Answer:
f(n) = 20 + 24n
Step-by-step explanation:
In slope-intercept form, y = mx + b, where m is the slope and b is the y intercept, you need to input the values you are given. f(n) is your "y" here.
The tricky part here is finding "b". Well, at the start, the bamboo shoot is 20 inches tall, so if you think about it, the equation should start with 20, which will be your "b".
Finally, you must show how the bamboo shoot will grow taller by 24 inches each day. Days in this case will be "n", which is like "x" in the general slope-intercept equation, and 24 is your slope ("m"). This will be positive because the height is <em>increasing.</em>
y = 24x + 20 ⇒ f(n) = 20 + 24n
Answer:
-19
Step-by-step explanation:
27x-19=-513
The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
<h3>How to determine the probability?</h3>
The given parameters are:
- Sample size, n = 100
- Population proportion, p = 82%
Start by calculating the mean:
![\mu = np](https://tex.z-dn.net/?f=%5Cmu%20%3D%20np)
![\mu = 100 * 82\%](https://tex.z-dn.net/?f=%5Cmu%20%3D%20100%20%2A%2082%5C%25)
![\mu = 82](https://tex.z-dn.net/?f=%5Cmu%20%3D%2082)
Calculate the standard deviation:
![\sigma = \sqrt{\mu(1 - p)](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cmu%281%20-%20p%29)
![\sigma = \sqrt{82 * (1 - 82\%)](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B82%20%2A%20%281%20-%2082%5C%25%29)
![\sigma = 3.84](https://tex.z-dn.net/?f=%5Csigma%20%3D%203.84)
Within ± 0.02 of the population proportion are:
![x_{min} = 82 * (1 - 0.02) = 80.38](https://tex.z-dn.net/?f=x_%7Bmin%7D%20%3D%2082%20%2A%20%281%20-%200.02%29%20%3D%2080.38)
![x_{max} = 82 * (1 + 0.02) = 83.64](https://tex.z-dn.net/?f=x_%7Bmax%7D%20%3D%2082%20%2A%20%281%20%2B%200.02%29%20%3D%2083.64)
Calculate the z-scores at these points using:
![z = \frac{x - \mu}{\sigma}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7Bx%20-%20%5Cmu%7D%7B%5Csigma%7D)
So, we have:
![z_1 = \frac{80.36 - 82}{3.84} = -0.43](https://tex.z-dn.net/?f=z_1%20%3D%20%5Cfrac%7B80.36%20-%2082%7D%7B3.84%7D%20%3D%20-0.43)
![z_2 = \frac{83.64 - 82}{3.84} = 0.43](https://tex.z-dn.net/?f=z_2%20%3D%20%5Cfrac%7B83.64%20-%2082%7D%7B3.84%7D%20%3D%200.43)
The probability is then represented as:
P(x ± 0.02) = P(-0.43 < z < 0.43)
Using the z table of probabilities, we have:
P(x ± 0.02) = 0.3328
Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
Read more about probability at:
brainly.com/question/25870256
#SPJ1
Explanation:
4x+3y=37
y=x-4
4x+3(x-4)=37
4x+3x-12=37
add 12 to both sides
7x=49
x=7
Now you use plug in x
4(7)+3y=37
28+3y=37
subtract 28 to both sides
3y=9
y=3
answer: x=7 and y=3