Based on the information given, it should be noted that the least number of marbles that can be in the bag will be 10 marbles.
<h2>
Solution to the probability.</h2>
If the bag contains 60 marbles, the number of red marbles will be:
= 1/5 × 60
= 12 marbles.
The number of white marbles will be:
= 3/10 × 60
= 18 marbles.
The number of blue marbles will be:
= 60 - (12 + 18)
= 60 - 30
= 30 marbles.
Furthermore, when the bag has 4 red marbles and 6 white marbles, there'll be 10 blue marbles.
Lastly, to find the probability of choosing a blue marble, we've to multiply 1/2 by the number given.
Learn more about probability on:
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(5,4)
On a system of 2 perpendicular axis with O as origine, the pair (5,4) means:
5 is the distance from the origin O and situated on x-axis (on the right of O)
4 is the distance from the origin O and situated on y-axis (above O)
Then the pair (5,4) is situated in the 1st Quadrant
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:
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I want to use Fanny, [FFE4B5] Matches 2592 Win Rate 97.%[-]
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
