Answer:
1. 4 categories are shown in the rows.
2. 2 categories are shown in the columns.
3. The number of 14 year olds that consider winter their favorite season is 12.
4. Total number of people polled is 82.
Step-by-step explanation:
The question is to test the ability of a student to group data using a frequency table accurately, and make appropriate deductions from it. Consider the attachment for the accurate table required to answer the given questions.
If the given information is grouped as required, thus the answers to the questions are:
i. 4 categories are shown in the rows.
ii. 2 categories are shown in the columns.
iii. The number of 14 year olds that considers winter their favorite season is 12.
iv. Total number of people polled is 82.
a triangle needs to have 180 degrees in all.
65 + 65 = 130
180 - 130 = 50
x = 50 degrees
I would recommend starting by turning 172 into 100+70+2. This makes it much easier to multiply it by 6.
(100+70+2) × 6 =
distributive property
(100×6) + (70×6) + (2×6) =
Simplify
600 + 420 + 12 =
Add it all together
1032
The answer would be 1032.
Answer: 
Step-by-step explanation:
Given
Curve is 
boundary is y=0 i.e.

The volume of solid generated when rotated about the x-axis is

Putting values we get
![\Rightarrow V=\int_{-1}^{1}\pi (3-3x^2)^2dx\\\\\Rightarrow V=\int_{-1}^{1}\pi(9+9x^4-18x^2)dx\\\\\Rightarrow V=\pi \left [ \frac{9x^5}{5} - 6 x^3 + 9 x\right ]_{-1}^{1}\\\\\Rightarrow V=9.6\pi](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D%5Cint_%7B-1%7D%5E%7B1%7D%5Cpi%20%283-3x%5E2%29%5E2dx%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cint_%7B-1%7D%5E%7B1%7D%5Cpi%289%2B9x%5E4-18x%5E2%29dx%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cpi%20%5Cleft%20%5B%20%20%5Cfrac%7B9x%5E5%7D%7B5%7D%20-%206%20x%5E3%20%2B%209%20x%5Cright%20%5D_%7B-1%7D%5E%7B1%7D%5C%5C%5C%5C%5CRightarrow%20V%3D9.6%5Cpi)