How many zeros does the function f(x) = 4x^11 − 20x^7 + 2x^3 − 15x + 14 have?
1 answer:
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Answer:
Width of intervals: 8
Step-by-step explanation:
We first look at how data is represented in a stem-leaf diagram.
Any number of the left (before -) is the stem and all numbers on right (after -) are the leaves. Each combination of stem and leaf represents one number. For example: 1 - 332 represents: 13, 13, 12.
Our data is as follows:
13, 13, 12, 24, 25, 31, 31, 35, 37, 42, 43, 41, 52, 51, 51, 52
To calculate the width of the frequency distribution chart, we have the following formula:
The range of any data set = Maximum value in the data set - Minimum value in the data set
Maximum value in this case as seen from the data is 52 and minimum is 12.
Range = 52 - 12 = 40
Since we had only 5 stems in the data, we shall use that as the number of classes required in the frequency distribution chart.
Hence, the class width in this data set will be 8.
To make the intervals, we begin from the minimum value and add 8 to it. The intervals will be:
12 - 20
20 - 28
28 - 36
36 - 44
44 - 52
Observe, that all the values of the stem lie within each interval.
For example, there are 3 values for stem 1: 12, 13, 13 and each lie in the first interval 12 - 20.
Next, the values of stem 2 are 24 and 25. Each of these value lie in the second interval 20 - 28; and henceforth.
Answer:
1)
2)
3) The greatest age that Sue could be is 7.
4) The smaller of the two integers is 92.
5) Don needs to earn at least 244 points in the fourth game.
Step-by-step explanation:
1) An rectangle has 2 dimensions: width(w) and length(l)
The perimeter P is:
The problem states that the length of a rectangle is three times its width. So l = 3w and:
The perimeter of the rectangle is at most 112 cm. It means that the perimeter can be 112, so the equal sign enters the inequality. So
2)
The problem states that he earns $850 per week in sales. His earnings is modeled by the following equation:
, in which w is the number of weeks.
The problem also states that he spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. So his expenses can be modeled by the following equation
, in which w is also the number of weeks.
He will make a profit when his earnings are bigger than his expenses, so: When they are equal, there is no profit, so the equal sign does not enter the inequality.
3)
I am going to call Jenny's age x and Sue's age y.
The problem states that Jenny is eight years older than twice her cousin Sue’s age. So
.
The sum of their ages is less than 32, so:
Sue's age has to be less than 8, so the greatest age that Sue could be is 7.
4)
The sum of two consecutive integers is at least 185.
There are two integers with sum of 185, so:
They are consecutive so:
Replacing in the sum equation:
The smaller of the two integers is 92.
5)
The average is the sum of all the scores divided by the number of games. So:
Don needs to earn at least 244 points in the fourth game.