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2 years ago

7

Matthew surveyed 600 of the students in his school about their favorite color. Students could choose between blue and purple. 11

% said their favorite color was purple. How many students' favorite color was blue?

1 answer:

yKpoI14uk [10]2 years ago

5 0

The answer is 534 students
89%

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$x=-\frac{-20+\sqrt{-20w+3600}}{10},\:x=-\frac{-20-\sqrt{-20w+3600}}{10}$

Step-by-step explanation:

$w=-5\left(x-8\right)\left(x+4\right)\\\mathrm{Expand\:}-5\left(x-8\right)\left(x+4\right):\quad -5x^2+20x+160\\w=-5x^2+20x+160\\Switch\:sides\\-5x^2+20x+160=w\\\mathrm{Subtract\:}w\mathrm{\:from\:both\:sides}\\-5x^2+20x+160-w=w-w\\Simplify\\-5x^2+20x+160-w=0\\Solve\:with\:the\:quadratic\:formula\\\mathrm{Quadratic\:Equation\:Formula:}\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-5,\:b=20,\:c=160-w:\quad x_{1,\:2}=\frac{-20\pm \sqrt{20^2-4\left(-5\right)\left(160-w\right)}}{2\left(-5\right)}\\x=\frac{-20+\sqrt{20^2-4\left(-5\right)\left(160-w\right)}}{2\left(-5\right)}:\quad -\frac{-20+\sqrt{-20w+3600}}{10}\\x=\frac{-20-\sqrt{20^2-4\left(-5\right)\left(160-w\right)}}{2\left(-5\right)}:\quad -\frac{-20-\sqrt{-20w+3600}}{10}\\The\:solutions\:to\:the\:quadratic\:equation\:are\\x=-\frac{-20+\sqrt{-20w+3600}}{10},\:x=-\frac{-20-\sqrt{-20w+3600}}{10}$

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2 years ago

the ratio of number of girls and boys in a class of 30 students is 7:8. if 5 new boys students admit in the class. what will be

Stells [14]

<h3>Given:</h3>

The ratio of number of girls and boys in a class of 30 students is 7:8

<h3>To Find:</h3>

The ratio of number of girls and boys if 5 new boys admit in the class.

<h3>Assumption:</h3>

Let the number of students be x.

<h3>Solution:</h3>

According to the question,

7x + 8x = 30

or, 15x = 30

or, x = $\large {\tt {\frac{30}{15}}}$

or, x = 2

7x = 7(2) = 14

8x = 8(2) = 16

There were 14 boys and 16 girls in the school.

After admitting 5 new boys, we get

14 + 5 = <u>19</u>

The ratio of number of girls and boys now is 16:19.

<h2>Answer:</h2>

<u>1</u><u>6</u><u>:</u><u>1</u><u>9</u>

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3 years ago