a crew of loggers cleared 1/2 acres of lumber in 4 days. How long will it take the same crew to clear 2 3/4 acres of lumber?
2 answers:
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There are a variety of methods of performing this subtraction, and corresponding different methods of regrouping.
If you're taught (as I was) to do the subtraction right-to-left, then the first regrouping you need to do is when you try to subtract 500 from 100. You must regroup the 8 thousands and 1 hundred to 7 thousands and 11 hundreds. Then, when you subtract 5 hundreds, you end with 7 thousands and 6 hundreds.
The next regrouping you need to do is when you try to subtract 6 ten-thousands from 5 ten-thousands. You must regroup the 2 hundred-thousands and 5 ten-thousands to 1 hundred-thousand and 15 ten-thousands. Then, when you subtract 6 ten-thousands, you end with 1 hundred-thousand and 9 ten-thousands.
The end result is
... 258,197 - 64,500 = 193,697
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If you use an abacus or soroban or similar tool to help you keep track of the numbers, you were likely taught to do the subtraction left-to-right. In this case, the first regrouping comes when you want to subtract 6 ten-thousands. Practitioners of this method know that -6 = -10 +4, so the number represented on the tool becomes (2-1) hundred-thousands and (5+4) ten-thousands plus the rest of the initial number, or 198,197 after subtracting the 6 ten-thousands.
The subtraction proceeds until you find you need to subtract 500 from 100. At this point, the tool is representing the partial result as 194,197. Again, if you practice this method, you know that -5 = -10 +5, so you reduce the thousands digit by 1 (to 3) and add 5 to the hundreds digit to get 193,697.
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An attempt is made to show the regroupings in the attachment. In each case there are two of them. However, working left-to-right, the result of the first subtraction of 6 ten-thousands is 19 ten-thousands, so you never actually write down anything else. Of course, if you're using an abacus or soroban, you don't write down anything—you simply change the position of the beads on the tool.
The average value of f over the region D is 243/4
To answer the question, we need to know what the average value of a function is
<h3>What is the average value of a function?</h3>The average value of a function f(x) over an interval [a,b] is given by
Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).
x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9
So,
So, the average value of f over the region D is 243/4
Learn more about average value of a function here:
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Answer:
a) σ/√n= 1.43 min
c) Margin of error 2.8028min
d) [30.1972; 35.8028]min
e) n=62 customers
Step-by-step explanation:
Hello!
The variable of interest is
X: Time a customer stays at a restaurant. (min)
A sample of 49 lunch customers was taken at a restaurant obtaining
X[bar]= 33 mi
The population standard deviation is known to be δ= 10min
a) and b)
There is no information about the distribution of the population, but we know that if the sample is large enough, n≥30, we can apply the central limit theorem and approximate the distribution of the sample mean to normal:
X[bar]≈N(μ;σ²/n)
Where μ is the population mean and σ²/n is the population variance of the sampling distribution.
The standard deviation of the mean is the square root of its variance:
√(σ²/n)= σ/√n= 10/√49= 10/7= 1.428≅ 1.43min
c)
The CI for the population mean has the general structure "Point estimator" ± "Margin of error"
Considering that we approximated the sampling distribution to normal and the standard deviation is known, the statistic to use to estimate the population mean is Z= (X[bar]-μ)/(σ/√n)≈N(0;1)
The formula for the interval is:
[X[bar]±*(σ/√n)]
The margin of error of the 95% interval is:
d= *(σ/√n)= 1.96* 1.43= 2.8028
d)
[X[bar]±*(σ/√n)]
[33±2.8028]
[30.1972; 35.8028]min
Using a confidence level of 95% you'd expect that the interval [30.1972; 35.8028]min contains the true average of time the customers spend at the restaurant.
e)
Considering the margin of error d=2.5min and the confidence level 95% you have to calculate the corresponding sample size to estimate the population mean. To do so you have to clear the value of n from the expression:
d= *(σ/√n)
= σ/√n
√n*()= σ
√n= σ* ()
n=( σ* ())²
n= (10*)²= 61.47≅ 62 customers
I hope this helps!