Answer:
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Step-by-step explanation:</h3>
<u>Given:</u>
To find the area of the rug, we need to use the formula "πr² or π(D/2)²"
<u>Where:</u>
Since we do not have the radius, we need to substitute the diameter in the formula "π(D/2)²" to determine the area of the rug.
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Substituting "22/7" as π:
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When finding the area of ANY shape, do not forget to include the units.
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If you're only provided with the lengths of a triangle, and you're asked to determine whether or not the triangle is right or not, you'll need to rely on the Pythagorean Theorem to help you out. In case you're rusty on it, the Pythagorean Theorem defines a relationship between the <em>legs</em> of a right triangle and its <em>hypotenuse</em>, the side opposite its right angle. That relationship is a² + b² = c², where a and b are the legs of the triangle, and c is its hypotenuse. To see if our triangle fits that requirement, we'll have to substitute its lengths into the equation.
How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.
So, substituting our values in, we have:
(2.6)² + (8.1)² = (8.6)²
Performing the necessary calculations, we have:
6.76 + 65.61 = 73.96
72.37 ≠ 73.96
Failing this, we know that our triangle cannot be right, but we <em>do </em>know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of <em>increasing the angle between a and b</em>. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be <em>obtuse</em>, which is to say: yes, there's an angle in it larger than 90°.
Answer:
3 Questions
Step-by-step explanation:
After MM students took a test, there was a total of 64% of correct answers.
The tests contained a total of 50 questions.
Number of questions gotten to score 64%= 64% X 50 = 32 questions
If the next student wants to score 70%, he has to score
70% of the total score = 70% X 50 = 35
Therefore the least number of question more the student has to get right
=35-32
= 3 questions
Answer: Here's the complete question.
calculate the future value of the annuity assuming that it is (1) an ordinary annuity (2) an annuity due. Comparing the two types of annuities, all else equal, which type is more preferable? Why? Amount of annuity Interest rate Deposit period (years) $500 12% 6
Ordinary annuity = 4545, annuity due = 4058 , ordinary annuity is better because it discounts for one less year
Ordinary annuity = 4058, annuity due = 4545, annuity due is better because it discounts for one less year.
Ordinary annuity = 4058, annuity due = 4545, annuity due is better because it compounds for one more year.
Ordinary annuity = 4545, annuity due = 4058 , ordinary annuity is better because it compounds for one more year.
Step-by-step explanation:
Future value of ordinary annuity = Amount*[{(1+r)n – 1}/r]
= 500*[{(1.12)6 – 1}/0.12]
= $4,057.59
i.e. $4,058
Future value of annuity due = (1+r)*Future value of ordinary annuity
= 1.12*4,058
= $4,545
Hence, the answer is
Ordinary annuity = 4058, annuity due = 4545, annuity due is better because it compounds for one more year.
Since payments are made at the beginning of the year
