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The inverse function is [tex]f^{-1} (g) = 10 - g[/tex]

Composition function is a type of function that is formed by combining two or more functions, where the output of one function becomes the input of another function. Composition function shown by the symbol "∘".

The composition function is a mathematical operation that combines two functions to produce a new function. Specifically, given two functions f and g, the composition function (also called function composition) creates a new function h(x) = f(g(x)) that applies the function g to an input x, and then applies the function f to the output of g(x).
We can start by finding the inverse function of f(g), which is [tex]f^{-1} (g)[/tex]. To do so, we need to solve the equation:

[tex]f(g) = x = 10 - g[/tex]

for g, in terms of x:

x = 10 - g

g = 10 - x

This gives us the inverse function:

[tex]f^{-1} (x) = 10 - x[/tex]

Now we can find f^-1(g) by replacing x with g in the above equation:

[tex]f^{-1} (g) = 10 - g[/tex]

Therefore, the function [tex]f^{-1} (g)[/tex] is given by:

[tex]f^{-1} (g) = 10 - g[/tex]

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Complete question is: f:g → 10 - g. Find f-1: g.

The other prime factor is even, the number is 30, and its prime factors are 2, 3, and 5.

To find the third prime factor and ultimately the number, we can use the fact that any integer greater than 1 can be expressed as a unique product of prime factors. We know that the number has three prime factors, and two of them are 3 and 5. So, we need to find the third prime factor.

Since the other prime factor is even, it must be 2 (the only even prime number). Therefore, the number can be calculated as:

Number = 3 x 5 x 2 = 30

So, the number is 30, and its prime factors are 2, 3, and 5.

Prime factors are the prime numbers that divide a given number exactly without leaving any remainder. For example, the prime factors of 12 are 2, 2, and 3, because 2 x 2 x 3 = 12 and these are the only prime numbers that divide 12 exactly. To factorize a number into its prime factors, we can use a method called prime factorization. We start by dividing the number by the smallest prime number that divides it exactly. We keep dividing the quotient by the smallest prime number that divides it exactly until we obtain only prime numbers. The prime factors are then the product of these prime numbers

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The equation to represent the number of guests at your party is 150 + 6x = 282 where, the number of guests at the party, x is 22.

Let

Cost of renting a roller rink = $150

Cost per person = $6

Total charge of the party = $282

Number of persons at the birthday party = x

The equation:

150 + 6x = 282

subtract 150 from both sides

6x = 282 - 150

6x = 132

divide both sides by 6

x = 132/6

x = 22

Therefore, there are 22 guests at the birthday party.

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7x ≤ 1, or x ≤ 1/7

(a) The probability that Thomas is selected for the position given that the company’s revenue did not improve is 4 out of 7.
(b) The probability that the company’s revenue will generally improve is the sum of the probabilities that Rachel, Sam and Thomas are hired multiplied by the probability that the company’s revenue will improve given that each individual is hired. This probability is given by (1/7)*(4/5) + (2/7)*(1/2) + (4/7)*(3/10) = 0.5.
(c) For the probabilities given for the second hiring process to be valid, the inequality x + 2x + 4x ≤ 1 must be satisfied. This inequality can be written as 7x ≤ 1, or x ≤ 1/7.

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The angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.

The 16-notch socket has a cylindrical shape with 16 notches or recesses machined into the interior of the socket. Each notch corresponds to a flat side of a 16-sided nut or bolt head. The notches are evenly spaced around the socket, providing a secure grip on the nut or bolt head and allowing for easy application of torque using a ratchet or wrench.

16-notch sockets are commonly used in automotive and industrial applications, particularly in heavy machinery where large bolts and nuts with 16-sided heads are often used. They are available in a range of sizes to fit different nut and bolt sizes and are typically made of durable materials such as chrome vanadium steel or high-grade aluminum.

Premise 1: Deondra is designing a 16-notch socket wrench.

Premise 2: The notches will be the same size.

Conclusion: Therefore, Deondra needs to know the angle measure for each notch.

To determine the angle measure for each notch, we can use the formula for the interior angle of a regular polygon, which is:

Interior angle = (n-2) x 180 / n

where n is the number of sides (or notches) in the polygon.

Applying this formula to a 16-sided polygon (or hexadecagon), we get:

Interior angle = (16-2) x 180 / 16

Interior angle = 1680 / 16

Interior angle = 105 degrees

Therefore, the angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.

