A production plant cost-control engineer is responsible for cost reduction. One of the costly items in his plant is the amount o
1 answer:
Answer:
248.96
Step-by-step explanation:
From this regression output we have the MS Residual or mean squared error to be equal to 61983.1
the question requires us to find the standard error of the estimate. The standard error of the estimate can be gotten by finding the square root of the MSE.
= 248.96
the standard error of the estimate = 248.96
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Answer:
The specific gravity of kerosene is 0.82
Step-by-step explanation:
Let
x -----> the weight in grams of a cubic centimeter of Kerosene
y ----> the weight in grams of a cubic centimeter of water
z ---> the specific gravity of a substance
so
we have
substitute the values
Answer:
2) x³ (x² + 1) (x + 1)
3) (x - 6) (x + 6)
6) (x + 3) (x - 4)
8) (5x + 3) (x - 2)
Step-by-step explanation:
I'm providing the solutions for numbers 2, 3, 6, and 8, in order to give you the opportunity to apply and practice the techniques demonstrated here for numbers 9 and 10.
<h3>2) x⁶ + x⁵ + x⁴ + x³ = 0 </h3>
Factor out the highest possible common term, applying the product rule of exponents,
x³ (x³ + x² + x¹ + 1) = 0
Next, apply the special factoring technique into the exponential expressions inside the parenthesis), the factor by grouping:
The factors for the given polynomial are: x³ (x² + 1) (x + 1)
<h3> 3) x² - 36 = 0 </h3>
Use the <u>difference of two squares factoring</u>, where it states: u² - v² = (u - v) (u + v)
Since 36 is a perfect square of 6², then we can establish the following factors using the difference of squares:
Factors: (x - 6) (x + 6).
<h3>6) x² - x - 12 = 0 </h3>
For this quadratic trinomial, find factors that will produce a product of <em>a</em> × <em>c</em> (1 × -12) and sum of b (-1):
The possible factors of -12 that also results to a sum of -1 are:
3 × -4 = -1
Hence, the possible factors of x² - x - 12 = 0 could be (x + 3) (x - 4). Verify whether this is correct by performing the FOIL method:
(x + 3) (x - 4) = x² - 4x + 3x - 12 = x² - x - 12
Therefore, the factors of x² - x - 12 = 0 are: (x + 3) (x - 4).
<h3>8) 5x² - 7x - 6 = 0 </h3>
where a = 5, b = -7, and c = -6
Given this quadratic trinomial, we can use the factoring by grouping, where it states: find the values of u and v such that the product of uv is the same as the product of <em>ac</em>: u × v = a × c, and that the sum of (<em>u</em> + <em>v </em>) is the same as <em>b</em>.
In other words, we must find the factors of u × v that have a product of a × c and a sum of b:
<em>u × v </em>= <em>a × c</em> = 5 × (-6) = -30
u + v = b = -7
The possible factors of -30 are:
-3 × 10 = -30
3 × -10 = -30
Out of these factors, the factors 3 × -10 = -30 will have the same sum as the value of b = -7:
3 + (-10) = -7
Hence, u = 3, v = -10.
Now, we can group the trinomial as follows:
(<em>ax</em>² + <em>ux </em>) + (<em>vx </em>+ <em>c </em>)
(5x² + 3x) + (-10x - 6)
For the last step, factor out the common terms from both groups:
(5x² + 3x) + (-10x - 6)
x (5x + 3) - 2(5x + 3)
Combine common terms together: (5x + 3) and (x - 2)
Therefore, the factors of the given quadratic trinomial are: (5x + 3) (x - 2).