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The probability of two correct out of five is (2/5)²(3/5)³ → 108/3125

However, there are ₅C₂ → 10 ways of choosing 2 from 5, so overall the probability is 10*108/3125 → 216/625

Hi rosala!

Calculating the fraction of space in an atom.?

The approximate radius of a H-atom is 0.05nm, and that of a proton is 1.5 x 10^-15m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by nucleus.

\(\frac{radius\ of\ a\ H-atom}{radius\ of\ a\ proton}=\frac{0.05nm}{1.5\times 10^{-15}m}\times\frac{10^{-9}m}{nm}=\frac{0.000\ 000\ 000\ 050}{1.5\times10^{-15}}\\ \color{blue}=\frac{1}{0.000\ 030}\)

The volumes behave like the third power of the radii.

\({\color{blue}\frac{volum\ of\ a\ H-atom}{volum\ of\ a\ proton}}=(\frac{1}{0.000\ 030})^3\\ \color{blue}=\frac{1}{0.000\ 000\ 000\ 000\ 027}=\frac{1}{2.7\times 10^{-14}}\)

  !

actually , the surprising this is that in the worksheet i received from school, 6.023 is given as answer so i was just wondering why that value was used, but thanks for the help, 

There is at least one online dictionary that mistakenly gives 6.023 instead of 6.022 Rosala, so it's possible Guest#1 came across this.  However, the important thing here is the process by which he/she obtained the answer - I'm sure you can easily modify the result using 6.022 yourself if necessary!

I assume these numbers represent the slopes of the two lines.

If the lines are parallel then the slopes are the same, so

n/9 = 3/2

Multiply both sides by 9 to get n = 27/2

If the lines are perpendicular then when the slopes are multiplied together the result is -1, so

(n/9)*(3/2) = -1

n/6 = -1

n = -6

why have you taken 6.023 instead of 6.022 ? 

share the link on social media! 

looks like it was answered, nvm! 

Note that the coordinates are stated this way:  ( x, f(x) )

First, let's find what  x  values cause  f(x)  to equal  2  .

There is the point (-3, 2).     So...     f( -3 )  =  2

There is the point ( 0, 2).     So...     f(  0 )  =  2

There is the point ( 3, 2).     So...     f(  3 )  =  2

Now we want to know what  x  values cause f(x)  to equal  -3, 0, and 3  .

There are no points where f(x) = -3  .

There is the point (-4, 0).     So...     f( -4 )  =  0

There is the point (-2, 3).     So...     f( -2 )  =  3

So...now we know that..

    f( f(-4) )             Since  f(-4)  =  0  , we can replace  " f(-4) "  with  " 0 " .

=  f(   0   )              Since  f(0)   =  2  , we can replace  " f(0)  "  with  " 2 " .

=  2

    f( f(-2) )             Since  f(-2)  =  3 ,  we can replace  " f(-2) "  with  " 3 ".

=  f(   3   )              Since  f(3)   =  2  , we can replace  " f(3)  "  with  " 2 " .

=  2

There are two  x  values that satisfy  f( f(x) ) = 2  . They are:  x = -4  and  x = -2

how did u post a priority question???

∠DEF  is an exterior angle of pentagon ABCDE.

The sum of all exterior angles in a polygon  =  360º

Since ABCDE is a regular pentagon, all 5 of its exterior angles have the same measure.

So..the measure of one exterior angle  =  360° / 5  =  72°

m∠DEF  =  72°

Since there are 180° in every triangle...

m∠DEF + m∠EFD + m∠FDE  =  180°

    72°    +    90°    + m∠FDE  =  180°                Subtract  72°  and  90°  from both sides.

                                m∠FDE  =  18°

Questions like this one appear to be asked frequently on this forum, so I will attempt to break it down for you so that you are not confused at all.

1. Identity Place Value The Decimal Extends To

\(0.3456\) extends until the ten thousandths. That is all this step entails. 

2. Take the Decimal Value over That

Since our decimal extends 4 decimal places, we want to make it equivalent to that number over ten thousand.

\(0.3456=\frac{3456}{10000}\)

3. Find the GCF of the Numerator and Denominator and Divide by It

GCF stands for "greatest common factor." Your goal in this step is to find what that is. If it is difficult to determine it, like it is here, you may want to try to reduce the fraction little by little.

For example, 3456 and 10000 are both even, so it is divisible by 2

However, someone more observant might notice that the last two digits of both numbers, 56 and 00, are divisible by 4, so the GCF is, at least, 4.

\(\frac{3456}{10000}\div\frac{4}{4}=\frac{864}{2500}\)

Yet again, 64 and 00 are divisible by 4, so divide it by 4 again.

