Answer:
theyre both the same rate.
Step-by-step explanation:
12months at 1% turns into 12% a year
There would be 5184 ways in which each subject books can be selected.
<u>Explanation:</u>
Number of geography books = 5
Number of chemistry books = 4
Number of Science books = 7
Different ways of selecting geography books = 5!
= 5 X 4 X 3 X 2 X 1
= 120
Different ways of selecting chemistry books = 4!
= 4 X 3 X 2 X 1
= 24
Different ways of selecting Science books = 7!
= 7 X 6 X 5 X 4 X 3 X 2 X 1
= 5040
Total different possible ways they can select them = 120 + 24 + 5040
= 5184
Answer:
48
Step-by-step explanation:
let s be the snowman, g be the girl, and t be the christmas tree
2s+g=24
2t+2ts=132
3t+2g=26
subtract 2 times the first equation from the third one to get
3t-4s=-22
from the second equation we can deduce
2t(1+s)=132
t(1+s)=66
t=66/(1+s)
Substitute:
3(66)/(1+s)-4s=-22
3(66)/(1+s)=4s-22
3(66)=(4s-22)(1+s)
3(66)=-18s+4s^2-22
4s^2-18s-220=0
using the quadratic formula, we get s = 10, s = -5.5.
2(10)+g=24
g=4
2t(1+10)=132
2t=12
t=6
So 2s+t*g= 20+6*4=48
you would get a different solution for the negative s, but since snowmen cannot be negative, 48 is the answe.r
It equals 276 but about 300
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
