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lozanna [386]
4 years ago
12

Professor Clayton hypothesizes that travel to other countries increases students' abilities to do well in advanced sociology cla

sses, so she conducts a survey study to test this. Which variable is her independent variable? - the survey - travel to other countries -the research methods -students' abilities
Mathematics
1 answer:
LenaWriter [7]4 years ago
7 0

Answer: travel to other countries

Step-by-step explanation:

The independent variable is the one which brings changes in the another variable or dependent variable. The dependent variable is variable which changes due to manipulative changes on the independent variable.

The independent variable is the travel to other countries which is going exert it's influence over the increase in the ability to do well in advanced sociological classes.

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What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?
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Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

\frac{\left(6x^4+15x^3+10x^2+10x+4\right)}{\left(3x^2+2\right)}

Now, we will find the quotient by factoring the numerator:

\mathrm{Use\:the\:rational\:root\:theorem}\\a_0=4,\:\quad a_n=6\\\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \\\mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2,\:3,\:6\\\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1,\:2,\:3,\:6}\\\\-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\\\\=\left(x+2\right)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}\\\\=\frac{6x^4+15x^3+10x^2+10x+4}{x+2}=6x^3+3x^2+4x+2\\\\

Now, we will factor it again:

=\left(6x^3+3x^2\right)+\left(4x+2\right)\\\\=2\left(2x+1\right)+3x^2\left(2x+1\right)\\\\=\left(2x+1\right)\left(3x^2+2\right)

At last we get our factorised form :

=\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)\\\\=\frac{\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)}{3x^2+2}\\\\=\left(x+2\right)\left(2x+1\right)\\\\=2x^2+5x+2

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