Answer:
b) 0.42
Step-by-step explanation:
Let A be the event that card is a heart card and B be the event that card is a face card.
We have to find P(A or B). P(A∪B)=?
P(A∪B)=P(A)+P(B)-P(A∩B)
There are 13 heart cards and 12 cards are face cards. There would be 3 face card in hearts. So,
P(A)=13/52=1/4=0.25
P(B)=12/52=3/13=0.231
P(A∩B)=3/52=0.058
P(A∪B)=0.25+0.231-0.058
P(A∪B)=0.481-0.058
P(A∪B)=0.423
So, the probability that the card is a heart or is a face card is about is 0.42.
Answer:
6
Step-by-step explanation:
expand
x-7= 1/4x-10/4
3/4x=18/4
multiply 4 on both sides to get rid of the denominator
3x=18
x=6
check work by substituting
6-7= 1/4(6-10)
-1= 1/4(-4)
-1=-1
they are equal, so it's correct
9) x= -17
10) n=0
11) x=-3
12) x=-21
as you already know, the slope of the tangent line is simply the derivative of the function, so
![r=2cos(3\theta )\implies \cfrac{dr}{d\theta }=2\stackrel{chain~rule}{\left[ -sin(3\theta )\cdot 3 \right]} \\\\\\ \left. \cfrac{dr}{d\theta }=-6sin(3\theta ) \right|_{\theta =\frac{\pi }{6}}\implies -6sin\left( 3\cdot \frac{\pi }{6} \right)\implies -6sin\left( \frac{\pi }{2} \right)\implies -6](https://tex.z-dn.net/?f=r%3D2cos%283%5Ctheta%20%29%5Cimplies%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D2%5Cstackrel%7Bchain~rule%7D%7B%5Cleft%5B%20-sin%283%5Ctheta%20%29%5Ccdot%203%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft.%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D-6sin%283%5Ctheta%20%29%20%5Cright%7C_%7B%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7D%5Cimplies%20-6sin%5Cleft%28%203%5Ccdot%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%5Cright%29%5Cimplies%20-6sin%5Cleft%28%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%5Cright%29%5Cimplies%20-6)
<span>−6a + 6a + 5 = 8
5 = 8 False
So, </span><span>No solution.</span>
