The diagram of the square below displays all the lines of symmetry for the square.
2 answers:
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Answer:
1. y = - 4 x + 5
2. x = -8
Step-by-step explanation:
1. (-1,9) (1,1)
y = mx + b
m = (y-y') / (x-x') = (1-9) / (1-(-1)) = -8 / 2 = - 4
b = y - mx = 9 - (-4) x (-1) = 5
equation: y = - 4 x + 5
check: (1,1) y=1 = (-4) x 1 + 5 = 1
2. Vertical line through (-8,6) is a line perpendicular to x axis
x = -8
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.