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Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

[tex]Z=\frac{x-u}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s=\frac{\sigma}{\sqrt n}[/tex]

u=8.4, sigma=1.8 n=32 s=0.3182

The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:

Z=1.57

Z = 1.57 has a p-value of 0.9418.

1 - 0.9418 = 0.0582.

0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.

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Answer:

g/7

Step-by-step explanation:

Answer:G/7

Step-by-step explanation:G/7

Answer:

75%

Step-by-step explanation:

write it as a fraction first, so 15/20.

make the bottom number 100 to get the mark out of 100.

to do this, multiply the bottom by 5 (20x5=100) and then do the same to the top.

you get 75/100. this equals 75%

Answer:

75%

Step-by-step explanation:

In this question, 20 is the highest score you can get on the test so 20 is 100%. We will now want to divide 100 by 20.

100 ÷ 20 = 5

Each score Amore got on the test was worth 5% of the test.

We know he scored 15 on the text, so now we want to multiply 15 with 5.

15 × 5 = 75

Amore scored 75% on his test.

Answer:

Each of the diagonals is 16

Step-by-step explanation:

The diagonals of a rectangular are equal

The two diagonals are QS and RT

QS = RT

→ 30 - 2x = 9 + x

Subtract 30 both sides:
30 - 30 - 2x = 9  -  30 + x

- 2x  = -21  + x

Subtract x both sides
-2x - x = -21 + x  -  x

-3x = -21

x = -21/-3 = 7

So the diagonal RT = 9 + 7 =16

should be the same as diagonal QS
Qs = 30 - 2(7) = 30 - 14 = 16

Total pay = Regular pay + Overtime pay = $280 + $616 = $896. Therefore, if Lisa works 42 hours in one week, she would be paid $896

The first step is to calculate Lisa's regular pay for the week. We know that her regular hourly rate is $8 per hour. If she works 35 hours or less in a week, then her pay is simply her hourly rate times the number of hours worked. Therefore, her regular pay for a week where she works 35 hours or less would be:

Regular pay = $8/hour * 35 hours = $280

However, we know that Lisa worked 42 hours in one week, which is more than 35 hours. This means she also worked 7 overtime hours. According to the problem, Lisa is paid 11 times her regular salary for any overtime hours worked. This means her overtime pay for the 7 overtime hours would be:

Overtime pay = $8/hour * 11 * 7 hours = $616

To get Lisa's total pay for the week, we simply add her regular pay and overtime pay together:

Total pay = Regular pay + Overtime pay = $280 + $616 = $896

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The surface area of the triangular prism is 156.5 inches².

The surface area of a triangular prism can be found as follows:

Therefore, the prism is a triangular prism. The prism has two triangular base with side length 5 inches each. The height of the triangular bases are 4.3 inches each.

The height of the triangular prism is 9 inches. The surface area of the triangular prism is the sum of the whole individual area of each surface of the prism.

Hence,

surface area of the prism = bh + l(s₁ + s₂ + s₃)

Therefore,

surface area of the prism = 4.3 × 5 + 9(5 + 5 + 5)

surface area of the prism = 21.5 + 9(15)

surface area of the prism = 21.5 + 135

surface area of the prism = 156.5 inches²

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The perimeter of the polygon with sides of lengths 18.6, 18.9, and 6.9 is 44.4 units.

What is the perimeter?

The perimeter of a polygon is the total distance around its boundary, which is equal to the sum of the lengths of all its sides. To find the perimeter of a polygon, you simply add up the lengths of all its sides.

The perimeter of any polygon is the sum of the lengths of its sides. In this case, we have three sides of lengths 18.6, 18.9, and 6.9.

To find the perimeter, we simply add these lengths together:

Perimeter = 18.6 + 18.9 + 6.9

Perimeter = 44.4

Therefore, the perimeter of the polygon with sides of lengths 18.6, 18.9, and 6.9 is 44.4 units.

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A is 0.8218

A is 0.6905.

