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#1 Re: Help Me ! » [ASK] Professional Goalkeeper » Today 19:34:15

One way is to use the binomial distribution.

Suppose that
represents the number of times that the goalkeeper saves a penalty. Then,
has a binomial distribution:

You want to calculate
. Do you see why?

#2 Re: Help Me ! » Probability Statistics: Please help! » 2018-03-14 00:18:34

Hi MellyBigD,

Welcome to the forum. You have posted 4 threads asking for help, but you have not shown any attempts at the problems or given any pointers about where you are stuck. We will endeavour to help you as best you can, and we happily volunteer our time to do so, but we will not do your homework for you. Can you please show some attempts at these problems, or be specific about what exactly you are stuck on?

#4 Re: Help Me ! » how can the sample space of rolling a two dice 36 ? isn't it 42? » 2018-03-08 09:57:17

Getting a 5 on the first die and a 5 on the second die is the same as getting a 5 on the second die and a 5 on the first die.

#5 Re: Help Me ! » math » 2018-02-13 17:40:05

What happens when x is greater than or equal to 1?

#6 Re: Help Me ! » Math » 2018-02-13 17:35:43

What is the limit of your function as x approaches 2?

#7 Re: This is Cool » the Mythical formula to calculate Numerical Derivatives! » 2018-02-12 08:14:24

These coefficients are part of a more general phenomenon called the Savitzky-Golay filter in numerical analysis. In fact the traditional five-point 'stencil' reads:

. You can derive this result simply by playing around with the Taylor series for
. It's a little tedious, but you can see the derivation here: … he_formula

There are analogous formulae for higher order derivatives too, and several published papers about the error term.

#8 Re: Help Me ! » Calculus 1 » 2018-02-11 19:27:27

Hi Sara,

Thanks for stopping by -- have you considered registering an account with us?

Have you heard of the chain rule, i.e.

#9 Re: Help Me ! » Please Check My Work Regarding Limit » 2018-02-07 20:01:15

Monox D. I-Fly wrote:

So, the approximation of x doesn't have to be 0 to make it equals 1?

#10 Re: Introductions » where is bobbym? » 2018-02-04 01:09:19

Bobbym sadly left us last year. We all miss him very much. There is a thread dedicated to him here:

#11 Re: Help Me ! » the largest interval on the following table » 2018-02-04 01:07:40

Hannibal lecter wrote:

and the second question is : Q2)  Find the largest time interval over which the actual US consumption of biodiesel was an increasing function of time. Interpret what increasing means, practically speaking, in this case.

I found the answer is for Q2 :-

The largest time interval was 2005–2007 since the percentage growth rates were positive for each of these three consecutive years. This means that the amount of biofuels consumed in the US steadily increased during the three year span from 2005 to 2007, then decreased in 2008

that don't make any sense? the first answer of Q1 say the largest interval is from 2008-2009
and the second answer for the Q2 said that the largest interval from 2005-2007? as well as it'a a decreasing function not increasing! ( over this interleave )

Because the table refers to percentage growth. If it grew by a positive percentage in 2005, 2006 and 2007, then the biodiesel consumption was still increasing in those years, but it was just growing more slowly in 2007 compared to 2006 and 2005.

The biodiesel consumption decreased in 2008, because its percentage is negative. Then it grew a little bit in 2009, because the percentage is positive.

#12 Re: Help Me ! » the largest interval on the following table » 2018-02-04 01:04:19

Hannibal lecter wrote:


The table shows the recent annual percent growth in US biodiesel consumption

find largest time interval over which the percentage growth in the US consumption of biodiesel was an increasing function of time

I found the answer is :  largest interval was 2008–2009 since the percentage growth rate increased from−11.7 to 7.3
(Note that the percentage growth rate was a decreasing function of time over 2005–2007.)

but why it's not from 2005 - 2006?
which gives  237 to 186.6 , isn't that the largest interval

The key word here is that we want to find the largest time interval where the percentage growth was an increasing function of time. Imagine plotting a graph with years on the x-axis and percentage growth on the y-axis -- what would it look like?

#13 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-04 00:56:51

Ah, I see -- my apologies, I misread the original equation. In that case, you are completely correct.

#14 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 23:05:47

No, it's -1/4: the gradient of a line and the gradient of the line perpendicular to it must multiply to make -1.

#15 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 20:42:40

Yes, so if the perpendicular line has a gradient of
, then the line must be of the form
. Given that the line passes through
, can you find the value of

#16 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 07:59:28

Correct! And you can check your answer by substituting x = 1 into your answer to get y = 5.

Now for the perpendicular line passing through (1,5). The line y = 4x + 7 has a gradient of 4. What is the gradient of the perpendicular line?

#17 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 06:15:40

Let's start with finding the parallel line through (1,5).

Can you write down a line which is parallel to y = 4x + 7?

#18 Re: Help Me ! » important question about Volum of sphare » 2018-02-03 03:53:32

Hannibal lecter wrote:

The average velocity, v, for a trip over a fixed distance, d, is inversely proportional to the time of travel, t.

which is v= d/t

there is no a constant of proportionality here why?

There is: it's
, the fixed distance. Since the distance doesn't change, that's the 'constant of proportionality'.

#19 Re: Help Me ! » determine slope of an equation without using dervitice » 2018-02-03 02:02:28

And what is the slope of a line with equation y = mx + c?

#20 Re: Help Me ! » can two lines be perpendicular and parallel at the same time? » 2018-02-03 02:01:37

No, you need to find two lines: one which is parallel to y = 4x + 7, and one which is perpendicular to it, each of which pass through (1,5).

#21 Re: Help Me ! » a montonic funtion » 2018-02-03 00:33:11

OK, take the line
. Do you see that

The '≤' sign accounts for the fact that the function doesn't have to be increasing at all points.

#23 Re: Help Me ! » a montonic funtion » 2018-02-03 00:22:58

Those inequalities are essentially saying everything that we've just discussed: imagine that
are points on the
-axis. In fact, let's use 

We know that
is to the right of
on the
-axis, i.e.
. Then,
is a point on the curve, and
is a point on the curve. So if
, this means that the point corresponding to
is 'below' the point corresponding to

The statement
just says that for any two different points you pick, one of them is always going to be 'below' the other -- which means that it's strictly increasing.

The difference between 'strictly increasing' and 'monotonically increasing' is virtually the same as the difference between '
' and '
' -- make sense?

#24 Re: Help Me ! » question about linear function form » 2018-02-02 20:30:17

Hannibal lecter wrote:

for example,  y = 10 + mx
b = 10
what is it intercept?

-intercept is the point at which the line crosses the

, then the coordinates of the
-intercept are
. Or sometimes people just say that the
-intercept is

#25 Re: Help Me ! » [ASK] Induction Again » 2018-02-02 20:27:52

Have you come across these formulae before?

If not, then one approach (which fits the title of the thread more accurately, I suppose) is to prove this result by induction:

and then once you have, set that equal to 364 and solve.

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