Answer:
99% confidence interval for the mean value from the random number generator is a lower limit of 85.87 and an upper limit of 110.93.
Step-by-step explanation:
Confidence interval = mean +/- margin of error (E)
mean = 98.4
sd = 16.3
n = 15
degree of freedom (df) = n - 1 = 15 - 1 = 14
confidence level (C) = 99% = 0.99
significance level = 1 - C = 1 - 0.99 = 0.01 = 1%
t-value corresponding to 14 df and 1% significance level is 2.977.
E = t×sd/√n = 2.977×16.3/√15 = 12.53
Lower limit = mean - E = 98.4 - 12.53 = 85.87
Upper limit = mean + E = 98.4 + 12.53 = 110.93
99% confidence interval for the mean is between 85.87 and 110.93
The reciprocal of 3/8 would be 8/3 (basically reversing the numbers).
When dividing fractions, you can just multiply the first fraction by the reciprocal of the second fraction instead of dividing by the second fraction.
3/4 ÷ 3/8
= 3/4 × 8/3
Simplifying gives us the final answer:
= 2
Let me know if you need any clarifications, thanks!
3(2x+5)=3
3 • 2x] + [3 • 5] = 3
6x + 15 = 3
6x = –12
x = –2
2x – 2(3x – 2) = 2(x –2) + 20
2x – 2(3x – 2) = 2(x –2) + 20
2x – 6x + 4 = 2x – 4 + 20
– 4x + 4 = 2x + 16
–4x + 4 – 4 –2x = 2x + 16 – 4 -2x
–6x = 12
x = –2
4. 4/6x +6 = -24
4/6 x = -24-6
4/6x = -30
x = -30*6/4
x = -45
5. 2/5x -4 = 10
2/5x = 10+4=14
x = 14*5/2
x = 35