4m = 12x + 40
8x + 8x + 12x + 40 + 4m = 360
28x + 40 + 12x + 40 = 360
x = 7
m = 12(7) + 40 = 124
Define unit vectors along the x-axis and the y-axis as

respectively.
Then the vector from P to Q is

In component form, the vector PQ is (-8,5).
The magnitude of vector PQ is
√[(-8)² + 5²] = √(89) = 9.434
Answer:
The vector PQ is (-8, 5) and its magnitude is √89 (or 9.434).
The value of z-score for a score that is three standard deviations above the mean is 3.
In this question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Let x be the score
let μ be the mean and
let σ be the standard deviations
Now, x = μ + 3σ
The formula of z-score is

⇒ 
⇒ 
⇒ 
Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.
Learn more about z-score here
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Answer:

-- Her equivalent weight on earth
Step-by-step explanation:
Given
The attached table
Required
Fill in the gaps
(a) The equation
First, we calculate the slope (m)

From the table, we can say that:


So, we have:




The equation is then calculated using:

This gives:




(b) When x = 54
Substitute 54 for x in 


40.75 - 7.05= 33.7
33.7 / 2 = 16.85
16.85 ft. should be on each side of the 7.05 ft. bench