If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answ
er to the nearest hundredth. triangles ABC and ADC in which angle C is a right angle, point D is on segment BC between points B and C, the measure of angle ABD is x degrees, and the measure of angle ADC is y degrees 0.74 units 1.17 units 1.64 units 2.14 units
1 answer:
Answer:
1.17 units
Step-by-step explanation:
Given :
If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD?
x= 45° ; y = 63° AC = 4 units
From trigonometry,
Taking triangle ADC;
sinθ = opposite / Hypotenus
Sin63° = 4 / AD
AD = 4 / 0.891 = 4.489 units
From triangle ABC;
sin45° = 4 / AB
AB = 4 / 0.7071
AB = 5.656 units
Difference = (5.657 - 4.489) units
= 1.167 units
= 1.17 units (nearest hundredth)
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Given Information:
Population mean = p = 60% = 0.60
Population size = N = 7400
Sample size = n = 50
Required Information:
Sample mean = μ = ?
standard deviation = σ = ?
Answer:
Sample mean = μ = 0.60
standard deviation = σ = 0.069
Step-by-step explanation:
We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10
np ≥ 10
50*0.60 ≥ 10
30 ≥ 10 (satisfied)
n(1 - p) ≥ 10
50(1 - 0.60) ≥ 10
50(0.40) ≥ 10
20 ≥ 10 (satisfied)
The mean of the sampling distribution will be same as population mean that is
Sample mean = p = μ = 0.60
The standard deviation for this sampling distribution is given by
Where p is the population mean that is proportion of female students and n is the sample size.
Therefore, the standard deviation of the sampling distribution is 0.069.