Answer:
12-5=7
12-7=5
Step-by-step explanation:
Say you have this problem.
4x=2x-4
First you would combine your like terms.
4x = 2x-4
-2x=-2x-4
---------------
2x=-4
Next you would divide
2x =-4
÷ -4 =-4
--------------
x = 0.5
Answer:

Step-by-step explanation:
Let r represent speed in the carpool.
We have been given that on the way to work Juan carpools with a fellow co-worker then takes the city bus back home in the evening. The average speed of the 20-mile trip is 5 miles per hour faster in the carpool.
We know that time is equal to distance over speed.
The total distance is 20 mile. Time taken to travel 20 miles using carpool would be 
The speed on the bus is 5 miles greater, so it will be
. Time taken to travel 20 miles using bus would be 
Total time will be equal to sum of both times that is:

Let us simplify our expression.


Combine numerator:


Therefore, our required expression would be
.
<h2>Steps:</h2>
So firstly, I will be factoring by grouping. For this, factor x⁶ - 9x⁴ and -x² + 9 separately. Make sure that they have the same quantity on the inside of the parentheses:

Now, you can rewrite the equation as:

However, it's not completely factored. Next, we will apply the formula for the difference of squares, which is
. In this case:

Next, we will apply the difference of squares once more with the second factor as such:

<h2>Answer:</h2>
<u>The factored form of this equation is:
</u>
Answer:
a) 0.623 (62.3%)
b) 0.764 (76.4%)
c) 0.6 (60%)
Step-by-step explanation:
a) defining the event F= the product is favorable , then the probability is
P(F) = probability that the study was sponsored by food industry * probability that the product is favorable given that it was sponsored + probability that the study had no corporate ties * probability that the product is favorable given that it was not sponsored = 0.70 * 0.68 + 0.30 * 0.49 = 0.623
b) for conditional probability we use the theorem of Bayes , then defining the event S= the study was sponsored by the food industry , we have:
P(S/F)=P(S∩F)/P(F)= 0.70 * 0.68/0.623 = 0.764 (76.4%)
where
P(S∩F)=probability that the study was sponsored by food industry and the product was found favorable
P(S/F)=probability that the study was sponsored by food industry given that the product was found favorable
c) for U= the product was found unfavourable , doing the same procedure as in a)
P(U)= 0.70 * 0.10 + 0.30 * 0.35 = 0.175
and the corresponding conditional probability is
P(N/U)=P(N∩U)/P(U)= 0.30 * 0.35 / 0.175 = 0.6 (60%)
where N represents the event = the study had no industry funding