9514 1404 393

**Answer:**

B. 3

**Step-by-step explanation:**

If all you want is a numerical result, sometimes a graphing calculator can provide that easily. The attachment shows it calculates the slope at x=4 to be 3.

** dy/dx = 3 at x = 4**

__

The derivative of the expression can be found from the quotient formula:

d(u/v) = (du·v -u·dv)/v²

y' = ((x -2)(2x -7) -(x^2 -7x +2)(1))/(x -2)^2

= (2x^2 -11x +14 -x^2 +7x -2)/(x -2)^2

= (x^2 -4x +12)/(x -2)^2

= ((x -4)x +12)/(x -2)^2

Then for x=4, we have ...

y' = 12/4 = 3

** dy/dx = 3 at x = 4**

**Answer:**

1/6

**Step-by-step explanation:**

We want to find how long it takes for the bacteria to lose half its size. We can do this by taking one point of the bacteria and finding how long it takes to go to half its size. When t=0, 9300 * (1/64)^t = 9300 * 1 = 9300 as anything to the power of 0 is 1. Therefore, we can solve for t when the end result of the bacteria is 9300/2= 4650, making our equation

4650 = 9300 * (1/64)^t

divide both sides by 9300

1/2 = (1/64)^t

First, we can tell that 2^6 = 64*. Because of this, we can say that (1/2)^6 = 1^6/2^6 = 1/64, so (1/64)^(1/6) = 1/2. We know this because

(1/2)^6 = 64

take the 6th root of both sides

(1/2) = (64)^(1/6)

. This means that t=1/6, so the bacterial culture loses 1/2 of its size every 1/6 seconds

* if this is harder to figure out, e.g. 3 and 729, we can plug (log₃729) into a calculator

Please give Brainiest.

**Answer:**

First, subtract the budgeted amount from the actual expense. If this expense was over budget, then the result will be positive. Next, divide that number by the original budgeted amount and then multiply the result by 100 to get the percentage over budget.

I hope that helps.

**Answer:**

a. The population of interest is:

xi. All workers in the U.S. who have participated in the job-sharing program

b. The variable that is being measured is:

viii. The percentage of the 1035 major firms surveyed which offer job-sharing to their employees

c. The sample selected is:

vi. The 1,035 firms surveyed

d. The parameter is:

v. Proportion of employees who are working mothers

e. The statistic is:

ix. 25% (stated as 23%)

**Step-by-step explanation:**

The parameter of a population is a fixed value calculated from every individual in the population. It is different from a statistic, which is computed from a sample of the population. The statistic is meant to approximate a population parameter.

900,000+60,000+60

is in expanded form