It sounds like your book is asking "what is the probability that the card is either a black card or a 9"
If so, there are 26 black cards (13 spades and 13 clubs) and four cards that have "9" on them (one in each suit). We have 26+4 = 30 cards that are either one or the other. There is overlap though. Namely the 2 black cards that have "9" on them (we count them twice), so we should subtract to get 30-2 = 28
There are 28 cards that either have a '9' on them, they are black, or both
This is out of 52 cards total
Divide the two values: 28/52 = 14/26 = 7/13 = 0.53846
Answer as a fraction: 7/13
Answer in decimal form: 0.53846
Answer as a percentage: 53.846%
Side note: the decimal form and percentage form are approximate
check the picture below.
so red line of BD is perpendicular to AC, hmmmm let's firstly find the slope of AC, bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.
![\bf A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{18}~,~\stackrel{y_2}{-8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-(-2)}{18-(-4)}\implies \cfrac{-8+2}{18+4} \\\\\\ \cfrac{-6}{22}\implies -\cfrac{3}{11} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20A%28%5Cstackrel%7Bx_1%7D%7B-4%7D~%2C~%5Cstackrel%7By_1%7D%7B-2%7D%29%5Cqquad%20C%28%5Cstackrel%7Bx_2%7D%7B18%7D~%2C~%5Cstackrel%7By_2%7D%7B-8%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B-8-%28-2%29%7D%7B18-%28-4%29%7D%5Cimplies%20%5Ccfrac%7B-8%2B2%7D%7B18%2B4%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B-6%7D%7B22%7D%5Cimplies%20-%5Ccfrac%7B3%7D%7B11%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
so we're really looking for the equation of a line whose slope is 11/3 and runs through B(4,4). Keeping in mind that
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
Answer:
69420333
Step-by-step explanation:
3 3/10 if you just add normally.
