Translate this phrase into an algebraic expression. The sum of 26 and twice a number
1 answer:
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Answer:
Shortest distance from A to C = 102.9005 m.
Step-by-step explanation:
It is given that, ABCD is a rectangular park.
The length of the park is 80 m.
The breadth of the park is 50 m.
The diameter of the circle = 15 m.
We have to calculate the shortest distance from A to C across the park.
The distance AC = = 94.339 m.
As one has to pass only through the lines shown, he cannot pass through the circle.
So, we have to subtract the diameter of 15 m from AC
=> 94.339 m - 15 m = 79.339 m.
One must pass through either half of the circumference of the circle.
Since, diameter of circle = 15 m, its radius(r) = = 7.5 m.
The circumference of the circle = 2×π×r = 47.123 m.
Half of the circumference = = 23.5615 m.
Distance from A to C passing through circumference = 79.339 m + 23.5615 m = 102.9005 m.
As we have to calculate the shortest distance from A to C, one cannot pass from A to C either through B or D,
since the distance ABC or ADC = 50+80 = 130 m.
Therefore, shortest distance from A to C = 102.9005 m.
Answer:
The 98% confidence interval for the population mean number of hours worked per year per person is (2146, 2193).
Step-by-step explanation:
The question is incomplete.
The number of hours registered in the sample are:
2051 2061 2162 2167 2169 2171
2180 2183 2186 2195 2196 2198
2205 2210 2211
The sample mean can be calculated as:
We have to calculate a 98% confidence interval for the mean.
The population standard deviation is know and is σ=39.
The sample mean is M=2169.67.
The sample size is N=15.
As σ is known, the standard error of the mean (σM) is calculated as:
The z-value for a 98% confidence interval is z=2.326.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 98% confidence interval for the population mean is (2146, 2193).