1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Diano4ka-milaya [45]
3 years ago
6

Record the data in a table with the rows representing the type of music and the columns representing the weeks.

Mathematics
1 answer:
Art [367]3 years ago
8 0

Answer:

150

Step-by-step explanation:

You might be interested in
Binomial Expansion/Pascal's triangle. Please help with all of number 5.
Mandarinka [93]
\begin{matrix}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\end{bmatrix}

The rows add up to 1,2,4,8,16, respectively. (Notice they're all powers of 2)

The sum of the numbers in row n is 2^{n-1}.

The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When n=1,

(1+x)^1=1+x=\dbinom10+\dbinom11x

so the base case holds. Assume the claim holds for n=k, so that

(1+x)^k=\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k

Use this to show that it holds for n=k+1.

(1+x)^{k+1}=(1+x)(1+x)^k
(1+x)^{k+1}=(1+x)\left(\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k\right)
(1+x)^{k+1}=1+\left(\dbinom k0+\dbinom k1\right)x+\left(\dbinom k1+\dbinom k2\right)x^2+\cdots+\left(\dbinom k{k-2}+\dbinom k{k-1}\right)x^{k-1}+\left(\dbinom k{k-1}+\dbinom kk\right)x^k+x^{k+1}

Notice that

\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!}{\ell!(k-\ell)!}+\dfrac{k!}{(\ell+1)!(k-\ell-1)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)}{(\ell+1)!(k-\ell)!}+\dfrac{k!(k-\ell)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)+k!(k-\ell)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(k+1)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{(k+1)!}{(\ell+1)!((k+1)-(\ell+1))!}
\dbinom k\ell+\dbinom k{\ell+1}=\dbinom{k+1}{\ell+1}

So you can write the expansion for n=k+1 as

(1+x)^{k+1}=1+\dbinom{k+1}1x+\dbinom{k+1}2x^2+\cdots+\dbinom{k+1}{k-1}x^{k-1}+\dbinom{k+1}kx^k+x^{k+1}

and since \dbinom{k+1}0=\dbinom{k+1}{k+1}=1, you have

(1+x)^{k+1}=\dbinom{k+1}0+\dbinom{k+1}1x+\cdots+\dbinom{k+1}kx^k+\dbinom{k+1}{k+1}x^{k+1}

and so the claim holds for n=k+1, thus proving the claim overall that

(1+x)^n=\dbinom n0+\dbinom n1x+\cdots+\dbinom n{n-1}x^{n-1}+\dbinom nnx^n

Setting x=1 gives

(1+1)^n=\dbinom n0+\dbinom n1+\cdots+\dbinom n{n-1}+\dbinom nn=2^n

which agrees with the result obtained for part (c).
4 0
3 years ago
3. The volume of a book is 60 cubic inches. If a large
saveliy_v [14]

Answer:

720 in^3.

Step-by-step explanation:

12 * 60 = 720.

6 0
2 years ago
Read 2 more answers
Simple geometry problem
vova2212 [387]

Answer:

Step-by-step explanation:

I gather that you need to find the area of the sector and then subtract from it the area of the segment to get the area of the triangle (although there are other ways in which to find the area of the triangle).

The area of a sector is:

A=\frac{\theta}{360}\pi r^2 where our angle is given as 34, pi is 3.1415, and the radius is 5:

A=\frac{34}{360}(3.1415)(25) and if you multiply and divide that all out you get that the area of the sector is:

A = 7.417

Now subtract from it the area of the segment, 2.209. to get the area of the triangle:

7.417 - 2.209 = 5.208

7 0
3 years ago
Read 2 more answers
Please Help!!!!!!! Emergency
Stolb23 [73]

Answer:

C

15 + x

Step by step explanation

For Company X, the initial cost is 30 cents  plus 5 cents per minute, so the expression would be 30 + 5x (x would represent minutes.

For Company Y, the initial cost is 15 cents  plus 4 cents per minute, so the expression would be 15 + 4x (x would represent minutes.)

Then subtract the expression of Y from the expression of X to show the difference in value between Y and X.

So, 30 + 5x - (15 +4x)

Distribute the subtraction sign.

30 + 5x - 15 - 4x

Solve across.

15 + x

6 0
3 years ago
What is 0.02349 written in standard form to 3 significant figures
Alinara [238K]

Answer: The answer is (B)

Explanation: The answer is (B) because, there are 2 zeros so that means that there would have to be a 2 behind the 10 and then there is 2,3,4,and 9. We take out the 9 and use the other numbers, bring over the decimal and now you have 2.34 x 10^{2} .

5 0
2 years ago
Read 2 more answers
Other questions:
  • Classify the system of equations 1/3x+y+2=0 1/2x+y-5=0 A. intersecting B. parallel C. coincident
    8·2 answers
  • Last month Marcus borrowed $74 from his roommate so far he has paid him back $33 which equation could be used to find X the amou
    8·2 answers
  • Samuel currently has an account balance of $3,439.96. He opened the account five years ago with a deposit of $3,104.31. If the i
    8·1 answer
  • To the nearest tenth, find the perimeter of ABC with vertices A (-2,-2) B (0,5) and C (3,1)
    8·1 answer
  • The value of a stock over a 12 year period form 2003 to 2015 is shown in the line graph. Which statement is not supported by the
    5·2 answers
  • Cada material en sus distintos estados de agregacion, cambia de volumen de forma diferente, sin embargo todos lo hacen en cierta
    9·1 answer
  • A potato chip manufacturer produces bags of potato chips that are supposed to have a net weight of 326 grams. Because the chips
    6·1 answer
  • Solve the equation.<br><br> 6 = c - 5
    12·2 answers
  • 14<br> 6<br> 4<br> 2<br> Y<br> -2<br> -2<br> -4
    6·1 answer
  • What is the mean score Score<br> 90<br> 80<br> 70<br> 60
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!