Answer:
Austin should use 8.2 gallons of 65% acid solution and 3.8 gallons 5% acid solution
Step-by-step explanation:
Let
x ----> the gallons of 65% acid solution needed
y ----> the gallons of 5% acid solution needed
Remember that
we know that
-----> equation A
-----> equation B
Solve the system by graphing
The solution is the intersection point both graphs
using a graphing tool
The solution is (8.2,3.8)
therefore
Austin should use 8.2 gallons of 65% acid solution and 3.8 gallons 5% acid solution
Answer:
The Region A represents p
The Region B represents p ∧ q
The Region C represents q
Step-by-step explanation:
The figure is as follows :
Given - The diagram represents two statements: p and q.
To find - Which represents regions A, B, and C?
A) p v q
B) p -> q
C) q ^ p
D) q -> p
Solution -
From the figure, we can see that,
The Region A represents p
The Region B represents p ∧ q
The Region C represents q
The truth table is as follows :
p q p ∧ q
T T T
T F F
F T F
F F F
Answer:
The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Step-by-step explanation:
We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.
The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.
<u><em>Let X = time for this event for boys in secondary school</em></u>
SO, X ~ Normal()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean time = 460 seconds
= standard deviation = 40 seconds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
<u>Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;</u>
P(X > x) = 0.10 {where x is the required time which boy need to beat}
P( >
) = 0.10
P(Z > ) = 0.10
<em>So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;</em>
<em> </em>
<em> </em> = 460 + 51.264 = <u>511.264 seconds</u>
Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.