Answer:
ASA congruence theorem
Step-by-step explanation:
WE know by given that <em>∠S ≅∠U</em> and<em> line ST ≅ line UT</em>
By the vertical angles theorem, we can find that ∠RTS ≅ ∠VTU.
They are in a form that when looking around the edge, you see congruent <em>angle, side, then angle</em>. That means that we can prove the triangles' congruence with ASA congruence.
Answer:
95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.
Step-by-step explanation:
Confidence interval is given by mean +/- margin of error (E)
Eggs from small nest
Sample size (n1) = 60
Mean = 37.2
Sample variance = 24.7
Eggs from large nest
Sample size (n2) = 159
Mean = 35.6
Sample variance = 39
Pooled variance = [(60-1)24.7 + (159-1)39] ÷ (60+159-2) = 7619.3 ÷ 217 = 35.11
Standard deviation = sqrt(pooled variance) = sqrt(35.11) = 5.93
Difference in mean = 37.2 - 35.6 = 1.6
Degree of freedom = n1+n2 - 2 = 60+159-2 = 217
Confidence level = 95%
Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132
E = t×sd/√(n1+n2) = 1.97132×5.93/√219 = 0.79
Lower limit = mean - E = 1.6 - 0.79 = 0.81
Upper limit = mean + E = 1.6 + 0.79 = 2.39
95% confidence interval for the difference in average mass is (0.81, 2.39)
The answer for the question in problem would be $125 is the price of hotel per night. This is computed by establishing the equations from the given statements, 3x + 4y = 625 and 4x +5y = 875. And by substitution you would get the answer of 125 as the price per night n the hotel and 75 per day for the rental of car.
