Answer:
50. 8 cm
51. 12π = 37.7 cm³
52. 113 cubic inches.
53. negative
54. non-linear
Step-by-step explanation:
50. Determine the height of a cylinder given radius = 3 cm and volume = 72 π cm³.
First we need to remember that the formula to calculate the volume of a cylinder is:
V = π * r² * h
Since know everything in this equation (we know V - 72π - and we know r - 3 -, we obviously know π ), we just need to isolate h and input the data we know.
[tex]h = \frac{V}{\pi * r^{2} } = \frac{72 \pi}{\pi * 3^{2} } = \frac{72}{9} = 8[/tex]
The height is then 8 cm.
51. Determine the volume of a cone, given radius = 2 cm, height = 9 cm.
First we need to remember that the formula to calculate the volume of a cone is:
V = (π * r² * h) / 3
Then we just have to enter our numbers in it and do the math:
[tex]V= \frac{\pi * r^{2} * h}{3} = \frac{\pi * 2^{2} * 9}{3} = 12 \pi = 37.7[/tex]
The volume of that cone is equivalent to 12 times π or about 37.7 cm³
52. Determine the volume of a grapefruit with a radius of 3 inches, round to the whole number.
A grapefruit is a sphere, we'll assume it's regular. First we need to remember that the formula to calculate the volume of a sphere is:
V = 4(π * r³) / 3
Then we enter our numbers in it:
[tex]V = \frac{4 * \pi * r^{3}}{3} = \frac{4 * \pi * 3^{3}}{3} = 4 * \pi * 9 = 36 * \pi = 113.097[/tex]
The volume of that sphere is 113.09, which we round down to the closest whole number: 113 cubic inches.
53. Determine whether there is a positive, negative or no correlation.
By looking at the graphic, you can see a series of dots downwards. If you were to trace a line following those points, a close approximation, you would have a rather straight line going down the Y axis while going further along the X axis.
If you were to calculate the slope of that imaginary line, you'll has a negative value, because the line is going down.
So, there's a negative correlation: the higher the X value, the lower the Y value.
54. Determine whether there is a linear or non-linear correlation.
By looking at the provided graphic, we can see it shows a curve, with a positive correlation, meaning the greater the X value, the greater the Y value.
However, you can see that it's not a straight line as it was in the previous question, it's a curve.
Since it's a curve, it's not a linear correlation.
