Which of the following is an example of an opposing force?

The length of aluminum rods produced by a company are approximated by a Gaussian distribution with a mean of 10 cm and a standar

ExtremeBDS [4]

Given Information:

Mean length of aluminum rods = μ = 10 cm

Standard deviation of length of aluminum rods = σ = 0.02 cm

Required Information:

a) P(9.98 < X < 10.02) = ?

b) P(9.90 < X < 10.1) = ?

Answer:

a) P(9.98 < X < 10.02) = 68.27%

b) P(9.90 < X < 10.1) = 100%

Explanation:

What is Normal Distribution?

Normal Distribution or also known as Gaussian Distribution, is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability

a) We want to find out the probability that the length of aluminum rods is between 9.98 and 10.02 cm.

$P(9.98 < X < 10.02) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9.98 < X < 10.02) = P( \frac{9.98- 10}{0.02} < Z < \frac{10.02 - 10}{0.02} )\\\\P(9.98 < X < 10.02) = P( \frac{-0.02}{0.02} < Z < \frac{0.02}{0.02} )\\\\P(9.98 < X < 10.02) = P( -1 < Z < 1 )\\\\$

The z-score corresponding to -1 is 0.15866 and 1 is 0.84134

$P(9.98 < X < 10.02) = P( Z < 1 ) - P( Z < -1 ) \\\\P(9.98 < X < 10.02) = 0.84134 - 0.15866 \\\\P(9.98 < X < 10.02) = 0.6827\\\\P(9.98 < X < 10.02) = 68.27 \%$

Therefore, the probability that the length of aluminum rods is between 9.98 and 10.02 cm is 68.27%

b) We want to find out the probability that the length of aluminum rods is between 9.90 and 10.1 cm.

$P(9.90 < X < 10.1) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9.90 < X < 10.1) = P( \frac{9.90- 10}{0.02} < Z < \frac{10.1 - 10}{0.02} )\\\\P(9.90 < X < 10.1) = P( \frac{-0.1}{0.02} < Z < \frac{0.1}{0.02} )\\\\P(9.90 < X < 10.1) = P( -5 < Z < 5 )\\\\$

The z-score corresponding to -5 is 0 and 5 is 1

$P(9.90 < X < 10.1) = P( Z < 5 ) - P( Z < -5 ) \\\\P(9.90 < X < 10.1) = 1 - 0 \\\\P(9.90 < X < 10.1) = 1\\\\P(9.90 < X < 10.1) = 100 \%$

Therefore, the probability that the length of aluminum rods is between 9.90 and 10.1 cm is 100%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.00 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

8 0

3 years ago

A child uses a rubber band to launch a bottle cap at an angle of 37.0° above the horizontal. The cap travels a horizontal distan

zavuch27 [327]

Answer:

Initial velocity will be 1.356 m/sec

Explanation:

Let the initial speed = u

Angle at which rubber band is launched = 37°

Horizontal component of initial velocity $u_x=ucos\Theta =ucos37^{\circ}=0.7986u$

Time is given as t = 1.20 sec

Distance in horizontal direction = 1.30 m

We know that distance = speed × time

So time $t=\frac{distance}{speed}$

$1.20=\frac{1.3}{0.7986u}$

$u=1.356m/sec$

So initial velocity will be 1.356 m/sec

3 0

2 years ago

A three branch parallel circuit has resistors of 27 W, 56 W, and 15 W. What is the total resistance?

Mekhanik [1.2K]

Answer:8.2 Ω

Explanation:

I ASSUME you mean Ω (ohms) and not W(atts)

Re = 1/(1 / 27 + 1/56 + 1/15) = 8.2263329... ≈ 8.2 Ω

6 0

2 years ago

A standing wave pattern is created on a string with mass density μ = 3.4 × 10-4 kg/m. A wave generator with frequency f = 61 Hz

uranmaximum [27]

Answer:

1) λ = 0.413 m , 2)v = 25,213 m / s , 3) T = 0.216 N , 4) m = 22.04 10-3 kg

Explanation:

1) The resonance occurs when the traveling wave bounces at the ends and the two waves are added, the ends as they are fixed have a node, the wavelength and the length of the string are related

λ = 2L / n n = 1, 2, 3 ...

In this case L = 0.62 m and n = 3

Let's calculate

λ = 2 0.62 / 3

λ = 0.413 m

2) the velocity related to wavelength and frequency

v = λ f

v = 0.413 61

v = 25,213 m / s

3) let's use the equation

v = √T /μ

T = v² μ

T = 25,213² 3.4 10⁻⁴

T = 0.216 N

4) the rope tension is proportional to the hanging weight

T-W = 0

T = W

W = m g

m = W / g

m = 0.216 / 9.8

m = 22.04 10-3 kg

5) n = 2

λ = 2 0.62 / 2

λ = 0.62 m

6) v = λ f

v = 0.62 61

v = 37.82 m / s

7) T = v² μ

T = 37.82² 3.4 10⁻⁴

T = 0.486 N

8) m = W / g

m = 0.486 / 9.8

m = 49.62 10⁻³ kg

9) n = 1

λ = 2 0.62

λ = 1.24 m

v = 1.24 61

v = 75.64 m / s

T = v² miu

T = 75.64² 3.4 10⁻⁴

T = 2.572 10⁻² N

m = 2.572 10⁻² / 9.8

m = 262.4 10⁻³ kg

5 0

3 years ago

If a racquet ball hits the wall with 20 N of force, how much force will it bounce back with?

loris [4]

Answer:

-20N

Explanation:

The racquet ball will bounce back with the same force.

This is in compliance with newton's third law of motion:

"action and reaction are equal but opposite"

If the ball hits the wall with an action force of 20N, the reaction force will be -20N.

The negative indicates an oppositely directed force.

8 0

3 years ago