Graph 4x minus 2y equals 10
1 answer:
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<h3>Answer: (a - 1)(2a² + a + 2)</h3>
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Explanation:
Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2
Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.
If we tried say a = -1, then,
2a³-a²+a-2 = 2(-1)³-(-1)²+(-1)-2 = -6
The result is not zero, so a = -1 is not an actual root.
But if we tried say a = 1, then,
2a³-a²+a-2 = 2(1)³-1²+1-2 = 0
We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.
Since a = 1 is a root, this makes (a-1) to be a factor.
From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.
Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.
Answer:
P(A | F) = 81.81%
There is 81.81% probability that worker was taught by method A given that he failed to learn it correctly.
Step-by-step explanation:
The failure rate is 15% for A which means that
P(F | A) = 0.15
The failure rate is 5% for B which means that
P(F | B) = 0.05
Method B is more expensive and hence is used only 40% of the time which means that
P(B) = 0.40
Which means that A is used the other 60% of the time
P(A) = 0.60
A worker is taught the skill by one of the methods but fails to learn it correctly.
We are asked to find the the probability that he was taught by method A.
So that means we want to find out
P(A | F) = ?
We know that according to Baye's rule,
Substitute the given probabilities into the above equation
Therefore, there is 81.81% probability that worker was taught by method A given that he failed to learn it correctly.
Answer:
a) area will be 1/4 of the original
b) 7 cm²
Step-by-step explanation:
<h3>a)</h3>Consider the equation for the area of a trapezoid:
A = 1/2(b1 +b2)h
Now, halve each of the dimensions:
A' = 1/2((1/2)b1 +(1/2)b2)((1/2)h)
A' = (1/4)(1/2(b1 +b2)h) = 1/4A
The area is multiplied by the square of the scale factor: (1/2)² = 1/4.
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<h3>b)</h3>The area of the smaller trapezoid will be ...
A' = 1/4A = (1/4)(28 cm²) = 7 cm²
