f(x) = x^2 + 16x
Completing the square.
f(x) = a(x-h)^2 + k
f(x) = (x + 8)^2 - 64
h = -8, k = -64
Vertex = (h,k)
Vertex = (-8, -64)
Not fully explained, just a quick summary.
Answer:
150 hombres juegan baloncesto.
Step-by-step explanation:
En una escuela hay 315 alumnos de los cuales 1/3 son mujeres y el resto son hombres.
Paso 1
Encontramos el número de estudiantes que son mujeres
= 1/3 × 315
= 105 mujeres.
Se nos dice que el resto son hombres. Por lo tanto, el número de hombres que son estudiantes se da como:
= 315 - 105 mujeres
= 210 hombres
Paso 2
2/7 de los hombres juegan fútbol y el resto baloncesto.
Esto significa que 2/7 de 210 hombres juegan al fútbol
= 2/7 × 210 hombres
= 60 hombres
Por tanto, 60 hombres juegan al fútbol.
Paso 3
También se nos dice que el resto juega al baloncesto.
El número de hombres que juegan baloncesto se calcula como:
210 - 60
= 150 hombres.
Por tanto, 150 hombres juegan baloncesto.
Answer: A) .1587
Step-by-step explanation:
Given : The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce.
i.e. 
and 
Let x denotes the amount of soda in any can.
Every can that has more than 12.50 ounces of soda poured into it must go through a special cleaning process before it can be sold.
Then, the probability that a randomly selected can will need to go through the mentioned process = probability that a randomly selected can has more than 12.50 ounces of soda poured into it =
![P(x>12.50)=1-P(x\leq12.50)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{12.50-12.30}{0.20})\\\\=1-P(z\leq1)\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.8413\ \ \ [\text{By z-table}]\\\\=0.1587](https://tex.z-dn.net/?f=P%28x%3E12.50%29%3D1-P%28x%5Cleq12.50%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5Cleq%5Cdfrac%7B12.50-12.30%7D%7B0.20%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq1%29%5C%20%5C%20%5B%5Cbecause%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%5C%5C%3D1-0.8413%5C%20%5C%20%5C%20%5B%5Ctext%7BBy%20z-table%7D%5D%5C%5C%5C%5C%3D0.1587)
Hence, the required probability= A) 0.1587
Answer:
A. D=sqrt( (x2-x1)^2+(y2-y1)^2 )
Step-by-step explanation:
The distance between two points is the root of the sum of the squares of the differences in their corresponding coordinates. The equation of choice A is the usual formulation.
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<em>Comment on answer choices</em>
Because the square of a number is the same as the square of its opposite, the formula in choice D is also correct.
