The geometry of a simple planar curve (ADB) is shown below. The value of the mid-ordinate of the curve in m is ______ (round off to 1 decimal place).
In the figure shown below, the friction coefficient between the block and the inclined plane is 0.2, and all the pulleys are weightless. The weight of the block is 10 N. The minimum force P in Newtons that is needed to slide the block up the inclined plane is ______ (round off to 2 decimal places).
An assignment problem is given below with the cost of assignment as shown.
| Task/Group | T1 | T2 | T3 | T4 |
|---|---|---|---|---|
| G1 | 6 | 10 | 5 | 4 |
| G2 | 4 | 100 | 6 | 4 |
| G3 | 6 | 9 | 6 | 2 |
| G4 | 3 | 7 | 6 | 4 |
If only one task can be assigned to one group, the minimum cost of assignment is ______.
A vertical stoping block of length 60.0 m, height 40.0 m, and average width 1.5 m has sharp boundary walls. However, the mining width of the stoping block is 2.0 m. The tonnage factors are 3.0 tonne/m³ for ore and 2.5 tonne/m³ for wall rocks. The average grade of ore is 10.0%. The overall grade of ore mined on account of dilution in percentage is ______ (round off to 2 decimal places).
A bauxite ore body has four boreholes as shown below. For each borehole, the grade of alumina, the thickness of the ore body, and the triangular area of influence are as shown.
The average grade of ore body in the region ABCD in percentage is ______ (round off to 1 decimal place).
The closest match of the scatter plot between the variables X and Y with the approximate attribute is
A 3-point borehole extensometer is installed to identify the location of a single discontinuity plane in a hanging wall rock by measuring deformations at three locations as shown in the figure. The absolute readings of deformations measured on two different dates are listed in the table. Based on the measured data the most likely inference is
| Date | Anchor-1 (mm) | Anchor-2 (mm) | Anchor-3 (mm) |
|---|---|---|---|
| May 2, 2021 (initial reading) | 34.52 | 29.04 | 43.11 |
| June 1, 2021 | 40.56 | 34.67 | 44.78 |
Match the semi-variogram shape with the model name and the property
| Semi-variogram model | Property |
|---|---|
| I. Pure nugget | E. reaches sill at finite range |
| II. Exponential | F. reaches sill asymptotically |
| III. Spherical | G. reaches sill instantaneously |
| IV. Gaussian |
= semi-variogram
= lag distance
Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences. Which one of the following is the correct logical inference based on the information in the above passage?
Consider the following inequalities.
(i)
(ii)
Which one of the following expressions below satisfies the above two inequalities?