Mark is making a decoration for a rally, using a string of triangular strips. Each strip is an isosceles triangle when flattened
out.
( by the way the picture is a triangle that is 70 degrees)
What is the measure of the third angle?
( by the way the picture is a triangle that is 70 degrees)
What is the measure of the third angle?
1 answer:
Solution:
Consider the Given Isosceles Triangle
Considering the Possibilities
Case 1. When two equal angles are of 70°
Let the third angle be x.
Keeping in mind , that sum of Interior angles of Triangle is 180°.
70° + 70° + x= 180°
140° +x= 180°
x= 180°- 140°
x= 40°
Case 2:
When an angle measures 70°, and two equal angles measure x°.
Keeping the same property of triangle in mind, that is sum of interior angles of triangle is 180°.
70° + x° + x° = 180°
⇒ 70° + 2 x° = 180°
⇒ 2 x° = 180° - 70°
⇒ 2 x° = 110°
Dividing both sides by 2, we get
x= 55°
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Answer:
(i) The estimated regression equation is;
≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that increase by a multiple of 0.0604 for each million dollar increase in sales, X
(ii) The estimated earnings for the company is approximately $4.7096 million
(iii) The standard error of estimate is approximately 29.34
The high standard error of estimate indicates that individual mean do not accurately represent the population mean
(iv) The coefficient of determination is approximately 0.57925
The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925
Step-by-step explanation:
The given data is presented as follows;
(i) From the data, we have;
The regression equation can be presented as follows;
= b₀ + b₁·x
Where;
b₁ = The slope given as follows;
b₀ = - b₁·
From the data, we have;
= 364.05
= 6,027.259
= 4.2
= 41.5625
∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005
b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69
Therefore, we have the regression equation as follows;
≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales
(ii) For the small company, we have;
X = $50.0 million, therefore, we get;
= 1.6896 + 0.0604 × 50 = 4.7096
The estimated earnings for the company, = 4.7096 million
(iii) The standard error of estimate, σ, is given by the following formula;
Where;
n = The sample size
Therefore, we have;
The standard error of estimate, σ ≈ 29.34
The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean
(iv) The coefficient of determination (R Square) is given as follows;
Where;
SSR = The Sum of Squared Regression ≈ 21.9884
SST = The total variation in the sample ≈ 37.96
Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925
The coefficient of determination, R² ≈ 0.57925.
Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925
Explanation:
<u>Part 1</u>
The total monthly payment will remain level at the amount currently scheduled for Month 1. The revised totals are shown at the bottom of the attachment.
When Card C is fully paid, the same total payment will continue to be used until all card debts are paid.
__
<u>Part 2</u>
The excess over the sum of minimum payments will be applied to Card C (24% rate). The minimum payment will continue to be made for the other credit cards. The revised Card C payments are shown at the bottom of the attachment.
When Card C is fully paid, the excess over the sum of minimum payments will be applied to Card B (20% rate).
_____
<em>Comment on the question</em>
You can't think too much about the given numbers. The minimum payment amounts given here decrease way faster than you would expect. For example, the $1.36 decrease in the minimum payment for Card A from Month 1 to Month 2 corresponds to a balance decrease of more than $90 when the interest rate is 1.5% per month. That is not possible if the payment is only $32.19.
Apparently, the question is not about the actual numbers. Rather, it is about the strategy of debt reduction. Some (bogus) numbers are given here just so you have something to think about.
The approach described in the problem statement has been given the name "debt avalanche" to distinguish the approach from Dave Ramsey's "debt snowball." The "debt snowball" approach pays off the <em>minimum balance</em> first, not the highest interest rate. It also includes some extra cash above the sum of minimum balances. ($100 is suggested; more is better.) The psychological effect of the quick win is considered to be more important than the extra cost of carrying the higher-rate debt for a longer period.
