Answer:
- The length = x = 15 units
- The width = x-5 = 10 units
Step-by-step explanation:
Let 'x' be the length of a rectangle
As the width of a rectangle is 5 units less than the length.
so
width of rectangle will be = w = x - 5 units
Area = 150 square units
Using the formula
Area = length × width



Subtract 50 from both sides



if



As length can not be negative. so
x = 15 units
Hence,
The length = x = 15 units
The width = x-5 = 15-5 = 10 units
Answer:
Yes
Step-by-step explanation:
Given,
Population mean Z = 600
Sample mean, µ = 586.50
Size of the sample, n = 10
Standard deviation, σ = 26.77
The testing hypothesis is,
Null hypothesis = µ<600
Alternative hypothesis = µ≥600
The test statistics is the calculated value of Z,
(Z- µ)/(σ/√n)
= (600-586.50)/(26.77/√10)
= (13.5*3.1623)/26.77
= 42.691/26.77
= 1.5947
And at 5% level of significance, the table value of Z = 1.644
Here, calculated Z<Table value of Z, so we accept the null hypothesis.
So, the null hypothesis is accepted. The mean value of the laptop is less than 600.
Answer:
Step-by-step explanation:
1/12^2 = 1/144
Answer:

Step-by-step explanation:
we know that
To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.
we will proceed to verify each case to determine the solution of the problem
<u>case A)</u> 
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y


Let


therefore
f(x) and g(x) are inverse functions
<u>case B)</u> 
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y


Let


therefore
f(x) and g(x) are inverse functions
<u>case C)</u> ![f(x)=x^{5}, g(x)=\sqrt[5]{x}](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B5%7D%2C%20g%28x%29%3D%5Csqrt%5B5%5D%7Bx%7D)
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y
fifth root both members
![y=\sqrt[5]{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B5%5D%7Bx%7D)
Let

![f^{-1}(x)=\sqrt[5]{x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B5%5D%7Bx%7D)
therefore
f(x) and g(x) are inverse functions
<u>case D)</u> 
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y





Let



therefore
f(x) and g(x) is not a pair of inverse functions
Answer:
The answer is 890 . ...... :D