Both of the Students are correct, where the units are the same in the beginning and at the end. If you divide 20 feet by 4, you get 5 feet or 60 inches. If you convert 20 feet to inches, you get 240 inches. When you divide 240 by 4, you get 60 inches. Therefore, they both are correct.
Answer:
Option B is correct.
Step-by-step explanation:
A = { 1, 3, 5, 7, 9 }
B = { 2, 4, 6, 8, 10 }
C = { 1, 5, 6, 7, 9 }
(B∩C) = {6} [Common element in set B and set C]
Now A∪(B∩C) = { 1, 3, 5, 6, 7, 9 }
Option B is the answer.
Answer: ![\sqrt[6]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B2%7D)
Step-by-step explanation:
You know that the expression is ![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D)
By definition we know that:
![\sqrt[n]{a}=a^{\frac{1}{n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%7B%5Cfrac%7B1%7D%7Bn%7D)
You also need to remember the Quotient of powers property:
Therefore, you can rewrite the expression:
Finally, you have to simplify the expression. Therefore, you get:
![=2^{(\frac{1}{2}-\frac{1}{3})}\\=2^{\frac{1}{6}}\\=\sqrt[6]{2}](https://tex.z-dn.net/?f=%3D2%5E%7B%28%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B1%7D%7B3%7D%29%7D%5C%5C%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%5C%5C%3D%5Csqrt%5B6%5D%7B2%7D)
Answer:
El primer paso será darle un nombre a nuestras variables:
x= Numero de libros comprados inicialmente
y=Precio inicial de los libros
Ahora analizamos el enunciado,
Lorena ha comprado libros todos del mismo precio por valor de 120 €
x*y=120 € (1)
El librero le regala 3 libros por lo que en realidad cada libro que cuesta 2 € menos
(x+3)(y-2)=120€ (2)
Tenemos entonces dos ecuaciones con dos incógnitas, así que podemos resolver,
Despejamos en (1)
x=120/y
Sustituimos en (2)
(120/y +3)(y-2)=120
120 - 240/y + 3y -6 =120
3y-240/y =120-120+6
3y -240/y =6
y- 80/y=6
y²-80=6y
y²-6y-80=0
Resolvemos la ecuación de segundo grado
a=1
b=-6
c=-80
Aplicando la resolvente,
(6+- √36+320)/2
6+-√356/2
(6+-18,86)/2
Como el valor de y no puede ser negativo la unica respuesta válida será:
y=12,43
Cada libro le costo 12,43€
Sustituyendo en (1)
x=120/12,43
x=9,65 como no puede ser un número racional
x=9
Lorena ha comprado 9 libros
Answer:
c: 1,335 yd³
Step-by-step explanation:
The formula for volume of a cylinder is V = πr²h where r is the radius of the base circle, and h is the height of the cylinder
We are given r = 5, and h = 17. Plug them in and solve for V...
V = π(5²)(17)
V = π(25)(17)
V = 425π
V = 425(3.14) = 1,334.5 yd³,
so 1,335 yd³ rounded to the nearest cubic yard
