15 POINTS! PLEASE HELP!

To measure the distance across a wide river surveyors use a technique of measuring angles to a fixed point on the other side of the river. In the diagram below, a survey starts a point A and find m

15 POINTS! PLEASE HELP!To Measure The Distance Across A Wide River Surveyors Use A Technique Of Measuring

Answers

Answer 1

Answer:

DC = 1332.95 feet

Step-by-step explanation:

From the figure attached,

Let the measure of DC = h ft

And measure of side BC = a ft

By applying tangent ratio in ΔBCD,

tan(56°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

             = [tex]\frac{DC}{BC}[/tex]

             = [tex]\frac{h}{a}[/tex]

h = a[tan(56°)] --------(1)

By applying tangent rule in ΔACD,

tan(22°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

tan(22°) = [tex]\frac{DC}{BC+AC}[/tex]

             = [tex]\frac{h}{a+2400}[/tex]

h = (a + 2400)tan(22°) ------- (2)

Equating the values of h from equations (1) and (2),

a[tan(56°)] = (a + 2400)tan(22°)

a[tan(56°) - tan(22°)] = 2400[tan(22°)]

1.0785a = 968.6629

a = 899.085 ft

From equation (1),

h = 899.085[tan(56°)]

h = 1332.948

h ≈  1332.95 ft


Related Questions

A radius is
the diameter

Answers

Answer:

Radius is the diameter divided by 2

Which is the correct equation for x:y=8:1

See picture attached.

Answers

Answer:

Step-by-step explanation:

Means of means = means of extremes 8y = x

x = 8y

Option B is the correct answer

What does the C equal to in -1/6 +7/6 = c

Answers

Answer:

c = 1

Step-by-step explanation:

we have -1/6 + 7/6

since 6 is a common denominator we can do

[tex]\frac{-1}{6} +\frac{7}{6} = c\\\frac{-1+7}{6} = c\\\frac{6}{6} = c\\1 = c\\c = 1[/tex]

The diameter of a circle is 6 kilometers. What is the area?

d=6 km

Give the exact answer in simplest form.

_____ square kilometers

Answers

Answer:

28.26

Step-by-step explanation:

6 divided by 2 = 3^2 = 9 x 3.14 = 28.26

A drawbridge has the shape of an isosceles trapezoid. The entire length of the bridge is 100 feet while the height is 25 feet. If the angle at which the bridge meets the land is approximately 60 degrees, how long is the part of the bridge that opens?

Answers

Answer:

The part of the bridge that opens is 50 ft.

Step-by-step explanation:

The given parameters of the drawbridge are;

The entire length of the bridge = 100 feet

The height of the isosceles trapezoid formed = 25 feet

The angle at which the drawbridge meets the land ≈ 60°

Therefore, the part of the bridge that opens = The top narrow parallel side of the isosceles trapezoid

The length of each half of the bridge = (The entire length)/2 = 100 ft./2 = 50 ft.

Let 'x' represent the path of the waterway still partly blocked by each half of the bridge inclined

∴ x = 50 × cos(60°) = 25

x = 25 ft.

The path covered by both sides of the drawbridge = 2·x = 2 × 25 ft. = 50 ft.

The part of the bridge that opens = The entire length - 2·x

∴ The part of the bridge that opens = 100 ft. - 50 ft. = 50 ft.

The part of the bridge that opens = 50 ft.

A car drove 5 miles in 30 minutes. How far will the car go in 1 hour? ​

Answers

Answer: 10 miles

Step-by-step explanation:

Practically, just look at it.  30 minutes = 5 miles, 60 minutes = 10 miles

Mathmatically, find the constant of proportionality.

30 minutes divided by 5 miles = 6 minutes per 1 mile. 60 minutes = 10 miles

I really need help!!!!!!​

Answers

Answer:

y = 1.50x + 4 ;

Step-by-step explanation:

Given that bike rental cost $4 plus $1.50 per hour

From the information given, the change in y per unit change in x is the value of the slope ;

Therefore, Given that total cost = y and x) number of hours

Change in cost per change in number of hours) 1.50 = slope ; intercept = constant = $4

The equation, in slope intercept form :

y = mx + c

y = 1.50x + 4

The perimeter of a piece of paper is 38 inches. Its length is 11 inches.

Find the area of the piece of paper.

Answers

Answer:

Buddy this might not be the correct answer but I got either 98 or 418 inches. Don't quote me on it though.

