Answer: Hence, Probability that a coffee maker will have a defective cord is 0.376=37.6%.
Step-by-step explanation:
Since we have given that
Let A be the event of getting a faulty switch.
Let B be the event of getting a defective cord.
Here, P(A∪B) = 4% = 0.04
P(A∩B) = 0.1% = 0.001
P(A) = 2.5% = 0.025
We need to find P(B):
As we know that
Hence, Probability that a coffee maker will have a defective cord is 0.376=37.6%.
Answer:
3/22
Step-by-step explanation:
-1/4 . (-6/11)
- You have to multiply the signs: As both are negative, the result will be positive.
- You have to multiply the numbers in the top part (numerators) and the numbers in the bottom part (denominators)
1 . 6 / 4 . 11 = 6/44
- Finally, you must simplify the answer by dividing both numbers among the same divisor, in this case the number is 2
6÷2 / 44÷2 = 3/22
Answer:
The first option
Step-by-step explanation:
slope is -2/6
I.e. -1/3
a = 6, is your answer.
Square both sides
<span><span><span>9=a−2<span>(6−a)(2a−3)</span>+3</span>9=a-2\sqrt{(6-a)(2a-3)}+3</span><span>9=a−2<span>√<span><span><span>(6−a)(2a−3)</span></span><span></span></span></span>+3
</span></span>2 .Separate terms with roots from terms without roots
<span><span><span>9−a−3=−2<span>(6−a)(2a−3)</span></span>9-a-3=-2\sqrt{(6-a)(2a-3)}</span><span>9−a−3=−2<span>√<span><span><span>(6−a)(2a−3)
</span></span><span></span></span></span></span></span>
3. Simplify <span><span><span>9−a−3</span>9-a-3</span><span>9−a−3</span></span> to <span><span><span>6−a</span>6-a</span><span>6−a
</span></span><span><span><span>6−a=−2<span>(6−a)(2a−3)</span></span>6-a=-2\sqrt{(6-a)(2a-3)}</span><span>6−a=−2<span>√<span><span><span>(6−a)(2a−3)
</span></span><span></span></span></span></span></span>
4 .Square both sides
<span><span><span><span><span>(6−a)</span>2</span>=4(6−a)(2a−3)</span>{(6-a)}^{2}=4(6-a)(2a-3)</span><span><span><span>(6−a)</span><span><span>2</span><span></span></span></span>=4(6−a)(2a−3)
</span></span>5 .Expand
<span><span><span>36−12a+<span>a2</span>=48a−72−8<span>a2</span>+12a</span>36-12a+{a}^{2}=48a-72-8{a}^{2}+12a</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>=48a−72−8<span>a<span><span>2</span><span></span></span></span>+12a
</span></span>6. Simplify <span><span><span>48a−72−8<span>a2</span>+12a</span>48a-72-8{a}^{2}+12a</span><span>48a−72−8<span>a<span><span>2</span><span></span></span></span>+12a</span></span> to <span><span><span>60a−72−8<span>a2</span></span>60a-72-8{a}^{2}</span><span>60a−72−8<span>a<span><span>2</span><span></span></span></span></span></span>
<span><span><span>36−12a+<span>a2</span>=60a−72−8<span>a2</span></span>36-12a+{a}^{2}=60a-72-8{a}^{2}</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>=60a−72−8<span>a<span><span>2
</span><span></span></span></span></span></span>
7. Move all terms to one side
<span><span><span>36−12a+<span>a2</span>−60a+72+8<span>a2</span>=0</span>36-12a+{a}^{2}-60a+72+8{a}^{2}=0</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>−60a+72+8<span>a<span><span>2</span><span></span></span></span>=0
</span></span>8. Simplify <span><span><span>36−12a+<span>a2</span>−60a+72+8<span>a2</span></span>36-12a+{a}^{2}-60a+72+8{a}^{2}</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>−60a+72+8<span>a<span><span>2</span><span></span></span></span></span></span> to <span><span><span>36−72a+9<span>a2</span>+72</span>36-72a+9{a}^{2}+72</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72</span></span>
<span><span><span>36−72a+9<span>a2</span>+72=0</span>36-72a+9{a}^{2}+72=0</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72=0
</span></span>9 .Simplify <span><span><span>36−72a+9<span>a2</span>+72</span>36-72a+9{a}^{2}+72</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72</span></span> to <span><span><span>−72a+9<span>a2</span>+108</span>-72a+9{a}^{2}+108</span><span>−72a+9<span>a<span><span>2</span><span></span></span></span>+108</span></span>
<span><span><span>−72a+9<span>a2</span>+108=0</span>-72a+9{a}^{2}+108=0</span><span>−72a+9<span>a<span><span>2</span><span></span></span></span>+108=0
</span></span>10.Factor out the common term <span><span>99</span>9</span>
<span><span><span>−9(8a−<span>a2</span>−12)=0</span>-9(8a-{a}^{2}-12)=0</span><span>−9(8a−<span>a<span><span>2</span><span></span></span></span>−12)=0
</span></span>11. Factor out the negative sign
<span><span><span>−9×−(<span>a2</span>−8a+12)=0</span>-9\times -({a}^{2}-8a+12)=0</span><span>−9×−(<span>a<span><span>2</span><span></span></span></span>−8a+12)=0
</span></span>12. Divide both sides by <span><span><span>−9</span>-9</span><span>−9</span></span>
<span><span><span>−<span>a2</span>+8a−12=0</span>-{a}^{2}+8a-12=0</span><span>−<span>a<span><span>2</span><span></span></span></span>+8a−12=0
</span></span>13. Multiply both sides by <span><span><span>−1</span>-1</span><span>−1</span></span>
<span><span><span><span>a2</span>−8a+12=0</span>{a}^{2}-8a+12=0</span><span><span>a<span><span>2</span><span></span></span></span>−8a+12=0
</span></span>14. Factor <span><span><span><span>a2</span>−8a+12</span>{a}^{2}-8a+12</span><span><span>a<span><span>2</span><span></span></span></span>−8a+12</span></span>
<span><span><span>(a−6)(a−2)=0</span>(a-6)(a-2)=0</span><span>(a−6)(a−2)=0
</span></span>15. Solve for <span><span>aa</span>a</span>
<span><span><span>a=6,2</span>a=6,2</span><span>a=6,2
</span></span>16 Check solution
When <span><span><span>a=2</span>a=2</span><span>a=2</span></span>, the original equation <span><span><span>−3=<span>6−a</span>−<span>2a−3</span></span>-3=\sqrt{6-a}-\sqrt{2a-3}</span><span>−3=<span>√<span><span><span>6−a</span></span><span></span></span></span>−<span>√<span><span><span>2a−3</span></span><span></span></span></span></span></span> does not hold true.
We will drop <span><span><span>a=2</span>a=2</span><span>a=2</span></span> from the solution set.
17. Therefore,
<span><span><span>a=6</span></span><span /></span>
The answer is 75% I used a calculator and Pen and Pencil and 75% is correct I even double checked with multiplication. If you want to check for yourself to find the % in the future divide the 300 by 400 and you'll get your decimal move the decimal to the right 2 times and you'll have your percent.
