Answer:
Option 2
Step-by-step explanation:
The account balance multiplier for the compound interest option is ...
(1 +r)^t = 1.05^8 ≈ 1.477455
The account balance multiplier for the simple interest option is ...
(1 +rt) = 1 +0.06·8 = 1.48
Jadwa should choose option 2 for this investment. It will earn about £5.09 more in interest over the 8-year period.
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£2000 · (1.48 -1.477455) ≈ £5.09
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In the above formulas, r is the interest rate, and t is the number of years.
Answer: 99°
explanation: first, we need to find angle T. we know that angle T and angle R are vertical angles, which means they’re the same. therefore, we solve the equation for x by doing angle T = angle R:
3x + 36 = 6x - 9
subtract 36 on both sides
3x = 6x - 45
subtract 6 on both sides
-3x = -45
divide both sides by -3
x= 15
then, plug in the value of x in 3x+36 to get angle T:
3(15) + 36= 81°
we found that angle T is 81°.
now, we need to find the supplementary angle of angle T. supplementary angles add up together to have a sum of 180°. to find the supplementary angle, subtract angle T from 180°:
180 - 81 = 99°
there we have the answer!
I’m pretty sure your answer is E
Answer:
(a) 156 cm²
Step-by-step explanation:
The total surface area of the 12 blocks can be computed by first finding the surface area of one block. That result can then be multiplied by 12. The area of one rectangular prism is given by the formula ...
A = 2(LW +H(L +W))
A = 2(4·1 +1/2(4+1)) = 2(4 +5/2) = 13 . . . cm²
The area of 12 such prisms will be ...
12 × (13 cm²) = 156 cm²
Victor needs 156 cm² of fabric to cover 12 blocks.
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<em>Additional comment</em>
This problem offers an opportunity to exercise your number sense. The area of the largest surface of one block is (4 cm)×(1 cm) = 4 cm². 12 of these surfaces will have an area of 48 cm². This is only part of the total area, so the only reasonable choice among those offered is 156 cm².
An if-then statement must hold under any condition. Let's take it case by case:
A. This one makes sense, and is perfect! If two angles are vertical, then they must be congruent. This holds no matter what. This is your answer.
B. This doesn't hold because Alternate Interior Angles can also be congruent (along with many others). Two angles don't <em>have </em>to be vertical to be congruent.
C. This one is also true because this is the contrapositive of Option A. (Read my reasoning on D to know what a contrapositive is). Therefore, this is correct.
D. This one is the contrapositive of B, which makes it the exact same as B. Thus, this is not the answer. Contrapositive, by the way, just means that it's the inverse and opposite of a given statement. Let's say P is the contrapositive of Q. If this is the case, then if Q is true, P must be true. In our case, Option D is the contrapositive of Option B and since Option B is not true, neither is D.
