Question 18 Item 18 The distribution of the number of moths captured per night by a certain moth trap is approximately normal wi

Answer:

The hourly rate for lectures is $7.33

Step-by-step explanation:

* Let's break down how to tackle the problem.

- For the level 3 course, examination hours are priced at double that of workshop hours.

- Workshop hours cost twice the rate of lecture hours.

- The total includes examination, workshop, and lecture hours.

- Examination lasts 3 hours, workshops 24 hours, and lectures 12 hours.

* Let’s denote the cost of lecture hours as $x per hour.

∴ The lectures cost $x per hour.

∵ Workshop charge is twice that of lectures

∴ Workshop hours cost 2(x) = 2x per hour.

∵ Examination fees are double that of workshop hours

∵ The workshop cost is 2x

∴ Examination fees are 2(2x) = 4x per hour.

- Combining costs for level 3 gives us the total of lecture, workshop, and examination hours.

∵ 12 hours for lectures

∵ 24 hours for workshops

∵ 3 hours for examinations

∵ Thus the total cost for level 3 = 12(x) + 24(2x) + 3(4x).

∴ Total cost for level 3 = 12x + 48x + 12x.

∵ Therefore, total cost = $528.

∴ 12x + 48x + 12x = 528.

∴ 72x = 528; hence we divide both sides by 72.

∴ x = 7.33.

∵ x represents the cost of lecture hours per hour.

∴ Therefore, the hourly price for lectures is $7.33.

Response:

a

    f'(t) is negative

b

 The unit is degC/min

c

At 35 minutes since the coffee was placed on the counter, the temperature is 68, and it will drop by approximately 0.75 in the next 30 seconds.

Detailed explanation:

According to the question, we are informed that

   The temperature of a cup of coffee on a counter is represented by the equation

where t indicates the time in minutes since the coffee was set on the counter.

In general, f(t)' denotes the derivative of f(t), indicating the change in temperature over time for the coffee

As the coffee rests on the counter, its temperature tends to decrease after a few minutes; thus, f(t)' is negative.

The temperature is measured in degrees Celsius while time is expressed in minutes.

Therefore, the change in temperature with respect to time, f(35)', will be given in degrees Celsius per minute (i.e., degC/min).

The question states that

which means the rate of temperature change after 35 minutes is 1.5.

And

indicating that the coffee's temperature after 35 minutes is 67 degrees Celsius.

Subsequently, after another t= 30 seconds = the rate at which the coffee's temperature changes is

=>        

=>            

Thus

At 35 minutes since the coffee was placed on the counter, its temperature is 68 and will drop by roughly 0.75 in the next 30 seconds.