Solve the following absolute value inequality
1 answer:
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Answer: the median is 6.
Please see the picture attached.
A line plot shows the number of occurrences (crosses) of each number of a data set.
The median is the central value, the middle number, of a data set ordered from least to greatest. When there are two middle numbers, the median will be the mean between the two.
In order to find the median, look at the line plot: count how many values you have (22), then add 1 (23) and divide by two (11.5). Since we have an even number of values, we will have two middle numbers, which will be in the eleventh and twelfth position.
Count the crosses from the left, the eleventh and twelfth crosses both correspond to the number 6, therefore the median is 6.
You can also write all the numbers in increasing order and divide them into two equal groups:
1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 | 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11
The median will be the average between the two central numbers, therefore 6 (again).
Please see the picture attached.
A line plot shows the number of occurrences (crosses) of each number of a data set.
The median is the central value, the middle number, of a data set ordered from least to greatest. When there are two middle numbers, the median will be the mean between the two.
In order to find the median, look at the line plot: count how many values you have (22), then add 1 (23) and divide by two (11.5). Since we have an even number of values, we will have two middle numbers, which will be in the eleventh and twelfth position.
Count the crosses from the left, the eleventh and twelfth crosses both correspond to the number 6, therefore the median is 6.
You can also write all the numbers in increasing order and divide them into two equal groups:
1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 | 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11
The median will be the average between the two central numbers, therefore 6 (again).
Answer:
- adult: $11
- children: $7
Step-by-step explanation:
The sales on the two days can be expressed using equations that can be solved for ticket prices.
<h3>Setup</h3>Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...
- 5x +7y = 104
- 7x +3y = 98
One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.
Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)
Yet another solution method can use the coefficients from the equations written in general form:
- 5x +7y -104 = 0
- 7x +3y -98 = 0
In this form, we define three products of "cross multiplication":
Δ1 = (5)(3) -(7)(7) = -34
Δ2 = (7)(-98) -(3)(-104) = -374
Δ3 = (-104)(7) -(-98)(5) = -238
Using those, we find the variable values to be ...
x = Δ2/Δ1 = -374/-34 = 11
y = Δ3/Δ1 = -238/-34 = 7
(adult price, children price) = ($11, $7)
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You can read more about the cross-multiplication method here:
