The value of the given expression (3m - n)² + 4m when m = 63 and n = 45 is equal to 20,916.
<h3>What is an expression?</h3>
An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
<u>Given the following variables:</u>
Substituting the given variables into the given expression, we have;
Expression = (3m - n)² + 4m.
Expression = (3(63) - 45)² + 4(45).
Expression = (189 - 45)² + 180
Expression = 144² + 180
Expression = 20,736 + 180
Expression = 20,916.
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Complete Question:
Evaluate the expression when m = 63 and n = 45. (3m - n)² + 4m.
Answer:
d. t distribution with df = 80
Step-by-step explanation:
Assuming this problem:
Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
a. t distribution with df = 82.
b. t distribution with df = 81.
c. t distribution with df = 41.
d. t distribution with df = 80
Solution to the problem
When we have two independent samples from two normal distributions with equal variances we are assuming that
And the statistic is given by this formula:
Where t follows a t distribution with 
degrees of freedom and the pooled variance 
is given by this formula:
This last one is an unbiased estimator of the common variance 
So on this case the degrees of freedom are given by:
And the best answer is:
d. t distribution with df = 80
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Answer:
Step-by-step explanation:
30. Given: rectangles QRST and RKST
Prove: ΔQSK is isosceles
An isosceles triangle is a triangle which has two sides and two angles to be equal.
Thus,
From rectangle QRST, the diagonals of rectangles are similar.
i.e RT ≅ QS (diagonal property)
Also, RT ≅ SK (opposite sides of rectangle RKST)
Thus,
RT ≅ QS ≅ SK
Therefore,
ΔQSK is an isosceles triangle.
31. Given: Rectangles QRST, RKST and JQST
Prove: JT ≅ KS
From rectangle QRST, the diagonals of rectangles are similar.
i.e RT ≅ QS (diagonal property)
But,
JT // QS and RT // KS
Thus,
JT ≅ QS (opposite sides of rectangle JQST)
also,
RT ≅ KS (opposite sides of rectangle RKST)
So that,
JT ≅ QS ≅ RT ≅ KS
Therefore,
JT ≅ KS
