A taxi cab costs $1.50 for the first mile and $0.75 for each additional mile. Which equation could be solved to find how many mi
1 answer:
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Answer:
- f(x) = 34.59 +3.74x
- 0.96
- very strong
- 8.93
Step-by-step explanation:
1. The selection of answers offers a choice of positive or negative slope, a slope of about 4 or about 35, and y-intercepts from the same set of values.
If you consider a couple of points (at the ends of the domain is usually a good choice), you see the slope is about 4 and the y-intercept is around 30.
For example, the points (5, 50) and (15, 91) have a slope of (91-50)/(15-5) = 4.1 so will give rise to the equation ...
y -50 = 4.1(x -5)
Filling in x=0 gives y = 50 -20.5 = 29.5
So, the nearest of the offered choices is ...
f(x) = 34.59 +3.74x
Please note that no calculator is involved. We simply estimated the parameters of the regression line based on a couple of the data points. This estimate is sufficient to allow us to find the correct answer choice.
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2. If we look at a few other data points, we see that they have a generally upward trend that matches the above equation pretty well. That suggests a very high value of correlation, so the appropriate choices would be 0.93 or 0.96. Of course, the correlation is positive, matching the sign of the slope of the regression line. (Since the data points do not fall exactly on a line, the correlation is not 1.00. My assessment is they fall close enough to the line to rate a correlation of .96 instead of .93.)
At this point, the output of your calculator can confirm that the correlation coefficient is closer to 0.96. Mine says r = 0.9624.
r = 0.96
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3. We have already determined by examining the data points that the correlation is "very strong." The correlation coefficient of 0.96 confirms this.
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4. Using the equation of part 1, we can find the number of study hours:
68 = 34.59 +3.74x
(68 -34.59)/3.74 = x ≈ 8.933
We expect a score of 68 is associated with about 8.93 study hours.
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Please note that we have used very little calculation to determine the answers to this question. The only requirement is a general understanding of what linear regression and correlation coefficients mean.
Answer:
The area and the perimeter of the picture are:
- <u>Area = 160 cm^2</u>
- <u>Perimeter = 67.31 cm</u>
Step-by-step explanation:
To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:
- Area of a rectangle = base * height
As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:
- Area of a rectangle = 16 cm * 12 cm
- Area of a rectangle = 192 cm^2
Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:
- Area of a triangle = (base * height) / 2
The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:
- Area of a triangle = (8 cm * 8 cm) / 2
- Area of a triangle = (64 cm^2) / 2
- Area of a triangle = 32 cm^2
We subtract to the found area:
- Area of the picture = 192 cm^2 - 32 cm^2
- <u>Area of the picture = 160 cm^2</u>
To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:
Where:
- a = Opposite leg (8 cm)
- b = Adjacent leg (8 cm)
So, we replace in the theorem:
(and we clear c)
-
- c = 11.3137085 cm
- c ≅ 11.31 cm
At last, we add all the sides of the picture begining by the base and going by the left side:
- Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
- <u>Perimeter of the picture = 67.31 cm approximately</u>.