What is the area of the trapezoid with height 11 units?

For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?

sergey [27]

Answer:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}$

Step-by-step explanation:

Given

$f(x) = \frac{7}{2}x - 16$

Required

The difference quotient for h

The difference quotient is calculated as:

$\frac{f(x + h) - f(x)}{ h}$

Calculate f(x + h)

$f(x) = \frac{7}{2}x - 16$

$f(x+h) = \frac{7}{2}(x+h) - 16$

$f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16$

The numerator of $\frac{f(x + h) - f(x)}{ h}$ is:

$f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)$

$f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16$

Collect like terms

$f(x + h) - f(x) = \frac{7}{2}x -\frac{7}{2}x + \frac{7}{2}h- 16 + 16$

$f(x + h) - f(x) = \frac{7}{2}h$

So, we have:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h$

Rewrite as:

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}$

$\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}$

5 0

2 years ago

If a denotes some event, what does upper a overbara denote? if p(a)equals=0.9930.993, what is the value of p(upper a overba

masya89 [10]

P(A) = 0.993 is the probability of event A
_
P(A) is the probability of not A (note that I am trying to place a bar over A. I hope you can see it, else it is because the editor did not show it as I intended)

Then, use the fact that the probability of A plus the probability not A is equal to 1:
                  _
=> P(A) + P(A) = 1
       _
=> P(A) = 1 - P(A) = 1 - 0.993 = 0.007

So, the answers are:
      _
1) P(A) = 0.07
             _
2) Yes, A is unlikely because its probability is very low.

5 0

3 years ago

Solve for a <br> A= (a+b) H<br> 2

Nastasia [14]

Answer:

Step-by-step explanation:

· To provide some context, for an employee who earns $4,000 in each bi-weekly pay period in September through December, approximately $2,200 of Social Security taxes would be deferred. This same amount, of course, will need to be repaid beginning in 2021 and the employee’s paycheck would be reduced accordingly.

4 0

3 years ago

Please help meeee!!!!!!!!

ivanzaharov [21]

Answer:

$840$

Step-by-step explanation:

This is a good example of permutations. For the first slot on his shelf, Dylan has 7 trophies to choose from. Then 6, 5, and so on. Since he is only fitting 4 trophies on his shelf, we only continue until we have the slots filled. Thus, we have $7\cdot 6 \cdot 5\cdot 4=\boxed{840\:\text{ways}}$ to do so.

*Note: We do not divide by $4!$ because in this case, order matters. A different order of the same four books still produces different arrangements, so the order matters.

6 0

3 years ago

A Customer Telephone Center receives 1,200 calls in a 24-hour period. Of these calls, 75% occur between 9:30 a.m. and 3:30 p.m.,

Volgvan

Divide Total time into two Time Periods. A regular Demand and a High Demand Time Period. Since 75% of the 1,200 calls occur between 9:30 am and 3:30 pm. We multiply .75 x 1,200 to get 900. We get an average of 900 calls every day between the hours of 9:30 am and 3:30 pm – Our net time for this time period is 6 hours.

Therefore, 6 Hours/900 becomes our quotient

Again, since the denominator is larger we invert it to 900 calls/6 Hours

To get a demand of 150 calls per hour.

We need to be able to handle 150 calls per hour.

So how Many Call Representatives are needed?

Again, our historical data tells us that each person can handle 10 calls an hour.

Therefore 150 calls per hour /10 Minutes = 15 Customer Service Representatives are needed during Peak Time!

Now, Subtract the Peak Hours from the 21 Hours Net Time Per day, gives us 15 Non-Peak hours we have to staff.

8 0

2 years ago