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jolli1 [7]
3 years ago
15

4(-2 1/3) + 7 1/6 simplified please help

Mathematics
1 answer:
Aliun [14]3 years ago
3 0

Answer:

1/20

Step-by-step explanation:

-2 1/3=-5/3=-10/6

7 1/6=43/6

-10/6*4=-40/6

-40/60+43/60=3/60=1/20

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Morgarella [4.7K]

Answer:

a) decreasing from (0,2),  increasing from (2,∞ )

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c) DNE. there is no inflexion point

Step-by-step explanation:

f(x) = x² - x - ln (x)

since ln(x) is defined for positive values only x must be greater than 0 (x>0)

also we will need the first derivative and the second derivative with respecto to x

f(x) = x² - x - ln (x)

df/dx (x) = 2x - 1 - 1/x

d²f /(dx)² (x) = 2 + 1/x²

a) to find the increasing and decreasing intervals we will need to evaluate the rate of change (df/dx) :

df/dx = 0 when 2x - 1 - 1/x = 0 →  2x² - x - 1 = 0   → x = (1±√(1+8))/2 = (1 ± 3)/2

→ x1 = 2 , x2 = -1 (discarded because x2<0)

therefore since 2x increases and 1/x decreases with increasing x

for x > 2  , df/dx is positive and thus f increases with increasing x

for 0<x< 2,  df/dx is negative and thus f decreases with increasing x

b) since f increases with increasing x for x> 2 and decreases with increasing x for, 0<x< 2 , f should be a minimum value.

we can verify it with the second derivative

d²f /(dx)² (x) =2 + 1/x² → for x >0 , d²f /(dx)² is always >0 therefore

d²f /(dx)² (x1) > 0 and df/dx (x1) =0 → thus f(x) is a local minimum of x

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3 years ago
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Step-by-step explanation:

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3 years ago
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Answer:

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3 years ago
It has been observed that a large percentage of professional hockey players have birthdays in the first part of the year. It has
vagabundo [1.1K]

Answer:

a

\mu  =  127

b

\sigma  =  9.76  

c

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d

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e

The correct option is  option 3

Step-by-step explanation:

From the question we are told that

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Generally the mean is  mathematically represented as  

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=>   \mu  =  508 * 0.25

=>   \mu  =  127

Generally the standard deviation is mathematically represented as

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=>   \sigma  =  \sqrt{ 508 * 0.25 (1-0.25)}    

=>    \sigma  =  9.76  

Generally the z-score of  158 is mathematically represented as

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=>  z-score  =  \frac{158 - 127}{9.76}

=>  z-score  =  3.18

Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158  is  greater than  3( Note :the probability of  z-score = 3 is  97%)

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