Answer with explanation: Given that Circle 1 has a center at (−4, −7) and a radius of 12 cm, while Circle 2's center is at (3, 4) with a radius of 15 cm. Two circles are similar if one can be transformed and scaled to fit over the other, creating identical circles. The circles qualify as similar because the transformation rule (x,y) → (x+7,y+11) can be applied to Circle 1, followed by dilation using a scale factor of 5/4. Since Circle 1's center is at (-4,-7), we translate it to (3,4) through (-4+7,-7+11). With Circle 1 having a radius of 12 and Circle 2 having 15 cm, we denote the scale factor as k.
The solution for y is y = \frac{a}{3(3 + x)}
When the stretch is proportional to the weight, it can be expressed as:
weight/(49 cm) = (135 N)/(21 cm)
weight = (49/21)×135 N
weight = 315 N
The fish's weight would be 315 N.
Answer:
(b)E(x)=1.3087
(c)Variance of x =1.7119
(d)E(y)=2.0447
Step-by-step explanation:
The random variable x refers to the average number of cups of coffee consumed daily.
The total number of respondents equals 1014
(a) Probability distribution for x.

(b) Expected value for x

E(x)=1.3087
(c) Variance for x
Variance 


(d)


E(y)=2.0447
The expected value for y surpasses that of x.
The result is 0.0129. The data to consider includes the mean and standard deviation for the random variable associated with the fleets' ages. Calculating the Z-score for x = 14 and using the standard normal distribution table yields the probability that the average age of the 40 sampled airplanes is at least 14 years, rounded to four decimal places as 0.0129.