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question 2 (but here i'm not sure, but will try):
probability that the first is on the north: 1/2
probability that the second is on the north is 1/2
probability that they are both on the north 1/4
on the north we have 5 trees: 5!
they have to be next to each other (it's like one tree): 4!
the can also change sides (one is on the left of another and vice versa) 2!
probability that they are on the northand next to each other: 1/4*(4!*2!)/5!=1/20
on the south: 1/4*(3!*2!)/4! = 1/8
north or south and next to each other: 1/20+1/8 = 2/40+5/40=7/40
but as i said i'm not sure
i would do it this way
you pick out the first tree - there are 9 posibilities and plant it on north or south - 2
so the first tree 9x2 ways
second 8x2
third; 7x2
fourth 6x2
fifth 5x2
sixth 4x2
seventh 3x2
eight 2x2
ninth 1x2
9x2x8x2x7x2x6x2x5x2x4x2x3x2x2x2x2 so 9!x2^10
a. 55pi
b. 2750pi
it's imposible. only numbers with 9 in the front will give you more!
if A= (b-c)(b-a)?
b=4c
c=b/4
A= (b-b/4)(b-a)= ((4b-b)/4)(b-a)=(3b(b-a))/4
132621
[x+abs(x)]/2x
positive = 1
negative = 0
only from 1962 we can form 24 different 4 digit numbers, 24 3-digit numbers, 12 2-digit numbers and 4 1-gigit numbers, 30 gives you only three numbers (30 3 and 0) so there are 65 different numbers!!
x^2=x
x^2-x=0
x(x-1)=0
x=1 v x=0
I would divide your irregular shape into basic shapes, such as rectangles, trapazium, triangles, semicircles etc.
Forgot to add that you find their areas and add them together :-(
you can't use binomial distriution with this problem :-(
you choose black ink for the card: 1/7;
you choose blue paper for the card: 1/6;
blue ink for the envelope: 1/7;
blue paper for the envelope: 1/7;
we have to multiply probabilities (black ink and blue paper and blue ink and blue paper) - we substitute and with multiplication:
so the answer is: 1/1764
absolute error: 0.015
relative error: 0.00187
1. P = (e^(-7)* 7^2)/2! = 0.02234121335
where 7 is expeted number of occurences and two the number of occurences we want to get.
2. P(0) + P(1) + P(2)
But I'm really not sure. Hope some guys here will be able to help you with this problem.
cos144 + cos72 = 2cos(144+72)/2*cos(144-72)/2=2cos108*cos36=
!!!!!!!!!!2cos(180-108)!!!!!!!!!!!
*cos36=-2cos72*cos36=(-cos72*2cos36*sin36)/sin36=
(-cos72*sin72)/sin36=(-1/2)*(sin144)/sin36=(-1/2)*(sin144)/(sin(180-36))=
(-1/2)(sin144)/(sin144)=-1/2
it should be 2cos(180-72)!!!
so:
the full mark is 100 points
grade 65 is worth 10% of the full mark which is 10 points. you scored 65/100 which is 6.5/100 of the full mark
grade 59 is worth 40% - 23.6/100 of the full mark
so all together you have 30.1/100 before your final.
you want to have more than 60 after your final so you have to score 29.9 on your final. 29.9/50 (the max on the final) is grade 59.8 on your final or more.
but if your final is worth 50% you need to get more than 59.8.
I'm sorry but I am not familiar with grades in the States. grade 65 means 65 out of 100?
10%+40%+60%=110%!!
what do you mean not allowed!?
you get the final answer, any way, as long as it is mathematically correct, can be used.