Answer:
The solutions to the system of the equations by the elimination method will be:
Step-by-step explanation:
Given the system of the equations
solving the system of the equations by the elimination method
Rearranging the equations
solve for z:
solve 
for y:
solve 
for x:
Therefore, the solutions to the system of the equations by the elimination method will be:
Answer:
A. Miguel has the greatest spread.
B. Considering the middle 50% of the training time, the person with the least spread is Adam.
C. Miguel is inconsistent with the time set for training compared to that of Adam.
Step-by-step explanation:
The spread of a data shows the range of the data.
Using the range to determine the spread of the given data:
A. The range of the two persons can be determined by:
Range = highest value - lowest value
So that:
Adam's range = 106 - 91
= 15
Miguel's range = 105 - 86
= 19
Comparing the range of the two, Miguel has the greatest spread.
B. Considering the middle 50% of the training time;
Adam - 103 105 104 106 100
Miguel - 88 86 89 93 105
Adam's 50% range = 106 - 100
= 6
Miguel's 50% range = 105 - 86
= 19
Considering the middle 50% of the training time, the person with the least spread is Adam.
C. The answers to parts 2(a) and 2(b) shows that; there is a wide variation (much inconsistency) in the time that Miguel spend during training, but a minimum variation in the time spent by Adam during training.
Let X be the score on an english test which is normally distributed with mean of 31.5 and standard deviation of 7.3
μ = 31.5 and σ =7.3
Here we have to find score that separates the top 59% from the bottom 41%
So basically we have to find here x value such that area above it is 59% and below it is 49%
This is same as finding z score such that probability below z score is 0.49 and above probability is 0.59
P(Z < z) = 0.49
Using excel function to find the z score for probability 0.49 we get
z = NORM.S.INV(0.49)
z = -0.025
It means for z score -0.025 area below it is 41% and above it is 59%
Now we will convert this z score into x value using given mean and standard deviation
x = (z* standard deviation) + mean
x = (-0.025 * 7.3) + 31.5
x = 31.6825 ~ 31.68
The score that separates the top 59% from the bottom 41% is 31.68
Answer:
32cm and 28cm
Step-by-step explanation:
Area of a trapezium=0.5 ( sum of parallel sides ) × height
600=0.5( 4+a+a)×20
where a is the length of the shorter side
600÷0.5=(4+2a)×20
1200=(4+2a)×20
1200÷20=4+2a
60=4+2a
60-4=2a
56=2a
56÷2=a
28=a.
since the longer side is 4 cm more than th shorter side , 28 +4=32
