A. homeostasis is the property of a system in which variables are regulated so that internal conditions remain stable and relatively constant.
I have to rewrite the expressions because they look very confusing.
1) The given fractions to add are:
4p² + 6 2p - 2
------------ + ------------
4p² 10p²
2) The statements to asses are:
<span>A) The least common denominator is 20p
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²
C) The second fraction rewritten with the LCD is (4p - 4) / 20p
D) The sum is (24p² -4p +30 ) / 20p² = (12p-2p+15) / 10p^2
E) The sum is a rational expression.
This is the result for each statement.
</span>
<span>A) The least common denominator is 20p
FALSE: THE LCD IS 20p², because it the least expression that contains all the prime factors of both denominators: 4p² and 10p.
See that you cannot divide 20p by 4p² but you can divide 20p² by 4p² and 10 p. So, 20p is not a common denominator.
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²
TRUE: you get this expression from the first fraction by multiplying both numerator and denominator by 20p² / 4p² = 5:
(4p² + 6)×5 = 20p² + 30
(4p²)×5 = 20p²
=>
20p² + 30
--------------
20p²
C) The second fraction rewritten with the LCD is (4p - 4) / 20p
FALSE: you have to multiply both numerator an denominator by 20p² / 10p = 2p
(2p - 2) × 2p = 4p² - 4p
10p × 2p = 20p²
So, the second fraction rewritten with the LCD is:
4p² - 4p
-----------
20p²
D) The sum is (24p² - 4p +30 ) / 20p² = (12p-2p+15) / 10p²
TRUE
</span>
<span><span> 20p² + 30 4p² - 4p 24p² - 4p + 30
-------------- + --------------- = ----------------------
20p² 20p² 20p²</span>
And when you simplify the last fraction dividing by 2 you get:
12p² - 2p + 15
-----------------------
10p²
E) The sum is a rational expression.
TRUE:
The sum of rational number has the closure property which means that by adding rational expression you will always ge a rational expression.
</span>
Answer:
price after discount and how much you saved...
Step-by-step explanation:
price after discount 9.60
you saved 2.40
please mark brainliest if correct :)
Answer:
Step-by-step explanation:
Alright, lets get started.
Tomas has four pieces of wood having each length = 5, 4, 6 and 3
The length of wood he needs to cut to make a model airplane =
Simplifying, it is 3.32 feet long
Means he needs more than 3 feet but less than 4 feet of wood piece.
So, he should select 4 feet length of wood because selcting 3 feet will not fulfilled to make his model and selcting 5 and 6 feet will have more unused wood.
4 feet piece of wood he should cut to have the least amount of unused wood. : Answer
Hope it will help :)
Answer:
He will need 4 newborns in the sample to be 95% confident.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.9}{2} = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.9%7D%7B2%7D%20%3D%200.05)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 1.645](https://tex.z-dn.net/?f=z%20%3D%201.645)
Now, find the margin of error M as such
![M = z*\sqrt{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Csqrt%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the length of the sample.
So:
![646 = 1.645*\frac{746}{\sqrt{n}}](https://tex.z-dn.net/?f=646%20%3D%201.645%2A%5Cfrac%7B746%7D%7B%5Csqrt%7Bn%7D%7D)
![646\sqrt{n} = 1227.17](https://tex.z-dn.net/?f=646%5Csqrt%7Bn%7D%20%3D%201227.17)
![\sqrt{n} = 1.90](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%201.90)
![\sqrt{n}^{2} = (1.90)^{2}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%5E%7B2%7D%20%3D%20%281.90%29%5E%7B2%7D)
![n = 3.61](https://tex.z-dn.net/?f=n%20%3D%203.61)
He will need 4 newborns in the sample to be 95% confident.