How many ways can a president, vis-president and treasurer be selected from a group of 15 students?
1 answer:
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Create a frequency chart by using a bar graph as shown in the picture below. A frequency chart is used when you want to present how much of the data belongs to one group. For this problem, it specifically represents how many people belong to a time interval. The y-axis is the number of people and the x-axis is the time expressed in intervals.
As you can see visually, the shape of the distribution graph is skewed to the right, although not uniformly. This is justified because the relatively high data are situated on the far right side of the graph. Also, there are no outliers in the data because they are all pretty close to each other. No bar is obviously different from the others. The center is the median of all the data. If you create a middle line as represented by the horizontal line, the center data point is 21. You can verify this by arranging all the data points from smallest to largest, and selecting the middle data. Lastly, the spread is from the lowest value to the highest value. The lowest value is at 12 to 1 pm with 19 people. The highest value is at 4 to 5 pm with 24 people. Therefore, the spread is from 19 to 24.
As you can see visually, the shape of the distribution graph is skewed to the right, although not uniformly. This is justified because the relatively high data are situated on the far right side of the graph. Also, there are no outliers in the data because they are all pretty close to each other. No bar is obviously different from the others. The center is the median of all the data. If you create a middle line as represented by the horizontal line, the center data point is 21. You can verify this by arranging all the data points from smallest to largest, and selecting the middle data. Lastly, the spread is from the lowest value to the highest value. The lowest value is at 12 to 1 pm with 19 people. The highest value is at 4 to 5 pm with 24 people. Therefore, the spread is from 19 to 24.
Answer:
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Step-by-step explanation:
Given that,
A box is being created out of a 15 inches by 10 inches sheet of metal.
The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.
The length of the metal box be = (15-2x) inches.
The width of the metal box be =(10-2x) inches
The height of the metal box be =x inches
Then, the volume of the metal box= length×width×height
=(15-2x)(10-2x)x cubic inches
=(150x-50x²+4x³) cubic inches
∴ V= 4x³-50x²+15x
Differentiating with respect to x
V'=12x²-100x+15
Again differentiating with respect to x
V''=24x-100
For maximum or minimum value, V'=0
12x²-100x+15=0
Apply quadratic formula , here a=12, b= -100 and c=15
For x= 8.18, The value of (15-2x) and (10-2x) will negative.
∴x=0.1528 .
Now,
∴At x=0.1528 inch, the volume of the metal box will be maximum.
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.