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
lorasvet [3.4K]
3 years ago
8

Find the number of ways in which a student can choose 5cource out of 9 course?​

Mathematics
1 answer:
Kaylis [27]3 years ago
7 0

Answer:

please mark as brainliest

You might be interested in
Solve these recurrence relations together with the initial conditions given. a) an= an−1+6an−2 for n ≥ 2, a0= 3, a1= 6 b) an= 7a
8_murik_8 [283]

Answer:

  • a) 3/5·((-2)^n + 4·3^n)
  • b) 3·2^n - 5^n
  • c) 3·2^n + 4^n
  • d) 4 - 3 n
  • e) 2 + 3·(-1)^n
  • f) (-3)^n·(3 - 2n)
  • g) ((-2 - √19)^n·(-6 + √19) + (-2 + √19)^n·(6 + √19))/√19

Step-by-step explanation:

These homogeneous recurrence relations of degree 2 have one of two solutions. Problems a, b, c, e, g have one solution; problems d and f have a slightly different solution. The solution method is similar, up to a point.

If there is a solution of the form a[n]=r^n, then it will satisfy ...

  r^n=c_1\cdot r^{n-1}+c_2\cdot r^{n-2}

Rearranging and dividing by r^{n-2}, we get the quadratic ...

  r^2-c_1r-c_2=0

The quadratic formula tells us values of r that satisfy this are ...

  r=\dfrac{c_1\pm\sqrt{c_1^2+4c_2}}{2}

We can call these values of r by the names r₁ and r₂.

Then, for some coefficients p and q, the solution to the recurrence relation is ...

  a[n]=pr_1^n+qr_2^n

We can find p and q by solving the initial condition equations:

\left[\begin{array}{cc}1&1\\r_1&r_2\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]

These have the solution ...

p=\dfrac{a[0]r_2-a[1]}{r_2-r_1}\\\\q=\dfrac{a[1]-a[0]r_1}{r_2-r_1}

_____

Using these formulas on the first recurrence relation, we get ...

a)

c_1=1,\ c_2=6,\ a[0]=3,\ a[1]=6\\\\r_1=\dfrac{1+\sqrt{1^2+4\cdot 6}}{2}=3,\ r_2=\dfrac{1-\sqrt{1^2+4\cdot 6}}{2}=-2\\\\p=\dfrac{3(-2)-6}{-5}=\dfrac{12}{5},\ q=\dfrac{6-3(3)}{-5}=\dfrac{3}{5}\\\\a[n]=\dfrac{3}{5}(-2)^n+\dfrac{12}{5}3^n

__

The rest of (b), (c), (e), (g) are solved in exactly the same way. A spreadsheet or graphing calculator can ease the process of finding the roots and coefficients for the given recurrence constants. (It's a matter of plugging in the numbers and doing the arithmetic.)

_____

For problems (d) and (f), the quadratic has one root with multiplicity 2. So, the formulas for p and q don't work and we must do something different. The generic solution in this case is ...

  a[n]=(p+qn)r^n

The initial condition equations are now ...

\left[\begin{array}{cc}1&0\\r&r\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]

and the solutions for p and q are ...

p=a[0]\\\\q=\dfrac{a[1]-a[0]r}{r}

__

Using these formulas on problem (d), we get ...

d)

c_1=2,\ c_2=-1,\ a[0]=4,\ a[1]=1\\\\r=\dfrac{2+\sqrt{2^2+4(-1)}}{2}=1\\\\p=4,\ q=\dfrac{1-4(1)}{1}=-3\\\\a[n]=4-3n

__

And for problem (f), we get ...

f)

c_1=-6,\ c_2=-9,\ a[0]=3,\ a[1]=-3\\\\r=\dfrac{-6+\sqrt{6^2+4(-9)}}{2}=-3\\\\p=3,\ q=\dfrac{-3-3(-3)}{-3}=-2\\\\a[n]=(3-2n)(-3)^n

_____

<em>Comment on problem g</em>

Yes, the bases of the exponential terms are conjugate irrational numbers. When the terms are evaluated, they do resolve to rational numbers.

6 0
3 years ago
A baker made 20 pies. A Boy Scout troop buys one–fourth of his pies, a preschool teacher buys one–third of his pies, and a cater
n200080 [17]

Answer:

The number of pies does the baker have left is 15.

Step-by-step explanation:

Given : A baker made 20 pies. A Boy Scout troop buys one–fourth of his pies, a preschool teacher buys one–third of his pies, and a caterer buys one–sixth of his pies.

To find : How many pies does the baker have left?

Solution :

Let x be the number of pies does the baker have left.

According to question,

Number of pies buys,

One-fourth =\frac{1}{4}

One-third =\frac{1}{3}

One-sixth =\frac{1}{6}

i.e. x=20-(20\times \frac{1}{4}+20\times \frac{1}{3}+20\times \frac{1}{6})

x=20-(5+20\times \frac{1}{3}+10\times \frac{1}{3})

x=20-(5+\frac{20+10}{3})

x=20-(5+ \frac{30}{3})

x=20-(5+10)

x=20-(15)

x=5

The number of pies does the baker have left is 15.

7 0
3 years ago
Tickets to a local circus cost $5 for students and $8 for adults. A group of 9 people spent a total of $60. How many adults were
S_A_V [24]

Answer:

5

Step-by-step explanation:

You need to set up and solve a system of linear equations here.

Let s and a represent the number of students and adults respectively.

Then s + a = 9, and s = 9 - a.

Total ticket cost for the adults was ($8/adult)(a)

and for the students ($5/student)(s).

Total cost of the tickets was then  ($8/adult)(a) + ($5/student)(s) = $60.

Then our system of linear equations is:

8a + 5s = 60

 a  +  s  = 9, or s = 9 - a.  Substituting 9 - a for s, we get:

8a + 5(9 - a) = 60.

Then 8a + 45 - 5a = 60, or 3a = 15.

Solving for a, we get a = 5.

Solving for s using s = 9 - a, we get   s = 9 - 5, or s = 4.

There were 5 adults in the group (and 4 students).

3 0
3 years ago
Find the degree of the monomial.<br> 3a4b3
steposvetlana [31]

Answer:

degree of the monomial is the sum of the exponents of all included variables

Step-by-step explanation:

please mark me as brainlist please

3 0
2 years ago
HELP ASAP 36 POINTS!!!!!
vodomira [7]

Answer:

48

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • I need help with these problems #3,4,5, and 6
    7·2 answers
  • I need help please?!!!
    10·2 answers
  • With a convenience sample, a population is broken up into different subgroups and then simple random samples are conducted withi
    13·1 answer
  • The manager of music is giving away 255 music downloads at its grand opening event.
    5·1 answer
  • PLEASE HELP!
    15·2 answers
  • (50pts + brainliest) Which postulate can be used to prove that △BCA and △DAC are congruent?
    5·2 answers
  • If your in k12 8th grade and you fail your exams which brings it down to a d or f do you have to take summerschool or retake the
    15·2 answers
  • Can someone help me please
    7·1 answer
  • Jim bought the game system on sale for $195. Kaylen bought the same system at full price for $250. How much was the sale for whe
    12·2 answers
  • NO LINKS A CELL PHONE COMPANY FOUND THAT 20 OF THEIR 150 PHONES WERE DEFECTIVE IN MAY. IF THEY PRODUCED 750 PHONES IN JUNE, HOW
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!