Step-by-step explanation:
Work out the value of x.
<h3>#12</h3>
<u>The angles are supplementary as same side interior angles, sum to 180°:</u>
- x + x - 26 = 180
- 2x = 206
- x = 103
<h3>#13</h3>
<u>The angles are corresponding, hence congruent:</u>
- 3x - 5 = x + 55
- 3x - x = 55 + 5
- 2x = 60
- x = 30
<h3>#14</h3>
<u>The angles are supplementary as same side interior angles, sum to 180°:</u>
- 2x + 24 + x = 180
- 3x = 180 - 24
- 3x = 156
- x = 52
<h3>#15</h3>
<u>The angles are corresponding, hence congruent:</u>
- 4x - 12 = 3x + 6
- 4x - 3x = 6 + 12
- x = 18
<h3>#16</h3>
<u>Corresponding with the right angle:</u>
- 4x + 12 = 90
- 4x = 78
- x = 19.5
<h3>#17</h3>
<u>Vertical angle of the bottom angle is supplementary with the top angle:</u>
- 2x + 12 + 3x + 23 = 180
- 5x + 35 = 180
- 5x = 145
- x = 49
Answer:
d) 16%
Step-by-step explanation:
The empirical rule states that for a normal distribution population with a mean (μ) and standard deviation (σ), the following conditions occur:
- 68% falls within one standard deviation μ ± σ
- 95% falls within two standard deviation μ ± 2σ
- 99.7% falls within three standard deviation μ ± 3σ
Given μ = 16 ounce and σ = 0.05 ounce.
68% falls within one standard deviation = μ ± σ = 16 ± 0.05 = (15.95, 16.05)
the number that falls outside one standard deviation = 100% - 68% = 32%
Therefore percentage of boxes have weights that are more than 1 standard deviation above the mean = 32% / 2 = 16%
Answer:
0.3
Step-by-step explanation:
0.8/y = 2 : 3/4
The value of y in the above expression can be obtained as follow:
0.8/y = 2 : 3/4
0.8/y = 2 ÷ 3/4
0.8/y = 2 × 4/3
0.8/y = 8/3
Cross multiply
0.8 × 3 = y × 8
2.4 = 8y
Divide both side by the coefficient of y i.e 8
y = 2.4/8
y = 0.3
Thus, the value of y is 0.3
