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Question 41549: Determine whether -4 satisfies each compound inequality
-3x > 0 and 3x - 4 < 11
Graph the solution set to each compound inequality.
x > -2 and x is less than or equal to 4
x > 3 or x < -3
Solve each compound inequality. Write the solution set in interval notation and graph it.
-1 is less than or equal to 3 - 2x < 11
Solve each problem by using a compound inequality.
Two tests only. Professor Davis counts his midterm as 2/3 of the grade, and his final as 1/3 of the grade. jason scored only 64 on the midterm. What range of scores on the final exam would put Jason's average between 70 and 79 inclusive?
Senior citizens. The number of senior citizens (65 and over) in the United States in millions n years after 1990 can be estimated by using the formula s - 0.38n + 31.2. The percentage of senior citizens living below the poverty level n years after 1990 can be estimated by using the formula p = -0.25n + 12.2.
a) how many senior citizens were ther in 2000?
b) In what year will the percentage of seniors living below the poverty level reach 7%?
c) What is the first year in which we can expect both the number of seniors to be greater than 40 million and fewer than 7% living below the poverty level?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Determine whether -4 satisfies each compound inequality
-3x > 0 and 3x - 4 < 11
-3(-4)? 0
12>0 So -4 satisfies the inequality -3x>0
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3x-4<11
3(-4)-4? 11
-12-4? 11
-16<11 So -4 satisfies the inequality 3x-4<11
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Graph the solution set to each compound inequality.
x > -2 and x is less than or equal to 4
Mark -2 and 4 on a number line.
Put an open circle at -2 and a solid circle at 4
Draw a heavy line segment from -2 to 4
That is your graph.
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x > 3 or x < -3
Mark -3 and 3 on a number line.
Put an open circle at 3 and at -3.
Draw a heavy line segment(ray) from -3 to the left.
Draw a heavy line segment(ray) from 3 to the right.
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Solve each compound inequality. Write the solution set in interval notation and graph it.
-1 is less than or equal to 3 - 2x < 11
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Solve each problem by using a compound inequality.
Two tests only. Professor Davis counts his midterm as 2/3 of the grade, and his final as 1/3 of the grade. jason scored only 64 on the midterm. What range of scores on the final exam would put Jason's average between 70 and 79 inclusive?
Let "m" be the midterm score and "f" be the final score.
ENEQUALITY:
70 < (2/3)m + (1/3)f < 79
Multiply thru by 3 to get:
210< 2(64) + f < 239
Subtract 128 from all segments of the inequality.
82 < f <108
The final grade must be between 82 and 108
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Senior citizens. The number of senior citizens (65 and over) in the United States in millions n years after 1990 can be estimated by using the formula s= 0.38n + 31.2. The percentage of senior citizens living below the poverty level n years after 1990 can be estimated by using the formula p = -0.25n + 12.2.
a) how many senior citizens were ther in 2000?
S=0.38(10)+31.2
S=3.8+31.2 = 35 million
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b) In what year will the percentage of seniors living below the poverty level reach 7%?
-0.25n+12.2=7
-0.25n=-5.2
n=20.8
1990+20.8=2010.8
Below 7% in the year 2011
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c) What is the first year in which we can expect both the number of seniors to be greater than 40 million and fewer than 7% living below the poverty level?
0.38n+31.2 > 40 and -0.25n+12.2<7
0.38n> 8.8 and 0.25n > 5.20
n>23.158 and n > 20.8
1990+23.158 =2013.158
The conditions will be met in the year 2014
Cheers,
Stan H.
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