Answer:
-102/7 as a mixed number is -14 4/7
Step-by-step explanation:
Answer:
(a) 4.148 x 10^(12) ways
(b) 5,827,360 ways
Step-by-step explanation:
Number of Demonstrators (D) = 44
Number of Repudiators (R) = 56
(a)
5 senate members must be Repudiators and 5 must be demonstrators, assuming that the order at which they are selected is irrelevant:
![N= C^{D}_{5} * C^{R}_{5}\\N=\frac{56!}{5!(56-5)!} *\frac{44!}{5!(44-5)!} \\N=3,819,816*1,086,008\\N=4.148 *10^{12}](https://tex.z-dn.net/?f=N%3D%20C%5E%7BD%7D_%7B5%7D%20%2A%20C%5E%7BR%7D_%7B5%7D%5C%5CN%3D%5Cfrac%7B56%21%7D%7B5%21%2856-5%29%21%7D%20%2A%5Cfrac%7B44%21%7D%7B5%21%2844-5%29%21%7D%20%5C%5CN%3D3%2C819%2C816%2A1%2C086%2C008%5C%5CN%3D4.148%20%2A10%5E%7B12%7D)
(b)
Since there are two different positions, (speaker and vice speaker), order is important in this situation, and the total number of ways to select two senators from each party is:
![N= P^{D}_{2} * P^{R}_{2}\\N=\frac{56!}{(56-2)!} *\frac{44!}{(44-2)!} \\N=3,080*1,892\\N=5,827,360](https://tex.z-dn.net/?f=N%3D%20P%5E%7BD%7D_%7B2%7D%20%2A%20P%5E%7BR%7D_%7B2%7D%5C%5CN%3D%5Cfrac%7B56%21%7D%7B%2856-2%29%21%7D%20%2A%5Cfrac%7B44%21%7D%7B%2844-2%29%21%7D%20%5C%5CN%3D3%2C080%2A1%2C892%5C%5CN%3D5%2C827%2C360)
Answer:
18 is the correct answer to this
Step-by-step explanation:
18/9=2
Answer:
11.33 feet
Step-by-step explanation:
The triangle for the given scenario is drawn below.
From the triangle ΔABC, AB is the length of the ladder, B is the foot of the ladder, AC is the wall, BC is the distance of the foot from the wall, and angle B is the angle of elevation of the ladder with ground.
Let the length of the ladder, ![AB = x](https://tex.z-dn.net/?f=AB%20%3D%20x)
As per question, BC = 6.5 ft,
°
Using cosine ratio of the angle B, we get
![\cos 55=\frac{BC}{AB}\\\\\cos 55=\frac{6.5}{x}\\\\x=\frac{6.5}{\cos 55}=11.33\textrm{ ft}](https://tex.z-dn.net/?f=%5Ccos%2055%3D%5Cfrac%7BBC%7D%7BAB%7D%5C%5C%5C%5C%5Ccos%2055%3D%5Cfrac%7B6.5%7D%7Bx%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B6.5%7D%7B%5Ccos%2055%7D%3D11.33%5Ctextrm%7B%20ft%7D)
Therefore, the length of the ladder is 11.33 ft.
Answer:
D: no solution
...because none of the answers work for both of the equations when you plug in the x and y values