Answer:
x = {-1/5, 1}
Step-by-step explanation:
(5x - 2)² - 1 = 8
Add 1 to both sides
(5x - 2)² = 9
Take the square root of both sides
5x - 2 = ±3
------------------------------
<u>Solution I</u> for 5x - 2 = +3
5x - 2 = 3
add 2 to both sides
5x = 5
Divide both sides by 5
x = 1
------------------------------
<u>Solution II</u> for 5x - 2 = -3
5x - 2 = -3
add 2 to both sides
5x = -1
Divide both sides by 5
x = -1/5
-------------------------------
x = {-1/5, 1}
Answer: 0.0386
Step-by-step explanation:
Given: The population of 400 tall women has a mean height
of 179.832 cm and a standard deviation
of 12.192 cm.
Let X be a random variable that represents the height of woman.
Sample size : n= 50
The probability that the mean for this sample group is above 182.88 will be :
![P(\overline{X}>182.88)\\\\=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{182.88-179.832}{\dfrac{12.192}{\sqrt{50}}})\\\\ =P(Z>1.7678)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(Z](https://tex.z-dn.net/?f=P%28%5Coverline%7BX%7D%3E182.88%29%5C%5C%5C%5C%3DP%28%5Cdfrac%7B%5Coverline%7BX%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%3E%5Cdfrac%7B182.88-179.832%7D%7B%5Cdfrac%7B12.192%7D%7B%5Csqrt%7B50%7D%7D%7D%29%5C%5C%5C%5C%20%3DP%28Z%3E1.7678%29%5C%20%5C%20%5C%20%5BZ%3D%5Cdfrac%7B%5Coverline%7BX%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%3D1-P%28Z%3C1.7678%29%5C%5C%5C%5C%3D1-0.9614%5C%20%5C%20%5C%20%5B%5Ctext%7BBy%20p-value%20table%7D%5D%5C%5C%5C%5C%3D%200.0386)
Hence, Required probability = 0.0386
<u><em>Answer</em></u>
length: 8 inch and width: 5 inch
<u><em>Explanation</em></u>
Let width be x,
then the length: x + 3
solve:
![\sf (x+3)(x) = 40](https://tex.z-dn.net/?f=%5Csf%20%28x%2B3%29%28x%29%20%3D%2040)
![\sf x^2+3x = 40](https://tex.z-dn.net/?f=%5Csf%20x%5E2%2B3x%20%3D%2040)
![\sf x^2+3x-40=0](https://tex.z-dn.net/?f=%5Csf%20x%5E2%2B3x-40%3D0)
![\sf x^2+8x-5x-40=0](https://tex.z-dn.net/?f=%5Csf%20x%5E2%2B8x-5x-40%3D0)
![\sf x(x+8)-5(x+8)=0](https://tex.z-dn.net/?f=%5Csf%20x%28x%2B8%29-5%28x%2B8%29%3D0)
![\sf (x-5)(x+8)=0](https://tex.z-dn.net/?f=%5Csf%20%28x-5%29%28x%2B8%29%3D0)
![\sf x = 5 \ or \ -8](https://tex.z-dn.net/?f=%5Csf%20x%20%3D%205%20%5C%20or%20%5C%20%20-8)
- As width cannot be negative, width will be 5.
Find for length:
![\sf x + 3](https://tex.z-dn.net/?f=%5Csf%20x%20%2B%203)
![\sf 5+ 3](https://tex.z-dn.net/?f=%5Csf%20%205%2B%203)
![\sf 8](https://tex.z-dn.net/?f=%5Csf%208)
Answer:
Interest: £23.4
Amount: £101.4
Step-by-step explanation:
6 × 5/100 × 78 = 23.4
Balance: 78 + 23.4 = 101.4