The solutions 71 and 72 are correct. Excellent!
73. The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking, it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.
74. A box contains 10 white, 6 red, and 10 black balls. A ball is drawn at random. Find the probability that the ball drawn is white or red.
The Answer #5355 is correct. Excellent!
#5357. Name the English polymath and engineer who made important contributions to automotive engineering, aerodynamics and co-invented the topic of operations research (23 October 1868 – 8 March 1946). He was also a pioneer British motor car builder, a hobby which resulted in his developing a successful car company, and is considered one of the "big three" English car engineers, the others being Harry Ricardo and Henry Royce.
#5358. Alessandro Giuseppe Antonio Anastasio Volta (February 18, 1745 – March 5, 1827) was an Italian physicist known for invention of the electric cell and Discovery of methane. Name the medal he was awarded in 1794.
The solutions 69 and 70 are correct. Spectacular!
71. Find two consecutive odd natural numbers, the sum of whose squares is 202.
72. The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.
The solutions 67 and 68 are correct. Stupendous!
69. Using the concept of slope, show shat the points (-2,-1), (4,0), (3,3), and (-3,2) taken in order form a parallelogram.
70. Find the equation of the straight lines passing through the point (2,2) and the sum of the intercepts is 9. (Two solutions).
The Answer is perfect. Marvelous!
#5355. Name the inventor (3 April 1693– 24 March 1776) who was a self-educated English carpenter and clockmaker. He invented the marine chronometer, a long-sought after device for solving the problem of establishing the East-West position or longitude of a ship at sea, thus revolutionising and extending the possibility of safe long-distance sea travel in the Age of Sail.
#5356. When did Lumière brothers, Auguste Marie Louis Nicolas and Louis Jean, who were the first filmmakers in history invent the cinema? They patented the cinematograph, which in contrast to Edison's "peepshow" kinetoscope allowed simultaneous viewing by multiple parties. Their first film, Sortie de l'usine Lumière de Lyon, is considered the first true motion picture.
The solutions 65 and 66 are correct. Brilliant!
67. A car left 30 minutes later than the scheduled time. In order to reach its destination 150 kilometers away, it has to increase its speed by 25 kilometers per hour from its usual speed. Find its usual speed.
68. Ifare the roots of the equation , form an equation whose roots are .
The Answer #5352 is correct. Magnificent!
#5353. What was invented by by an Italian, Luigi De Cristoforis, in 1876? (It was developed by Enrico Bernardi at the University of Padua in 1882).
#5354. What inverntion/discovery was made in 1774 by Carl Wilhelm Scheele, who supposed it to be an oxide of a new element? In 1809, chemists suggested that the gas might be a pure element, and this was confirmed by Sir Humphry Davy in 1810.