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andrey2020 [161]

2 years ago

8

Which statements about the clock are accurate? Select three options. The central angle formed when one hand points at 1 and the

other hand points at 3 is 30°. The circumference of the clock is approximately 62.8 inches. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°. The length of the major arc between 3 and 10 is approximately 31.4 inches. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

2 answers:

Svet_ta [14]2 years ago

8 0

Answer:

2,3,5

EDGE 2021

Step-by-step explanation:

Kitty [74]2 years ago

7 0

Answer:

Option 2, 3 and 5 are correct.

Step-by-step explanation:

Given question is incomplete, here is the complete question.

The face of a clock is divided into 12 equal parts.

Which statements about the clock are accurate? Select three options.

The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.

The circumference of the clock is approximately 62.8 inches.

The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

The length of the major arc between 3 and 10 is approximately 31.4 inches.

The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Option 1. "Central angle when one hand points at 1 and the other hand points at 3."

Since, face of the clock has been divided in 12 equal parts.

So, central angle at the center for each part = $\frac{360}{12}$

= 30°

Number of parts between 1 and 3 = 3

So central angle between 1 and 3 = 3 × 30°

= 90° (False)

Option 2. "Circumference of the clock = 62.8° inches."

Formula to be used

Circumference = 2πr of a circle

r = radius of the circle

Therefore circumference of he circle = 2π(10)

= 20π

= 62.8 inches (True)

Option 3. "Minor arc measure when one hand points at 12 and the other hand points at 4 is 120°."

Number of parts between 12 and 4 = 4

So Central angle formed = 4 × 30°

= 120° (True)

Option 4. "Length of major are between 3 and 10 = 31.4 inches."

Number of parts between 3 and 10 = 7

Central angle formed by hands = 7 × 30°

= 210°

$\text{Length of arc}=\frac{\pi }{360{^\circ}} \times (2\pi r)$

$=\frac{210}{360}\times (2\pi )(10)$

= 39.65 inches (False)

Option 5. "The length of the minor arc between 6 and 7 is approximately 5.2 inches."

Number of parts between 6 and 7 = 1

Central angle between 6 and 7 = 30°

Length of minor arc = $\frac{30}{360}\times (2\pi )(10)$

$=\frac{20\pi }{12}=5.24$

≈ 5.2 inches (True)

Option 2, 3 and 5 are correct.

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3 years ago

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

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Answer:

a) $\hat p=\frac{471}{1024}=0.460$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Data given and notation

n=1024 represent the random sample taken

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

$\hat p=\frac{471}{1024}=0.460$ estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

Part b

If we replace the values obtained we got:

$0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429$

$0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491$

The 99% confidence interval would be given by (0.429;0.491)

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