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iogann1982 [59]

2 years ago

15

A theater wants to take in 2000 dollars for a certain matinee. Children's tickets cost 5 dollars each and adult tickets cost 10

dollars each. If the theater has a maximum of 350 seats, write a system of equations that can be solved to determine the number of both children and adult tickets the theater can sell.

1 answer:

tensa zangetsu [6.8K]2 years ago

8 0

Answer:

We have the following system of equations:

$\left \{ {5x + 10 y = 2.000 (1)} \atop {x + y = 350 (2)} \right.$

(2) = x = 350-y . Replace x in equation (1 )

=> 5(350-y)+10y=2000 => y = 241

Replace y=241 in equation (2 ) => x = 350-241 = 109

the number of both children and adult tickets the theater can sell.

Children tickets : 109

Adult tickets : 241

Step-by-step explanation:

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Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. Afte

natka813 [3]

Answer:

(a) 8 balls

(b) 4 balls

Step-by-step explanation:

Let

$N \to$ Number of balls

For a box, the probability that there are N balls in it is:

$Pr = 0.5^N$

For 2 boxes, it is:

$Pr = 2 * 0.5^N$

From the question, we have:

$\frac{80}{10000} \to$ Favorable outcome

To solve for N, we have:

$2 * 0.5^N = \frac{80}{10000}$

$2 * 0.5^N = 0.008$

Divide both sides by 2

$0.5^N = 0.004$

Take log of both sides

$\log(0.5^N) = \log(0.004)$

Apply law of logarithm

$N\log(0.5) = \log(0.004)$

Make N the subject

$N = \frac{\log(0.004)}{\log(0.5)}$

$N =7.966$

Approximate

$N = 8$

Solving (b): Balls in one of the two boxes.

Here, we assume that each ball will have almost the same number of balls at a given instance;

Hence, we have:

$Balls \approx \frac{N}{2}$

$Balls \approx \frac{8}{2}$

$Balls \approx 4$

<em>4 balls in each box</em>

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3 years ago

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sattari [20]

Answer:

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7 0

2 years ago

'-(x^2/2)-x-(5/2)' simplify

Lilit [14]

Answer:

-1 by x^2/2

Step-by-step explanation:

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6 0

3 years ago

Johny Deposited 50000 rupees, Jaleel 40000 and Jaleel 20000 rupees to start a business together.They got 3300 rupees as a profit

Andrews [41]

Step-by-step explanation:

Step one:

Johny Deposited 50000 rupees,

Jaleel 40000 and

Jaleel 20000 rupees

total deposits = 110,000

They got 3300 rupees as a profit in a month

Johny's investment in percent

50000/110000= 0.45%

Jaleel's investment in percent

40000/110000= 0.36%

Jaleel's(2) investment in percent

50000/110000= 0.18%

They will get

Johny =0.45*33000= 1485 rupees

Jaleel= 0.36*3300= 1188 rupees

Jaleel(2)= 0.18*3300=594 rupees

7 0

3 years ago

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans an

Y_Kistochka [10]

Answer: a) 15, b) 1.

Step-by-step explanation:

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?

(a) 10% of all adult Americans support the changes

Here, $np>5\ and\ n(1-p)>5$

And , $p=0.10$

So, consider the equality, to find the value of 'n'.

$np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50$

So, there are $50-35=15$ more adult Americans needed.

(b) 15% of all adult Americans supports the changes

Here, $p=0.15$

So, again we get that

$np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34$

So, there are $35-34=1$ more adult Americans needed.

Hence, a) 15, b) 1.

5 0

3 years ago