What is the value x² + 3y / xy, if x=4 and y=2?
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Answer:
Step-by-step explanation:
we would like to solve the following equation:
in order to do so do cross multiplication:
divide both sides by √3:
since we ended up with a square root on the denominator so we can consider rationalising the denominator to do so multiply both numerator and denominator by √3 which yields:
simplify multiplication:
reduce fraction:
and we are done!
Answer and Step-by-step explanation: Scaterplot is a type of graphic which shows the relationship between to variables. In this question, you want to determine if there is a linear relationship between overhead widths of seals and the weights. So, the hypothesis are:
H₀: no linear correlation;
H₁: there is linear correlation;
In this hypothesis test, to reject H₀, the correlation coefficient r of the data set has to be bigger than the critical value from the table.
With α = 0.05 and n = 6, the critical value is 0.811.
The linear correlation is calculated as:
r = n∑xy - ∑x.∑y / √[n∑x² - (∑x)²] [n∑y² - (∑y)²]
r =
r = 0.9485
Since r is bigger than the critical value, H₀ is rejected, which means there is enough evidence to conclude that there is linear correlation between overhead widths and the weights.
In the attachments is the scaterplot of the measurements, also showing the relationship.
