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Genrish500 [490]
3 years ago
13

Tickets for a cinema cost £a for adults and £c for children. 2 adults and 3 children cost £42.70. 3 adults and 5 children cost £

67.30.
How much does it cost for 1 adult and 1 child?​
Mathematics
1 answer:
svetoff [14.1K]3 years ago
8 0

Answer:

c = 6.5, a = 11.6

Step-by-step explanation:

2a + 3c = 42.7

3a + 5c = 67.3

Elimination

(2a+3c = 42.7)*3

(3a+5c = 67.3)*2

(1) 6a+9c = 128.1

(2) 6a+10c = 134.6

(2) - (1)

c = 6.5

Substitue 'c' in any of the equation

2a + 3(6.5) = 42.7 or 3a + 5(6.5) = 67.3

2a + 19.5 = 42.7 3a + 32.5 = 67.3

2a = 42.7 - 19.5 3a = 67.3 - 32.5

2a = 23.2 3a = 34.8

a = 11.6 a = 11.6

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bogdanovich [222]

Answer:

a) \sigma_{\bar x} = 1.414

b) \sigma_{\bar x} = 1.414

c) \sigma_{\bar x} = 1.414

d) \sigma _{\bar x} = 1.343

Step-by-step explanation:

Given that:

The random sample is of size 50 i.e the population standard deviation  =10

Size of the sample n = 50

a) The population size is infinite;

The standard error is determined as:

\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}

\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}

\sigma_{\bar x} = 1.414

b) When the population size N= 50000

n/N = 50/50000 = 0.001 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}

\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}

\sigma_{\bar x} = 1.414

c)  When the population size N= 5000

n/N = 50/5000 = 0.01 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}

\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}

\sigma_{\bar x} = 1.414

d) When the population size N= 500

n/N = 50/500 = 0.1 > 0.05

So; the finite population of the standard error is applicable in this scenario;

Therefore;

The standard error is determined as:

\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }

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3 years ago
A rental car company charges $60.00 just to rent a car, and $70.00 for each day you keep the car.
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Answer:

$200

Step-by-step explanation:

70 x 2 = 140.00 + 60.00 = $200

8 0
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Naddik [55]

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

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→ Plot point (-1, 8)

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→ Plot point (0, 3)

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→ Plot point (4, 3)

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→ Plot point (5, 8)

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∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

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∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

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