Same denominator.
Add only the numerators.
5/12 + 8/12
13/12~~~
Words to the wise: Please express exponentials as x^2, not x2.
x2 + y2 = 81 should be <span>x^2 + y^2 = 81 = 9^2
Comparing this to x^2 + y^2 = r^2, we see that r= radius=9. y-intercepts are where x=0, so purposely set x=0 and solve for y:
0^2 + y^2 = 9^2. Then y = 9 or y = -9.
The graph intersects the y-axis at (0,9) and (0, -9).</span>
W+b=30
5.50w+8.75b=204
Use simultaneous equations to solve. Replace w with 30-b and plug into the second equation.
5.50(30-b)+8.75b=204
165-5.5b+8.75b=204
3.25b=39
b=12
She sold 12 belts.
Answer:
0.8554 is the probability that the proportion of students living in dormitories is between 0.70 and 0.85
Step-by-step explanation:
We are given the following in the question:
Proportion of students who live in dormitories = 80%
![p= 0.80](https://tex.z-dn.net/?f=p%3D%200.80)
Sample size, n = 80
Thus, the number of students follow a binomial distribution,
We use normal approximation to the binomial distribution to find the probability.
Parameters of Normal distribution:
![\mu = np = 80\times 0.80 = 64\\\sigma = \sqrt{np(1-p)} = \sqrt{80(0.80)(1-0.80)} = 3.58](https://tex.z-dn.net/?f=%5Cmu%20%3D%20np%20%3D%2080%5Ctimes%200.80%20%3D%2064%5C%5C%5Csigma%20%3D%20%5Csqrt%7Bnp%281-p%29%7D%20%3D%20%5Csqrt%7B80%280.80%29%281-0.80%29%7D%20%3D%203.58)
We have to find the probability that the sample proportion (the proportion living in the dormitories) is between 0.70 and 0.85.
![P(0.70\leq p \leq 0.85)\\\\=P(0.70(80)\leq x \leq0.85(80))\\\\=P(56 \leq x \leq 68) \\\\= P(\displaystyle\frac{56 - 64}{3.58} \leq z \leq \displaystyle\frac{68-64}{3.58})\\\\ = P(-2.2346 \leq z \leq 1.1173)\\\\= P(z \leq 1.1173) - P(z < -2.2346)\\\\= 0.8681 - 0.0127 = 0.8554](https://tex.z-dn.net/?f=P%280.70%5Cleq%20p%20%5Cleq%200.85%29%5C%5C%5C%5C%3DP%280.70%2880%29%5Cleq%20x%20%5Cleq0.85%2880%29%29%5C%5C%5C%5C%3DP%2856%20%5Cleq%20x%20%5Cleq%2068%29%20%5C%5C%5C%5C%3D%20P%28%5Cdisplaystyle%5Cfrac%7B56%20-%2064%7D%7B3.58%7D%20%5Cleq%20z%20%5Cleq%20%5Cdisplaystyle%5Cfrac%7B68-64%7D%7B3.58%7D%29%5C%5C%5C%5C%20%3D%20P%28-2.2346%20%5Cleq%20z%20%5Cleq%201.1173%29%5C%5C%5C%5C%3D%20P%28z%20%5Cleq%201.1173%29%20-%20P%28z%20%3C%20-2.2346%29%5C%5C%5C%5C%3D%200.8681%20-%200.0127%20%3D%200.8554)
Thus, 0.8554 is the probability that the proportion of students living in dormitories is between 0.70 and 0.85