For the fish bowl the first answer is correct.
(1/2)(4/3)(22/7)(12^3)
For the second problem
(1/3)(3.14)(6^2)(10) - (4/3)(3.14)(1.5^3)
The second answer.
Answer:
A(-6,-1) B(-6, -5) C(-4, -1)
Step-by-step explanation:
When a coordinate is rotated 180 degrees, they go from (x,y) to (-x,-y), so all you need to do is multiply every coordinate by -1
Answer:
a. 2.28%
b. 30.85%
c. 628.16
d. 474.67
Step-by-step explanation:
For a given value x, the related z-score is computed as z = (x-500)/100.
a. The z-score related to 700 is (700-500)/100 = 2, and P(Z > 2) = 0.0228 (2.28%)
b. The z-score related to 550 is (550-500)/100 = 0.5, and P(Z > 0.5) = 0.3085 (30.85%)
c. We are looking for a value b such that P(Z > b) = 0.1, i.e., b is the 90th quantile of the standard normal distribution, so, b = 1.281552. Therefore, P((X-500)/100 > 1.281552) = 0.1, equivalently P(X > 500 + 100(1.281552)) = 0.1 and the minimun SAT score needed to be in the highest 10% of the population is 628.1552
d. We are looking for a value c such that P(Z > c) = 0.6, i.e., c is the 40th quantile of the standard normal distribution, so, c = -0.2533471. Therefore, P((X-500)/100 > -0.2533471) = 0.6, equivalently P(X > 500 + 100(-0.2533471)), and the minimun SAT score needed to be accepted is 474.6653
Answer:
27, 26
Step-by-step explanation:
27^2 -26^2 = 729 -676 = 53
If the numbers are integers, they must differ by an odd number. For some odd number k, we will have ...
(x +k)^2 -x^2 = 53
2xk +k^2 = 53
x = (53 -k^2)/(2k)
x = 53/(2k) -k/2
The second term is an odd multiple of 1/2. The first term will be an odd multiple of 1/2 only for k=1. For k = 1, we have ...
x = (53 -1)/2 = 26
The two numbers are 26 and 27.
