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Hi;

The solution #6078 is correct. Neat work, bobbym!

#6079. A(3,2) and B(-2,1) are the two vertices of triangle ABC, whose centroid G has coordinates (5/3,-1/3). Find the coordinates of the third vertex C of the triangle.

Hi;

The solution 577 (four parts) is correct. Excellent, bobbym!

578. A semicircular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and the capacity of the cup.

Hi;

The solution #6077 (two parts) is correct. Excellent, bobbym!

#6078. Find the points which divide the line segment joining (8,12) and (12,8) into four equal parts.

Hi;

577. A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the bag at random. Find the probability that the drawn ball is

(i) white

(ii) red

(iii) not black

(iv) red or white

Hi;

The solution 575 (three parts) is correct. Excellent, bobbym!

576. A hemispherical tank, full of water, is emptied by a pipe at the rate of 25/7 liters per second. How mach time will it take to empty half the tank if diameter of the tank is 3 m?

Hi;

#6077. Find the ratio in which C(p,1) divides the join of A(-4,4) and B(6,-1) and hence find the value of p.

Hi;

The solution #6075 is correct. Well done, bobbym!

#6076. If the points A(4,3) and B(x,5) are on the circle with the center O(2,3), find the value of x.

Hi;

The solution 574 (two parts) is correct. Excellent, bobbym!

575. All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is drawn at random from the remaining pack. Find the probability of getting

(i) a black face card

(ii) a queen

(iii) a black card

Hi;

The solution #3681 is correct. Good work, bobbym!

#3682. Find the diameter of a circle whose circumference is 628 cm. Use

#3683. If the perimeter of a semi-circle is 36 cm, find the diameter.

Hi;

The solution 573 is correct. Excellent, bobbym!

574. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag. Find the probability of

(i) a white ball or a green ball

(ii) neither a green ball nor a red ball

Hi;

The solutions #6073 and #6074 are correct. Neat work, bobbym!

#6075. A die is thrown once. Find the probability of getting

(i) an even number

(ii) a prime number

(iii) a number greater than 4

Hi;

The solution #3680 is correct. Neat work, bobbym!

#3681. If the nth term of an Arithmetic Progression is (2n + 1), then the sum of first three terms is ____________

Hi;

Corrected : 573. Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of **0.4 m/s**. Determine the rise in level of water in the tank in half an hour.

Sorry for the inconvenience, bobbym!

Hi;

The solutions 572(i) and 572(ii) are correct. Excellent, bobbym!

573. Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 cm m/s. Determine the rise in level of water in the tank in half an hour.

Hi;

The solution #6072 is correct. Excellent, bobbym!

#6073. A number is chosen at random from among the first 30 natural numbers. The probability of the number chosen being prime is ________.

#6074. A card is drawn at random from a well shuffled pack of 52 playing cards. The probability of getting a red face card is ________.

Hi;

The solution 571 is correct. Excellent, bobbym!

572. (i) A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be

(i) red?

(ii) white?

(iii) not green?

572. (ii) There are 30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card is drawn out of the bag at random. Find the probability that the number on the selected cards divisible by 3.

Hi;

The solution #6071 is correct. Excellent, bobbym!

#6072. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, the the water level rises (in cm) by __________

Hi;

The solution #6070 is perfect. Neat work, bobbym!

#6071. Find the value of k for which the points with coordinates (2,5), (k,-11/2) and (4,6) are collinear.

Hi;

The solution 570 is correct. Excellent, bobbym!

571. One card is drawn from a well shuffled deck of 52 playing cards. Find the probability of getting

(i) a non-face card

(ii) a black king or a red queen

Hi;

The solution #6069 is correct. Good work, bobbym!

#6070. The coordinates of the mid-point of the line joining the points (2p + 2,3) and (4,2q + 1) are (2p,2q). Find the value of p and q.

Hi;

The solution 569 is correct. Neat work, bobbym!

570. From a point 100 m above a lake, the angle of elevations of a stationary helicopter is 30 degrees and the angle of depression of reflection of the helicopter in the lake is 60 degrees. Find the height of the helicopter.

Hi;

The solution #3679 is correct. Good work, bobbym!

#3680. The common difference of the Arithmetic Progression 1/p, (1 - p)/p, (1 - 2p)/p is ______-.

Hi;

The solution #6068 is correct. Neat work, bobbym!

#6069. If P(2,p) is the mid-point of the line segment joining the points A(6,-5) and B(-2,11), find the value of p.

Hi;

The solution #6067 is correct. Good work, bobbym!

#6068. What is the distance between the points A(c,0) and B(0,-c)?

Hi;

The solution 568 (four parts) is correct. Excellent, bobbym!

569. Find an A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40. (first four terms)