Answer: On average, a pet's weight during this vet visit is approximately 2.4 pounds away from 12.9 pounds.
If the MAD for another day's weights was 1.5, then that day’s weights would be less variable compared to the weights of pets seen today.
Step-by-step explanation:
Given: The data in the table outlines the weights of animals visiting a vet one day, in pounds.
Mean = 12.9
Median= 12.0
Mode = 12.0
Mean Absolute Deviation = 2.4
It’s understood that the mean absolute deviation (MAD) of a dataset indicates the average distance between each data point and the mean. It reflects the variation present in the dataset.
Therefore, the average weight of a pet visiting this vet on this day is about 2.4 pounds away from 12.9 pounds.
Moreover, if another day had a MAD of 1.5, and since 1.5 < 2.4,[TAG_42]]
it implies that the weights on that day would be less variable compared to those of pets encountered on this day.
Answer:
Davide is 10 years old.
L'età di Davide è 10.
Step-by-step explanation:
The average ages of Aldo, Bruno, Carlo, and Davide amount to 16 years.
Let’s denote:
x for Aldo's age.
y for Bruno's age.
z for Carlo's age.
w for Davide's age.
The average for all four is 16 years.
This gives us:
Excluding Davide, the average age of the other three is 18. Therefore:
Substituting into the original equation:
Hence, Davide’s age is indeed 10.
L'età di Davide è 10.
In detail: Based on the central limit theorem, the distribution appears normal due to the large sample size. The confidence interval is presented in the format: (Sample mean - margin of error, sample mean + margin of error). The sample mean, denoted as x, serves as the point estimate for the population mean. The confidence interval is computed as: mean ± z × σ/√n, where σ represents the population standard deviation. The formula transforms into confidence interval = x ± z × σ/√n, with specific values: x = $75, σ = $24. To find the z score, we subtract the confidence level from 100% which gives α as 1 - 0.96 = 0.04; halving this results in α/2 = 0.02, signifying the tail areas. To ensure we account for the center area, we have 1 - 0.02 = 0.98, corresponding to a z score of 2.05 for the 96% confidence level. The confidence interval becomes 75 ± 2.05 × 24/√64 = 75 ± 2.05 × 3 = 75 ± 6.15. The lower limit is 75 - 6.15 = 68.85, while the upper limit stands at 75 + 6.15 = 81.15. For n = 400, with x = $75 and σ = $24, the z score remains 2.05, resulting in the confidence interval calculated as 75 ± 2.05 × 24/√400 = 75 ± 2.05 × 1.2 = 75 ± 2.46. Subsequently, the lower bound becomes 75 - 2.46 = 72.54, and the upper limit adds up to 75 + 2.46 = 77.46. Lastly, when n = 400, x = $200, and σ = $80, the z score tied to a 94% confidence level is 1.88. Thus, the confidence interval is expressed as 200 ± 1.88 × 80/√400 = 200 ± 1.88 × 4 = 200 ± 7.52, giving us a margin of error of 7.52.
Applying the cosine law, we can determine:
<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a, b, and c represent the sides of the triangle and C indicates the angle opposite to side c</span>
<span>Thus, we have:</span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>
<span>Now we solve for C</span>
<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500 - 57,600 - 40,000 = -96,000cos(C)
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)→ C=38.53°
<span>Therefore, the direction the captain should head towards island B is
180 - 38.53 </span><span>= 141.47 degrees</span>
Answer:
The solution yields a number equal to -136.
Step-by-step explanation:
Let x represent the number, leading to the following equation:
x + 2 = 7/8 x - 15
Rearranging gives:
x - 7/8 x = -15 - 2
1/8 x = -17
x = -17 * 8 resulting in -136.
