claire was able to verify that x=3 was a solution to her teacher's linear equation, but the equation got erasted from thw board.
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The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)
<h3>How to interpret Cycle Graphs?</h3>
From the diagram attached, we can say that;
Period = 2π/k
where;
k = 2π/2.25
k = 8π/9
Thus;
h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)
h(t) = -24cos (8π/9)t + 24.5
Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;
41 = -24cos (8π/9)t + 24.5
41 - 24.5 = -24cos (8π/9)t
16.5 = -24cos (8π/9)t
-0.6875 = cos (8π/9)t
cos⁻¹0.6875 = (8π/9)t
t = 0.834 min
Thus, time interval is between;
0.834 < t < (2.25 - 0.834)
⇒ 0.834 < t < 1.416 and
(2.25 + 0.834) < t < (2.25 + 1.416)
⇒ (3.084, 3.666)
Read more about Cycle Graphs at; brainly.com/question/24461724
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Z value is a numerical measurement that describe a value relationship to the mean of a group of values. The standard deviations is 1.25 above the mean is 14,500 hours.
<h3>Given information-</h3>The mean for the bulb is 12,000 hours.
The standard deviation for the bulb is 2000 hours.
Sample value is 14500.
To find out the how many standard deviation is 14500 mean away from the mean the z value of the mean should be calculated.
<h3>Z value</h3>Z value is a numerical measurement that describe a value relationship to the mean of a group of values. Z value is the ratio of the difference of the sample value and mean
to the standard deviation. Thus the z value for the given mean
is,
Thus the standard deviations is 1.25 above the mean is 14,500 hours.
Learn more about the z value here;