sin(x+y)=sin(x)cos(y)-cos(x)sin(y)
also, remember pythagorean rule, 
given that sin(Θ)=4/5 and cos(x)=-5/13
find sin(x) and cos(Θ)
sin(x)
cos(x)=-5/13
using pythagorean identity
(sin(x))^2+(-5/13)^2=1
sin(x)=+/- 12/13
in the 2nd quadrant, sin is positve so sin(x)=12/13
cos(Θ)
sin(Θ)=4/5
using pythagrean identity
(4/5)^2+(cos(Θ))^2=1
cos(Θ)=+/-3/5
in 1st quadrant, cos is positive
cos(Θ)=3/5
so sin(Θ+x)=sin(Θ)cos(x)+cos(Θ)sin(x)
sin(Θ+x)=(4/5)(-5/13)+(3/5)(12/13)
sin(Θ+x)=16/65
answer is 1st option
Considering that the subjects are chosen without replacement, they are not independent, and the probability cannot be found using the binomial distribution.
The binomial distribution and the hypergeometric distribution are quite similar, as:
- They find the probability of exactly x successes on n repeated trials.
- For each trial, there are only two possible outcomes.
- The difference is that the binomial distribution is for independent trials, that is, in each trial, the probability of success is the same, while the hypergeometric distribution is for dependent trials.
- If the sample is without replacement, the trials are not independent, thus the hypergeometric distribution is used, not the binomial.
A similar problem is given at brainly.com/question/21772486
Step-by-step explanation:
divide 3.5 by 5.0 (3.5 ÷ 5.0 = 0.7), then multiply 0.7 by 15.0 (0.7 × 15.0 = 10.5), and check by dividing (10.5 ÷ 15.0 = 7.0) the answer is 10.5
left means subtracting
6 7/8 - 2 5/8
Whole numbers subtract each other
Numerators subtract each other
The denominators stay the same.
6-2= 4
7-5=2
4 2/8
Reduce 2/8. Divide by 2. 2/2= 1, 8/2= 4
4 2/8=4 1/4
Answer: 4 2/8 = 4 1/4 cups left
