We have that
<span>p(t)=-3t^2+18t-4
using a graphing tool, we can see the maximum of the graph
(see the attached figure)
A) </span><span>In what year of operation does Mr. Cash’s business show maximum profit?
</span>
Mr. Cash’s business show maximum profit at year 3 (maximum in the parabole)
<span>B) What is the maximum profit?
23 (hundred of thousand of dollars) = 2.300.000 dollars
</span>c) What time will it be two late?
(This is the time when the graph crosses zero and the profits turn into losses )
5.77 years, or an estimate of about 69 months.
Answer:
The attached image shows the graph for the given function.
Step-by-step explanation:
We are given the following function in the question:

We have to graph the given function.
Properties of the given function are:
- It is an exponential function of the form

- Here, a = 2, b = -1
- The y-intercept of the given function is (0,0.5)
- There is no x-intercept.
- The domain of the given function is all real numbers.
- The range of given function is

The attached image shows the graph for the given function.
The number of bins in the histogram determines the width of the bins and
the frequency (number of members) in a bin.
- Please find attached the graph of the histogram of Gretchen's data created with MS Excel.
<h3 /><h3>Method used to create the histogram of Gretchen's data</h3>
Given:
The table from Gretchen's data is presented as follows;
![\begin{tabular}{|c|c|} \underline{ Member}& \underline{Number of Days}\\x_1&2\\x_2&4\\x_3&7\\x_4&8\\x_5&12\\x_6&15\\x_7&10\\x_8&7\\x_9&9\\x_{10}&6\\x_{11}&13\\x_{12}&3\\x_{13}&8\\x_{14}&10\\x_{15}&10\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%7B%7Cc%7Cc%7C%7D%20%5Cunderline%7B%20Member%7D%26%20%5Cunderline%7BNumber%20of%20Days%7D%5C%5Cx_1%262%5C%5Cx_2%264%5C%5Cx_3%267%5C%5Cx_4%268%5C%5Cx_5%2612%5C%5Cx_6%2615%5C%5Cx_7%2610%5C%5Cx_8%267%5C%5Cx_9%269%5C%5Cx_%7B10%7D%266%5C%5Cx_%7B11%7D%2613%5C%5Cx_%7B12%7D%263%5C%5Cx_%7B13%7D%268%5C%5Cx_%7B14%7D%2610%5C%5Cx_%7B15%7D%2610%5Cend%7Barray%7D%5Cright%5D)
The required number of bins = 8 bins
The steps to create the histogram using MS Excel;
- Enter the 15 dataset for the number of days as presented in the above table in a column on the worksheet.
- Select the dataset entered into the cells from above then select the Insert menu.
- In the Chart section of the insert menu click on the Histogram icon to view the quick options for histograms type charts.
- Select the Histogram option from the drop down menu from the quick options for histograms, to create an histogram chart.
- Right-click the histogram created from the previous step, then select Format Chart Area from the pop up menu.
- In the Format Chart Area task pane, click on the arrow next to Chart Options, then select Horizontal Axis from the options menu.
- Click on the histogram icon under Axis Options, then click on arrow button besides Axis Option sub menu, to display the axis options.
- Click on the Number of bins radio button then enter 8, to create an histogram having 8 bins.
The histogram of Gretchen's data having eight bins created with MS Excel is attached.
Learn more about creating a histogram chart here:
brainly.com/question/25069221
brainly.com/question/4601962
Answer:
x = ± 1 , x = ± 
Step-by-step explanation:
Let u = x² , then
- 3x² + 2 = 0 , can be expressed as
u² - 3u + 2 = 0 ← in standard form
(u - 1)(u - 2) = 0 ← in factored form
Equate each factor to zero and solve for u
u - 1 = 0 ⇒ u = 1
u - 2 = 0 ⇒ u = 2
Change the variable u back to x
x² = 1 ( take square root of both sides )
x = ± 1
or
x² = 2 ( take square root of both sides )
x = ± 