What is the equation of the line? please help...
1 answer:
You might be interested in
Answer:
a)
b) 3,624.25 pounds
Step-by-step explanation:
a)
Since 4300/25 = 172, in average every single person should weight 172 pounds to exceed the design limit.
The probability that one person weights 172 pounds or more is the area under the Normal curve with mean 160 pounds and standard deviation 30 pounds to the right of 172.
<em>In Excel and OpenOffice Calc, this value is found with the formula </em>
<em>=1-NORMDIST(172;160;30;1) </em>
<em> (NORMDIST(172;160;30;1) gives the area to the left of 172, so 1-NORMDIST(172;160;30;1) gives the area to the right of 172) </em>
and equals 0.3446
(see picture 1)
Hence, the probability that all the 25 people exceeds 172 pounds equals
b)
Similarly, we must find a weight w such that if p is the area to the left of w, then
so
w would be the point such that the area under the Normal curve with mean 160 pounds and standard deviation 30 pounds to the right of w equals 0.6918.
<em>In Excel and OpenOffice Calc this is found with </em>
<em>=NORMINV(1-0.6918;160;30) </em>
and equals 144.97 pounds
(See picture 2)
and the design limit that is exceeded by 25 occupants with probability 0.0001 is 25*144.97 = 3,624.25 pounds
Answer:
3) rate of change = -5/4
4) rate of change = 3
5) rate of change = 1
6) steepest slope = #4
7) Please see the attached graph and explanation below
8) Please see the attached graph and explanation below
Step-by-step explanation:
<h3><u>Note:</u> </h3>I will do questions 3, 4, 6, 7, and 8, and will let you work on question 5 (since it involves the same process of solving for the rate of change as questions 3 and 4). However, the rate of change for question 5 is 1.
<h3>3) Calculate the Rate of Change from the Graph: </h3>The <u>rate of change</u> is essentially the same as the <em>slope</em> of a linear equation, where it represents the ratio of a change in y to a corresponding change in x.
In order to solve for the rate of change, choose two points from the given graph.
Let (x₁, y₁) = (0, 200)
(x₂, y₂) = (80, 100)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (100 - 200)/(80 - 0)
m = -100/80
Reduce to lowest terms by dividing the numerator and the denominator by 20/20:
m = -5/4
Therefore, the rate of change is -5/4.
<h3>4) Calculate the Rate of Change from the Table: </h3>Similar to what we did in question 3, choose two ordered pairs from the given table:
Let (x₁, y₁) = (0, -1)
(x₂, y₂) = (3, 8)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = 3
Therefore, the rate of change from the given table is 3.
<h3>6) Which linear function has the steepest slope? </h3>The positive-sloped lines whose rate of change has the highest value will have the steepest slope. For lines with negative slopes (downward-tilting lines), the highest absolute value for its rate of change will have the steepest negative slope.
Hence, the linear function with the steepest slope is #4 because the value of y changes by 3 units for every unit of change in x values.
<h3>7) Graph the equation: y = -6x - 4:</h3>The linear equation, y = -6x - 4, where the slope, m = -6, and the y-intercept is (0, -4).
- To graph this equation, start by plotting the y-intercept.
- Then, use the slope, m = -6/1 (down 6 units, run 1 unit to the right) to plot other points on the graph. In doing so, your next graph should occur at point, (1, -10). Connect the two points to create a line that will represent the given equation, y = -6x - 4.
Technically, two points are sufficient enough to connect and create a line with. Please see the attached screenshot of the graph for y = -6x - 4.
<h3>8) Graph the following equation: 3x - 4y = 12</h3>The given linear equation is in its <u>standard form</u>, Ax + By = C. It is easier to graph when the equation is in its <u>slope-intercept form,</u> y = mx + b.
In order to transform the given standard equation to slope-intercept form, start by subtracting 3x from both sides:
3x - 4y = 12
3x -3x - 4y = -3x + 12
-4y = -3x + 12
Divide both sides by -4 to isolate y:
y = ¾x - 3 ⇒ This is the slope-intercept form where the slope, m = ¾, and the y-intercept is (0, -3).
<h3><u>Graph:</u></h3>Similar to how we graphed the equation from question 7, start by plotting the y-intercept (0, -3) on the graph. Then, use the slope, m = ¾ (3 units up, 4 units run), to plot other points on the graph. Your next point occurs at the <u>x-intercept</u>, (4, 0). The <em>x-intercept</em> is the point on the graph where it crosses the x-axis. Connect the two points to create a line that will represent the given equation, 3x - 4y = 12.
Please see the attached screenshot of the graph for 3x - 4y = 12.
