Answer:
14. x=21, GK=167°, HJ=98°, HGJ=262°, GKJ=201°
15. x=9, AD=108°, BC=23°, DC=139°, DBC=221°
Step-by-step explanation:
In each case, the sum of the arcs around the circle is 360°.
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14. 61 +(5x -7) +34 +(9x -22) = 360
14x = 294 . . . . . subtract 66, simplify
x = 21 . . . . . . . . divide by 14
(5x -7) = 98
(9x -22) = 167
- x = 21
- arc GK = 167°
- arc HJ = 98°
- arc HGJ = 360° -98° = 262°
- arc GKJ = 167° +34° = 201°
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15. 90 +(2x +5) +(17x -14) +(12x) = 360
31x = 279 . . . . subtract 81, simplify
x = 9 . . . . . . . . divide by 31
(2x+5) = 23
(17x -14) = 139
(12x) = 108
- x = 9
- arc AD = 108°
- arc BC = 23°
- arc DC = 139°
- arc DBC = 360° -139° = 221°
The 90th percentile is 1.2816 standard deviations from the mean. That tells you the standard deviation is ...
... (40 in - 38 in)/(1.2816) ≈ 1.56 in
The standard deviation for height for 4-year olds seems to be 1.56 inches.
By the law of sines, m∠<em>EFG</em> is such that
sin(m∠<em>EFG</em>) / (8 in.) = sin(m∠<em>G</em>) / (7.5 in)
so you need to find m∠<em>G</em>.
The interior angles to any triangle sum to 180°, so
m∠<em>DEG</em> = m∠<em>D</em> + m∠<em>G</em> + 43°
m∠<em>DEG</em> + m∠<em>D</em> + m∠<em>G </em>= 2 (m∠<em>D</em> + m∠<em>G</em>) + 43°
180° = 2 (m∠<em>D</em> + m∠<em>G</em>) + 43°
137° = 2 (m∠<em>D</em> + m∠<em>G</em>)
68.5° = m∠<em>D</em> + m∠<em>G</em>
But ∆<em>DEG</em> is isosceles, so m∠<em>D</em> = m∠<em>G</em>, which means
68.5° = 2 m∠<em>G</em>
34.25° = m∠<em>G</em>
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Then
sin(m∠<em>EFG</em>) = (8 in.) sin(34.25°) / (7.5 in)
m∠<em>EFG</em> ≈ sin⁻¹(0.600325) ≈ 36.8932°
Let's call x the price of a box of slime.
Gianna spent 4 × $58 for art supplies so 4(58) + 8x all together. We have
392 ≤ 4(58) + 8x ≤ 472
We can work with both inequalities at once. 4(58)=232 so we subtract that from all three sides.
160 ≤ 8x ≤ 240
Divide all three sides by 8, a positive number so the inequalities don't flip.
20 ≤ x ≤ 30
Answer: Least: $20, Most: $30
