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
Nataly [62]
3 years ago
6

Five adult tickets and three child tickets for a movie costs £55. The cost of buying two adult tickets and three child tickets i

s £31. Work out each of the costs of an adult and child ticket.
Mathematics
1 answer:
Allisa [31]3 years ago
7 0

Answer:

  • adult £8
  • child £5

Step-by-step explanation:

If you look at the numbers you are given, you see that the first purchase has 3 more adult tickets than the second purchase, and its cost is £24 more. This means an adult ticket costs £24/3 = £8.

Two adult tickets will cost 2×£8 = £16, so three child tickets cost ...

  £31 -16 = £15

Each child ticket is then £15/3 = £5.

An adult ticket costs £8; a child ticket costs £5.

You might be interested in
a) Γ(n) =∫[infinity]0tn−1e−tdta)Show that Γ(n+ 1) =nΓ(n) using integration by parts.b) Show that Γ(n+ 1) =n! , wherenis a positi
Nataliya [291]

\Gamma(n)=\displaystyle\int_0^\infty t^{n-1}e^{-t}\,\mathrm dt

a. Integrate by parts by taking

u=t^{n-1}\implies\mathrm du=(n-1)t^{n-2}\,\mathrm dt

\mathrm dv=e^{-t}\,\mathrm dt\implies v=-e^{-t}

Then

\displaystyle\Gamma(n)=-t^{n-1}e^{-t}\bigg|_0^\infty+(n-1)\int_0^\infty t^{n-2}e^{-t}\,\mathrm dt

We have

\displaystyle\lim_{t\to\infty}\frac{t^{n-1}}{e^t}=0

and so

\Gamma(n)=(n-1)\displaystyle\int_0^\infty t^{n-2}e^{-t}\,\mathrm dt=(n-1)\Gamma(n-1)

or, replacing n\to n+1, \Gamma(n+1)=n\Gamma(n).

b. From the above recursive relation, we find

\Gamma(n+1)=n\Gamma(n)=n(n-1)\Gamma(n-1)=n(n-1)(n-2)\Gamma(n-2)=\cdots=n(n-1)(n-2)\cdots2\cdot1\Gamma(1)

Now,

\Gamma(1)=\displaystyle\int_0^\infty e^{-t}\,\mathrm dt=1

and so we're left with \Gamma(n+1)=n!.

c. Using the previous result, we find \Gamma(5)=4!=24.

d. If the question is asking to find \Gamma(12), then you can just use the same approach as in (c).

But if you're supposed to find \Gamma\left(\frac12\right), we have

\displaystyle\Gamma\left(\frac12\right)=\int_0^\infty t^{-1/2}e^{-t}\,\mathrm dt

Substitute

u=t^{1/2}\implies u^2=t\implies 2u\,\mathrm du=\mathrm dt

Then

\displaystyle\Gamma\left(\frac12\right)=\int_0^\infty\frac1ue^{-u^2}(2u\,\mathrm du)=2\int_0^\infty e^{-u^2}\,\mathrm du=\frac{2\sqrt\pi}2=\sqrt\pi

7 0
3 years ago
Please help me with these 2 answers!
fgiga [73]
7 is 71+7/3+78
8 is 60x2x2
4 0
3 years ago
Read 2 more answers
2 less than a number
Umnica [9.8K]

Answer:

-2

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Fiona joins a fruit of the month club. The entry cost is $25 and then she pays $18 per month. If she participates for 8 months,
xeze [42]

Answer: $169

Step-by-step explanation: The expression 25 + 18 x 8 represents the amount she will pay if she participates for 8 months.

Multiply 18 x 8 to find the cost for 8 months. $18 x 8 = $144.

Now add $25 to $144, which equals $169

5 0
3 years ago
Read 2 more answers
Stuck in this problem help please
marta [7]
Use trigonometry.

tan30° = perpendicular / base

Here for angle 30° , x is perpendicular while 10 is the base.

tan30° = 1/√3
1/√3 = x/10
x = 10/✓3

By rationalising
x = 10√3/3

Hope This Helps You!
3 0
4 years ago
Other questions:
  • You want to buy a $ 351,749 home. You plan to pay 15 % as a down payment, and take out a 15 year loan for the rest. What will yo
    8·1 answer
  • Which equations represent this fact family ? Check all that apply
    10·1 answer
  • HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    7·2 answers
  • What is the solution to the inequality _ 6 w < 84​
    8·1 answer
  • Express the following in the form p/q , where p and q are integers and q is not equal to 0<br> 0.47
    9·1 answer
  • Cuando es 5765446+686-56
    11·1 answer
  • Sarah makes 1/2 pound of caramel popcorn and puts it in a bag that holds 1/8 of a pound. Which equation can be used to find how
    7·1 answer
  • The sum of two numbers is 54 and the difference is 8. What are the numbers?
    10·1 answer
  • The table below shows the meal cost and tip for the last 10 tables that a waiter served.
    9·1 answer
  • What is the slope of the line graphed above?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!