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3 years ago

1.9 An electronics store buys media from customers

Mathematics

1 answer:

Marina CMI [18]3 years ago

8 0

The store pays $2 for each Blu-ray disc, $0.75 for each DVD, and

$0.1 for each VHS cassette

Step-by-step explanation:

An electronics store buys media from customers to resell.

The given is:

1. The store pays one customer $5.30 for one Blu-ray disc, four DVDs,

and three VHS cassettes

2. The store pays the second customer $11.50 for five Blu-ray discs

and two DVDs

3. The store pays the third customer $10.20 for two Blu- ray discs, eight

DVDs, and two VHS cassettes

We need to find the amount the store pays for each item

Assume that:

The cost of a Blue-ray disc is $x

The cost of a DVD is $y

The cost of a VHS cassette is $z

∴ x + 4y + 3z = 5.3 ⇒ (1)

∴ 5x + 2y = 11.5 ⇒ (2)

∴ 2x + 8y + 2z = 10.2 ⇒ ÷ 2

∴ x + 4y + z = 5.1 ⇒ (3)

- Subtract equation (3) from equation (1)

∵ x + 4y + 3z = 5.3 ⇒ (1)

∵ x + 4y + z = 5.1 ⇒ (3)

∴ 2z = 0.2

- Divide both sides by 2

∴ z = 0.1

Substitute the value of z in equation (3)

∴ x + 4y + 0.1 = 5.1

- Subtract 0.1 from both sides

∴ x + 4y = 5 ⇒ (4)

Let us solve equations (2) and (4)

∵ 5x + 2y = 11.5 ⇒ (2)

∵ x + 4y = 5 ⇒ (4)

- Multiply equation (2) by -2 to eliminate y

∴ -10x - 4y = -23 ⇒ (5)

- Add equations (4) and (5)

∴ -9x = -18

- Divide both sides by -9

∴ x = 2

- Substitute the value of x in equation (2)

∴ 5(2) + 2y = 11.5

∴ 10 + 2y = 11.5

- Subtract 10 from both sides

∴ 2y = 1.5

- Divide both sides by 2

∴ y = 0.75

The store pays $2 for each Blu-ray disc, $0.75 for each DVD, and

$0.1 for each VHS cassette

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Finger [1]

Answer:

Part A: The population are the American adult citizens, excluding the ones from Alaska and Hawaii. The population is the people which the sample is trying to represent, as a hole.

The sample is a portion of this population, and in this case is represented by a randomly selected amount of people whose response to the interview has been selected.

Part B: The sample here has been selected in two steps. The first step is the one that we must pay attention to: the numbered list of one million responses from around the US (excluding Alaska and Hawaii). Because these responses were obtained by an online survey, the sample looks like a convenience sampling, as it depends on the availability and willingness from participants to take part of the study (is not compulsory for everyone, so not everyone is going to response, then there are people that is not going to be represented by). The second step is the random selection of a part of the previous responses. This last part will ensure that, the individuals that took part of the group that was interviewed, are well represented in the results.

Part C: As it was mentioned, there is a selection bias, because the information from the sample comes from a specific group of people that has certain features that may not represent all American adults citizens. For example, the opinion of those people who do not use internet, will not be considered (and they may be a large number of persons). This situations weaken the conclusions obtained in the study, as they are not representative of the hole population.

Step-by-step explanation:

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2 years ago

The ratio of boys to girls in a school is 9:11. If there are 400 pupils in the school,how many boys are there

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I believe its 180.

I have seen this question before and the amount of girls was 220, so 400-220 is 180

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3 years ago

To add 20.4 + 3.75 + 4.25, Crystal first added 3.75 and 4.25. Which property did Crystal use to add mentally?

Black_prince [1.1K]

Answer:

A) Associative Property of Addition

Step-by-step explanation:

Associative Property of Addition

Let A, B and C be any three real numbers

A+(B+C) = (A+B) + C

Given data

(20.4 + 3.75) + 4.25 = 20.4 + (3.75 + 4.25)

= 20.4 + 8.0

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3 years ago

The height of a punted football can be modeled with the quadratic function 0.01x^2 + 1.18x+2.

Fantom [35]

The function of the path of the punted ball is a quadratic function which

follows the path of a parabola.

The correct responses are;

Part A: The coordinates of the vertex is $\underline {(59, \, 36.81)}$

Part B: The maximum height of the punt is 36.81 ft.

Part C: The defensive player must reach up to 7.65 feet to block the punt.

Part D: The distance down the field the ball will go without being blocked is approximately 119.67 ft.

Reasons:

The function for the height of the punted ball is; h = -0.01·x² + 1.18·x + 2

Assumption; The distances are feet.

Part A: By completing the square, we have;

f(x) = -0.01·x² + 1.18·x + 2

100·f(x) = -x² + 118·x + 200

-100·f(x) = x² - 118·x - 200

x² - 118·x + (118/2)²= 200 + (118/2)²

(x - 59)² = 200 + (59)² = 3681

(x - 59)² - 3681

At the vertex, -3281 = -100·f(x)

∴ f(x) at the vertex = -3681/-100 = 36.81

$\mathrm{\underline{Coordinate \ of \ the \ vertex = (59, \, 36.81)}}$

Part B: The maximum height is given by the y-value at the vertex = 36.81 ft.

Part C: When x = 5, we have;

h = -0.01·x² + 1.18·x + 2

h = -0.01 × 5² + 1.18 × 5 + 2 = 7.65

The defensive player must reach up to 7.65 feet to block the punt

Part D: The distance the ball will go before it hits the ground is given by

the function, for the height as follows;

h = -0.01·x² + 1.18·x + 2 = 0

From the completing the square method, above, we get;

-0.01·x² + 1.18·x + 2 = 0

x² - 118·x - 200 = 0

x² - 118·x + (118/2)²= 200 + (118/2)²

x² - 118·x + (59)²= 200 + (59)² = 3681

(x - 59)² = 3681

x - 59 = ±√3681

x = 59 ± √3681

x = 59 + √3681 ≈ 119.67

The distance down the field the ball will go without being blocked, x ≈ 119.67 ft.

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