Answer: 0.4667
Step-by-step explanation:
According to 68–95–99.7 rule , About 99.7% of all data values lies with in 3 standard deviations from population mean (
).
Here , margin of error = 3s , where s is standard deviation.
As per given , we have want our sample mean 
to estimate μ μ with an error of no more than 1.4 point in either direction.
If 99.7% of all samples give an within 1.4 , it means that
Divide boths ides by 3 , we get
Hence, So must have 0.4667 as standard deviation so that 99.7 % 99.7% of all samples give an within 1.4 point of μ .
a. Recall that
For , we have
By integrating both sides, we get
If , then
so that
We can shift the index to simplify the sum slightly.
b. The power series for can be obtained simply by multiplying both sides of the series above by .
c. We have
Answer:
If all three digits need to be the same (I assume that's what aaa means) it's 333
Step-by-step explanation:
For a number XYZ to be divisible by 9, X+Y+Z must be divisible by 9. Here's why:
X*100 + Y * 10 + Z = X + Y + Z + 99*X + 9*Y = X + Y + Z + 9(11X + Y)
So we need to find the smallest a so that a+a+a = 3a is divisible by 9. The smallest would be 0, but 000 is not a real 3-digit number. The next one is 3.
Answer:
The area of the rectangle is 4 sq yards.
Step-by-step explanation:
Given that,
The length of the rectangle, 
The breadth of the rectangle, B = 26 yards
We need to find the area of the rectangle. The formula for the area of a rectangle is given by :
A = LB
Put all the values,
So, the area of the rectangle is 4 sq yards.
Answer:
A
Step-by-step explanation:
The constant of proportionality is the ratio between the two proportional variables in a directly proportional relationship. In this case, the variables are 
and 
.
To find the constant of proportionality, all we have to do is divide any value of by its corresponding value of . Let's take the values in the first row of the table. We know that 
and 
, so the constant of proportionality is 
. Hope this helps!
