The perimeter of the semicircle is 25.71 cm. Calculate the value of radius x. Take pi to be 3.142

Mathematics

1 answer:

yan [13]3 years ago

5 0

Answer:

5 cm

Step-by-step explanation:

$Perimeter of semicircle = \frac{1}{2} \times 2\pi \: x +2x\\ 25.71 = 3.14 2\times x+ 2x\\ 25.71 = 5.14 2 x\\ x = \frac{25.71}{5.142} \\ x = 5 \: cm$

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There are 169 million registered voters in the us. determine an interval for the number (how many) of registered democrats in th

VashaNatasha [74]

Part A:

Given that in a sample of 400 registered voters, 204 were democrats, i.e. n = 400, $\hat{p}= \frac{204}{400} =0.51$

The 95% confidence interval for the proportion of registered democrats voters in the population is given by:

$95\%\ C.I.=\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ =0.51\pm1.96\sqrt{\frac{0.51(1-0.51)}{400}}=0.51\pm1.96\sqrt{\frac{0.2499}{400}} \\ \\ =0.51\pm1.96(0.025)=0.51\pm0.049=(0.51-0.049,\ 0.51+0.049) \\ \\ =\bold{(0.461,\ 0.559)}$

Part B:

Given that there are 169 million registered voters in the US, the interval for the number of registered democrats in the population is given by

[0.461(169,000,000), 0.559(169,000,000)] = (77,909,000, 94,471,000)

6 0

3 years ago

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Kisachek [45]

Answer:

1. c

2. b

3. a

4. d

5. e

6. f

Step-by-step explanation: