document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184905>Question 1184905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The maximum heart rate of a person, in beats per minute, can be estimated using the expression 220 − 𝑥, where 𝑥 is the person's age in years for 20≤𝑥≤70. If it is generally recommended that at least 50% but not more than 80% of the maximum heart rate be achieved during exercise, what inequality represents the target heart rate, 𝒉, in beats per minute, over a 30-minute period years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815591 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The maximum heart rate of a person, in beats per minute, can be estimated using the expression 220 − 𝑥, where 𝑥 is the person's age in years for 20≤𝑥≤70. If it is generally recommended that at least 50% but not more than 80% of the maximum heart rate be achieved during exercise, what inequality represents the target heart rate, 𝒉, in beats per minute, over a 30-minute period years?\r<BR>\n" );
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document.write( "maximum heart rate = 220 - x, for 20 <= x <= 70.\r<BR>\n" );
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document.write( "h = the target heart rate for exercise, in beats per minute, over a 30 minute period.\r<BR>\n" );
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document.write( "your inequality will be:\r<BR>\n" );
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document.write( "h >= .50 * (220 - x)<BR>\n" );
document.write( "h <= .80 * (220 - x)\r<BR>\n" );
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document.write( "this inequality can also be expressed at:\r<BR>\n" );
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document.write( ".50 * (220 - x) <= h <= .80 * (220 - x)\r<BR>\n" );
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document.write( "for a person who is 20 years old, the target heart rate during exercise is:\r<BR>\n" );
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document.write( ".50 * (220 - 20) <= h <= .80 * (220 - 20), which equals:<BR>\n" );
document.write( ".50 * 200 <= h <= .80 * 200, which equals:<BR>\n" );
document.write( "100 <= h <= 160.\r<BR>\n" );
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document.write( "for a person who is 70 years old, the target heart rate during exercise is:\r<BR>\n" );
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document.write( ".50 * (220 - 70) <= h <= .80 * (220 - 70), which equals:<BR>\n" );
document.write( ".50 * 150 <= h <= .8 * 150, which equals:<BR>\n" );
document.write( "75 <= h <= 120.\r<BR>\n" );
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document.write( "the inequality can be graphed, as shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/092011.jpg\" >\r<BR>\n" );
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document.write( "the opposite of the inequalities would be graphed.\r<BR>\n" );
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document.write( "inequalities for graphing are:\r<BR>\n" );
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document.write( "y <= .5 * (220 - x)<BR>\n" );
document.write( "y >= .8 * (220 - x)<BR>\n" );
document.write( "y <= 0<BR>\n" );
document.write( "x <= 20<BR>\n" );
document.write( "x >= 70\r<BR>\n" );
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document.write( "the area on the graph that is not shaded is the region of feasibility.\r<BR>\n" );
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document.write( "the coordinate points are in (x,y) format.<BR>\n" );
document.write( "x represents the age of the person.<BR>\n" );
document.write( "y represents the target heart rate.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "a person who is 45 shows coordinates of (45,87.5) and (45,140).<BR>\n" );
document.write( "(45,87.5) shows that his minimum target heart rate for exercise is 87.5<BR>\n" );
document.write( "(45,140) shows that his maximum target heart rate for exercise is 140.\r<BR>\n" );
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document.write( "this is based on the inequalities of:\r<BR>\n" );
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document.write( "y >= .50 * (220 - x)<BR>\n" );
document.write( "y <= .80 * (220 - x)\r<BR>\n" );
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document.write( "x is equal to 45.\r<BR>\n" );
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document.write( "y >= .50 * (220 - 45) becomes y >= .50 * 175 which becomes y >= 87.5.<BR>\n" );
document.write( "y <= .80 * (220 - 45) becomes y <= .80 * 175 which becomes y <= 140.\r<BR>\n" );
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document.write( "keep in mind that the opposite of the inequalities are being graphed.<BR>\n" );
document.write( "this allows the feasible region to be the unshaded region of the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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