Rename 3 1/2 as the sum of 2 fractions
2 answers:
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Answer:
382.925 feets
Step-by-step explanation:
The solution diagram is attached below :
Converting radian measurement to degree :
radian angle * 180/π = degree angle
1.2 * 180/π = 68.755°
0.9 * 180/π = 51.566°
Height of dam is h:
Using trigonometry :
Tan θ = opposite / Adjacent
Tan 68.755° = h / x
h = x Tan 68.755° - - - (1)
Tan 51.566° = h / (155+x)
h = (155+x) tan 51.566° - - - (2)
Equate (1) and (2)
x Tan 68.755 = (155+x) Tan 51.566
x Tan 68.755 = 155tan 51.566 + x tan 51.566
x Tan 68.755 = 195.32311 + x Tan 51.566
x Tan 68.755 - x Tan 51.566 = 195.32311
x(tan 68.755 - tan 51.566) = 195.32311
x * 1.3120110 = 195.32311
1.3120110x = 195.32311
x = 195.32311 / 1.3120110
x = 148.87307
Using :
h = x Tan 68.755
h = 148.87307 * tan(68.755)
h = 382.92539
h = 382.925 feets
Answer:
The statement is True.
Step-by-step explanation:
In this case we need to determine whether the rubber bands in a package of a particular brand of rubber band can hold a weight of 7 lbs or less.
A one-sample test can be used to perform the analysis.
The hypothesis can be defined as follows:
<em>H₀</em>: The mean weight the rubber bands can hold is 7 lbs, i.e. <em>μ</em> = 7.
<em>Hₐ</em>: The mean weight the rubber bands can hold is less than 7 lbs, i.e. <em>μ</em> < 7.
The information provided is:
As the population standard deviation is provided, we will use a <em>z</em>-test for single mean.
Compute the test statistic value as follows:
The test statistic value is -1.20.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the <em>p</em>-value for the two-tailed test as follows:
*Use a z-table for the probability.
The p-value of the test is 0.1151.
The <em>p</em>-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the mean weight the rubber bands can hold is 7 lbs.
Hence, the statement is True.