\(\frac{864}{2500}\div\frac{4}{4}=\frac{216}{625}\)

4. You're done!

what is .3456 as a simplied fracion

\(0.3456=\frac{3456}{10000}\color{blue}=\frac{216}{625}\)

  !

You will have a field day with this

Ok ... fine ...

I'll do as you please.

yes but you still didnt leave a like

Simply subtract the width from the length. 

\(72.25-51.5=20.75ft\)

Don't forget the units of measure, either!

72.25-51.5=20.75

Ok, here you go!

\(1gal=16cups\)

\(1qrt=4cups\)

\(1pint=2cups\)

Good?

a) 

Let's think about this problem. Before we do, though, we must understand a few things.

An obtuse angle is defined by an angle wherein its measure follows the rule \(90^{\circ} . In other words, an angle that is obtuse is larger than 90 degrees and is less than 180 degrees.

Another thing to consider is the combined number of degrees of the interior angles of an 11-gon (known as a hendecagon). To do this, there is a formula for it. It is the following:
 

\(S=180(n-2)\)

Let S = sum of all interior angles in polygon

Let n = number of sides of the polygon.

An 11-gon has 11 sides total, so let's plug that into the formula:
 

I will assume that the angle I will use is 90 degrees. Divide the sum of the interior angles of degrees by 90 and see what you get. \(\frac{1620}{90}=18\). Of course, I can't have right angles as that does not fit the definition of an obtuse angle, so that means that there can only be 17 obtuse angles. 

But wait! An 11-gon only has 11 sides and subsequently 11 angles, which means that every angle can be obtuse!

B)

I actually found b easier than A) but that is OK.

There can only be, at most, 3 acute angles in a convex polygon. Only 3. This is because the exterior angle of an acute angle is greater than 90 degrees, and a 4th angle would make the exterior angle measure passed the limit of 360 degrees. Does this make sense?

x + 3y - 24  =  0

a)     Plug in  y  for  x  and solve for  y  .

y + 3y - 24  =  0

4y - 24  =  0

4y  =  24

y  =  6 

The coordinate  =  (x, y)  =  (y, y)  =  (6, 6)

b)     Plug in  3y  for  x  and solve for  y  .

(3y) + 3y - 24  =  0

6y - 24  =  0

6y  =  24

y  =  4

The coordinate  =  (x, y)  =  (3y, y)  =  (3*4, 4)  =  (12, 4)

c)     Plug in  x + 4  for  y  and solve for  x  .

x + 3y - 24  =  0

x + 3(x + 4) - 24  =  0

x + 3x + 12 - 24  =  0

4x - 12  =  0

4x  =  12

x  =  3

The coordinate  =  (x, y)  =  ( x,  x + 4  )  =  ( 3,  3 + 4  )  =  (3, 7)

If we are getting technical here, this is the meaning of life.

An organismic state characterized by capacity for metabolism, growth, reaction to stimuli, and reproduction.

Now that is the meaning of life, don't you think?

Can you tell me which part is incorrect?

Not all authorities agree on the standard form of a line; some believe it to be \(Ax+By=C\)while others believe it to be \(y=mx+b\). Regardless of which form you use as your standard, the answer will not be different. For this problem, I will use the form \(Ax+By=C\) because the equations are already in that form. I will, therefore, use 2 different method to solve this problem because of the likelihood of ambiguity.

Method 1

For a system, however, we have this form:

{ \(A_1x+B_1y=C_1\)

{ \(A_2x+B_2y=C_2\) 

Before I start solving, I need to straighten out a rule 

1. If \(\frac{A_1}{A_2}=\frac{B_1}{B_2}\neq\frac{C_1}{C_2}\), then the system has no solution. 

2. If \(\frac{A_1}{A_2}=\frac{B_1}{B_2}=\frac{C_1}{C_2}\), then the system has infinitely many solutions.

Why is this knowledge beneficial? Well, if a system has no solution or has infinitely many of them, then that means that the lines of each equation must be parallel. And by definition, if two lines are parallel, they must have the same slope. Therefore, let's look at your system:

{\(6x-ay=8\)

{\(2x+3y=12\)

Let's see what happens when we try to put the numbers over one another:
 

Does \(\frac{6}{2}=\frac{-a}{3}\neq\frac{8}{12}\)? Yes, 6/2=3, and that is definitely not equivalent to 8/12, so we know that we have the first case. To solve for a, though, we must set it equal to \(\frac{A_1}{A_2}\), which is equal to 3. Let's do that:

What if you want to check your answer? To check your answer, you can graph it and see if the lines ever intersect. If they do not intersect, then you have done the problem correctly.