14 x 2000
Basic multiplication fact:
14 x 2=28
Total number of zeros=3
So, 14 x 2000=28,000
Answer:
p²q³ + pq and pq(pq² + 1)
Step-by-step explanation:
Given
3p²q² - 3p²q³ +4p²q³ -3p²q² + pq
Required
Collect like terms
We start by rewriting the expression
3p²q² - 3p²q³ +4p²q³ -3p²q² + pq
Collect like terms
3p²q² -3p²q² - 3p²q³ +4p²q³ + pq
Group like terms
(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq
Perform arithmetic operations on like terms
(0) - (-p²q³) + pq
- (-p²q³) + pq
Open bracket
p²q³ + pq
The answer can be further simplified
Factorize p²q³ + pq
pq(pq² + 1)
Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)
The inverse of the function x^7 is x^-7 and it is also a function.
An inverse function or an anti function is defined as a function, which can reverse into another function.
A standard method to find inverse of a function is to set y=f(x)
let y= f(x)=x^7
thus
=x
thus
(y)=![\sqrt[7]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7By%7D)
thus ![f^{-1} (x)=\sqrt[7]{x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%20%28x%29%3D%5Csqrt%5B7%5D%7Bx%7D)
(To verify this if a function is inverse or not we are required to check for the identity)
f(
(x))=
(f(x))=x
Therefore, The inverse of the function x^7 is x^-7 and it is also a function.
For further reference:
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Answer:
a) ![s^2 =30^2 =900](https://tex.z-dn.net/?f=%20s%5E2%20%3D30%5E2%20%3D900)
b)
c)
Step-by-step explanation:
Assuming the following question: Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms
Part a
For this case the best point of estimate for the population variance would be:
![s^2 =30^2 =900](https://tex.z-dn.net/?f=%20s%5E2%20%3D30%5E2%20%3D900)
Part b
The confidence interval for the population variance is given by the following formula:
The degrees of freedom are given by:
Since the Confidence is 0.90 or 90%, the significance
and
, the critical values for this case are:
And replacing into the formula for the interval we got:
Part c
Now we just take square root on both sides of the interval and we got: