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Elden
5 days ago
7

Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random

sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for Inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month? 32 +1.645,8908 32 + 1.9620 0.64 + 1.282,16.620.) © 264 265 CHAT 0.04 + 1.00, layanan
Mathematics
1 answer:
zzz [4K]5 days ago
5 0

Answer:

0.64 ± 0.1117 or

0.64\pm 1.645*\sqrt{\frac{0.64*(0.36)}{50}}

Step-by-step explanation:

Sample size (n) = 50

Z-score for a 90% confidence level (z) = 1.645

Proportion of students who read at least one book (p):

p=\frac{32}{50}=0.64

The confidence interval is calculated as:

p\pm z*\sqrt{\frac{p*(1-p)}{n} }

By applying the provided information:

0.64\pm 1.645*\sqrt{\frac{0.64*(1-0.64)}{50}}\\ 0.64\pm 0.1117

The confidence interval results in 0.64 ± 0.1117

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Tracie's bus moves towards home at an average pace of one-half mile for every minute.

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When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is t
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The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

\boxed{u \ or \ v_i = initial \ velocity}

\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}

\boxed{a = acceleration \ (constant)}

\boxed{d = distance \ travelled}

We know the flea attains a takeoff velocity of 1.0 m/s over a distance of 0.50 mm.

The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

\boxed{ \ v^2 = u^2 + 2ad \ }

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  • v = takeoff velocity = 1.0 m/s
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First, convert 0.50 mm to meters: \boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}

Solution steps:

Rearrange the formula to isolate acceleration (a).

\boxed{ \ v^2 = u^2 + 2ad \ }

\boxed{ \ v^2 - u^2 = 2ad \ }

\boxed{ \ 2ad = v^2 - u^2 \ }

\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }

Insert the given values into the rearranged equation.

\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }

\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }

\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }

\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }

This yields the flea's acceleration as 1,000 m/s².

Additional resources

  1. Scientific notation: brainly.com/question/7263463
  2. Determining substance mass: brainly.com/question/4053884
  3. Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

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