Write the standard form of the line that contains a slope of -3/8 and passes through the point (5, -4). Include your work in you

<span>Denote x as the interval, then: 186 = 50 + 3 + (3+x) + (3+2x) + (3+3x) + (3+4x) + (3+5x) + (3+6x) + (3+7x) 186 = 74 + 28x x = 4 Age of the eldest son = 3+7x = 3+28 = 31.</span>

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.

     

To resolve this issue, you simply multiply base 1 by height 1, which equals base 2 multiplied by height 2. Inserting our values yields 24 * 4 = 5 * height 2. By solving, we find the missing height to be 19.2. 

Response:  a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

Detailed explanation:

In Problem 8-4, the computer time-sharing system experiences teleport inquiries at an average rate of 0.1 per millisecond. We are tasked with determining the probabilities of the inquiries over a specific period of 50 milliseconds:

Given that

Applying the Poisson process, we find that

(a) at most 12

probability=  

(b) exactly 13

probability=

(c) more than 12

probability=

(d) exactly 20

probability=

(e) within the range of 10 to 15, inclusive

probability=

Thus, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

An airplane flying at a speed of 950 kilometers per hour would take 0.0010526 hours to travel 1.00 kilometer.