Answer:
y= -3/2x+9
Step-by-step explanation:
Well we have to know that to find a line perpendicular to a given line, you have to have opposite slopes. So that makes the equation begin as y=-3/2x because it's opposite of y=2/3x. Then we have to make sure it goes through the point (4,3). To do that, I tweaked the numbers in my graphing calculator and it worked with 9! So the equation is y= -3/2x+9
Answer: D) 77 mph to 117 mph
Step-by-step explanation:
Given that:
Mean serve speed(m) = 97 miles per hour
Standard deviation of serve speed = 10 mph
Shape of distribution is not known ; interval that will contain the speeds of at least three-fourths of the player's serves
Using Chebyshev's rule:
(1 - 1/k²) = 3 / 4
1 / k² = 3/4 - 1
- 1/k² = - 1 / 4
1/k² = 1/4
Cross multiply:
k² = 4
Square root of both sides :
k = 2
Hence, number of standard deviation = 2
(-k*sd) + m ; (k*sd)+m
(-2*10) + 97 ; (2*10)+97
-20 + 97; 20 + 97
77 ; 117
77mph ; 117mph
In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are
possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by
. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability
![\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cbinom%7B13%7D1%5Cbinom44%5Cbinom%7B48%7D1%7D%7B%5Cbinom%7B52%7D5%7D%3D%5Cdfrac%7B624%7D%7B2%2C598%2C960%7D%5Capprox0.00024)
There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing
possible hands. Exactly 2 aces are drawn in
hands. And so on. This gives a total of
![\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Ba%3D1%7D%5E4%5Cbinom4a%5Cbinom%7B48%7D%7B5-a%7D%3D886%2C656)
possible hands containing at least 1 ace, and hence B occurs with probability
![\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csum%5Climits_%7Ba%3D1%7D%5E4%5Cbinom4a%5Cbinom%7B48%7D%7B5-a%7D%7D%7B%5Cbinom%7B52%7D5%7D%3D%5Cdfrac%7B18%2C472%7D%7B54%2C145%7D%5Capprox0.3412)
The product of these probability is approximately 0.000082.
A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e.
. This happens if
- the hand has 4 aces and 1 non-ace, or
- the hand has a non-ace 4-of-a-kind and 1 ace
The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So
consists of 96 possible hands, which occurs with probability
![\dfrac{96}{\binom{52}5}\approx0.0000369](https://tex.z-dn.net/?f=%5Cdfrac%7B96%7D%7B%5Cbinom%7B52%7D5%7D%5Capprox0.0000369)
and so the events A and B are NOT independent.
Answer:
29/6
Step-by-step explanation: