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1 year ago

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If biology is 40% and chemistry is 24% and earth science is blank and so is physics. There are 4% more students signed up for an

earth science project than a physics project. How can I write an equation to find the percent of students ,x, that a re e signed ti do a physics project?

1 answer:

san4es73 [151]1 year ago

6 0

Given data:

The given biology percentage is B=40%.

The given chemistry percentage is C=24%.

The percenage of earth science as compare to physics is E=P+4%.

The expresion for the sum of all subjects is,

B+C+E+P=100%

40%+24%+E+P=100%

E+P=36%.............................(I)

Substitute given value in the above expression.

P+4%+P=36%

2P=32%

P=16%

The nummber of students assigned earth science is,

E=16%+4%

=20%

Thus, the percentage of the students assigned to the physics subject is 16%.

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The value of T₂₀ - T₁₅ is <u>-20</u>.

Step-by-step explanation:

<u>Given</u> :

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

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>> T₂₀ - T₁₅

<u>Using Formula</u> :

General term of an A.P.

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

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

<u>Solution</u> :

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 :

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

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

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

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

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

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

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

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

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

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

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▹ Answer

<em>x = -7</em>

▹ Step-by-Step Explanation

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<u>Distribute</u>

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5x = -35

<u>Final Answer</u>

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