Answer:
the probability that all tomatoes are sold is 0.919 (91.9%)
Step-by-step explanation:
since the random variable X= number of tomatoes that are demanded, is normally distributed we can make the standard random variable Z such that:
Z=(X-μ)/σ = (83 - 125)/30 = -1.4
where μ= expected value of X= mean of X (since X is normally distributed) , σ=standard deviation of X
then all tomatoes are sold if the demand surpasses 83 tomatos , therefore
P(X>83) = P(Z>-1.4) = 1- P(Z≤-1.4)
from tables of standard normal distribution →P(Z≤-1.4)=0.081 , therefore
P(X>83) = 1- P(Z≤-1.4) = 1 - 0.081 = 0.919 (91.9%)
thus the probability that all tomatoes are sold is 0.919 (91.9%)
Let
x--------> <span>the speed of the boat in mph
we know that
</span>going upstream the speed is x-7
<span>going downstream the speed is x+7
</span>
let the distance be d
<span>time to go upstream = d/(x-7) </span>
<span>time to go downstream = d/(x+7)
</span>
time going upstream is 3 times going downstream
so
<span>3d/(x+7) = d/(x-7) </span>
<span>divide by d </span>
<span>3/(x+7) = 1/(x-7) </span>
<span>3x-21 = x+7 </span>
<span>2x = 28 </span>
<span>x = 14
</span>
the answer is
<span>the speed of the boat in still water is 14 mph</span>
Firstly, let's factorise each equation individually - to do this, find 2 numbers that when summed add to the value of the second term, and when multiplied give the value of the third term.
7 and 12 give us 4 and 3 (4+3=7, 4*3=12) -- 8 and 15 give us 5 and 3 (5+3=8, 5*3=15)
Now we can rewrite these equations as (y+4)(y+3) and (y+5)(y+3) respectively.
Putting this in a fraction: (y+4)(y+3)/(y+5)(y+3) -- We can clearly see that there is a y+3 on both sides of the fraction, and given there are no terms outside of the brackets being multiplied, we can directly cancel.
This gives us our final answer:
(y+4)/(y+5)
