Joe wants to enlarge the rectangular pumpkin patch located on his farm. The pumpkin patch is currently 40 meters wide and 60 met

Answer:

The equation will be altered by doubling the angular velocity of motion, resulting in d(s) = 7·sin(720s)

Step-by-step explanation:

The current equation of the pendulum-like motion of the pocket watch is d(s) = 7sin(360s)

The formula for simple harmonic motion is x = A·sin(ω₁t + ∅)

By comparing, we find;

x = d(s)

A = 7

ω₁t = 360

∅ = 0

The period of oscillation is the duration needed for a complete cycle, calculated as  2·π/ω₁.

Thus;

ω₁ = 2·π/T₁

When the frequency of the swing doubles, the time taken to complete one cycle is halved, hence, the new period is T₂ = T₁/2.

Consequently, ω₂ = 2·π/T₂  = 2·π/(T₁/2) = 4·π/T₁ = 2ω₁.

The revised equation becomes:

x = A·sin(ω₂t) =  A·sin(2ω₁t) leading to;

d(s) = 7·sin(2 × 360s) = 7·sin(720s).

This illustrates the modification due to an increase in the angular frequency of motion.

Response:

The probability that a student has a pet, given they do not have any siblings is:

Option: D ( 60%)

Step-by-step breakdown:

Let A represent the situation where a student lacks a sibling.

Let B signify the occurrence that a student has a pet.

Consequently, A∩B refers to the event in which a student is without siblings but possesses a pet.

Let P denote the chance of an event happening.

We need to determine:

P(B|A)

From our knowledge:

From the data provided:

P(A)=0.25

and P(A∩B)=0.15

Thus,

which expressed as a percentage is:

Therefore, the probability is:

60%

Answer:

57.2 g

Step-by-step explanation:

Organizing the data in increasing order to find the outlier and compute the mean

Detailed explanation:

The provided data consists of: [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]

Arranging it in ascending sequence

                               [1, 3, 4, 4, 9, 10, 12, 15, 16, 18, 32 ]

The outlier is identified as 32

Calculating the mean;

Mean=total of data set/quantity of data set

Total= 1 + 3+ 4+ 4+ 9+ 10+ 12+ 15+ 16+ 18+ 32=124

Quantity of data set=11

Mean=124/11=11.27