From past experience, it is known 90 percent of one year’s old children can distinguish their mother’s voice of a similar sounding female. A random sample of one year’s old are given this voice recognize test. Find the standard deviation that all 20 children recognize their mother’s voice.

From past experience it is known 90 percent of one year old children can distinguish their mothers voice of a similar sounding female. A random sample of one year’s old are given this voice recognize test. Find the probability that at least 3 children didn’t recognize their mother’s voice.

From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice of a similar sounding female. A random sample of 20 one year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their Mother's voice. Find the mean of x.

In a hotel it is known that 20% of the total reservation will be cancelled in the last minute. What is the probability that out of 15 reservation that there will be more than 8 but less than 12 will cancelled?

In a hotel it is known that 20% of the hotel reservation will be cancelled in the last minute. What is the probability that there will be less than 2 reservations cancelled out of 4 reservations?

In a hotel it is known than 20% of the total reservation will be cancelled in the last minute. What is the probability that these will be fewer than 2 reservation cancelled out of 4 resevations?

3 randomly chosen senior high school students were administered a drug test. Each student was evaluate as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the 3 students drug test evaluation as PPP,PPN,PNP,NPP,PNN,NPN,NNP,NNN. Assume the possible combination is equally likely and knowing that 1 student get a negative result, what is the probability that all 3 students get a negative result?

3 randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test(P) or negative to the drug test (N). Assume the possible combinations of the three student’s drug test evaluation as PPP,PPN,PNP,NPP,PNN,NPN,NNP,NNN. Assuming each possible combination is equally likely what is the probability that all 3 students get positive results?

Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three students' drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that all three students get negative results ?

Express in polar form : -3 -4 i

Find all values of z for which $$e^{4z=i}$$ .

If cos ƶ = 2, find cos 3z.

If cos ƶ = 2, find cos 2z.

if z=6 $$e^{ipi/3}$$ , evaluate| iz |.

Find the acute angle between two vectors z1 = 3 – 4i and z2 = -4 + 3i.

For a complex number z = 2 + 2 (sqrt. Of 3)i, the modulus is:

The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as

Find the area of the first octant part of the plane x/a + y/b + z/c = 1; where a, b and c are positive.

What percentage of the volume of a cone is the maximum right circular cylinder that can be inscribed in it?

Find the volume generated by revolving the area cut off the parabola y=4x- $$x^2$$ by the x axis about the line y=6.

The area of the second quadrant of the circle $$x^2$$ + $$y^2$$ =36 is revolved about the line y+10=0. What is the volume generated?

Find the height of a right circular cylinder of maximum volume which can be inscribed in a sphere of radius 10 cm.

The area bounded by the curve $$y^2$$ = 12x and the line x = 3 is revolved about the lone x = 3. What is the volume generated?

Find the volume of the solid generated when the region bounded by y = $$x^2$$ – 4x + 6 and y = x + 2 revolved about the x-axis.

Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150 degrees.

Sand is pouring to form a conical pile such that’s its radius is always twice its height. If a volume of a conical pile is increasing at the rate of 2 cu. m./sec, how fast is the height is increasing when the height is 4m?

Sand is pouring to form a conical pile such that its altitude is always twice its radius. If the volume of a conical pile is increasing at a rate of 25pi cu. ft./min, how fast is the radius is increasing when the radius is 5 feet?

Find the ratio of the surface area of the cube to its volume, if the side is s.

Find the volume (in cubic units) generated by rotating a circle $$x^2$$ + $$y^2$$ + 6x + 4y + 12 = 0 about the y-axis.

Find the volume generated by revolving about the x-axis, the area bounded by the curve y = cosh x from x = 0 to x =1.

Find the volume generated when the area bounded by y = $$2^{-x}$$ and y = $$(x-1)^2$$ is revolved about the x-axis.

The parabola $$y^2$$ = 4ax and the line x = p enclosed an area with the centroid at the focus of parabola. Find p in terms of a.

Find the height of the right circular of maximum volume which can be inscribed in a sphere of radius.

If the radius of the sphere is inscribed by the factor of 3, by what factor does the volume of the sphere change?

An equilateral triangle with side “a” is revolved about its altitude. Find the volume of the solid generated.

If the area bounded by the parabolas y = $$x^2$$ – $$c^2$$ and y = $$c^2$$ – $$x^2$$ is 576 square units, find the volume of C.

A solid has circular base of radius r. Find the volume of the solid if every planer section perpendicular to a fixed diameter is a semicircle.

Find the volume generated by the circle $$x^2$$ + $$y^2$$ = 25 if it is revolved about the line 4x + 3y = 40.

A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8 cm/hr. If the icicle is currently 4 cm in radius and 20 cm long, is the volume of the icicle incr easing, and at what rate?

Find the volume of the solid of revolution obtained by revolving the region bounded by y = $$x$$ – $$x^2$$ and the x-axis about the x- axis.

Find the height of the right circular cone of least volume that can be circumscribed about a sphere of radius “a”.

Find the moment of inertia with respect to the y-axis of the area bounded by y= $$x^2$$ and y=2x.

Find the moment of inertia with respect to the y-axis of the first quadrant area bounded by the parabola $$x^2$$ = 4y and the line y=x.

Find the moment of the inertia of the area bounded by the parabola $$y^2$$ = 4x and the line x = 1, with respect to the line x-axis.

Find the area bounded by r = 2 / ( 1 + cos θ ) andcos θ = 0.

A line through (0,0) intersects y= $$x^2$$ at a point (a, $$a^2$$ ). The area of the upper region bounded above by the line and below by the curve is 27. Find a.

Find the area enclosed by the lemniscate of Bernoulli $$r^2$$ = $$a^2$$ cos 2θ.

Find the area bounded by y = $$x^3$$ , the x-axis and the lines x = -2 and x = 1.

Identify the curve described by r = 6