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A sports apparel company makes basketball shirts in 15 sizes. For each
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12 Sep 2023, 04:00
12 Sep 2023, 04:00
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66% (02:36) correct
33% (02:36) wrong based on 12 sessions
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A sports apparel company makes basketball shirts in 15 sizes. For each of the 14 sizes, the ratio of the length of a shirt to that of its next larger size shirt is a fixed constant.
The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?
A. \(20 \sqrt{2}\)
B. \(20 \sqrt[14]{2^5}\)
C. \(20 \sqrt[4]{2^7}\)
D. \(20 \sqrt[2]{2^8}\)
E. \(20 \sqrt[2]{2^{14\)
The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?
A. \(20 \sqrt{2}\)
B. \(20 \sqrt[14]{2^5}\)
C. \(20 \sqrt[4]{2^7}\)
D. \(20 \sqrt[2]{2^8}\)
E. \(20 \sqrt[2]{2^{14\)
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Re: A sports apparel company makes basketball shirts in 15 sizes. For each
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15 Sep 2023, 14:13
15 Sep 2023, 14:13
Hi! I'm not sure how to do this problem. Why are there square roots in the answer choices?
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Re: A sports apparel company makes basketball shirts in 15 sizes. For each
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15 Sep 2023, 21:58
15 Sep 2023, 21:58
3
A sports apparel company makes basketball shirts in 15 sizes. For each of the 14 sizes, the ratio of the length of a shirt to that of its next larger size shirt is a fixed constant. The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?
The problem is based on Geometric Progression(GP) with first term (a) as 20 and number of terms (n) as 15.
Size of \(15^{th}\) shirt, \(T_{15}\) = 40.
Let r be the ratio between consecutive sizes.
We need to find the size of \(8^{th}\) shirt, \(T_8\)
Using, GP formula for \(T_n\) we get
\(T_n = a*r^{n-1}\)
=> \(T_{15} = a*r^{15-1}\) = 20 * \(r^{14}\)
=> \(r^{14}\) = \(\frac{40}{20}\) = 2
\(T_8 = a*r^{8-1}\) = 20 * \(r^7\)
We know that \(r^{14}\) = 2
Taking square root on both the sides we will get
\(r^7\) = \(\sqrt{2}\)
=> \(T_8\) = 20 * \(\sqrt{2}\)
So, Answer will be A
Hope it helps!
The problem is based on Geometric Progression(GP) with first term (a) as 20 and number of terms (n) as 15.
Size of \(15^{th}\) shirt, \(T_{15}\) = 40.
Let r be the ratio between consecutive sizes.
We need to find the size of \(8^{th}\) shirt, \(T_8\)
Using, GP formula for \(T_n\) we get
\(T_n = a*r^{n-1}\)
=> \(T_{15} = a*r^{15-1}\) = 20 * \(r^{14}\)
=> \(r^{14}\) = \(\frac{40}{20}\) = 2
\(T_8 = a*r^{8-1}\) = 20 * \(r^7\)
We know that \(r^{14}\) = 2
Taking square root on both the sides we will get
\(r^7\) = \(\sqrt{2}\)
=> \(T_8\) = 20 * \(\sqrt{2}\)
So, Answer will be A
Hope it helps!
