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3 years ago

A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of

Mathematics

1 answer:

Rainbow [258]3 years ago

8 0

Answer:

The attendance was 198 children, 90 students and 99 adults.

Step-by-step explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

$5c+7s+12a=2808$

We also know that the children attendance doubles the adult attendance:

$c=2a$

The third equation is the seating capacity, which we assume is full:

$c+s+a=387$

We start by replacing variables in two of the equations:

$c=2a\\\\s=387-c-a=387-2a-a=387-3a$

Then, we solve the remaining equation for a:

$5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99$

Then, we solve for the other two equations:

$c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90$

The attendance was 198 children, 90 students and 99 adults.

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On the day you retire you have $1,000,000 saved. You expect to live another 25 years during which time you expect to earn 6.19%

serious [3.7K]

Answer:

OUR ANSWER IS $61,334.36

Step-by-step explanation:

The real rate of return = 6.19% - 2.5% = 3.69%

We assume the annual withdrawal is P and the same will be withdrawn at the end of each year, so that the present value of the regular annuity will be $1,000,000

Total tenure = 25 Years

PV = 1 × [(1-(1 + r)⁻ⁿ] /r = P × [1 +(1.0369)⁻²⁵] /0.0369 =P× 16.147

But as per the condition, PV = $1,000,000

So P =$1000,000 /16.147 =$61,334.36

4 0

3 years ago

Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean an

vovangra [49]

Let's assume initial population is in 1999

so, production of passenger cars in Japan is 3.94 million in 1999

so, P=3.94 million

and the production of passenger cars in Japan is 6.74 million in 2009

so, A=6.74 million in t=2009-1999=10 years

now, we can use formula

$A=P(1+r)^t$

here , r is interest rate

so, we can plug values

$6.74=3.94(1+r)^{10}$

now, we can solve for

$\left(1+r\right)^{10}=\frac{337}{197}$

$r=0.05516$

so,

the geometric mean annual percent increase is 5.516%............Answer

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3 years ago

Plz answer these questions<br> Answer should be with explanation

yan [13]

Answer:

2/3

Step-by-step explanation:

In the game of chance, the possibility of winning it is 1/3. This is one of two outcomes, winning or losing. Since there is a 1/3 chance of winning it, there leaves only one outcome, losing it. Since 1/3 is a third of a whole, that leaves 2/3 for the other possibility, losing it. We then find that winning it has the chance of 1/3 and losing it has a 2/3 chance.

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3 years ago

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Ilia_Sergeevich [38]

Here is ur perfect answer