2(4x – 3) ≥ –3(3x) + 5x?Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
1 answer:
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Answer:
- width: 18 in
- length: 27 in
Step-by-step explanation:
The relations between length (L) and width (W) are ...
W +9 = L
LW = 486
Substituting gives ...
(W+9)W = 486
W^2 +9W -486 = 0 . . . put in standard form
(W +27)(W -18) = 0 . . . . factor
W = 18 . . . . the positive solution
The width of the rectangle is 18 inches; the length is 27 inches.
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<em>Comment on factoring</em>
There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.
486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.
Answer:
a) S = {1, 2, 3}
b) P(odd number) =
c) No
d) Yes
Step-by-step explanation:
a) The sample space is the set of all possible outcomes. By definition, the elements of a set should not be repeated. Hence, the sample space S = {1, 2, 3}
However, the sample is not equiprobable because each element has different probabilities.
b) P(odd number) =
Note that the odd numbers are 1 (on three faces) and 3 (on one face).
c) The fact the die has been biased does not change the possible outcomes. It only changes the probability of getting any given number.
d) Because the 3-face has been loaded, this probability changes. In fact, it is calculated thus:
Let's assume the probability for 1 or 2 is . Then that of 3 is
(because it is twice the others). The sum of probabilities must be 1.
P(odd number) = Prob(1) + Prob(3)
= =