Step-by-step explanation:

Somebody know this? thanks

Answers

Answer:

4 right angles

Step-by-step explanation:

a straight light intersects  another straight line= creating 4 right angles

Two ordinary dice are thrown simultaneously. Determine the n
of throws necessary to obtain at least once with probability 0.49.
at least once the pair (6;6)

Answers

Two ordinary dice are thrown simultaneously. Determine the number of throws necessary to obtain at least once with probability 0.49 at least once the pair (6,6).

Solution: The probability of getting a pair of 6s in a single throw is 1/36.The probability of not getting a pair of 6s in a single throw is 1 - 1/36 = 35/36.

The probability of not getting a pair of 6s in n throws is (35/36)^n.

The probability of getting a pair of 6s in n throws is 1 - (35/36)^n.

So, for at least one pair of 6s with probability 0.49 in n throws, we have:

1 - (35/36)^n = 0.49⇒ (35/36)^n = 0.51⇒ n ln (35/36) = ln 0.51⇒ n = ln 0.51/ln (35/36) = 72.5 ~ 73So, at least 73 throws are necessary to obtain at least once with probability 0.49 at least once the pair (6,6).

Answer: At least 73 throws are necessary to obtain at least once with probability 0.49 at least once the pair (6,6).

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Just give me some ideas for this please.
Using what you know about fair and unfair games, as well as expected value, design a game that will be fair to both you and the player. Be creative in your design, trying not to mimic anything that you have already seen in this course or in searching the internet. Include a thorough description as well as a visual representation of the game that includes evidence of fairness.

Answers

Answer:

For game ideas, try to make a game that everyone will want to play. Make it fun, challenging, but still beatable, but not too easy. One thing you could do is a trivia game! With lots of different subjects so people can choose what they get questions about. Also, do a lot of research to get the questions! Hope this helped :)

Step-by-step explanation:

Answer:

KING OF QUESTIONS!!!

Step-by-step explanation:

Each player starts out with 10 tokens ( tokens can be anything I recommend spare change or coins. ) the tokens will be used as point tallies at the end of the game.  But to determine who goes first the question master asks a question from the starting deck( The easiest questions) and starting with player one the players answer and whoever answers with the correct answer will go first, the other players will form an orderly line from closest to the correct answer to farthest. ( If there are more than 1 successful answers you pull another card from the next deck. This is an increase in difficulty. And it will keep increasing until there is one person with the correct or closest answer or until they reach the end of the final deck. Remember that this event is highly unlikely) After this is done the game begins.  The question master asks a question the players will answer. The players that get it correct will receive 2 token. The players that do not but are close get 1 and the player to get the farthest from the correct answer loses 1 token. ( Tokens are worth 1 point.)

Roles:

Player 1 ( Answers the questions.)

Player 2 ( Answers the questions.)

Player 3 ( Answers the questions.)

Player 4 ( Answers the questions.)

Question Master & Token Master ( Asks the questions and gives the token to the correct answer. )

How to Win:

Quick Match- Play until a player reaches 30 tokens.

Long Match- Play until all but one player is eliminated.

Ways to Lose-  If a player loses all of there tokens or is cheating they are eliminated, this happens only when the player is caught cheating or stealing tokens from other players or when the player loses all of these tokens due to incorrect answers.

what is the inverses operation needed to solve for P?
800=p-275
A subtraction
B addition
C multiplication
D division ill mark brainlist

Answers

Addition is needed because of the subtraction sign.

Rationalise √2+√3/3√2-2√3=a-b√6

Answers

Answer: 3√6-6/6 + √2=a-b√6

Step-by-step explanation: multiply radicals in the denominator by conjugate to get (a+b)(a-b)=a^2-B^2 pattern.

the circumference of a circle is 64π. what is the radius of the circle?

Answers

The radius of the circle can be found by dividing the circumference by 2π. In this case, the radius is 32.

The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 64π.

To find the radius, we can rearrange the formula as r = C / (2π). Substituting the given value of the circumference, we have r = 64π / (2π) = 32.

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Use The Figure Below to Solve For x.

Answers

Answer:

x=-1

Step-by-step explanation:

Hello there!

