Answer:
Possible values for X include;
15, 30, 45, 60, and so on
Step-by-step explanation:
The parameters provided are
Number of chocolates Tanmay possessed = X
Number of chocolates given to Akash = 1/3 × X
Number of chocolates given to Sharad = 1/5 × X
Consequently, since both 3 and 5 divide X,
3 × 5 = 15 is the smallest single factor of X.
Thus, the values of X based on this minimum factor are as follows;
15 × 1 = 15
15 × 2 = 30
15 × 3 = 45
15 × 4 = 60
Therefore, potential values for X form an arithmetic series: a + (n - 1) × d
Where:
a = 15
n = 1, 2, 3, 4,...
d = 15
This results in;
15, 30, 45, 60
Answer:
89
Step-by-step explanation:
Given that
2 O, 2 T and 1 M
Now based on this, the following arrangements exist
1
Three arrangements i.e. {M,T,O}
2
XX or XY
XX in 2C1 = two arrangements i.e. {OO or TT}
XY in 3C2 × 2! = six arrangements
3
XXY or XYZ
XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve arrangements
XYZ in 3C3 × 3! = six arrangements
4
XXYY or XXYZ
XXYY = 4! ÷ (2! × 2!) = six arrangements
XXYZ in 2C1 × 4! ÷ 2! = twenty four arrangements
5
= 5! ÷ (2! ×2!)
= 120 ÷ 4
= 30
Thus, the overall total is
= 3 + (2 +6)+ (12 +6) + (6 +24) + 30
= 89
Answer:
Katherine will create at least 8 playlists. Each of these will feature 4 pop songs and 9 rock songs.
Detailed Explanation:
Katherine has a library of 32 pop songs and 72 rock songs on her mp3 player. She intends to distribute these into playlists, ensuring an equal count of pop and rock songs in each.
To determine the minimum number of playlists, we find the GCF of the two numbers provided.
For 32, we can express it as 2^5, and 72 can be described as 2^3*3^2
Thus, the GCF for the two figures is 2^3, equaling 8.
Consequently, she will generate 8 playlists, with each containing 4 pop songs and 9 rock songs.
<span>The system of equations that can determine if the commuter jet’s flight path crosses the restricted airspace is:
y = \frac{1}{4}(x - 10)^2 + 6 (i)
y = \frac{-27}{34}x - \frac{5}{17} (ii)
</span><span>
Here's why:
</span><span>
The closed airspace boundary is defined by points (10, 6) and (12, 7).
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The commuter jet’s linear path runs from (-18, 14) to (16, -13).
Equation (i) describes the boundary since it fits both (10, 6) and (12, 7):
For (10, 6):
\frac{1}{4}(10-10)^2 + 6 = 6 (true)
For (12, 7):
\frac{1}{4}(12-10)^2 + 6 = 1 + 6 = 7 (true)
Equation (ii) represents the commuter jet’s path as it fits both (-18, 14) and (16, -13):
For (16, -13):
-13 = \frac{-27}{34} \times 16 - \frac{5}{17} = -13 (true)
For (-18, 14):
14 = \frac{-27}{34} \times (-18) - \frac{5}{17} = 14 (true)
By solving this system, we can confirm that the jet’s flight path intersects the closed airspace.
