The perimeter of a rectangle is 60. The length is twice the width. Find the length and width.
1 answer:
Step-by-step explanation: Our first task in this problem is to setup variables representing <em>length</em> and <em>width</em> and we do that by using the second sentence.
<em><u>The length is twice the width</u></em>
So if we call our width <em>x</em>, that means that our length is 2 times <em>x</em> or 2x
Width of the rectangle ⇒ <em>x</em>
Length of the rectangle ⇒ <em>2x</em>
Before moving on, go ahead and draw a picture of your
rectangle so that you can visualize what's going on.
I have done this for you below.
We label our widths <em>x</em> and our lengths <em>2x</em>.
Now we can use the first sentence to setup our equation.
The perimeter of a rectangle is the distance
around the outside of the figure.
So if our perimeter is 60, that means that x + x + 2x + 2x = 60.
Simplifying by combining like terms, we get 6x = 60.
Now dividing both sides by 6, we find that <em>x = 10</em>.
Since <em>x</em> represents width, our width is 10.
Our length therefore with be <em>2(10)</em> or 20.
So our width is 10 and our length is 20.
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<h3>Answer: </h3>
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Explanation:
The data set for Ali is
8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8,
8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9
which when on a single line looks like this
8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8, 8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9
Let's sort the values from smallest to largest
4.7, 5.8, 5.9, 6.5, 6.5, 7.0, 7.2, 7.7, 8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9, 9.1, 9.8, 9.9
Now lets break the data up into separate rows such that each time we get to a new units value, we move to another row
4.7
5.8, 5.9
6.5, 6.5
7.0, 7.2, 7.7
8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9
9.1, 9.8, 9.9
We have these stems: 4, 5, 6, 7, 8, 9 which represent the units digit of the values. The leaf values are the tenths decimal place.
For example, a number like 4.7 has a stem of 4 and leaf of 7 (as indicated by the key below)
This is what the stem-and-leaf plot looks like for Ali's data only
The stem-and-leaf plot condenses things by tossing out repeated elements. Instead of writing 8.1, 8.1, 8.3 for instance, we can just write a stem of 8 and then list the individual leaves 1, 1 and 3. We save ourselves from having to write two more copies of '8'
Through similar steps, this is what the stem-and-leaf plot looks like for Kumar's data set only
Kumar doesn't have any leaves for the stem 6, so we will have that section blank. It's important to have this stem so it aligns with Ali's stem plot.
Notice that both stem plots involve the same exact set of stems (4 through 9 inclusive).
What we can do is combine those two plots into one single diagram like this
Then the last thing to do is reverse each set of leaves for Ali (handle each row separately). The reason for this is so that each row of leaf values increases as you further move away from the stem. This is simply a style choice. This is somewhat similar to a number line, except negative values aren't involved here.
This is what the final answer would look like
The fact that Ali is on the left side vs Kumar on the right, doesn't really matter. We could swap the two positions and end up with the same basic table. I placed Ali on the left because her data set is on the top row of the original table given.
The thing you need to watch out for is that joining the stem and leaf for Ali means you'll have to read from right to left (as opposed to left to right). Always start with the stem. That's one potential drawback to a back-to-back stem-and-leaf plot. The advantage is that it helps us compare the two data sets fairly quickly.
Answer:
832
Step-by-step explanation:
standard deviation =228 minute
error =13 minute given
confidence level =905% =0.90
α=1-0.90=0.1
we know that sample size should be greater than
n=832