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2 years ago

15. A band expects to have 16 songs on their next

Mathematics

1 answer:

stepladder [879]2 years ago

8 0

Answer:

There will be 13 songs in the final album.

Step-by-step explanation:

i) number of songs expected = 16 songs

ii) the band wrrites 62.5% more

therefore the band writes $16 \times ( 1 + 0.625) = 16 \times 1.625 = 26$ songs

iii) During the editing process 50% of the songs are removed.

Therefore there will be in the final album = $( 1 - 0.5) \times 26 = 0.5 \times 26 = 13$ songs.

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OleMash [197]

Answer:

The value of T₂₀ - T₁₅ is -20.

Step-by-step explanation:

Given :

>> If for an A.P, d = -4

To Find :

>> T₂₀ - T₁₅

Using Formula :

General term of an A.P.

$\star{\small{\underline{\boxed{\sf{\red{ T_n = a + (n - 1)d}}}}}}$

>> Tₙ = nᵗʰ term
>> a = first term
>> n = no. of terms
>> d = common difference

Solution :

Firstly finding the A.P of T₂₀ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{20} = a + (20 - 1) d}}}$

${\dashrightarrow{\sf{ T_{20} = a + (19)d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19 \times d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19d}}}$

${\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a + 19d}}}}}}$

Hence, the value of T₂₀ is a + 19d.

$\rule{190}1$

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{15}= a + (15 - 1) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + (14) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14 \times d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14d}}}$

${\star{\underline{\boxed{\sf \pink{ T_{15}= a + 14d}}}}}$

Hence, the value of T₁₅ is a + 14d

$\rule{190}1$

Now, finding the difference between T₂₀ - T₁₅ :

${\dashrightarrow{\pmb{\sf{T_{20} - T_{15}}}}}$

${\dashrightarrow{\sf{(a + 19d) - (a + 14d)}}}$

${\dashrightarrow{\sf{a + 19d - a - 14d}}}$

${\dashrightarrow{\sf{a - a + 19d - 14d}}}$

${\dashrightarrow{\sf{0+ 19d - 14d}}}$

${\dashrightarrow{\sf{19d - 14d}}}$

${\dashrightarrow{\sf{5 \times - 4}}}$

${\dashrightarrow{\sf{ - 20}}}$

${\star \: \underline{\boxed{\sf{\pink{T_{20} - T_{15} = - 20}}}}}$

Hence, the value of T₂₀ - T₁₅ is -20.

$\underline{\rule{220pt}{3.5pt}}$

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