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Sorry, I don't understand why the distance between Delta Junction and Haines Junction is subtracted with the distance between the two destinations travelled on Thursday?

Because 1016 -1202 = -186  is negative. Using the absolute value is -(-186) = + 186

Sorry, I don't understand why the distance between Delta Junction and Haines Junction is subtracted with the distance between the two destinations travelled on Thursday?

Using absolute value to determine distance

\(\begin{array}{|rcll|} \hline && (1422-1016)-(1016-1202)+(1202-918)+(918-496)+(496-51) \\ &=& 406 + 186 + 284 +422 +445 \\ &=& 1743 \\ \hline \end{array}\)

Find the least common multiple of 9x^2-16 and 3x^2+x-4

\(9x^2-16=(3x-4)(3x+4)\)

\(3x^2+x-4\\=3x^2+4x-3x-4\\=x(3x+4)-1(3x+4)\\=(x-1)(3x+4)\)

So the lowest common multiple is

  \((3x-4)(3x+4)(x-1)\\ =(9x^2-16)(x-1)\\ =9x^3-16x-9x^2+16\\ =9x^3-9x^2-16x+16\\ \)

I'll take a stab at this one.....if the number of dice showing a two-digit number  = the number of dice showing a one-digit number, then  2 must show a two-digit number and 2  must show a one-digit number

There are 3 two-digit numbers and 9 one-digit numbers on each die

So....the probabiity is

C(4,2) (3/12)^2 (9/12)^2    =  

C(4,2) (1/4)^2 (3/4)^2  =

27/128 

l 6 - x  l  = 2

We actually have two equations here

6 - x  = 2               and              6 - x  =  -2

                           subtract 6 from both sides

-x  = - 4                                      -x   =  -8

                          multiply through by  -1

x  = 4                                           x  = 8

Thanks so much Hectictar, Chris and Gavin,

I am ever so pleased.  You have put a great big smile on my face 

Thanks, hectictar.....!!!!

Yeah....GYangg...I just decided to expand it...but..we can see it this way.....

C(6,3)  (6x)^3 (1 / (3x))^3

Notice that the  x^3  terms will cancel   and we will be left with

C(6,3) * 6^3  / 3^3  =

20 * 216 / 27  

20 * 8  = 

160

Here we go:

Which undergoes HA<=> H+ + A- 
ka = [H][A] / [HA] 
you know [H+], but what are the others? 
Write the electroneutrality equation for the entire reaction (including water's dissociation) 
[H+] = [OH-] + [A-] ....we know that [H]>>>[OH], so 
[H+] = [A-] 
next write the total concentration equation (mass balance equation) 
Ct = 0.5M = [A-] + [HA] 
[HA] = 0.5 - [A-] = 0.5 - [H+] 

all together you have: 
ka = [H]^2 / (0.5 - [H+]) 
ka = 0.0001*0.0001/(0.5-0.0001) = 2.00x10^-8 

Hope you can understand this approach

HA<=> H+ + A- 
ka = [H][A] / [HA] 
you know [H+], but what are the others? 
Write the electroneutrality equation for the entire reaction (including water's dissociation) 
[H+] = [OH-] + [A-] ....we know that [H]>>>[OH], so 
[H+] = [A-] 
next write the total concentration equation (mass balance equation) 
Ct = 0.5M = [A-] + [HA] 
[HA] = 0.5 - [A-] = 0.5 - [H+] 

all together you have: 
ka = [H]^2 / (0.5 - [H+]) 
ka = 0.0001*0.0001/(0.5-0.0001) = 2.00x10^-8 

I hope this helps!

A small typo in radians. It should read 0.49 radians.

B

88 / (17 + 88 + 25 + 57) = 0.4705882353...

Round to the nearest whole percent, we have 0.47 or 47%.

The answer would be B. 

Hey Chris!

Just a quick question, if I do the problem, I will probably hard expand it, but is there are better way that just isolates the constant?

A way that doesn't require you to expand the whole expression?

P(placebo and improvement)  =  \(\frac{\text{number who received placebo and reported improvement}}{\text{total number who participated in the study}}\)

Let the total number of people who participated in the study  =  t

80% of those who participated in the study received med A .  So…
20% of those who participated in the study received a placebo.

number of those who received the placebo   =   0.2t

62% of those who received the placebo reported no improvement.  So…
38% of those who received the placebo reported improvement.

number who received placebo and reported improvement  =  0.38( 0.2t )

P(placebo and improvement)  =  \(\frac{0.38(0.2t)}{t}\)   =   0.38(0.2)   =   0.076   =   7.6%

Well...let's see!!!

(6x  +  1/ (3x) )^6   =

(6x)^6  +  6 * (6x)^5 (1/ (3x) )  +  15* (6x)^4 (1/(3x))^2  + 20* (6x)^3*(1 /(3x))^3

+ 15(6x)^2 * (1/(3x))^4 +   6* (6x)(1/(3x) )^5  + (1/ (3x))^6

The constant term is in red  

20 * 216x^3 / (27x^3)  =  20 *216 / 27   =  20 *24 / 3  =  20 * 8   =  160

sin( angle )   =   length of side opposite / length of hypotenuse

sin P   =   15 / 17

                                     Take the inverse sin of both sides of the equation.

P   =   arcsin( 15/17 )

                                     Plug  arcsin(15/17)  into a calculator to get...

P   ≈   61.93°

yup, thank you

The two factors of the first number that you are looking for is 11 and 5.

We first prime factorize 55, and we get 5 * 11.

So we can immediately test 5 and 11.

5 * 11 = 55 and 5 + 11 = 16.

it works!

i hope this helped.

Here you go:

 ∠ R = α = 28.072° = 28°4'21″ = 0.49 rad

This is a trigonometry problem. We have to use inverse oprations.

We can use any of the sine, cosine, tangent, cotangent, secant, and cosecant since we know all of the 3 sides.

Let's just say we use sine. 

It is basically the ratio of the side opposite to the angle to the hypotenuse.

In this case, it is 8 : 17. 

The inverse of sine of 8/17 is 49 rad or about 28 degrees.

I hope this helps. 

To find the expected value, we do this:

(20/100)*5 + (80/100)*2 = 13/5

13/5 is the expected value. 

This means, that the special ticket should cost 13/5 more than the regular ticket to cover the cost of the refunds.

If you need help with expected values problems, you should watch this video explaining how to find the expected value:

https://m.youtube.com/watch?v=DAjVAEDil_Q

hope this helped!

If you are trying to find the mean, or average, of the numbers, I can help you! 

To find the mean, you add up all the numbers in the list, and divide the total by how many numbers there are in the list. 

Adding the numbers in the list, we have:

4 + 3 + 5 + 12 + 13 +16 = 53

Then we divided 53 by the total numbers there are in the list, which is 6

53 / 6 is rounded up to 9.

The answer you are looking for is 9.