How does the stratosphere protect us?

Which data set has the smallest standard deviation?

hjlf

Answer:

B. 22,22,23,23,22,22,23

Explanation:

The standard deviation is a measure of dispersion or variability of a data set. In order to determine the data set that has the smallest standard deviation, we shall investigate on the ranges of the data sets given. The range of a data set is simply the difference between the maximum and minimum values in a data set. A data set that has a smaller range also has a smaller standard deviation.

From the alternatives given, the data set given by alternative B has the smallest range and consequently the smallest standard deviation.

The maximum value is 23 while the minimum is 22. The range is 1.

5 0

3 years ago

A student adds two vectors of magnitudes 48 m and 22 m. What are the maximum and minimum possible values for the resultant of th

Julli [10]

Answer:

Maximum=70 m

Minimum=26 m

Explanation:

Vector Addition

Since vectors have magnitude and direction, adding them takes into consideration not only the magnitudes but also their respective directions. Two vectors can be totally collaborative, i.e., point to the same direction, or be totally opposite. In the first case, the magnitude of the sum is at maximum. Otherwise, it's at a minimum.

Thus, the maximum magnitude of the sum is 48+22 = 70 m and the minimum magnitude of the sum is 48-22= 26 m

4 0

3 years ago

Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bu

vlada-n [284]

Answer:

$\frac{1}{10}$ M

Explanation:

To apply the concept of angular momentum conservation, there should be no external torque before and after

As the asteroid is travelling directly towards the center of the Earth, after impact ,it does not impose any torque on earth's rotation, So angular momentum of earth is conserved

⇒ $I_{1} \times W_{1} =I_{2} \times W_{2}$

$I_{1}$ is the moment of interia of earth before impact
$W_{1}$ is the angular velocity of earth about an axis passing through the center of earth before impact
$I_{2}$ is moment of interia of earth and asteroid system
$W_{2}$ is the angular velocity of earth and asteroid system about the same axis

let $W_{1}=W$

since $\text{Time period of rotation}∝$ $\frac{1}{\text{Angular velocity}}$

⇒ if time period is to increase by 25%, which is $\frac{5}{4}$ times, the angular velocity decreases 25% which is $\frac{4}{5}$ times

therefore $W_{1}$ $=$ $\frac{4}{5} \times W_{1}$

$I_{1}=\frac{2}{5} \times M\times R^{2}$ (moment of inertia of solid sphere)

where M is mass of earth

R is radius of earth

$I_{2}=\frac{2}{5} \times M\times R^{2}+M_{1}\times R^{2}$

(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)

where $M_{1}$ is mass of asteroid

⇒ $\frac{2}{5} \times M\times R^{2} \times W_{1}=}(\frac{2}{5} \times M\times R^{2}$ $+$ $M_{1}\times R^{2})\times(\frac{4}{5} \times W_{1})$

$\frac{1}{2} \times M\times R^{2}$ = $(\frac{2}{5} \times M\times R^{2}$ + $M_{1}\times R^{2})$

$M_{1}\times R^{2}=$ $\frac{1}{10} \times M\times R^{2}$

⇒ $M_{1}=}$ $\frac{1}{10} \times M$

3 0

3 years ago

A toy cannon launches a 46-g golf ball straight up into the air with a kinetic energy of 6.8 J. What must the

Shkiper50 [21]

Answer : The correct option is, (C) 17 m/s

Explanation :

Formula used :

$K.E=\frac{1}{2}mv^2$

where,

K.E = kinetic energy = 6.8 J

m = mass of object = 46 g = 0.046 kg (1 kg = 1000 g)

v = velocity

Now put all the given values in the above formula, we get:

$K.E=\frac{1}{2}mv^2$

$6.8J=\frac{1}{2}\times 0.046kg\times v^2$

$6.8kg.m^2/s^2=\frac{1}{2}\times 0.046kg\times v^2$

$v=17.19m/s\approx 17m/s$

Therefore, the ball's velocity be as it leaves the cannon is, 17 m/s

3 0

3 years ago

Estimate the power you produce in running up a flight of stairs. Give your answer in horsepower (1 hp = 746 W). Suppose you clim

GarryVolchara [31]

The first thing you should do is calculate the work done when climbing the stairs. This work by definition will be given by:
W = F * d
W = (m * g) * (d)
W = ((71) * (9.8)) * (3) = 2087.4J
Then, you can calculate the power that in this case is given by
P = W / t
P = (2087.4) / (10) = 208.74W
To have the result in HP we use the fact that 1HP = 746W
P = (208.74) / (746)
P = 0.28 HP
answer
the power you produce in running up a flight of stairs is 0.28 HP

3 0

3 years ago

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