Listing out a few elements of the set of perfect squares, we get the following values
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...}
we can stop there because 82 is between 81 and 100
So if x^2 = 82, then x^2 is between 81 and 100 meaning
81 < x^2 < 100
apply the square root to all sides of the compound inequality and we get
9 < x < 10
So the square root of 81 is between 9 and 10
Answer: the value falls between 9 and 10
Answer:
(c) ![f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Cleft%20%5C%7B%20%7B%7B%5Cfrac%7B1%7D%7B35-25%7D%3D%5Cfrac%7B1%7D%7B10%7D%3B%5C%2025%3CX%3C35%7D%20%5Catop%20%7B0%3B%5C%20Otherwise%7D%7D%20%5Cright.)
(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Step-by-step explanation:
The random variable <em>X</em> follows a Uniform (25, 35).
(a)
The probability density function of an Uniform distribution is:
![f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Cleft%20%5C%7B%20%7B%7B%5Cfrac%7B1%7D%7BB-A%7D%3B%5C%20A%3CX%3CB%7D%20%5Catop%20%7B0%3B%5C%20Otherwise%7D%7D%20%5Cright.)
Then the probability density function of the random variable <em>X</em> is:
![f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Cleft%20%5C%7B%20%7B%7B%5Cfrac%7B1%7D%7B35-25%7D%3D%5Cfrac%7B1%7D%7B10%7D%3B%5C%2025%3CX%3C35%7D%20%5Catop%20%7B0%3B%5C%20Otherwise%7D%7D%20%5Cright.)
(b)
Compute the value of P (X > 33) as follows:
![P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20](https://tex.z-dn.net/?f=P%28X%3E33%29%3D%5Cint%5Climits%5E%7B35%7D_%7B33%7D%20%7B%5Cfrac%7B1%7D%7B10%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B10%7D%5Ccdot%5Cint%5Climits%5E%7B35%7D_%7B33%7D%20%7B1%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B10%7D%5Ctimes%20%5Bx%5D%5E%7B35%7D_%7B33%7D%5C%5C%5C%5C%3D%5Cfrac%7B35-33%7D%7B10%7D%5C%5C%5C%5C%3D%5Cfrac%7B2%7D%7B10%7D%5C%5C%5C%5C%3D0.20)
Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c)
Compute the mean of <em>X</em> as follows:
![\mu=\frac{A+B}{2}=\frac{25+35}{2}=30](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7BA%2BB%7D%7B2%7D%3D%5Cfrac%7B25%2B35%7D%7B2%7D%3D30)
Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:
![P(30-2](https://tex.z-dn.net/?f=P%2830-2%3CX%3C30%2B2%29%3DP%2828%3CX%3C32%29)
![=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B32%7D_%7B28%7D%20%7B%5Cfrac%7B1%7D%7B10%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B10%7D%5Ccdot%5Cint%5Climits%5E%7B32%7D_%7B28%7D%7B1%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B10%7D%5Ctimes%20%5Bx%5D%5E%7B32%7D_%7B28%7D%5C%5C%5C%5C%3D%5Cfrac%7B32-28%7D%7B10%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B10%7D%5C%5C%5C%5C%3D0.40)
Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Answer:
$37.50
Step-by-step explanation:
I said 50 x .75 (I wanted to see how much was left on) and I got 37.5.
Tell me if I am wrong.
Can I get brainliest
Answer:
686.94
Step-by-step explanation:
first year, 42 interest
second year, 44.94 interest
Total=686.94