You have to pick at least one even factor from the set to make an even product.
There are 3 even numbers to choose from, and we can pick up to 3 additional odd numbers.
For example, if we pick out 1 even number and 2 odd numbers, this can be done in
![\dbinom 31 \dbinom 32 = 3\cdot3 = 9](https://tex.z-dn.net/?f=%5Cdbinom%2031%20%5Cdbinom%2032%20%3D%203%5Ccdot3%20%3D%209)
ways. If we pick out 3 even numbers and 0 odd numbers, this can be done in
![\dbinom 33 \dbinom 30 = 1\cdot1 = 1](https://tex.z-dn.net/?f=%5Cdbinom%2033%20%5Cdbinom%2030%20%3D%201%5Ccdot1%20%3D%201)
way.
The total count is then the sum of all possible selections with at least 1 even number and between 0 and 3 odd numbers.
![\displaystyle \sum_{e=1}^3 \binom 3e \sum_{o=0}^3 \binom 3o = 2^3 \sum_{e=1}^3 \binom3e = 8 \left(\sum_{e=0}^3 \binom3e - \binom30\right) = 8(2^3 - 1) = \boxed{56}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Be%3D1%7D%5E3%20%5Cbinom%203e%20%5Csum_%7Bo%3D0%7D%5E3%20%5Cbinom%203o%20%3D%202%5E3%20%5Csum_%7Be%3D1%7D%5E3%20%5Cbinom3e%20%3D%208%20%5Cleft%28%5Csum_%7Be%3D0%7D%5E3%20%5Cbinom3e%20-%20%5Cbinom30%5Cright%29%20%3D%208%282%5E3%20-%201%29%20%3D%20%5Cboxed%7B56%7D)
where we use the binomial identity
![\displaystyle \sum_{k=0}^n \binom nk = \sum_{k=0}^n \binom nk 1^{n-k} 1^k = (1+1)^n = 2^n](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bk%3D0%7D%5En%20%5Cbinom%20nk%20%3D%20%5Csum_%7Bk%3D0%7D%5En%20%5Cbinom%20nk%201%5E%7Bn-k%7D%201%5Ek%20%3D%20%281%2B1%29%5En%20%3D%202%5En)
Answer:
La respuesta esta abajo
Step-by-step explanation:
La pregunta no está completa porque no contiene gráficos, pero te mostraré cómo responderla.
La ecuación de un gráfico de línea recta viene dada por:
y = mx + b; donde y y x son variables, m es la pendiente de la gráfica y b es la intersección en y (que es el valor de y cuando x es 0)
Dado que la ecuación de la gráfica es y = mx, comparando con la ecuación de una línea recta (y = mx + b), podemos concluir que la gráfica con una ecuación y = mx, tiene una pendiente de my una intersección con y de 0.
Esto significa que la gráfica pasa por el origen sin tocar el eje y. Además, la gráfica tiene una pendiente positiva.
Answer:
C
Step-by-step explanation:
-8 14 = 42 (He subtracted 14 from 42)
-8p = 28 (Which is how he got 28)
p = -3.5 (He took 28 divide by -8 which got him -3.5)
I will show you how to do #5:
a). -20 + 2(n-1) Original Expression
-20 +2n - 2 Distributive Property
-22 + n Combine Like Terms
Final Expression: -22 + n
b). 1.5 + (-2.5)(n -1) Original Expression
1.5 + -2.5n + 2.5 Distributive Property
4 - 2.5n Combine Like Terms
Final Expression: 4 - 2.5n
Answer:
She has 5 candles left.
Step-by-step explanation:
Total of candy Sarah has = 25candies
If Sarah gave 2/5 of the candies to her sister, the total amount she gave her sister will be 2/5 of 25
2/5 of 25 = 10
The remaining candy left will be 25-10 which is 15.
If she gave 2/3 of the amount left to her friend, the amount she gave her friend will be 2/3×15 = 10candies.