<span>the equation -2x² + 5x -3=0, we notice that the sum of the coefficient equals 0, -2+5-3=0, if such a case happens, the solution of the previous equation will be, x=1 (always) and x= c/a, a=-2, and c=-3, so x=-3/-2, finally, the answer is: the 2 in the denominator should be -2</span>
Answer:
22.5 miles
Step-by-step explanation:
No traffic :
Let speed = x
Time taken = 30 = 30/60 = 0.5 hour
Speed = distance / time
Distance = d
x = d / 0.5 - - - (1)
With traffic :
Speed = x - 30
Time taken = 1 hour 30 minutes = 1.5 hour
x - 30 = d / 1.5
x = d/1.5 + 30 - - - - (2)
Equating (1) and (2)
d / 0.5 = d/1.5 + 30
d /0.5 - d /1.5 = 30
(1.5d - 0.5d) / 0.75 = 30
1.5d - 0.5d = 22.5
1d = 22.5
Hence,
d = 22.5 miles
Answer:
Question 13: For age groups y=1 and y=1.3 response is 8 microseconds.
Question 14: The club was making a loss between 11.28 and 4.88 years.
Step-by-step explanation:
Question 13:
The age group y for which the response rate R is 8 microseconds is given by the solution of the equation

We graph this equation and find the solutions to be

Since only positive solutions for y are valid in the real world we take only those.
Thus only for age groups y=1 and y=1.3 the response is 8 microseconds.
Question 14:
The footbal club is making a loss when 
Or

We graph this inequality and find the solutions to be
and 
Since in the real world only positive values for t are valid, we take the the second solution to be true.
Thus the club was making a loss in years 
Answer:
a) 90.695 lb
b) 85.305 lb
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

(a) The 65th percentile
X when Z has a pvalue of 0.65. So X when Z = 0.385.




(b) The 35th percentile
X when Z has a pvalue of 0.35. So X when Z = -0.385.




For the first investment. A = P(1 + rt); where p = 9,720, r = 0.0316 and t = 1/12
A = 9720(1 + 0.0316/12) = 9720(1.0026) = $9,746
For the second investment,
A = 8140(1 + 0.0323 x 2) = 8140(1.0646) = $8,666
Total amount she had = $9,746 + $8,666 = $18,412