The answer to number 9 please

Danny is riding his bike at 12m/s he tries to pop a wheelie but he fails hits a curb flies through the air and comes to a comple

maxonik [38]

Answer:

a = -0.4m/s²

Explanation:

v_f = v_I + (a)(t)

a(t) = v_f-v_I

a = (v_f-v_I)/t

a = (0m/s-12m/s)/30s

a = -0.4m/s²

8 0

2 years ago

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

An electromagnetic wave has a frequency of 4.0 x 1018 Hz. What is the

trapecia [35]

Answer: D

Wavelength λ = 7.5 × 10^-11 m

Explanation:

You are given the frequency of an electromagnetic wave to be:

F = 4.0 x 1018 Hz. And the speed of light C to be

C = 3 × 10^8 m/s

From wave speed formula:

Wave speed is the product of waves frequency and wavelength. That is,

V = fλ

Where

f = frequency

λ = wavelength

V = C = speed of light

Substitute the values of the parameters into the formula

C = fλ

3 × 10^8 = 4 × 10^18 × λ

Make λ the subject of formula

λ = (3×10^8)/(4×10^18)

λ = 7.5 × 10^-11 m

Therefore, the wavelength of the wave is 7.5 × 10^-11 m

8 0

3 years ago

HELP PLS!!!! Light travels approximately 982,080,000 ft/s, and one year has approximately 32,000,000 seconds. A light year is th

maw [93]

You've already told us the speed in ft/s . It's right there in the question. You said that light travels about 982,080,000 ft/s.

We don't know how accurate that number is, but for purposes of THIS question, that's the number we're going with.

In scientific notation, it's written . . . <em>9.8208 x 10⁸ ft/s .</em>

We don't know where you were going with the number of seconds in a year. But to answer the question that you eventually asked, it turned out that we don't even need it.

6 0

3 years ago

How o astronomers gather information to establish the hubble law?

Novay_Z [31]

<span>they had originally used einsteins therory of relativity and his field equations to figure out their information</span>

8 0

3 years ago