Answer:
P = 57°
Step-by-step explanation:
Given the following :
PQ = 17
QR = 15
PR = 14
Using the cosine formula since the length of the three sides are given:
a2 = b2 + c2 – 2bccos(A)
To find P:
QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)
15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)
225 = 289 + 196 - 476 cosP
476*CosP = 485 - 225
476*CosP = 260
CosP = 260/476
CosP = 0.5462184
P = Cos^-1(0.5462184)
P = 56.892029
P = 57°
It is a 4 by 8 grid. So there are 32 squares total.
Now, count how many x's are on the boxes.
I counted 14 x'ed boxes.
Divide 14 by 32
14/32=0.4375
Now convert to a percent. Move the decimal two places to the left.
You get 43.75% as the answer.
192 ÷ 15 = 12 and 8/10 (simplified: 4/5)
the fraction ia there because ( i think) 8 people have one less marble
The given expression is ![^7P_6-2(^6C_2)](https://tex.z-dn.net/?f=%20%5E7P_6-2%28%5E6C_2%29%20)
Here P represents Permutation and C represents Combination
Thus, the given expression can be rewritten as:
![^7P_6-2(^6C_2)=\frac{7!}{(7-6)!}-2\frac{6!}{(6-2)!2!} =\frac{7!}{1!}-2\frac{6!}{4!2!}](https://tex.z-dn.net/?f=%20%5E7P_6-2%28%5E6C_2%29%3D%5Cfrac%7B7%21%7D%7B%287-6%29%21%7D-2%5Cfrac%7B6%21%7D%7B%286-2%29%212%21%7D%20%3D%5Cfrac%7B7%21%7D%7B1%21%7D-2%5Cfrac%7B6%21%7D%7B4%212%21%7D%20)
![\therefore ^7P_6-2(^6C_2)=7!-\frac{2\times 6\times 5\times 4!}{4!\times 2}=5040-30=5010](https://tex.z-dn.net/?f=%20%5Ctherefore%20%5E7P_6-2%28%5E6C_2%29%3D7%21-%5Cfrac%7B2%5Ctimes%206%5Ctimes%205%5Ctimes%204%21%7D%7B4%21%5Ctimes%202%7D%3D5040-30%3D5010%20%20)
Therefore, for the given expression
, it's value is 5010
Answer:
k = 66
Step-by-step explanation:
To solve this problem, subtract 301 from 367.
369 - 301 = 66
Therefore, k is equal to 66.
Hope this helps!