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liraira [26]
3 years ago
12

A ladder is sliding down a wall so that the distance between the top of the ladder and the floor is decreasing at a rate of 9 fe

et per second. How fast is the base of the ladder receding from the wall?
Mathematics
1 answer:
bixtya [17]3 years ago
4 0
Use Pythagorean theorm

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The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amo
Aloiza [94]

Answer:

a)\ \ \bar x_m-\bar x_f=67.03\\\\b)\ \ E=15.7416\\\\c)\ \ CI=[51.2884, \ 82.7716]

Step-by-step explanation:

a. -Given that:

n_m=41\ , \ \sigma_m=33, \bar x_m=135.67\\\\n_f=37. \ \ ,\sigma_f=20, \ \ \bar x_f=68.64

#The point estimator of the difference between the population mean expenditure for males and the population mean expenditure for females is calculated as:

\bar x_m-\bar x_f\\\\\therefore \bigtriangleup\bar x=135.67-68.64\\\\=67.03

Hence, the pointer is estimator 67.03

b. The standard error of the point estimator,\bar x_m-\bar x_f is calculated by the following following:

\sigma_{\bar x_m-\bar x_f}=\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}

-And the margin of error, E at a 99% confidence can be calculated as:

E=z_{\alpha/2}\times \sigma_{\bar x_m-\bar x_f}\\\\\\=z_{0.005}\times\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\\\=2.575\times \sqrt{\frac{33^2}{41}+\frac{20^2}{37}}\\\\\\=15.7416

Hence, the margin of error is 15.7416

c. The estimator confidence interval is calculated using the following formula:

\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}

#We substitute to solve for the confidence interval using the standard deviation and sample size values in  a above:

CI=\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\=(135.67-68.64)\pm 15.7416\\\\=67.03\pm 15.7416\\\\=[51.2884, \ 82.7716]

Hence, the 99% confidence interval is [51.2884,82.7716]

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