(a) The probability that the student is a woman.The number of women in the class is 31 while the total number of students is 42. The probability of a randomly selected student being a woman is given as:P(woman) = (Number of women in the class) / (Total number of students in the class)P(woman) = 31 / 42P(woman) = 0.7381(b) The probability that the student received an A.The number of men and women that received an A is given as follows:Men that received an A = 6Women that received an A = 7The total number of students that received an A is:Total number of students that received an A = (Number of men that received an A) + (Number of women that received an A)Total number of students that received an A = 6 + 7Total number of students that received an A = 13The probability of a randomly selected student receiving an A is given as:P(A) = (Number of students that received an A) / (Total number of students in the class)P(A) = 13 / 42P(A) = 0.3095(c) The probability that the student is a woman or received an A.The probability of the student being a woman or received an A is given as:P(woman or A) = P(woman) + P(A) - P(woman and A)From parts (a) and (b), we know that:P(woman) = 0.7381P(A) = 0.3095Now, we have to determine the probability that the student is a woman and received an A.The number of women that received an A = 7 while the total number of women in the class is 31.The probability of a woman receiving an A is given as:P(woman and A) = (Number of women that received an A) / (Total number of women in the class)P(woman and A) = 7 / 31P(woman and A) = 0.2258Therefore:P(woman or A) = P(woman) + P(A) - P(woman and A)P(woman or A) = 0.7381 + 0.3095 - 0.2258P(woman or A) = 0.8218(d) The probability that the student did not receive an A.The probability that the student did not receive an A is given as:P(not A) = 1 - P(A)From part (b), we know that:P(A) = 0.3095Therefore:P(not A) = 1 - P(A)P(not A) = 1 - 0.3095P(not A) = 0.6905Therefore, the answers are given as follows:(a) The probability that the student is a woman is 0.7381.(b) The probability that the student received an A is 0.3095.(c) The probability that the student is a woman or received an A is 0.8218.(d) The probability that the student did not receive an A is 0.6905.

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The equation of the parabola with focus (4,5) and directrix y=-1 is

[tex](y-5)^2=4(x-4) or (y+1)^2=4(x-4).[/tex]

The equation of a parabola is defined by its focus and directrix. The focus is the point on the parabola that is used to determine its shape, while the directrix is the line used to determine its orientation. The equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex]. This equation can be expressed in terms of the focus and directrix by substituting the x and y values of the focus and directrix into the equation. Substituting the x value of the focus (4) into the equation gives us[tex](y-5)^2=4(4-4)[/tex], which simplifies to[tex](y-5)^2=0[/tex]. This equation can be rearranged to give us y=5, which is the y value of the focus. Substituting the y value of the directrix (-1) into the equation gives us [tex](y+1)^2=4(x-4)[/tex]. This equation can also be rearranged to give us y=-1, which is the y value of the directrix. Therefore, the equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex] or[tex](y+1)^2=4(x-4)[/tex].

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Part A: The proportion of Iron Bank customers who invest in neither stocks nor futures is 27%.

Part B: Of the Iron Bank customers who invest in futures, 61.54% also invest in stocks.

Part C: The probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%.

Part A:  This can be calculated by subtracting the combined proportion of those who invest in stocks (36%) and those who invest in futures (22%) from 100%.

Part B: This can be calculated by dividing the proportion of those who invest in both stocks and futures (15%) by the proportion of those who invest in futures (22%).

Part C: This can be calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).

Given, that 36% of the customers are investing in stocks and 15% of those customers are also investing in futures.

So, 21% of the customers invest in stocks and not futures, while 79% of the customers either invest in futures, or in neither stocks nor futures.

Therefore, the probability is 21/100, or 18.18%.

In conclusion, the probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%. This is calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).

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The third column of the inverse of the matrix, A = [tex]\begin{bmatrix}-2 & -5 & -13 \\4 &5 &11 \\1 &2 &6 \\\end{bmatrix}[/tex], obtained using the product of A and the third column of A⁻¹ is; [tex]\begin{bmatrix} 1 \\ -3\\ 1 \\\end{bmatrix}[/tex]

The product of a matrix and the inverse of the matrix is the multiplicative identity.

The specified matrix can be presented as follows;

A = [tex]\begin{bmatrix}-2 & -5 & -13 \\4 & 5 & 11 \\1 &2 & 6 \\\end{bmatrix}[/tex]

The third columns of the inverse of the matrix, A, A⁻¹, can be obtained without computing the other two columns, as follows;

The inverse of the matrix A, A⁻¹ is the solution of the following matrix equation;

Ax = [tex]e_i[/tex]

Where;

[tex]e_i[/tex] = The column i of the identity matrix

x = The third column of the inverse matrix

Therefore, for the third column, we get;

[tex]e_i[/tex] = [tex]e_3[/tex] = [tex]\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}[/tex]

Ax = [tex]e_3[/tex] = [tex]\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}[/tex]

Therefore;

x = [tex]e_i[/tex]/X, which using a graphing calculator, indicates;

[tex]x = \frac{\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}}{\begin{bmatrix}-2 & -5 & -13 \\4 & 5 & 11 \\1 &2 & 6 \\\end{bmatrix}} = \begin{bmatrix}1 \\ -3\\1\\\end{bmatrix}[/tex]

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The missing y value in the table can be found to be 19. 5.

To find the missing value, you need to find the relationship that x and y have with each other on the table.

We find that when 4 increases to 11, 2. 5 as y, increases to 9. 5. The difference in both is:

= 11 - 4                                                 = 9. 5  - 2.5

= 7                                                        = 7

We see this common difference again with 15 and 11 being 4 and the difference between the y - values of 13. 5 and 9. 5 being 4 as well.

The y value corresponding to 21 as x would be:

= ( 21 - 15 ) + 13. 5

= 19. 5

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The answer of the given question based of a suggestive survey the answer is  "What do you like and don’t like about the CEO?"

The CEO or Chief Executive Officer is  highest-ranking executive in  company who is responsible for making major corporate decisions, managing  overall operations, and leading  organization towards achieving its goals and the objectives. The CEO reports to board of directors and is responsible for success or failure of company.

The suggestive survey question is: "What do you like and don’t like about the CEO?"

This question is suggestive because it implies that the respondent should have opinions about the CEO, and it encourages the respondent to share both positive and negative opinions. This can bias the responses towards certain answers, rather than allowing the respondent to express their own thoughts freely.

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Answer:

[tex]\large\boxed{ \sf Area = 25\ ft .^2}[/tex]

Step-by-step explanation:

We need to find out the area of the triangle which has a base of 12.5ft and s height of 4ft.

We know that the formula for calculating the area of the triangle is ,

[tex]\sf:\implies \pink{Area_{\triangle}=\dfrac{1}{2}\times (b)\times (h)}\\[/tex]

where,

F I G U R E : -

[tex] \setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){$\large\bf 4\ ft $}\put(2.8,.3){$\large\bf 12.5\ ft$}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\end{picture}[/tex]

Now on substituting the respective values, we have;

[tex]\sf:\implies Area = \dfrac{1}{2}\times (12.5) \times (4) \ ft.^2 \\[/tex]

Simplify,

[tex]\sf:\implies \underline{\underline{\boxed{\sf Area = \frak{25\ ft.^2} }}} \\[/tex]

Hence the area of the triangle is 25ft.²

Let's first find the total cost of transportation and admission tickets:

$200 (transportation) + $6.50 (admission ticket) x n (number of students) = $750

$6.50n = $550

n = 84.62

So, the maximum number of students that can go to the game is 84.62. However, we cannot have a fractional number of students, so we can round down to 84 students.

Now, let's find the cost of the meal for each student:

$2.50 (medium sandwich) + $2.00 (drink) + $1.50 (popcorn) = $6.00

If the booster club pays for a large sandwich, drink, and popcorn for each student, the cost will be:

$3.00 (large sandwich) + $2.50 (drink) + $2.00 (popcorn) = $7.50

The difference in cost between the two options is $1.50 per student.

To find how many more students can go to the game with the cheaper meal option, we can divide the total amount of money available ($750) by the difference in cost per student ($1.50):

$750 ÷ $1.50 = 500

So, with the cheaper meal option, the booster club can take 500/6 students = 83 students.

Therefore, the booster club can take 1 more student to the game if they pay for a medium sandwich, drink, and popcorn for each student.

The volume of the part of the cone that is filled with sand is 2/9 times the total volume of the cone.

To do this, we need to first determine the total volume of the cone. The formula for the volume of a cone is:

V = 1/3 x π x r² x h

Where V is the volume, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant (approximately equal to 3.14).

Since we know that the paper cup is cone-shaped, we can assume that it has a circular base. Let's say that the radius of the base of the cone is r and the height of the cone is h.

