Time After 3:00 O'clock When The Hands Of The Clock Are Perpendicular
Problem
How many minutes after 3:00 o’clock will the hands of the clock be perpendicular to each other for the 1st time?
| A. 35 | C. 32.73 |
| B. 33.15 | D. 34.12 |
October 2018
Smallest Part From The Circle That Was Divided Into Four Parts By Perpendicular Chords
Problem
Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.
Continuous Beam With Equal Support Reactions
Situation
A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length x is so calculated in order that the reactions at all supports shall be the same.
1. Find x in meters.
| A. 1.319 | C. 1.217 |
| B. 1.139 | D. 1.127 |
2. Find the moment at B in N·m.
| A. -240 | C. -242 |
| B. -207 | D. -226 |
3. Calculate the reactions in Newton.
| A. 843.4 | C. 863.8 |
| B. 425.4 | D. 827.8 |
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Probability that a Point Inside a Square Will Subtend an Obtuse Angle to Adjacent Corners of the Square
Problem
Point P is randomly chosen inside the square ABCD. Lines AP and PB are then drawn. What is the probability that angle APB is obtuse?
Continuous Beam With a Gap and a Zero Moment in Interior Support
Situation
A beam of uniform cross section whose flexural rigidity EI = 2.8 × 1011 N·mm2, is placed on three supports as shown. Support B is at small gap Δ so that the moment at B is zero.
1. Calculate the reaction at A.
| A. 4.375 kN | C. 5.437 kN |
| B. 8.750 kN | D. 6.626 kN |
2. What is the reaction at B?
| A. 4.375 kN | C. 5.437 kN |
| B. 8.750 kN | D. 6.626 kN |
3. Find the value of Δ.
| A. 46 mm | C. 34 mm |
| B. 64 mm | D. 56 mm |
Probability that a Large Shipment is Accepted or Not Accepted due to Defective Items
Problem
A stationery store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. Find the probability that this shipment is...
- accepted if 5% of the total shipment is defective.
- not accepted if 15% of the total shipment is defective.
1 - Probability for cars to pass through a point on road in a 5-minute period
Problem
The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (a) two cars go past and (b) fewer than 3 cars go past.
Poisson Probability Distribution
The number of occurrences in a given time interval or in a given space can be modeled using Poisson Distribution if the following conditions are being satisfied:
- The events occur at random.
- The events are independent from one another.
- The average rate of occurrences is constant.
- There are no simultaneous occurrences.
The Poisson distribution is defined as
$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$
where x is a discrete random variable
μ = the mean number of occurrences
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