Step-by-step explanation:
Given that,
We have to find the value of m∠E.
Here, two sides are equal, thus it is an isosceles triangle. As the two sides are equal, so their angles must be equal. So, ∠E and ∠D will be equal. Let us assume the measures of both ∠E and ∠D as x.
→ Sum of all the interior angles of ∆ = 180°
→ ∠E + ∠D + ∠F = 180°
→ 116° + x + x = 180°
→ 2x = 180° – 116°
→ 2x = 64°
→ x = 64° ÷ 2
→<u> x = 32°</u>
Henceforth,
→ m∠E = x
→ m∠E = 32°
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(4u+3) (u-1) is the answer
The answer is: [C]: " y = 3x + 1 " .
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Note: By looking at the graph, we see that it passed through the point, " (0, 1) " (at the y-intercept).
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Consider choice: [A]: "y = 3x" ; When "x = 0" ; what does "y" equal ?
→ y = 3x = 3(0) = 0 ; → "(0, 0)" is a solution; NOT "(0, 1)" ; so rule out "[A]" .
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Consider choice: [B]: "y = 3x − 1" ; When "x = 0" ; what does "y" equal ?
→ y = 3(0)−1 =0−1 = -1; → "(0, -1)" is a solution; NOT "(0, 1)" ; so rule out "[B]" .
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Consider choice: [C]: "y = 3x + 1" ; When "x = 0" ; what does "y" equal ?
→ y = 3(0)+1 = 0+1 = 1; → "(0, -1)" is a solution; so "choice [C]" is possible.
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Consider choice: [D]: "y = 3x² + 1"; When "x = 0" ; what does "y" equal ?
→ y = 3(0²)+1 = 0+1 = 1; → "(0, 1)" is a solution; so "choice [D]" is possible.
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However; choice: [D]: is a parabola, not a line; so we determine that the correct answer is: Choice [C]: "y = 3x + 1" .
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Sample = 75 printers, Printers used by small businesses = 15
p(15) = 15/75 = 0.2
At 90% limit, Z =1.64
Limit of proportion of printers used by small business = p +/- Z Sqrt [p(1-p)/n]
=0.2 +/- 1.64 * Sqrt [0.2(1-0.2)/75] = 0.2 +/- 0.0757
Limit of proportion => (0.2-0.0757) to (0.2+0.0757) => 0.1243 to 0.2757 or 12.43% to 27.57%
