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3 years ago

The length of a rectangular mailing

Mathematics

1 answer:

anygoal [31]3 years ago

7 0

ANSWER

Let the width be y

2(L + W) = Perimeter

2(2y - 5cm + y) = 62cm

(2×2y) + (2×-5cm) + (2×y) = 62cm

4y + - 10cm + 2y = 62cm

4y - 10cm + 2y = 62cm

4y + 2y - 10cm = 62cm

6y - 10cm + 10cm = 62cm + 10cm

6y = 72cm

6 6

y = 12cm

WIDTH

= y

= 12cm

LENGTH

= 2y - 5cm

= 2×y - 5cm

= 2×12cm - 5cm

= 24cm - 5cm

= 19cm

Providence

19cm + 19cm + 12cm + 12cm = 62cm which is the perimeter

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2 years ago

Suppose that 50% of the watches produced by a certain factory are defective. A store buys a box with 400 watches produced by thi

tiny-mole [99]

Answer:

$(a)\ P(x \ge 215)$

$(b)\ P(x \ge 214.5) = 0.07353$

Step-by-step explanation:

Given

$p = 0.50$ ---- proportion of watches with defects

$n = 400$ --- Number of watches

Solving (a): Represent at least 215 of 400 are defective

In inequalities, at least means: $\ge$

So, the probability is represented as: $P(x \ge 215)$

Solving (b): Calculate $P(x \ge 215)$

Normal or Poisson: Normal distribution is characterized by 2 parameters $\mu$ and $\sigma$ .

These two parameters can be easily calculated from the given parameters in the question. So, we solve using normal distribution

Start by calculating the mean

$\mu =np$

$\mu = 0.50 * 400$

$\mu = 200$

Calculate standard deviation

$\sigma = \sqrt{\mu (1 - p)$

$\sigma = \sqrt{200 * (1 - 0.50)$

$\sigma = \sqrt{200 * 0.50$

$\sigma = \sqrt{100$

$\sigma = 10$

By continuity correction, we have:

$x \to x - 0.5$

$x \to 215 - 0.5$

$x \to 214.5$

So, we have:

$P(x \ge 215) = P(x \ge 214.5)$

Calculating $P(x \ge 214.5)$ , we have:

$P(x \ge 214.5) = 1 - P(x < z)$

Calculate z score

$z = \frac{x - \mu}{\sigma}$

$z = \frac{214.5 - 200}{10}$

$z = \frac{14.5}{10}$

$z = 1.45$

So, we have:

$P(x \ge 214.5) = 1 - P(x < 1.45)$

Using the z score probability table, we have:

$P(x < 1.45) = 0.92647$

So, we have:

$P(x \ge 214.5) = 1 - 0.92647$

$P(x \ge 214.5) = 0.07353$

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