Answer:
At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.
Step-by-step explanation:
Hello!
Considering the dependent variable:
Y: Ductility in steel.
And the independent variable:
X: Carbon content of the steel.
The linear regression was estimated and a prediction interval was calculated.
The prediction interval is calculated to predict a value that the variable Y (response variable) can take for a given value of the variable X (predictor variable) in the definition range of the linear regression line. Symbolically [Y/X=
]
In this case 95% prediction interval for Y/X=0.5
At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.
I hope it helps!
You've got five different problems in this photo ... four on top and the word problem on the bottom ... and they're all exactly the same thing: Taking two points and finding the slope of the line that goes through them.
In every case, the procedure is the same.
If the two points are (x₁ , y₁) and (x₂ , y₂) , then
the slope of the line that goes through them is
Slope = (y₂ - y₁) / (x₂ - x₁) .
This is important, and you should memorize it.
#1). (8, 10) and (-7, 14)
Slope = (14 - 10) / (-7 - 8) = 4 / -15
#2). (-3, 1) and (-17, 2)
Slope = (2 - 1) / (-17 - -3) = (2 - 1) / (-17 + 3) = 1 / -14
#3). (-20, -4) and (-12, -10)
Slope = [ -10 - (-4) ] / [ -12 - (-20) ]
=========================================
The word problem:
This question only gives you one point on the graph,
and then it wants to know what's the slope ?
What are you going to do for another point ?
A "proportional relationship" always passes through the origin,
so another point on the line is (0, 0) .
Now you have two points on THAT line too, and you can easily
find its slope.
After paying 4 tolls, Tony will have 4×$1.25 = $5.00 less change in his car. At that point, he will have $1 in change. The appropriate choice is
graph of line going through (0, 6) and (4,1)
Triangle 3 because its length is longer than the others.
In a rational function, holes are located where f(x) is undefined(the denominator is 0), but the undefined points can be factored out. In f(x), when x is 4 or -3, f(x) is undefined. But, x+3 can be factored out, so it is a hole. The hole is located at (-3,-1/7)
