is the radius of the circle, and we can use the distance formula to find it:
r = √((-6 - (-1))^2 + (6 - 2)^2)
r = √((-5)^2 + (4)^2)
r = √(25 + 16)
r = √41

So the equation of the circle is:
(x - (-1))^2 + (y - 2)^2 = (√41)^2
(x + 1)^2 + (y - 2)^2 = 41

Therefore, the equation of the circle that has center(-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.

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Answer: 3rd option

Step-by-step explanation:

5500        55

-------- = ----------  

   p          100

Answer:

To find the volume of the container in cubic centimeters, we multiply its length, width, and height:

Volume = 60 cm x 20 cm x 45 cm = 54,000 cubic centimeters

To convert cubic centimeters to liters, we divide by 1,000:

54,000 cubic centimeters ÷ 1,000 = 54 liters

Therefore, the container can hold 54 liters of water before it overflows.

Step-by-step explanation:

The effective annual IRR (internal rate of return) is 8%. If the dollars invested and withdrawn and the inflation rate for the 19-year time span of the investment is 9% per year the inflation-free IRR is -0.92%.

To calculate this, we need to use the IRR formula: IRR = [Sum of cash flows / (-initial investment)]1/n - 1, where n is the number of periods.

a. To find the effective annual IRR earned on this investment, we can use the following formula:

0 = -10,000/(1+IRR) - 10,000/(1+IRR)^2 - 10,000/(1+IRR)^3 - 10,000/(1+IRR)^4 + 10,000/(1+IRR)^5 + 10,000(1-0.05)/(1+IRR)^6       + 10,000(1-0.05)^2/(1+IRR)^7 + ... + 10,000(1-0.05)^14/(1+IRR)^18

The effective annual IRR earned on this investment to the nearest percent is 8%.

b. To find the inflation-free IRR earned on this investment, we can use the following formula:

Inflation-free IRR = (1 + IRR)/(1 + inflation rate) - 1

Plugging in the values we found in part (a), we get:

Inflation-free IRR = (1 + 0.08)/(1 + 0.09) - 1 = -0.0092

So the inflation-free IRR earned on this investment is approximately -0.92%.

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Answer:

80 and 2x + 9

Step-by-step explanation:

to evaluate g(f(1)) , evaluate f(1) then substitute the value obtained into g(x)

f(1) = 3(1) + 7 = 3 + 7 = 10 , then

g(10) = 10² - 2(10) = 100 - 20 = 80

------------------------------------------------------

to calculate (g ￮ f)(x) , substitute x = f(x) into g(x)

(g ￮ f)(x)

= g(f(x))

= g(x + 4)

= 2(x + 4) + 1

= 2x + 8 + 1

= 2x + 9

This is because the x-coordinate of a point on the graph of y = x^2 - x is given by the value of x that satisfies the equation. Similarly, the x-coordinate of a point on the graph of y = 20 is constant and equal to some value c.

To find the x-coordinates of the points where the graphs of the equations y = x^2 - x and y = 20 intersect, we need to solve the system of equations:

y = x^2 - x

y = 20

Since both equations are equal to y, we can set them equal to each other:

x^2 - x = 20

Now, if we solve for x, we will get the x-coordinates of the points where the two graphs intersect.

Hence, the x-coordinates of the points of intersection are the solutions of the equation x^2 - x = 20.

This is because the x-coordinate of a point on the graph of y = x^2 - x is given by the value of x that satisfies the equation. Similarly, the x-coordinate of a point on the graph of y = 20 is constant and equal to some value c.

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Answer:

5 compact discs on sale.

Step-by-step explanation:

To solve this you'll need to set up a system of equations. Let's use x or the original price and y for sale price. Here's what your equations will look like:

14.95x + 12.95y = 139.50

x + y = 10

Now, cancel out x so you can solve for y. You can choose either variable, but canceling out x gets you to your answer in less steps. Remember to multiply by a negative so you can cancel out the variable.

Here's what your work will look like:

14.95 + 12.95y = 139.50

-14.95 (x + y = 10)

Here's what your new equations will look like after distributing:

14.95x + 12.95y = 139.50

-14.95x - 14.95y = -149.5

Now, add these two equations together. When you do that, x cancels out and you can solve for y.

