Select the statements that describe a normal distribution.

Mathematics

1 answer:

Snezhnost [94]2 years ago

3 0

Answer: The statements that describe a normal distribution are;

a. The density curve is symmetric and bell-shaped.

b. The normal distribution is a continuous distribution.

Step-by-step explanation: The normal distribution is the most commonly used and important statistic tool. It is referred to as the "Bell Curve" because of its bell-shape and the the fact that it is symmetric density curve. A continuous distribution defines the possibilities of a continuous random variable and a prime example of a continuous distribution is the Normal distribution.

The normal distribution is not a discrete distribution because it does not have discrete variables. The normal distribution is not a flat line that extends from a minimum to a maximum but it is a continuous distribution that extends in a bell shape from one minimum value going up to a maximum value before descending back to another minimum value.

68% of a normal distribution curve falls with one standard deviation from the mean not 32%.

The two parameters that define a normal distribution is the mean and the standard deviation.

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a ball is shot straight upward. with it's height, in feet, after t seconds given by the function f(t)=-16t^2+192t. Find the aver

jekas [21]

ANSWER

$80 {ms}^{ - 1}$

EXPLANATION

The average velocity of the ball is the rateof displacement over the total time.

The height of the ball, in feet, after t seconds is given by the function:

$f(t)=-16t^2+192t$

At time t=1, the height of the ball is

$f(1)=-16(1)^2+192(1)$

$f(1)=-16+192 = 176ft$

At time t=6, the height of the ball is

$f(6)=-16(6)^2+192(6)$

$f(6)=-16(36)+192(6)$

$f(6)=-576+1152 = 576$

The average velocity

$= \frac{f(6) - f(1)}{6 - 1}$

$= \frac{576- 176}{6 - 1}$

$= \frac{400}{5}$

$= 80 {ms}^{ - 1}$

7 0

2 years ago

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a

belka [17]

Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s
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