Answer:
3
Step-by-step explanation:
if she can cut the 126 cm length rope into 42 pieces and 291 cm rope into 97 pieces she will have no remainders
42*3=126
97*3=291
Answer:
x = 2 or x = -5
Step-by-step explanation:
x² + 3x - 4 = 6
x² + 3x -4 - 6 = 0
x² + 3x - 10 = 0 (Here you find two numbers that have a sum of 3 and a product of -10. These two numbers would be 5 and -2. 5 - 2=3 and 5×-2 =-10.)
x² + 5x - 2x -10 = 0 (They you replace 3x by 5x and -2x)
(x² + 5x) (-2x -10) =0 - (You find common terms)
x(x + 5) -2(x + 5) = 0
(x - 2) (x + 5) = 0
So
x - 2 = 0 or x + 5 = 0
x =2 x = -5
Answer:
The probability of picking exactly 4 of the 6 numbers correctly is ![\frac{15}{5245786}=2.859 \times 10^{-6}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B5245786%7D%3D2.859%20%5Ctimes%2010%5E%7B-6%7D)
Step-by-step explanation:
As order is unimportant, we have to calculate the different outcomes with combinations formula:
![C^{n}_{r}=\frac{n!}{(n-r)! \ r!}](https://tex.z-dn.net/?f=C%5E%7Bn%7D_%7Br%7D%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%20%5C%20r%21%7D)
The total outcomes of picking exactly 4 of the 6 numbers is:
![C^{6}_{4}=\frac{6!}{(6-4)! \ 4!}=\frac{6 *5*4*3*2*1}{(2*1) \times (4*3*2*1)}=\frac{30}{2}=15](https://tex.z-dn.net/?f=C%5E%7B6%7D_%7B4%7D%3D%5Cfrac%7B6%21%7D%7B%286-4%29%21%20%5C%204%21%7D%3D%5Cfrac%7B6%20%2A5%2A4%2A3%2A2%2A1%7D%7B%282%2A1%29%20%5Ctimes%20%284%2A3%2A2%2A1%29%7D%3D%5Cfrac%7B30%7D%7B2%7D%3D15)
The probability of picking exactly 4 of the 6 numbers correctly is given by:
Total outcomes by picking 6 numbers from 1 to 42: 5245786
P(4 of the 6 numbers are correct)= ![\frac{15}{5245786}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B5245786%7D)
Answer:
16n2−10n+22
Step-by-step explanation:
3) Missing in 3): ∠EDF and ∠ADC = "Vertical angles"
Calculate x°:
∠ EDF = 120°
∠ EDF = ∠ ADC (Vertical) , but ∠ ADC = 3x° + 2x°,
Then 3x°+2x° =120°
5x° = 120° and x° =120/5, so x° =24°