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3 years ago

The minute had of a clock is 8 in. long.

Mathematics

1 answer:

DaniilM [7]3 years ago

3 0

Answer:

P=8.378in

Step-by-step explanation:

Let Distance travelled be P

Time,t=10mins

Lenth of minute hand be l

1 hr= 60 mins, Therefore t is time taken to cover $\frac{1}{6} of \ the \ distance$

$P=\frac{2}{6}\pi*r\\P=\frac{2}{6}*\pi*8\\ =8.378$

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3 years ago

You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are

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Answer:

0.8809

Step-by-step explanation:

Given that:

The population proportion p = 4% = 4/100 = 0.04

Sample mean x = 16

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The sample proportion $\hat p =\dfrac{x}{n}$

= 16/300

= 0.0533

∴

$P(\hat p \leq 0.0533) = P\bigg ( \dfrac{\hat p - p}{\sqrt{\dfrac{P(1-P)}{n}}}\leq\dfrac{0.0533 - 0.04}{\sqrt{\dfrac{0.04(1-0.04)}{300}}}\bigg )$

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$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{1.28 \times 10^{-4}}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{0.0113}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )$

From the z tables;

= 0.8809

Let X be the random variation that follows a normal distribution;

Then;

population mean $\mu$ = n × p

population mean $\mu$ = 300 × 0.04

population mean $\mu$ = 12

The standard deviation $\sigma = \sqrt{np(1-p)}$

The standard deviation $\sigma = \sqrt{300 \times 0.04(1-0.04)}$

The standard deviation $\sigma = \sqrt{11.52}$

The standard deviation $\sigma = 3.39$

The z -score can be computed as:

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

$z = \dfrac{16 -12}{3.39}$

$z = \dfrac{4}{3.39}$

z = 1.18

The required probability is:

P(X ≤ 10) = Pr (z ≤ 1.18)

= 0.8809

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Answer:

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