The information we are given:

We are told that the distance from point a to c is x + 10

We are told that the distance from a to b is 5

we are also told that the distance from b to c is 2x+6

Because from point A to B and B to C is inside the total of A to C we can add the two together and create a equation to solve for x

so the sum of the two parts 5 + 2x + 6

*combine like terms*

11 + 2x

is equal to the total distance (x+10)

now we solve for x

11 + 2x = x + 10

step 1 subtract x from each side by

2x - x =  x

x -x cancels out

now we have 11 + x = 10

step 2 subtract 11 from each side

11-11 cancels out

10 - 11 = -1

we're left with x = -1

Now lets plug in x and see if A to C is equal to A to B + B to C

(-1) + 10 = 5 + 2(-1) + 6

10 - 1= 9

2*-1=-2

6-2=4

4+5=9

9=9

which is true so we can conclude that x = -1




1. Find the solution to the recurrence relation an = 3an-1 + 4an-2 with initial values ao = 2 and a₁ = 3.

Answers

The solution to the recurrence relation an = 3an-1 + 4an-2 with initial values ao = 2 and a₁ = 3 is given byan = (-1)4ⁿ - 4(4)ⁿ-¹/16

Given recurrence relation is an = 3an-1 + 4an-2, with initial values ao = 2 and a₁ = 3.

The characteristic equation of the recurrence relation is given byr² - 3r - 4 = 0

Solving the characteristic equation, we get

r² - 4r + r - 4 = 0

r(r - 4) + 1(r - 4) = 0

(r - 4)(r + 1) = 0

r1 = 4, r2 = -1

So, the general solution of the recurrence relation is given by

an = Ar¹ + Br²

For r1 = 4, a4 = 3

a3 + 4a2a4 = 3a3 + 4a2 = 3(4a2 + 4a1) + 4a2= 16a2 + 12a1 ....(1)

For r2 = -1, aₙ₊₁ = 3an + 4an-1aₙ₊₁ = 3an + 4an-1 = 3(A(-1)^n + B(4)^n) + 4(A(-1)^(n-1) + B(4)^(n-1))= 3A(-1)^n - 4A(-1)^(n-1) + 12B(4)^n + 4B(4)^(n-1)= A(-1)^n + 4B(4)^n ....(2)

Putting n = 0 in (2), we get

a1 = A - 4A = -3A = 3 => A = -1

Substituting A = -1 in (1), we get

a4 = 16a2 + 12a1=> a4 = 16a2 + 12(2) => a4 = 16a2 + 24a4 = 16a2 + 24 => a2 = (a4 - 24)/16

Thus the solution to the recurrence relation an = 3an-1 + 4an-2 with initial values ao = 2 and a₁ = 3 is given by

an = (-1)4ⁿ - 4(4)ⁿ-¹/16

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Jenica bowls three games and scores an average of 116 points per game. She scores 105 on her first game and 128 on her second game. What does she need to score on her third game to get a mean score of ?

Answers

Answer:

230

Step-by-step explanation:230

I dont know how to do this​

Answers

Answer:

a) 55°

b) 125°

c) 55°

d) 55°

Step-by-step explanation:

a) 180-(90+35) = 55

b) this angle forms a straight angle with ∡a

c) this angle is vertical, and congruent, with ∡a

d) 180-(70+55) = 55

Draw a two-dimensional representation of each prism. Then find the area of the entire surface of each prism

Answers

Answer:

Surface area of cuboid = 78 unit²

Step-by-step explanation:

Given diagram is a cuboid prism

Given:

Length of cuboid = 5 unit

Width of cuboid = 3 unit

Height of cuboid = 3 unit

Find:

Surface area of cuboid

Computation:

Surface area of cuboid = 2[lb + bh + hl]

Surface area of cuboid = 2[(5)(3) + (3)(3) + (3)(5)]

Surface area of cuboid = 2[15 + 9 + 15]

Surface area of cuboid = 2[39]

Surface area of cuboid = 78 unit²

Find the distance between the points (–7,–9) and (–2,4).

Answers

Answer:

√194 or 13.9

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√[-2 - (-7)² + [4 - (-9)]

√(5)² + (13)²

√25 + 169

√194

= 13.9

What is the perimeter of thjs

Answers

Answer:73 ft

Step-by-step explanation:

Answer:

(120 + 12.5pi) ft^2

Step-by-step explanation:

10ft x 12 ft = 120ft^2

10ft/2 = 5 ft (Radius)

Area of semi circle:

[tex]\frac{\pi r^{2} }{2} = \frac{\pi 5^{2} }{2} = 12.5\pi ft^{2}[/tex]

Area = (120 + 12.5pi) ft^2

Which expression represents the length of the spring after Gerard removes some weight? Gerard adds weight to the end of the hanging spring D-- The song stretches to a length of p centimeters. Gerard removes some weight and the song moves up by a 8 E-p) - 9 D-9--​

Answers

Answer: p+(-q)

Step-by-step explanation:

Helppppp it’s due today

Answers

C I’m pretty sure. Sorry if wrong but I did the work.

approximately what interest rate to the nearest whole percentage would you need to earn in order to turn $3,500 into $7,000 over 10 years?
a. 5%
b. 7%
c. 9%
d. 10%

Answers

The approximate interest rate needed to turn $3,500 into $7,000 over 10 years is 9%. Correct answer is C.

