Based on the provided information about the metals' melting point, boiling point, and density, the response is A. The gold sample transitions from liquid to gas at the highest temperature, while the copper sample occupies the most volume. Gold's boiling point is the highest at 2660, and copper has the lowest density, which correlates with a larger volume since density is defined as mass divided by volume.
Define x as the price for each bed sheet and y as the price for every towel. The linear equations representing the scenario are:
38x + 61y = 791.50
54x + 50y = 923
When solving for x and y in the equations, the results are x = 12 and y = 5.5. Consequently, one bedsheet costs $12, and each towel is priced at $5.5.
A. Mean and standard deviation.
The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.
The standard deviation of the sampling distribution is:
σₓ̄ = σ / √n
Plugging in values:
σₓ̄ = 6.9 / √25 = 1.38
b. Calculate z-scores for both values:
z = (value - mean) / standard deviation
For 172.5:
z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068
For 175.8:
z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83
The difference between these probabilities is 0.762.
Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.
c. Z-score for 172 cm:
z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03
Hence, samples with means below 172 cm equal 0.03 × 200 = 6.
Answer:
Review the explanation
Step-by-step explanation:
The triangles ΔABC and ΔBAD are congruent, establishing:
- AB ≅ BA;
- AC ≅ BD;
- BC ≅ AD;
- ∠ABC ≅ ∠BAD;
- ∠BCA ≅ ∠ADB;
- ∠CAB ≅ ∠DBA.
Now, consider triangles AEC and BED. In these triangles, we have:
- AC ≅ BD;
- ∠EAC ≅ ∠EBD (due to ∠CBA ≅ ∠BAD);
- ∠AEC ≅ ∠BED (being vertical angles).
Therefore, ΔAEC ≅ ΔBED, which leads to the conclusion that:
AE ≅ EB.
This indicates that line segment CD bisects segment AD.
