Answer:
-7
Step-by-step explanation:
Answer:
The factorized form of the given expression is ![4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]](https://tex.z-dn.net/?f=4%20%5B%28a-1%29%5E2%20-%20b%28a%20-%201%20%2B%20%5Cfrac%7Bb%7D%7B4%7D%29%5D)
Step-by-step explanation:
Given;
4a² + b² - 4ab - 8a + 4b + 4
This expression is factorized as follows;
(4a² - 8a + 4) + (b² - 4ab + 4b)
(4a² - 4a - 4a + 4) + b² - 4b(a - 1)
(4a - 4)(a - 1) + b² - 4b(a - 1)
(4a - 4)(a - 1) - 4b(a - 1) + b²
4(a - 1)(a - 1) - 4b(a - 1) + b²
4(a - 1)² - 4b(a - 1 + b/4)
![4(a- 1)^2 - 4b(a - 1 + \frac{b}{4} )\\\\4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]](https://tex.z-dn.net/?f=4%28a-%201%29%5E2%20-%204b%28a%20-%201%20%2B%20%5Cfrac%7Bb%7D%7B4%7D%20%29%5C%5C%5C%5C4%20%5B%28a-1%29%5E2%20-%20b%28a%20-%201%20%2B%20%5Cfrac%7Bb%7D%7B4%7D%29%5D)
John is correct because 0.5 is equal to one half and multiplying something by its half is just same as dividing something in two and half of 1.4 is 0.5
(sorry if it's too long feel free to shorten it)
The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.
<h3>What is a proportional relationship?</h3>
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
From the table, the rate is:
k = $8.8/4.4 = 2.
From the market, the rate is:
k = $4.8/3 = $1.6.
Hence the equation is y = 1.6x.
More can be learned about proportional relationships at brainly.com/question/10424180
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Answer:
The interval [32.6 cm, 45.8 cm]
Step-by-step explanation:
According with the <em>68–95–99.7 rule for the Normal distribution:</em> If
is the mean of the distribution and s the standard deviation, around 68% of the data must fall in the interval
![\large [\bar x - s, \bar x +s]](https://tex.z-dn.net/?f=%5Clarge%20%5B%5Cbar%20x%20-%20s%2C%20%5Cbar%20x%20%2Bs%5D)
around 95% of the data must fall in the interval
around 99.7% of the data must fall in the interval
![\large [\bar x -3s, \bar x +3s]](https://tex.z-dn.net/?f=%5Clarge%20%5B%5Cbar%20x%20-3s%2C%20%5Cbar%20x%20%2B3s%5D)
So, the range of lengths that covers almost all the data (99.7%) is the interval
[39.2 - 3*2.2, 39.2 + 3*2.2] = [32.6, 45.8]
<em>This means that if we measure the upper arm length of a male over 20 years old in the United States, the probability that the length is between 32.6 cm and 45.8 cm is 99.7%</em>