Answer:
F= (9C+160)/5
Step-by-step explanation:
C=5(F-32)/9
make F the subject of the formula= isolate F
5(F-32)=9C
5F-160=9C
5F=9C+160
F= (9C+160)/5
check: a, b, c are all positive integers (a=9, b=160, c=5)
85−(6x+11)=6(x+8)+x
Step 1: Simplify both sides of the equation.<span><span>85−<span>(<span><span>6x</span>+11</span>)</span></span>=<span><span>6<span>(<span>x+8</span>)</span></span>+x</span></span><span><span>85+<span><span>−1</span><span>(<span><span>6x</span>+11</span>)</span></span></span>=<span><span>6<span>(<span>x+8</span>)</span></span>+x</span></span>(Distribute the Negative Sign)<span><span><span>85+<span><span>−1</span><span>(<span>6x</span>)</span></span></span>+<span><span>(<span>−1</span>)</span><span>(11)</span></span></span>=<span><span>6<span>(<span>x+8</span>)</span></span>+x</span></span><span><span><span><span><span>85+</span>−<span>6x</span></span>+</span>−11</span>=<span><span>6<span>(<span>x+8</span>)</span></span>+x</span></span><span><span><span><span><span>85+</span>−<span>6x</span></span>+</span>−11</span>=<span><span><span><span>(6)</span><span>(x)</span></span>+<span><span>(6)</span><span>(8)</span></span></span>+x</span></span>(Distribute)<span><span><span><span><span>85+</span>−<span>6x</span></span>+</span>−11</span>=<span><span><span>6x</span>+48</span>+x</span></span><span><span><span>(<span>−<span>6x</span></span>)</span>+<span>(<span>85+<span>−11</span></span>)</span></span>=<span><span>(<span><span>6x</span>+x</span>)</span>+<span>(48)</span></span></span>(Combine Like Terms)<span><span><span>−<span>6x</span></span>+74</span>=<span><span>7x</span>+48</span></span><span><span><span>−<span>6x</span></span>+74</span>=<span><span>7x</span>+48</span></span>Step 2: Subtract 7x from both sides.<span><span><span><span>−<span>6x</span></span>+74</span>−<span>7x</span></span>=<span><span><span>7x</span>+48</span>−<span>7x</span></span></span><span><span><span>−<span>13x</span></span>+74</span>=48</span>Step 3: Subtract 74 from both sides.<span><span><span><span>−<span>13x</span></span>+74</span>−74</span>=<span>48−74</span></span><span><span>−<span>13x</span></span>=<span>−26</span></span>Step 4: Divide both sides by -13.<span><span><span>−<span>13x</span></span><span>−13</span></span>=<span><span>−26</span><span>−13</span></span></span><span>x=2</span><span>Answer:
x=2</span>
Assume that each material in each category has an equal chance of being selected.
Categories:
(a) Type of wood used to make the cabinet: birch, maple, cherry.
Each type of wood has a probability of 1/3 to be selected.
(b) Type of finish: transparent, semi-transparent.
Each type of finish has a probability of 1/2 to be selected.
(c) Knob: bronze, steel, wood.
Each material has 1/3 probability to be selected.
Each event (selecting material for the cabinet, for the finish, and for the knob) is an independent event.
Therefore
Probablity(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cheryy wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6