The value of money increases over time with the help of compounding interest. If one puts in a principal amount in an account, the amount will increase over time as interest accrues. Let's use the future value formula for the calculation. Let’s assume that the interest rate needed to turn $3,500 into $7,000 over 10 years is x percent. P = $3,500 (principal)FV = $7,000 (future value)

N = 10 years (duration of the investment)Using the future value formula:

FV = P(1 + r/n)^(nt)where, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the duration of the investment in years.

Substituting the given values, we have: $7,000 = $3,500(1 + x/n)^(n × 10)We can solve for x by approximating the interest rate using each of the answer options given in the question until we find an answer that is close to $7,000. A calculator can also be used to calculate the compound interest for each option. If the interest rate is 7%, then the interest is compounded annually. Therefore, n = 1$7,000

= $3,500(1 + 0.07/1)^(1 × 10) If the interest rate is 10%, then the interest is compounded annually.

Therefore, n = 1$7,000 = $3,500(1 + 0.1/1)^(1 × 10)Thus, x ≈ 9.57%, greater than the required amount.

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Characterization of Random Processes in Time Domain Let Y(t) = 2X(t) + sin(2t) where X(t) is a wide-sense stationary (WSS) random process with mean à = E[X(t)] = 0 and autocorrelation Rx (T) = E[X(t + 7)X(t)] = e¯|7|. (a) (5) Find the mean ÿ(t) = E[Y(t)] and the autocorrelation Ry(t +7,t) = E[Y(t + 7)Y(t)] of Y (t). (2) Is Y (t) wide-sense stationary? Why? (b) (5)Find the crosscorrelation Rxy(t+7,t) = E[X(t+7)Y(t)]. (2) Are X and Y jointly wide sense stationary? Why? (c) (5) Find the autocovariance Cy (t +7,t) = E[(Y(t + 7) − ÿ(t + 7))(Y(t) − y(t))] of Y (t). (2) Is Y (t) white? Why?

Answers

A. The mean ÿ(t) = 0 and the autocorrelation Ry(t + 7, t) = 4e⁻⁷. Y(t) is wide-sense stationary.

B. the cross-correlation Rxy(t + 7, t) = 2e⁻⁷. X and Y are jointly wide-sense stationary.

C. The autocovariance Cy(t + 7, t) = 4e⁻⁷. Y(t) is not a white process because autocovariance Cy(t + 7, t) is not a Dirac delta function.

How did we arrive at these assertions?

To find the mean ÿ(t) = E[Y(t)] and the autocorrelation Ry(t + 7, t) = E[Y(t + 7)Y(t)], we substitute the expression for Y(t) into the formulas:

(a) Mean of Y(t):

ÿ(t) = E[Y(t)] = E[2X(t) + sin(2t)]

= 2E[X(t)] + E[sin(2t)]

= 2(0) + 0

= 0

(b) Autocorrelation of Y(t + 7, t):

Ry(t + 7, t) = E[Y(t + 7)Y(t)]

= E[(2X(t + 7) + sin(2(t + 7)))(2X(t) + sin(2t))]

Expanding the expression:

Ry(t + 7, t) = E[4X(t + 7)X(t) + 2X(t + 7)sin(2t) + 2sin(2(t + 7))X(t) + sin(2(t + 7))sin(2t)]

Since X(t) is a WSS random process with mean 0, its autocorrelation Rx(T) = E[X(t + 7)X(t)] = e^(-|7|).

Using the properties of expectation and the independence of X(t) and sin(2t):

Ry(t + 7, t) = 4E[X(t + 7)X(t)] + 2E[X(t + 7)]E[sin(2t)] + 2E[sin(2(t + 7))]E[X(t)] + E[sin(2(t + 7))]E[sin(2t)]

= 4Rx(7) + 2(0)(0) + 2(0)(0) + 0

= 4e⁻⁷

Therefore, the mean ÿ(t) = 0 and the autocorrelation Ry(t + 7, t) = 4e⁻⁷.

