Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. How many miles is he, in a direct line, from his star
ting point? Express your answer as a decimal to the nearest hundredth.
1 answer:
Answer:
1.25 mi
Step-by-step explanation:
Think of this in terms of a graph in the x-y axis
Bill starts out at point (0,0)
He walks 1/2 mile south (i.e 0.5 miles in the -y direction) and ends up at (0,-0.5)
Next he walks 3/4 mile (0.75 miles) in the +x direction and ends up at (0.75, -0.5)
Then he continues to walk 1/2 mile (0.5 miles) in south in the -y direction and ends up at (0.75, -1).
His final distance from the starting point (0,0) from his end point (0.75,-1) is simply the distance between the 2 coordinates (see picture for formula).
hence,
D = √ (0.75 -0)² + (-1 - 0)²
D = √ (0.75)² + (-1)²
D = 1.25
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Answer:
The 98% confidence interval would be given by (0.326;0.354)
Step-by-step explanation:
1) Notation and definitions
number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
random sample taken
estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
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.
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The population proportion have the following distribution
2) Confidence interval
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 98% confidence interval would be given by (0.326;0.354)
Answer:
$1210
Step-by-step explanation:
Let x be total amount
First John spent $110 on a radio and 4/11 of what was left on presents for his friends so he was left with
Then he put 2/5 of his remaining money into a checking account
Rest he donated to charity
Hence total amount of money John originally had was $1210