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3 years ago

A birthday cake has a circumference of 14n.

Mathematics

1 answer:

Murljashka [212]3 years ago

5 0

a) The length of the outside of one piece of birthday cake is 3.64

b) The area of one piece is 12.8

Step-by-step explanation:

The given information are,

A birthday cake has a circumference of 14π.
The slices are cut at 30 degree angles.
The birthday cake is in the shape of a circle.

The formula for the circumference of the circle is 2πr.

⇒ 2πr = 14π

⇒ 2r = 14

⇒ r = 14/2

⇒ r = 7

The radius of the birthday cake is 7.

To find the length of outside of one piece :

Length of the arc = (central angle / 360) × 2πr

⇒ (30/360) × 14π

⇒ (1/12) × 14π

⇒ (7/6)π

⇒ 1.16 × 3.14

⇒ 3.64

Therefore, the length of the outside of one piece of birthday cake is 3.64

To find the area of one piece :

Area of the arc = (central angle / 360) × πr²

⇒ (30/360) × π(7)²

⇒ (1/12) × 49π

⇒ (49/12) × (3.14)

⇒ 4.08 × 3.14

⇒ 12.8

Therefore, the area of one piece is 12.8

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Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is $\\ P(z>0.48) = P(x>533.2) = 0.3156$

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a sample mean. The distribution for sample means follows a normal distribution with mean $\\ \mu$ and standard deviation $\\ \frac{\sigma}{\sqrt{n}}$ . Mathematically

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The probability that the mean battery life would be greater than 533.2 minutes

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$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}$

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With this value of z we can consult a cumulative standard normal table (or use some statistic program) to find the cumulative probability for z (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

$\\ P(z$

However, in the question we are asked for $\\ P(z>0.48) = P(x>533.2)$ . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

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Rounding to four decimal places, we have

$\\ P(z>0.48) = 0.3156$

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