Here's what your new equation will look like after adding:

-2y = -10

Now, divide both sides by -2. After doing so, you should get y = 5. This means that you bought 5 compact discs on sale.

Hope this helps!

Answer: :)

Step-by-step explanation:

Let's start by setting up a proportion to represent the ratio of black tiles to white tiles:

1 black tile : 4 white tiles

We know that Eddie wants a total of 25 tiles in the design, so we can set up another proportion to represent the ratio of white tiles to the total number of tiles:

white tiles : 25 total tiles

To solve for the number of white tiles, we need to find the equivalent ratio of white tiles in terms of the total number of tiles. We can do this by cross-multiplying our two proportions:

1 black tile * (white tiles/4 black tiles) = white tiles/4

white tiles/25 total tiles = (white tiles/4) / (1 black tile + white tiles/4)

Simplifying this expression, we get:

white tiles/25 = (white tiles/4) / (5/4)

white tiles/25 = (1/4) * (white tiles/5)

5 * white tiles = 100

white tiles = 20

Therefore, Eddie will use 20 white tiles in his design.

The two possible solutions for the given triangle are:

Case 1: $B = 51.92°$, $C = 107.08°$, $c = 25.93$

Case 2: $B = 128.08°$, $C = 30.92°$, $c = 13.45$

Both solutions exist and are rounded to two decimal places.

The Law of Sines states that for any triangle ABC, the following equation holds:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Using this equation, we can solve for the missing angles and side lengths in the given triangle.

Case 1:
To find angle B, we can rearrange the equation to get:

$\sin B = \frac{b \sin A}{a}$

Plugging in the given values:

$\sin B = \frac{22 \sin 21°}{9.5}$

$\sin B = 0.789$

Taking the inverse sine of both sides:

$B = \sin^{-1}(0.789)$

$B = 51.92°$

To find angle C, we can use the fact that the sum of the angles in a triangle is 180°:

$C = 180° - A - B$

$C = 180° - 21° - 51.92°$

$C = 107.08°$

Finally, to find side c, we can use the Law of Sines again:

$\frac{c}{\sin C} = \frac{a}{\sin A}$

Rearranging and plugging in the given values:

$c = \frac{a \sin C}{\sin A}$

$c = \frac{9.5 \sin 107.08°}{\sin 21°}$

$c = 25.93$

So the solution for Case 1 is:

$B = 51.92°$, $C = 107.08°$, $c = 25.93$

Case 2:
In this case, we need to consider the possibility of an obtuse angle B. To find this angle, we can use the fact that the sine of an obtuse angle is the same as the sine of its supplement:

$\sin B = \sin (180° - B)$

So we can find the supplement of the angle we found in Case 1:

$B = 180° - 51.92°$

$B = 128.08°$

Plugging this value back into the Law of Sines equation, we can find the other missing values:

$C = 180° - A - B$

$C = 180° - 21° - 128.08°$

$C = 30.92°$

$c = \frac{a \sin C}{\sin A}$

$c = \frac{9.5 \sin 30.92°}{\sin 21°}$

$c = 13.45$

So the solution for Case 2 is:

$B = 128.08°$, $C = 30.92°$, $c = 13.45$

Therefore, the two possible solutions for the given triangle are:

Case 1: $B = 51.92°$, $C = 107.08°$, $c = 25.93$

Case 2: $B = 128.08°$, $C = 30.92°$, $c = 13.45$

Both solutions exist and are rounded to two decimal places.

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The cost of a cylindrical pole is $3462

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, a solid cylinder has a density of 6.1 g/cm³, the dimension is a diameter of 41.2 cm and a height of 710 cm, this metal can be purchased for $0.60 per kilogram.

we need to find the cost of the cylinder,

Finding the volume first,

Cylinder's volume = π × radius² × height

= 3.14 × 20.6² × 710

= 946,068 cm³

∵ density = mass / volume

mass = density × volume

= 6.1 × 946,068

= 5771014.8 grams

= 5771 kg

Now, the cost of the cylinder = 5771 × 0.60 = 3462

Hence, the cost of a cylindrical pole is $3462

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