MATH MULTIVECTOR

32問 • 1年前

問題一覧

A steel girder & a long is noved on rollers along a walkway 4 wide and into a corridor perpendicular to the walkway. How wide must the corridor be to successfully move the girder?

1.8m

From past experience, it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year-olds is 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 variance of X..

1.8

Fron past experience, it is known 908 of one year old children can distinguish their mother's voice of a similar sounding female. A random sample of 20 one year old are given this voice recognition test. Find the probability that all children recognize their mother's voice.

0.122

One end of a 32-meter ladder resting on a horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2 meters per minute. How fast is the top of the ladder rising when its foot is 10 meters from the wall?

0.66 m/min

The area enclosed by the ellipse 4x 9y 36 is revolved about the line x3, what is the volume generated?

355.3

A ball bounces 2/3 of the altitude from which it falls. Suppose the ball is dropped from a height of 18 ft. Bow far will it travel at the instant it strikes the ground for the 5th time?

75.78 ft

About how many quarts of water will a 3.25-1iter container hold?

3.445

The rectangular coordinate system in space is divided into eight compartments, which are known as

octants

Two hundred single-sport athletes were cross-classified according to gender as follows What is the probability that the athlete is male or a swimmer or both?

0.650

A rectangular tank with a square hase, an open top, and a volume of 108 ft 3 is to be constructed of slieet steel. Find the dimensions of the tank that has the minimum surface area.

6 ft x 6 ft x 4.32 ft

A man 5 ft tall walks at a rate of 6 ft/sec directly away from a street light that is 20 ft above the street. At what rate is the tip of his shadow moving

8 ft/s

All circles having the same center but with unequal radit are called

concentric circles

If the sides of a right triangle is in arithmetic progression, what is the ratio of its sides?

3:4:5

Three zen, Jhun, Noel, and Ryan can do a piece of work in t hours working together. Working alone, A can do the work in 6 hours more, B in 1 hour more, and C in twice the time if all working together. How long would it take to finish the work if all work together?

40 min

Evaluate the integral log of a to base 10 dx from x = 1 to x = 10.

2.0

If a bug noves a distance of 3 cm along a circular arc and if this arc subtends a central angle of 45 degrees, what is the radius of the circle?

12 cm

Find all the values of z for which 1

-1/6 pi 1 + 1/2 kpl 1

An unlimited sequence of squares are inscribed one within another by joining the midpoints of the perimeters of these squares. sides of each preceding square. If the initial square is 8 cm on a side, find the sum of the

109.25 cm

Two engineers facing each other with a distance of 5 km from each other, the angles of elevation of the balloon from the two engineers are 56 degrees and 58 degrees, respectively. What is the distance of the balloon from the two engineers?

4.64 km, 4.54 km

A water tank is shaped in such a way that the volume of water in the tank is V 2y^3/2 cu. in. When its depth is y inches. If water flows out through a hole at the bottom of the tank at the rate of 3(sqrt. of yl cu. in/min. At what rate does the water level in the tank fall?

1 in/min

Joseph gave his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally

A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. Let event A denote that the consumers had seen an ad for the new soap, and event B denote that the consumers had tried the new soap. What is the probability a randomly selected consumer had either seen an advertisement or tried the new soap?

0.4500

What is the conic section whose eccentricity is equal to 1

parabola

Find the area under one arch of the hypocycloid x a (theta sin theta), ya(1 cos theta).

3pi a

Laura has a rectangular garden whose width is x + 3 and whose length is x^4. In terms of x, what is the area of her garden

x^7

Find the area bounded by 2/11 cos theta) and cos theta = 0.

8/3

what is the greatest common factor of 24 and 64?

The segnent from (-1, -4) to (2, -2) is extended three times its own length. The terminal point is

(11, -20)

The tangent of an angle of a right triangle is 0.75. What is the cosecant of the angle?

1.667

A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lbs of dissolved salt per gallon. Assuming that the mixture is kept uniform, by stirring, a drain pipe draws out of the tank the mixture at 2 qua. Pind the amount of salt in the tank at the end of 30 minutes.

171.24 lbs

Classify the conic section 9x 167 32 1280.

ellipse

IF y arctan (in x), find y' when x 1/e.

e/2

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premopremo remo · 75問 · 2年前

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