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@Guest any number number of letters

1) Words consisting of how many letters? Just 3 and 2-letter "words"? How about 4-letter "words"?

And how about repeats such as:"MMA", "AAM"....etc.

idk, thats why i asked this question

is it right?

ty for at least trying

So the answer is B: 4

I am not sure if this is right but:

I noticed that 6y is2 times 3y and 18 is 2 times 9 so I think that bx will be two times 2x so 4x so 4. (They have to be the same equation to have an infinite amount of solutions so yeah)

Thank you All!

it doesn't make sense. What is a logarithm and how does it work.

See the answer to Question # 1 here:

https://web2.0calc.com/questions/please-explain-thoroughly-so-i-could-understand-the-procedures

Let the the length of each side of the square=D

Let the time it takes him to walk one side of the square =T

Then the time it takes him to walk 3 legs of the square =3T

D =6T x 3 = 18T - distance of the first 3 legs of his walk.

The time it takes him to walk the last leg of his walk =6/5T =1.2T

1.2T x 5 =6T - distance covered in the last leg

Total distance covered / Time taken = Average speed

[18T + 6T] / [3T + 1.2T] =24T / 4.2T =5 5/7 - feet/sec - his average speed around the block.

Guest #6 is Mr. BB.  He’s a semi-skilled plagiarist, and he tends to copy and paste a posted answer/solution that’s defective.   Of course, there is no explanation for its derivative, and in this case, the binomials are wrong. The counts should be from 4 to 7, not 4 to 1.  When Mr. BB serves porkbutt roasts the anuses are still attached. Nothing too unusual, here.

GA

Yes, that is the correct answer. 

sum(nCr(7, k)*0.6^k*0.4^(7-k),k,4,7)

Enter this into the forum’s calculator for a confirmation.  

If you are going to paste LaTex code on here, you should also open a LaTex box and paste it in there so that it renders. You should also give a source for your code!

You may hope it helps, but it does not help very much.

While this is the correct result, without an explanation of its origination, it’s of little help to a student trying to learn how to solve these types of probability questions. 

GA

Solution:

\(\text {The series ends after a team has a fourth win.}\\ \text{Here are the four scenarios with derived probabilities }\\ \text{where the Cubs win the series. }\\ \text{1) The Cubs win the first four games.}\ \text{ }\\ \hspace{35 mm} \rho(\text {Cbs win on } 4^{th} \text{game )= }\ \text{ }\\ \hspace{35 mm} (3/5)^4 = (81/625) = 12.96\%\\ \text{ }\\ \text{2) Cubs win series in game five. }\\ \text{For the Cubs to win the series in game five,}\\ \text{ they need to win three games in four trials and then win the fifth game. }\\ \text{ } \hspace{34 mm} \rho \text {(Cbs win 3 in 4})*\rho \text{(Cbs win 5th game}) =\\ \text{ } \hspace{35 mm} \ \binom{4}{3}(3/5)^3*(2/5) *(3/5) = (648/3125) \approx 20.74\% \\ \text{ }\\ \text{3) Cubs win series in game six. }\\ \text{For the Cubs to win the series in game six, }\\ \text{they need to win three games in five trials and then win the sixth game. }\\ \text{ } \hspace{34 mm} \rho \text {(Cbs win 3 in 5})* \rho\text{(Cbs win 6th game}) =\\ \text{ } \hspace{34 mm} \binom{5}{3}(3/5)^3*(2/5)^2 *(3/5) = (648/3125) \approx 20.74\% \\ \text{ }\\ \text{4) Cubs win series in game seven. }\\ \text{For the Cubs to win the series in game seven, }\\ \text{they need to win three games in six trials and then win the seventh game. }\\ \text{ } \hspace{34 mm} \rho \text {(Cbs win 3 in 6})* \rho \text{(Cbs win 7th game}) =\\ \text{ } \hspace{34 mm} \binom{6}{3}(3/5)^3*(2/5)^3 *(3/5) \approx 16.59\% \\ \text{ }\\ \text{ The sum of the individual probabilities gives }\\ \text{ the overall probability of the Cubs winning the series.}\\ \text {Sum of individual probabilities: } \\ (20.74+20.74+16.59+12.96) \bf \approx 71.0\% \)

GA

-2x+y = k     and .5x + y = 14        Use the second equation to find y when x = -8.4

                          .5(-8.4) + y = 14      results in y = 18.2

Sub this into the FIRST equation to comput value for k

-2(-8.4) + 18.2 = k         k=35

Here is a graph:

Each handle will exert the same FOOT-POUNDS of torque to loosen the bolt...

9/12 ft * 375 lbs = 281.25 foot-pounds  of torque required

15/12 ft * ? lbs = 281.25 ft-lbs      solve for ? = 225 lbs

Side 1    6 fps

         2   6 fps

         3   6 fps

         4   5 fps

Let x = distance of each side (it will cancel out)

x ft  / 6 ft/sec   x 3     +   x ft / 5ft/sec = 4x / (avg)

(3/6 sec + 1/5 sec ) x  = 4x / avg        Divide both sides by 'x'

15/30 + 6/30  = 4/avg                         Solve for avg  (which is average speed in ft/sec)

avg = 4 / (21/30) = 120/21 ft/sec = 40/7 ft/sec

1>   Area shaded is included in Fish circle and Dog circle but NOT Cat circle    so   fish AND dog but NOT cat

2>  17 are listed as taking band....of these 8 ALSO take art....the remaining ones do not take art    17-8 = 9

3>  175

       86

       52

       18+25     (18 can ALSO speak French)

       32 + 18    (Again 18 can ALSO speak French...but it didn't ask this)

Use Geometric Series formula:

S =F x ( 1 - R^N) / (1 - R), where S =Sum of the series, F = First term, R = Common ratio, N = Number of terms. The first term = 310, the common ratio =1.17. I don't know what you mean by "actual value of the ratio". 363 - 310 =53 extra phones, or 17%, were sold at the end of the 2nd week compared to the 1st week. But this number will go up by 17% every week. So, at the end of the 3rd week, you will have 53 x 1.17 =62 extra phones sold, and 62 x 1.17 =73 extra phones sold at the end of the 4th week....and so on. 

