Correct question is;
Caitlin purchased a prepaid phone card for $20. Long distance calls cost 7 cents a minute using this card. Catin used her card only once to make a long distance all the remaining credit on her card is $16.8. how many minutes did her call last?
Answer:
45 minutes 43 seconds
Step-by-step explanation:
We are told that she purchase the prepaid phone card for $20.
Now she has $16.8 after making the call.
Therefore;
Amount spent on the call = 20 - 16.8 = $3.2
We are told that the long distance call costs 7 cents per minute. Which is $0.07 per minutes
Thus, time spent = $3.2/$0.07 = 45.714 minutes or 45 minutes 43 seconds
Answer: median: 23 Frequency: 1 is 1 2 is 1 3 is 2
<h3>
First Method:</h3>
<u>Using cosine rule</u>:
![\rightarrow \sf cos(30 ) = \dfrac{YZ}{12}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20cos%2830%20%29%20%3D%20%5Cdfrac%7BYZ%7D%7B12%7D)
![\rightarrow \sf YZ = 12cos(30 )](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20YZ%20%3D%2012cos%2830%20%29)
![\rightarrow \sf YZ = 6\sqrt{3}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20YZ%20%3D%206%5Csqrt%7B3%7D)
![\rightarrow \sf YZ = 10.4](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20YZ%20%3D%2010.4)
<h3>
Second Method:</h3>
<u>First find XY using sine rule</u>:
![\rightarrow \sf sin(30)=\dfrac{XY}{12}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20sin%2830%29%3D%5Cdfrac%7BXY%7D%7B12%7D)
![\rightarrow \sf XY = 12sin(30)](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20XY%20%3D%2012sin%2830%29)
![\rightarrow \sf XY =6](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20XY%20%3D6)
Then use Pythagoras Theorem:
⇒ XY² + YZ² = XZ²
⇒ (6)² + YZ² = 12²
⇒ YZ² = 144 - 36
⇒ YZ = √108
⇒ YZ = 6√3
⇒ YZ = 10.4
Commutative property of multiplication3x4 = 4x3 = 12
Answer:
![4b + 2m = 2(2b + m)](https://tex.z-dn.net/?f=4b%20%2B%202m%20%3D%202%282b%20%2B%20m%29)
Step-by-step explanation:
Given
![4b + 2m](https://tex.z-dn.net/?f=4b%20%2B%202m)
Required
Write an equivalent expression
To do this, we simply write
as a product of two factors.
Express 4b as 2 * 2b
![4b + 2m = 2 * 2b + 2m](https://tex.z-dn.net/?f=4b%20%2B%202m%20%3D%202%20%2A%202b%20%2B%202m)
Express 2m as 2 * m
![4b + 2m = 2 * 2b + 2 * m](https://tex.z-dn.net/?f=4b%20%2B%202m%20%3D%202%20%2A%202b%20%2B%202%20%2A%20m)
Factor 2 out of the expression:
![4b + 2m = 2 *(2b + m)](https://tex.z-dn.net/?f=4b%20%2B%202m%20%3D%202%20%2A%282b%20%2B%20m%29)
![4b + 2m = 2(2b + m)](https://tex.z-dn.net/?f=4b%20%2B%202m%20%3D%202%282b%20%2B%20m%29)
Hence:
An equivalent expression is: ![2(2b + m)](https://tex.z-dn.net/?f=2%282b%20%2B%20m%29)