∠K = ∠N = 60°
∠L = ∠M = 120°
<h3>Step-by-step explanation:</h3>In the attached, we have renamed F to G so Brainly will let us talk about it more easily. We have also added altitude MX.
AG is also a midsegment of ΔKLM, so LM = 2×AG = 4. Then ...
... NX = AB - LM = 7 -4 = 3
and we have right ΔMXN with hypotenuse 6 and leg 3. This is recognizable as a 30°-60°-90° triangle, with the 60° angle at N.
The angle at M is supplementary to that at N (because LM ║ KN), so measures 120°
The trapezoid is isosceles, so angles K and L have the same measures as angles N and M.
Answer:
Option C. $6,012
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
where
V is the the depreciated value
P is the original value
r is the rate of depreciation in decimal
t is Number of Time Periods
in this problem we have
t = 7 years
P = $8,000
r = 0.04
substitute in the formula above
Hope this helps :)
Answer:
a. Descriptive statistics for the sample.
n= 9
mean X[bar]= 20.36
median Me= 20.30
min: 19.70
max: 21.40
standad deviation S= 0.61
b. 95% Confidence interval [19.88; 20.83]
c. Decision: Support H₀
Step-by-step explanation:
Hello!
I don't have excel so I cannot install PHstat, I've used a statistic software called Infostat for the calculations.
There was a random sample of 9 bottles of shampoo taken to test if the process is operating correctly. If it is, the bottles should weight on average 20 ounces (this would be our study parameter)
The study variable is X: the weight of a bottle of shampoo.
X~N(μ;σ²)
a.
Descriptive statistics for the sample.
n= 9
mean X[bar]= 20.36
median Me= 20.30
min: 19.70
max: 21.40
standad deviation S= 0.61
b. 95% Confidence interval.
Since the variable has a normal distribution and the population variance is unknown, the statistic to use to construct this interval is the Students t:
X[bar] ± * (S/√n)
20.36 ± * (0.61/√9)
[19.88; 20.83]
c. You have to test the hypothesis that the production is operating correctly, if it is so, then:
H₀: μ = 20
H₁: μ ≠ 20
α: 0.05
The statistic value is t= 1.74
p-value: 0.1198
When you use the p-value to decide on a statistical hypothesis, you should always contrast it with the level of significance using the following rule:
If p-value ≤ α, then you reject the null hypothesis.
If p-value > α, then you do not reject the null hypothesis.
Since the p-value is greater than the significance level, you do not reject the null hypothesis. This means that the average weight of the shampoo bottles is 20 ounces, i.e. the process is operating correctly.
I hope it helps!