The 37th term will be =F x R^(N - 1), so sales for week 37 will be:

310 x 1.17^(37 -1) =310 x 1.17^36 =310 x 285 =88,350 - cell phones will be sold for week 37.

Use the above Geometric Formula to find total sales for the year:

S =310 x (1 - 1.17^52) / (1 - 1.17)

S =310 x (1 - 3,513) / (-0.17)

S =310 x  (-3,512) / (-.17)

S =310 x   20,659

S =6,404,290 - cell phone sold during the first year.

Note: Because of rounding off to whole numbers, the final total will be out by about 251. You may wish to check these calculations yourself and round off as you see appropriate.

2.   Let's look at each pair of numbers.

Could  (4, 6)  represent event A?

Is  4 + 6  greater than  7  ?  yes

Is  4 + 6  a multiple of  4  ?  no

Therefore (4, 6) could not represent event A.

Could  (4, 3)  represent event A?

Is  4 + 3  greater than  7  ?  no

Is  4 + 3  a multiple of  4  ?  no

Therefore  (4, 3)  could not represent event A.

Could  (6, 6)  represent event A?

Is  6 + 6  greater than  7  ?  yes

Is  6 + 6  a multiple of  4  ?  yes

Therefore  (6, 6)  could represent event A.

Could  (5, 4)  represent event A?

Is  5 + 4  greater than  7  ?  yes

Is  5 + 4  a multiple of  4  ?  no

Therefore  (5, 4)  could not represent event A.

Could  (3, 5)  represent event A?

Is  3 + 5  greater than  7  ?  yes

Is  3 + 5  a multiple of  4  ?  yes

Therefore  (3, 5)  could represent event A.

Could  (1, 5)  represent event A?

Is  1 + 5  greater than  7  ?  no

Is  1 + 5  a multiple of  4  ?  no

Therefore (1, 5) could not represent event A.

1.

num of students that like TV but not video games  =  num of students that like TV - num of students that like both TV and video games

num of students that like TV but not video games  =  34 - 8

num of students that like TV but not video games  =  26

Let the number of days for Bob to finish the job = B

Let the number of days for Carl to finish the same job = C, then we have:

1/B + 1/C = 1/12. But Bob works 1.5 times faster than carl, or it takes him 2/3 the time it takes Carl.

B = 2/3C. Subbing this into first equation we have:

1/(2/3C) + 1/C = 1/12

5/2C =1/12

2C = 60

C = 30 - days - that would take Carl to finish the Job.

B =2/3 x 30 = 20 days - that would take Bob to finish the job.

Thanks so much everyone this was very helpful!

A function $f$ has a horizontal asymptote of y = -4,$ a vertical asymptote of x = 3,$ and an x-intercept at S(1,0).

(a): Let f be of the form f(x) = \frac{ax+b}{x+c}.

      Find an expression for f(x). 

(b): Let f be of the form f(x) = \frac{rx+s}{2x+t}.

      Find an expression for f(x).

I believe this is answer already, but I think I have a better solution:

$\bold{Part (a)}$: A Logical Approach

First of all, a number with an odd number of positive divisors must be a perfect square.

For example, $9=3^2$, and its factors are: 1, 3, and 9. A total of 3 numbers. 

However, a number that is not a perfect square, will have an even number of factors.

For example, $6=2\cdot3$, and its factors are : 1, 2, 3, and 6. A total of 3 numbers. 

Logically, this makes sense, because when you look at 6’s factors, $1\cdot6=6$ and $2\cdot3=6$.

When you look at 9’s factors, $1\cdot9=9$ and $3\cdot3=9$.

In the factors of 6, every number has another number to pair itself with, making pairs of 2, which makes an even number of

factors. 

On the other hand, in the factors of 9, 1 and 9 can pair with each other to make 9, but 3 must pair with itself to make 9, hence

the even number of factors. 

This problem does not ask of odd number of factors, but asks for 3 factors. This must mean that the number must be a prime

number squared. This is because when you take a composite number, $n$, and square it, you will come across miscellaneous factors other than 1, $\sqrt{n}$. and n. For example, take 16 or $4^2$. The factors are 1, 2, 4, 8, and 16. There are an odd number of factors, just not exactly three. 

This is because when you are taking $4^2$, you are actually take (2^2)^2, and you will see other powers of two, for example

$2^3$, 8.

So the answer for part (a), is a positive integer that have exactly 3 positive divisors, must be the square of a prime number:

$$p^2$$where $p$ is any prime.

$\bold{Part(b)}$:

The first step in this problem is to prime factorize 8400. 

$$8400=2^4\cdot3\cdot{5^2}\cdot7.$$

Instead of counting all of the possible numbers, it is easier to count the numbers that have three divisors or fewer.

1, has one divisor.

All the prime numbers: 2,3,5, and 7 have two divisors. 

All the perfect squares of primes: 4 and 25 have three divisors. 

Now the rest have four or more divisors.

There are a total of $(4+1)(1+1)(2+1)(1+1)=60$ positive divisors of 8400.

But since this list includes those who are four or less, the answer will be:

$60-7=\boxed{53}$.

I hope this helped!