a blue print of a house is drawn using a scale of 1/4 in=3 ft. If the bedroom of the actual house is 16 in by 12 in, what are th
1 answer:
Answer:
64 feet × 48 feet
Step-by-step explanation:
Dimensions refers to the measurements of the house including length and breadth of the house.
Given:a blue print of a house is drawn using a scale of
To find:the dimensions of the bedroom on the blueprint
Solution:
Length of the bedroom = 16 in
So, length of the bedroom in the blueprint = 16×4=64 feet
Breadth of the bedroom = 12 in
So, breadth of the bedroom in the blueprint = 12×4 = 48 feet
Therefore, dimensions of the bedroom in the blue print = 64 feet × 48 feet
You might be interested in
Answer:
The definition for the given piecewise-defined function is: .
Step-by-step explanation:
<h3>General Concepts:</h3>- Piecewise-defined functions.
- Interval notations.
<h3>What is a piecewise-defined function?</h3>
A piecewise-defined function represents specific rules over different intervals of the domain.
<h3>Symbols used in expressing interval notations:</h3>Open interval: This means that the endpoint is <em>not</em> included in the interval.
We can use the following symbols to indicate the <u>exclusion</u> of endpoints in the interval:
- Left or right parenthesis, "( )" (or both).
- Greater than (>) or less than (<) symbols.
- Open dot "
" is another way of expressing the exclusion of an endpoint in the graph of a piecewise-defined function.
Closed interval: This implies the inclusion of endpoints in the interval.
We can use the following symbols to indicate the <u>inclusion</u> of endpoints in the interval:
- Open- or closed brackets (or both), "[ ]."
- Greater than or equal to (≥) or less than or equal to (≤) symbols.
- Closed circle or dot, "•" is another way of expressing the <em>inclusion</em> of the endpoint in the graph of a piecewise-defined function.
The best way to determine which piecewise-defined function represents the graph is by observing the <u>endpoints</u> and <u>orientation</u> of both partial lines.
- Open circle on (-1, 2): The graph shows that one of the partial lines has an <em>excluded</em> endpoint of (-1, 2) extending towards the <u>right</u>. This implies that its domain values are defined when x > -1.
- Closed circle on (-1, 1): The graph shows that one of the partial lines has an <em>included</em> endpoint of (-1, 1) extended towards the <u>left</u>. Hence, its domain values are defined when x ≤ -1.
Based on our observations from the previous step, we can infer that x > -1 or x ≤ -1 apply to piecewise-defined functions A or D. However, only one of those two options represent the graph.
<h2>Solution:</h2><h3>a) Test option A:</h3>
We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a <u>closed dot</u>.
Substitute x = -2 into f(x) = 2x + 2:
- f(x) = 2x + 2
- f(-2) = 2(-2) + 2
- f(-2) = -4 + 2
- f(-2) = -2 ⇒ <em>False statement</em>.
⇒ The output value of f(-2) = -2 is <u>not</u> included in the graph of the partial line whose endpoint is at (-1, 1).
<h3>Piece 2: If x > -1, then it is defined by f(x) = x + 4. </h3>
We must choose a domain value that falls within the interval of x > -1 whose output is included in the graph of the partial line with an <u>open dot</u>.
Substitute x = 0 into f(x) = x + 4:
- f(x) = x + 4
- f(0) = (0) + 4
- f(0) = 4 ⇒ <em>True statement</em>.
⇒ The output value of f(0) = 4 <u>is</u> included in the graph of the partial line whose endpoint is at (-1, 2).
Conclusion for Option A:
Option A is not the correct piecewise-defined function because one of the pieces, f(x) = 2x + 2, does not specify the interval (-∞, -1].
<h3>b) Test option D:</h3>
We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a <u>closed dot</u>.
Substitute x = -2 into f(x) = x + 2:
- f(x) = x + 2
- f(-2) = (-2) + 2
- f(-2) = 0 ⇒ <em>True statement</em>.
⇒ The output value of f(-2) = 0 <u>is</u> included the graph of the partial line whose endpoint is at (-1, 1).
<h3>Piece 2: If x > -1, then it is defined by f(x) = 2x + 4.</h3>
We must choose a domain value that falls within the interval of x > -1 whose output is included is included in the graph of the partial line with an <u>open dot</u>.
Substitute x = 0 into f(x) = 2x + 4:
- f(x) = 2x + 4
- f(0) = 2(0) + 4
- f(0) = 0 + 4 = 0 ⇒ <em>True statement</em>.
⇒ The output value of f(0) = 4 <u>is</u> included in the graph of the partial line whose endpoint is at (-1, 2).
<h2>Final Answer: </h2>
We can infer that the piecewise-defined function that represents the graph is:
.
________________________________________
Learn more about piecewise-defined functions here:
Answer:
Mean of the data set in the dot plot would be: 3.6
Step-by-step explanation:
As we know that Mean from the dot plot can be obtained by:
- adding the numbers and then
- divide the resulting sum by the number of addends.
Please check the attached figure where the dot plot is also plotted.
From the dot plot, it is clear that
There are 3 dots at 1.
There are 4 dots at 2.
There are 3 dots at 3.
There are 4 dots at 4.
There are 5 dots at 5.
There are 3 dots at 6.
All we have to do is to add the dots and divide the sum by the number of addend dots.
In other words:
There are 3 dots at 1 ⇒ 1+1+1
There are 4 dots at 2 ⇒ 2+2+2+2
There are 3 dots at 3 ⇒ 3+3+3
There are 4 dots at 4 ⇒ 4+4+4+4
There are 5 dots at 5 ⇒ 5+5+5+5+5
There are 3 dots at 6 ⇒ 6+6+6
As there are total 22 dots.
And the sum of all the dots with respect to their plot number = 79
i.e. 1+1+1+2+2+2+2+3+3+3+4+4+4+4+5+5+5+5+5+6+6+6 = 79
Thus
Mean of the data set in the dot plot = 79/22
= 3.6
Therefore, Mean of the data set in the dot plot would be: 3.6
