PLZ HELP FIND R AND EXPLAIN
1 answer:
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Answer:
see explanation
Step-by-step explanation:
(a)
Sum the parts of the ratio , 1 + 2 + 3 = 6 parts
Divide sum of angles in a triangle by 6 to find the value of one part of the ratio.
180° ÷ 6 = 30° ← value of 1 part of the ratio
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Since there is an angle of 90° then the triangle is right.
(b)
The shortest side is the side opposite the smallest angle of 30°
Using the sine ratio and the exact value
sin30° = , then
sin30° = =
=
( cross- multiply )
2 opp = 19 ( divide both sides by 2 )
opp = 9,5
Shortest side in the triangle is 9.5 cm
Answer:
The probability that the sample mean would differ from the population mean by more than 0.5 millimeters is 0.2420.
Step-by-step explanation:
Let <em>X</em> = the diameter of the steel bolts manufactured by the steel bolts manufacturing company Thompson and Thompson.
The mean diameter of the bolts is:
<em>μ</em> = 149 mm.
The standard deviation of the diameter of bolts is:
<em>σ</em> = 5 mm.
A random sample, of size <em>n</em> = 49, of steel bolts are selected.
The population of the diameter of bolts is not known.
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
The mean of the sampling distribution of sample mean is:
The standard deviation of the sampling distribution of sample mean is:
Compute the probability that the sample mean would differ from the population mean by more than 0.5 millimeters as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the sample mean would differ from the population mean by more than 0.5 millimeters is 0.2420.