Answer: (80% , 85%)
Step-by-step explanation:
We know that, confidence interval for population proportion is given by :-
(p-E , p+E)
, where p = sample proportion , E = Margin of error.
Given : Proportion of elementary school teachers who are female = 82%.
The article also states the maximum error of their estimate = 3%.
Then, the 90% confidence interval for the proportion of elementary school teachers who are female will be :
(82%-2% , 82%+3%)
= (80% , 85%)
Hence, the resulting 90% confidence interval for the proportion of elementary school teachers who are female = (80% , 85%)
<h2>SOLVING</h2>
What is the slope of the line passing through the point (1,2) and (5,4)
Formula used, here
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| simplify
| reduce
Answer:
-4m + 4
Step-by-step explanation:
you distribute the -4 to the m making -4m and then distribute -4 to the -1 which makes +4
Answer: 117.6° ; 32.4° .
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Explanation:
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Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.
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We are given the following:
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We have a triangle.
Angle 1: m∡1 = (8x) ;
Angle 2: m∡2 = (2x + 3) ;
Angle 3: m∡3 = 30.
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We are asked to find: "m∡1" and " m∡2" .
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Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
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So, " m∡1 + m∡2 + m∡3 = 180 " .
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Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ;
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m∡1 + m∡2 + m∡3 = 180 ;
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8x + (2x + 3) + 30 = 180 ;
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8x + 2x + 3 + 30 = 180 ;
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Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
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+8x + 2x = +10x ;
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+3 + 30 = +33 ;
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Rewrite the entire equation, as:
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10x + 33 = 180 ;
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Now, subtract "33" from EACH SIDE of the equation:
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10x + 33 − 33 = 180 −<span> 33 ;
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to get:
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10x = 147 ;
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Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" :
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10x / 10 = 147 / 10 ;
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to get:
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x = 14.7 ;
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Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2"; as follows:
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Angle 1: "(8x)" = 8*(14.7) = 117.6° ;
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Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
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These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° .
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Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
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Let us check:
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m∡1 + m∡2 + m∡3 = 180 ;
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Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
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→ 117.6 + 32.4 + 30 = ? 180 ??
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→ 117.6 + 32.4 = 150 ; → 150 + 30 =? 180 ? Yes!
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