What is the best method to solve the system of equations? 2x + 3y = 8 4x - 6y = 2?
1 answer:
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The obtained answers for the given frequency distribution are:
(a) The formula for the mean in sigma notation is where n is the number of observations;
are the n observations.
The mean for the given monthly plan price is $16.1.
(b) The frequency distribution for given data is {$9.99 - 2; $10 - 5; $12 - 1; $12.75 - 2; $14.99 - 6; $20 - 4; $25 - 5}
(c) The formula for the mean using the frequency distribution table is where
and on applying this formula for the given data, the mean is $16.1.
(d) The median for the given data is , and the mode for the given data is $14.99
The frequency distribution has sample observations and frequencies
.
Then, the mean is calculated by
Where (Sum of frequencies)
The median is calculated by
The mode is calculated by
Mode = highest frequency value
<h3>Calculation:</h3>The given list of data is
{$14.99, $12.75, $14.99, $14.99, $9.99, $25, $25, $10, $14.99, $10, $20, $10, $20, $14.99, $10, $25, $20, $12, $14.99, $25, $25, $20, $12.75, $10, $9.99}
(a) Formula for the mean using sigma notation and use it to calculate the mean:
The formula for the mean is
Where n = 25; - n observations
On substituting,
Mean
=1/25(14.99+12.75+14.99+14.99+9.99+25+25+10+14.99+10+20+10+20+14.99+10+25+20+12+14.99+25+25+20+12.75+10+9.99)
= 1/25(402.42)
= 16.09 ≅ 16.1
(b) Constructing a frequency distribution for the data:
Cost - frequency - cumulative frequency
$9.99 - 2 - 2
$10 - 5 - 7
$12 - 1 - 8
$12.75 - 2 - 10
$14.99 - 6 - 16
$20 - 4 - 20
$25 - 5 - 25
Sum of frequencies N = 25;
(c) Using frequency distribution, calculating the mean:
The formula for finding the mean using frequency distribution is
Where N = 25;
On substituting,
<em> </em>= 1/25 (2 × 9.99 + 5 × 10 + 1 × 12 + 2 × 12.75 + 6 × 14.99 + 4 × 20 + 5 × 25)
= 1/25 (402.42)
= 16.09 ≅ 16.1
Therefore, the mean is the same as the mean obtained in option (a).
(d) Calculating the median and the mode:
Since N = 25(odd) i.e., 2· 12 + 1; k = (12 + 1)th term = 13th term
So, the median = 14.99. (frequency at 13th term)
Since the highest frequency is 6 occurred by the cost is $14.99,
Mode = 14.99
Learn more about frequency distribution here:
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Answer:
The Perimeter of the Figure to the nearest tenth is 18.7 units
Step-by-step explanation:
Please note I have attached an edited version of your sketch to aid my solution. Now this question can be solved in multiple ways. Here, we shall see one of them. Looking at the original sketch, we can see that the figure is actually a combination of a Triangle (Figure 1 in my sketch) and a rectangle (Figure 2 in my sketch). So we can simply find the sides of a Triangle and the sides of a Rectangle and add them. Perimeter on Figure 1:The Perimeter of a Triangle is given by the Sum of the three sides as:
AT=a+b+c
Perimeter on Sketched Figure:The perimeter of the total figure will be two sides of the triangle and the three sides of the rectangle (as the one adjacent between Fig. 1 and 2 can not be taken into account). Thus we need to find 5 different sides and add them together. Now since the figure is on a graph paper, we can read of the size of some sides, thus the left side of the triangle is units and the base of the triangle is also units. Now to find the last unknown side we can take Pythagorian theorem, since our triangle is a Right triangle, (i.e. one angle is 90°). Pythagoras states that the squared of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs of the triangle (where the hypotenuse side is always across the 90° angle. So here we can say that: where is the hypotenuse and our unknown side. So plugging in values and solving for we have: units.
Perimeter on Figure 2:
The Perimeter of the Rectangle is given by:
Ar=2(w+l)
