Answer:
1) (c)∠ G = 34°
2) (a) x = 33°
3) (d) The perpendicular segments are JM, KL, PQ AND NR.
Step-by-step explanation:
Here in the given questions:
1) p II r
⇒ ∠ G = 34° (ALTERNATE EXTERIOR ANGLES)
Hence, the measure of ∠ G = 34°
2) In the given triangle:
The measure of exterior angle is always the sum of interior opposite angles.
⇒ Here, x + 72° = 105°
or, x = 105° - 72° = 33° , or x = 33°
3) The given plane in the cube is JKPN
The segments which have J , K , P and N as their one vertex are perpendicular to the given plane.
Hence, the segments are JM, KL, PQ AND NR.
![S=\{\varnothing,d,\{d\},\{\{d\}\},\{\{\{d\}\}\}\}=\{v,w,x,y,z\}](https://tex.z-dn.net/?f=S%3D%5C%7B%5Cvarnothing%2Cd%2C%5C%7Bd%5C%7D%2C%5C%7B%5C%7Bd%5C%7D%5C%7D%2C%5C%7B%5C%7B%5C%7Bd%5C%7D%5C%7D%5C%7D%5C%7D%3D%5C%7Bv%2Cw%2Cx%2Cy%2Cz%5C%7D)
A set containing
![n](https://tex.z-dn.net/?f=n)
elements has a power set containing
![2^n](https://tex.z-dn.net/?f=2%5En)
elements; here,
![|S|=5](https://tex.z-dn.net/?f=%7CS%7C%3D5)
so
![|\mathscr P(S)|=2^5=32](https://tex.z-dn.net/?f=%7C%5Cmathscr%20P%28S%29%7C%3D2%5E5%3D32)
.
The elements of the power set are all possible combinations of up to 5 of the total 5 elements to choose from:
0 choices (1):
![v](https://tex.z-dn.net/?f=v)
(since
![v=\varnothing](https://tex.z-dn.net/?f=v%3D%5Cvarnothing)
)
1choice (5):
![\{v\},\{w\},\{x\},\{y\},\{z\}](https://tex.z-dn.net/?f=%5C%7Bv%5C%7D%2C%5C%7Bw%5C%7D%2C%5C%7Bx%5C%7D%2C%5C%7By%5C%7D%2C%5C%7Bz%5C%7D)
2 choices (10):
![\{v,w\},\{v,x\},\{v,y\},\{v,z\},\{w,x\},\{w,y\},\{w,z\},\{x,y\},\{x,z\},\{y,z\}](https://tex.z-dn.net/?f=%5C%7Bv%2Cw%5C%7D%2C%5C%7Bv%2Cx%5C%7D%2C%5C%7Bv%2Cy%5C%7D%2C%5C%7Bv%2Cz%5C%7D%2C%5C%7Bw%2Cx%5C%7D%2C%5C%7Bw%2Cy%5C%7D%2C%5C%7Bw%2Cz%5C%7D%2C%5C%7Bx%2Cy%5C%7D%2C%5C%7Bx%2Cz%5C%7D%2C%5C%7By%2Cz%5C%7D)
3 choices (10):
![\{v,w,x\},\{v,w,y\},\{v,w,z\}](https://tex.z-dn.net/?f=%5C%7Bv%2Cw%2Cx%5C%7D%2C%5C%7Bv%2Cw%2Cy%5C%7D%2C%5C%7Bv%2Cw%2Cz%5C%7D)
and so on
4 choices (5);
![\{v,w,x,y\},\{v,w,x,z\}](https://tex.z-dn.net/?f=%5C%7Bv%2Cw%2Cx%2Cy%5C%7D%2C%5C%7Bv%2Cw%2Cx%2Cz%5C%7D)
and so on
5 choices (1):
![\{v,w,x,y,z\}](https://tex.z-dn.net/?f=%5C%7Bv%2Cw%2Cx%2Cy%2Cz%5C%7D)
(1 + 5 + 10 + 10 + 5 + 1 = 32)
Answer:
One example: 1.29
Step-by-step explanation:
Any number with 9 at the second decimal place
Answer:
x = 2.25 (Approximately)
Step-by-step explanation:
4 + 3x^4 = 81
4 - 4 + 3x^4 = 81 - 4
3x^4 = 77
(3x^4)/3 = 77/3
x^4 = 25.67 (Approximately)
x = 2.25 (Approximately)
There are 11 letters in Mississippi. One letter is an M. You have a 1/11 chance of drawing an M if you randomly pick a letter.