Question Solved1 Answer Scientists at the Hopkins Memorial Forest in western Massachusetts have been collecting meteorological and environmental data in the forest data for more than 100 years. In the past few years, sulfate content in water samples from Birch Brook has averaged 7.48 mg/L with a standard deviation of 1.60 mg/L. 1. [35%] What is the standard error of the sulfate in a collection of 10 water samples? 2. [35%] If 10 students measure the sulfate in their samples, what is the probability that their average sulfate will be between 6.49 and 8.47 mg/L? 3.130%] What do you need to assume for the probability calculated in (2) to be accurate?

What side of the bed do you get out of when you wake up? An analyst asked a random sample of 80 teenagers what side of the bed they get out of and 52 said that they get out of the right side of the bed. Construct and interpret a 90% confidence interval for the proportion of all teenagers that get out of the right side of the bed. STATE: 90% CI for = the of teenagers that get out of the right side of the bed. PLAN: Select 3 true statements. The sample size, 80, is less than 10% of all teenagers. We have a random sample of 80 teenagers The Random condition is not met. One-sample z interval for u The 10% condition is not met. One-sample z interval for p Large Counts: no = n(1 - 2) = The Large Counts condition met because the number of successes, np, and the number of failures, n(1-P), both at least 10. DO: DO: p = (Enter 2 decimal places) (Enter 3 decimal places) The 90% CI is ( ). CONCLUDE: We are 90% confident that the interval from to captures = the of all teenagers that get out of the right side of the bed.

242 Equipotential Surfaces and the Electric Field Two large, parallel conducting plates are 10.0 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. The plates are oriented so that an electrostatic force of 5.96 x 10-15 acts to the right on an electron placed anywhere between the two plates (Neglect fringing.) Find the magnitude of the electric field between the plates. Enter a positive number if the field points to the right and a negative number if the field points to the left. N c Save for Later Submit Answer

Parts E and B please 5. Compute the power Px and the energy Ex for each of the following signals: (a) x(t) = e-3tu(t) (b) x(t) = ej(2t+31/4) (c) x(t) = cos(t/2) (d) x[n] = (?)"u[n] (e) x[n] = ej(1/2+31/8) (f) x[n] = cos (31n/4)

1. Derive an expression for the horizontal distance of a vertical staff from a tacheometer if the line of sight of the telescope is horizontal 2. Derive expressions for the horizontal distance D and the vertical intercept (difference) V when the staff is (a) elevation and (b) depression. 3. The distance between a tachometer station and a staff station is measured to be 50.85 m. with the line of sight horizontal, the stadia hair readings are found to be 1.99 m and 1.395 m. Determine the instrument constant. 4. The following readings were taken with a tacheometer on to a vertical staff and zero vertical angle. Horizontal Distance Stadia Readings 46.2 m 0.78; 1.01; 1.24 51.2 m 1.86; 2.16; 2.47 Calculate the tacheometric constants. 5. The following readings were taken with tachometers on a vertical staff stand on three points, if the elevation the station point is 45.9 m and the height of instrument is 17.6 dm. Stadia readings Vertical angle 0.795, 1.025, 1.255 1.875, 2.180, 2.485 5 30 1.368, 2.359, 3.35 -6° 45' Find the distance from station to each staff point and their reduced levels? 6. In determining the elevation of point A and the distance between two points, A and B, a theodolite is set up at A and the following data are obtained: Z or a = 92° 45', stadia interval = 1.311m, hi = 1.28 m, and the line of sight at 2.62 m (central staff reading). The instrument constant K = 100 and C = 0.03 m. The elevation of B is 38.28 m. compute the distance AB and elevation of point A. 7. The elevation of station P is 345.67m. The height of theodolite over that station is 1.23m. When observing a rod held on station Q, the following data are recorded, Vertical angle - - 9° 45', lower staid hair = 0.83, center hair = 1.23, upper stadia hair = 1.63. Determine the distance between P and Q, and elevation of Q. 8. Stadia readings were taken with a theodolite on a vertical staff with the telescope inclined at a V.C.R of 93°30'. The staff readings were 299, 205 and 112 cm. The reduced level of the staff station is 100.75m, and the height of the instrument is 14 Dm. What is the reduced level of the ground at the instrument? Take constants as 100 and zero. 9. A tacheometer is setup at an intermediate point on a traverse course PQ and the following observations are made on a staff held vertical. Staff Station V.C.R + 279° 30' + 275900 Staff Intercept (S) Central Hair Readings 2.250 2.105 2.055 1.975 The constants are 100 and 0. Compute the length PQ and the reduced level of Q. if RL of P- 350.50 m. 10. From an instrument station Pof R.L 218.56 m two depressed lines of sight were taken to a staff held vertically over a station Q. The staff readings obtained is 3.160 m and 1.310m. The angels of depression of the lines of sight are 7 15 and 87. Find the horizontal distance between the two stations. Find also the R.L of the station Q. The height of instrument above the station P is 1.51m. 11. A theodolite was set over a station A of reduced level 44.620m, the instrument height being 1.425m. Observations were taken by tangent method to the 3m and 0.60m marks on each staff held vertically at three stations B, C and D with the following results. Instrument station Staff Station V.C.R 27910 885 95°15 273 30 9224 112 10 Find the distances from A to each station and their reduced levels? 12. Observations with a tachometer gave staff intercepts of 0.595m and 1.490m with telescope Horizontal and the staff held vertically at Horizontal distance of 61.062m and 152.40m respectively from the instrument, calculate the instrument constant and additive constant of the tachometer. The instrument was then set over a station with R.L 80.559m. the height of the instrument axis above the station point being 1.29 m. the readings of the three hairs on a vertical staff were 0.915m, 1895m and 2.875m, the telescope being inclined at 8 above the Horizontal. Determine the R.L of the staff station and its distance from the center the instrument.

Question 2 From the table below, calculate the actual distance for each point given the multiplying and additive constants equivalent to 98.4 and 0.5, respectively. Point Top stadia Middle stadia Below stadia Distance А 2.00 1.50 1.00 a) B 1.95 1.55 0.25 b) с 2.35 1.85 0.95 c) D 1.98 1.78 0.48 d) E 1.56 1.26 0.76 e)

em 6 Find the direction of the line normal to the surface defined by the function \[ f(x, y, z)=x^{2} y+y^{2} z+z^{2} x+1=0, \] at the point \( (1,2,-1) \). Find the equation of the tangent plane and the normal line at this point. Make a 3D plot to show the surface, the tangent plane, and the normal line.