The total volume of the cone can be calculated using the formula above:

V = 1/3 x π x r² x h

Now we need to determine the volume of the part of the cone that is filled with sand. We know that the cup is 2/3 full of sand, so the volume of sand in the cup is 2/3 of the total volume of the cup. We can express this as:

V = 2/3 x V

We can substitute the formula for V into this equation to get:

V  = 2/3 x (1/3 x π x r² x h)

Simplifying this equation, we get:

V = 2/9 x π x r² x h

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The line of best fit for the given points is y = -1.35x + 9.62, where x is the independent variable and y is the dependent variable. This line represents the linear relationship between the two variables that best fits the given data.

To find the line of best fit for the given points, we can use linear regression. Using a calculator or statistical software, we obtain the following results:

Slope (m) = -1.35

Y-intercept (b) = 9.62

Therefore, the equation of the line of best fit is:

y = -1.35x + 9.62

Rounding to two decimal places, we get:

y = -1.35x + 9.62

The line of best fit for the given points is y = -1.35x + 9.62, which represents the linear relationship between the variables.

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The simple interest she will have to pay equals R 1275, and the total she will pay equals R 9775 for her TV over the past 3 years.

Thuli wants to buy TV, and a bank offers to loan her the money at an interest rate.

Principal, P = R 8,500

Interest Rate, R = 5%

Time, t = 3 year

Simple interest is defined as an interest charge that borrowers pay their lenders for a loan. It is calculated using the principal only. Formula for SI is written as SI = (P×T×R)/100

Here, SI = Simple interest

P = Principal (sum of money borrowed)

R = Rate of interest p.a

T = Time (in years)

We have to calculate simpled interest she will have to pay also calculate the total she will pay.

So, Simple interest = (8500×3×5)/100

= 85× 15 = R 1275

Now, total she will have to pay = Principle + SI

= 8500 + 1275

= R 9775

Hence, required total she will pay is R9775.

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Answer:

the answer is 7,21

Step-by-step explanation:

a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is 0.095.

b. The probability that at most 23 of them live in cities with population greater than 100,000 people is 0.0332.

c. The probability that at least 22 of them live in cities with population greater than 100,000 people is 0.9876.

d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is 0.8782.

Let X be the number of Americans out of 34 who live in cities with population greater than 100,000 people.

Then X follows a binomial distribution with n = 34 and p = 0.6.

a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is:

P(X = 23) = (34C₂₃) x (0.6)²³ x (0.4)¹¹ = 0.095

b. The probability that at most 23 of them live in cities with population greater than 100,000 people is:

P(X <= 23) = P(X = 0) + P(X = 1) + ... + P(X = 23)

= ∑(34Ci) x (0.6)^i x (0.4)^(34-i), i = 0 to 23

= 0.0332

c. The probability that at least 22 of them live in cities with population greater than 100,000 people is:

P(X >= 22) = 1 - P(X < 22) = 1 - P(X <= 21)

= 1 - ∑(34Ci) * (0.6)^i x (0.4)^(34-i), i = 0 to 21

= 0.9876

d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is:

P(18 <= X <= 24) = P(X <= 24) - P(X < 18)

= ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 24

- ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 17

= 0.8782

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Radius is the distance in a straight line from the centre of the circle to its circumference. The diameter is twice the radius. Therefore,  radius and diameter of the circle are 7 and 14 yards respectively.

The above figure is a circle. The area of the circle is given as 49π yard squared. The question want us to find the radius and diameter of the circle.

Hence,

area of a circle = πr²

where

Therefore,

area of the circle = 49π

Hence,

49π = π × r²

divide both sides by π

r² = 49

square root both sides

r = √49

r = 7 yards

The diameter of a circle is twice the radius.

Hence,

diameter of the circle = 7 × 2 = 14 yards

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:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3

Answer:Given, csc θ = 3 and θ lies in [0, π/2]We need to find the values of the remaining 5 trigonometric functions.Here is how we can find them:We know that csc θ = 3. csc θ = 1/sin θ. Hence, we can say sin θ = 1/csc θ = 1/3.In the first quadrant, sin θ is positive (All are positive except tan θ and cot θ). Hence, sin θ = 1/3, and cos θ = √(1 - sin²θ) = √(1 - 1/9) = √8/3 = (2/3)√2.The remaining trigonometric functions are:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3

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Answer:

the answer is 18

Step-by-step explanation:

volume of triangular prism =l×w×h

9×2×1=18