To determine if Y(t) is wide-sense stationary, we need to check if the mean and autocorrelation are independent of time:

Mean: The mean ÿ(t) is constant and does not depend on time t. Thus, Y(t) has a constant mean.

Autocorrelation: The autocorrelation Ry(t + 7, t) depends only on the time difference of 7. It is independent of the absolute values of t. Therefore, Y(t) has a stationary autocorrelation.

Since Y(t) has a constant mean and a stationary autocorrelation, it is wide-sense stationary.

Moving on to part (b), we need to find the cross-correlation Rxy(t + 7, t) = E[X(t + 7)Y(t)].

Rxy(t + 7, t) = E[X(t + 7)Y(t)]

= E[X(t + 7)(2X(t) + sin(2t))]

Expanding the expression:

Rxy(t + 7, t) = E[2X(t + 7)X(t) + X(t + 7)sin(2t)]

Since X(t) is a WSS random process, its autocorrelation Rx(T) = e|⁻⁷|.

Using the properties of expectation and the independence of X(t) and sin(2t):

Rxy(t + 7, t) = 2E[X(t + 7)X(t)] + E[X(t + 7)]E[sin

(2t)]

= 2Rx(7) + 0

= 2e⁻⁷

Therefore, the cross-correlation Rxy(t + 7, t) = 2e⁻⁷.

To determine if X and Y are jointly wide-sense stationary, we need to check if the cross-correlation Rxy(t + 7, t) is independent of time:

Cross-correlation: The cross-correlation Rxy(t + 7, t) depends only on the time difference of 7. It is independent of the absolute values of t. Therefore, X and Y have a stationary cross-correlation.

Since the cross-correlation is stationary, X and Y are jointly wide-sense stationary.

Moving on to part (c), we need to find the autocovariance Cy(t + 7, t) = E[(Y(t + 7) - ÿ(t + 7))(Y(t) - ÿ(t))].

Expanding the expression:

Cy(t + 7, t) = E[(2X(t + 7) + sin(2(t + 7))) - 0][(2X(t) + sin(2t)) - 0]

= E[(2X(t + 7) + sin(2(t + 7)))(2X(t) + sin(2t))]

Using the same approach as in part (b), we expand the expression and evaluate the expectation:

Cy(t + 7, t) = 4E[X(t + 7)X(t)] + 2E[X(t + 7)]E[sin(2t)] + 2E[sin(2(t + 7))]E[X(t)] + E[sin(2(t + 7))]E[sin(2t)]

= 4Rx(7) + 0 + 0 + 0

= 4e⁻⁷

Therefore, the autocovariance Cy(t + 7, t) = 4e⁻⁷.

To determine if Y(t) is white, we check if the autocovariance Cy(t + 7, t) is a Dirac delta function. Since Cy(t + 7, t) = 4e⁻⁷ ≠ 0, it is not a Dirac delta function. Hence, Y(t) is not a white process.

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please help 6th grade math please please help

Answers

i: 1

ii: 6

iii: 3

iv: 2

v: 4.5

vi: 2.5

I’m doing this in my class too!
Least value is 1 kilometer
Median is 3 kilometers
Upper quartile is 4.5 kilometers
Greatest value is 6 kilometers
Lower quartile is 2 kilometers
Interquartile range is 2.5 kilometers

Find the area of the parallelogram
Height=4cm
Base=5cm

Answers

Answer:

The area of the parallelogram is 20cm²

Answer:

A = 20 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the height ) , then

A = 5 × 4 = 20 cm²

Solve the following ordinary differential equations using Laplace trans- forms: (a) y(t) + y(t) +3y(t) = 0; y(0) = 1, y(0) = 2 (b) y(t) - 2y(t) + 4y(t) = 0; y(0) = 1, y(0) = 2 (c) y(t) + y(t) = sint; y(0) = 1, y(0) = 2 (d) y(t) +3y(t) = sint; y(0) = 1, y(0) = 2 (e) y(t) + 2y(t) = e';y(0) = 1, y(0) = 2

