The weights (to the nearest pound) of some boxes to be shipped are found to be:. Weight 65 68 69 70 71 72 90 95 frequency 1 2 5

The toddler weighs 12.5 kg.

In-depth explanation:

The formula for gravitational potential energy is Ep=mgh where;

Ep=gravitational potential energy

m=mass of an object

g=gravitational field strength

h=height in meters

Given that; h= 1.5m, Ep=187.5J, g=10 N/kg then finding m;

Ep=mgh

187.5=m*10*1.5

187.5=15m

187.5/15 =15m/15

m=12.5 kg

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• Gravitation potential energy:

Keywords: Mass, gravitational potential energy

Answer:

120*2.75*60/5280

= 3.75

Step-by-step explanation:

Considering James takes 120 steps in a minute, with 60 minutes in an hour and a mile consisting of 5,280 feet, we can establish his walking pace. By multiplying his steps per minute by the distance of each step (120 * 2.75), we determine the distance he covers in one minute. This value is then multiplied by 60 to account for the total hour. Finally, the total distance is divided by the feet in a mile (5,280), which results in a speed of 3.75 miles per hour. Thus, the calculation becomes 120*2.75*60/5280

Answer:

1.21 g/day

Step-by-step explanation:

We start with the fact that

The mass of the bacterial colony (in grams) is described by

Where t=Time(in days)

Next, we differentiate with respect to t

Using the formula

We know that P(t)=6

Now, substitute this value

Insert the given value of t

We understand that

Applying the formula

By employing

g/day

Consequently, the instantaneous rate at which the mass of the colony changes is=1.21g/day

Answer:

We have defined functions:

f(x) = IxI + 1

g(x) = 1/x^3.

Currently, it is evident that the composite functions are not commutative.

How can we demonstrate this?

To determine if two composite functions are commutative, the following must hold true:

f(g(x)) = g(f(x))

One could apply brute force (simply substituting values to see if the composite functions commute),

but I will opt for a more sophisticated approach.

There are two notable observations:

g(x) has a point of discontinuity at x = 0.

Thus:

f(g(x)) = I 1/x^3 I + 1

remains discontinuous at x = 0, whereas:

g(f(x)) = 1/(IxI + 1)^3

shows that the denominator IxI + 1 can never reach zero.

At this point, there is no discontinuity.

Consequently, the composite functions cannot be commutative.