Answers

(a) The ordinary differential equation is given by y(t) + y(t) + 3y(t) = 0. Using Laplace transform, we have(L [y(t)] + L [y(t)] + 3L [y(t)]) = 0L [y(t)] (s + 1) + L [y(t)] (s + 1) + 3L [y(t)] = 0L [y(t)] (s + 1) = - 3L [y(t)]L [y(t)] = - 3L [y(t)] /(s + 1)Taking the inverse Laplace of both sides, we have y(t) = L -1 [- 3L [y(t)] /(s + 1)]y(t) = - 3L -1 [L [y(t)] /(s + 1)]

On comparison, we get y(t) = 3e^{-t} - 2e^{-3t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(b) The ordinary differential equation is given by y(t) - 2y(t) + 4y(t) = 0. Using Laplace transform, we have L [y(t)] - 2L [y(t)] + 4L [y(t)] = 0L [y(t)] = 0/(s - 2) + (- 4)/(s - 2)

Taking the inverse Laplace of both sides, we have y(t) = L -1 [0/(s - 2) - 4/(s - 2)]y(t) = 4e^{2t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(c) The ordinary differential equation is given by y(t) + y(t) = sint. Using Laplace transform, we have L [y(t)] + L [y(t)] = L [sint]L [y(t)] = L [sint]/(s + 1)

Taking the inverse Laplace of both sides, we have y(t) = L -1 [L [sint]/(s + 1)]y(t) = sin(t) - e^{-t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(d) The ordinary differential equation is given by y(t) + 3y(t) = sint. Using Laplace transform, we have L [y(t)] + 3L [y(t)] = L [sint]L [y(t)] = L [sint]/(s + 3)Taking the inverse Laplace of both sides, we have y(t) = L -1 [L [sint]/(s + 3)]y(t) = (1/10)(sin(t) - 3cos(t)) - (1/10)e^{-3t}.

The initial conditions are y(0) = 1 and y(0) = 2 respectively.(e) The ordinary differential equation is given by y(t) + 2y(t) = e^{t}. Using Laplace transform, we have L [y(t)] + 2L [y(t)] = L [e^{t}]L [y(t)] = 1/(s + 2)Taking the inverse Laplace of both sides, we havey(t) = L -1 [1/(s + 2)]y(t) = e^{-2t}The initial conditions are y(0) = 1 and y(0) = 2 respectively.

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You roll a single 6 sided die. What are the odds of rolling a 9?

A. 1/6
B. 0
C. 1/9
D. 9

Answers

Answer:

B. 0

Step-by-step explanation:

There aren't enough sides for you to roll a nine

Calculate the 90% confidence interval for the following sample Sample: 7.9, 8.3, 8.4, 9.6, 7.7, 8.1, 6.8, 7.5, 8.6, 8, 7.8,7.4, 8.4, 8.9, 8.5, 9.4, 6.9,7.7. Assume normality of the data.

Answers

The 90% confidence interval for the given sample is (7.58, 8.60).

To calculate the 90% confidence interval for the given sample assuming normality of the data, we need to use the formula as follows;Confidence interval = X ± Z α/2(σ/√n)Where, X is the sample meanZ α/2 is the Z-score for the desired level of confidenceσ is the population standard deviationn is the sample sizeFirst, we need to calculate the sample mean and standard deviation.Sample mean,

X= (7.9 + 8.3 + 8.4 + 9.6 + 7.7 + 8.1 + 6.8 + 7.5 + 8.6 + 8 + 7.8 + 7.4 + 8.4 + 8.9 + 8.5 + 9.4 + 6.9 + 7.7) / 18

= 8.09

Sample standard deviation,

σ = √[Σ(xi - X)² / (n - 1)]σ = √[(7.9 - 8.09)² + (8.3 - 8.09)² + (8.4 - 8.09)² + (9.6 - 8.09)² + (7.7 - 8.09)² + (8.1 - 8.09)² + (6.8 - 8.09)² + (7.5 - 8.09)² + (8.6 - 8.09)² + (8 - 8.09)² + (7.8 - 8.09)² + (7.4 - 8.09)² + (8.4 - 8.09)² + (8.9 - 8.09)² + (8.5 - 8.09)² + (9.4 - 8.09)² + (6.9 - 8.09)² + (7.7 - 8.09)² / (18 - 1)]σ = 0.761

Now, we need to find the Z α/2 value from the standard normal distribution table.

Z α/2 = 1.645 (for 90% confidence level)Putting the values in the formula,Confidence interval =

X ± Z α/2(σ/√n)

= 8.09 ± 1.645(0.761/√18)

= 8.09 ± 0.511

= (8.09 - 0.511, 8.09 + 0.511)

= (7.58, 8.60).

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