Answer:
The dimension of the open rectangular box is 
.
The volume of the box is 8.217 cubic inches.
Step-by-step explanation:
Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.
To find : The dimensions and the volume of the open rectangular box ?
Solution :
Let the height be 'x'.
The length of the box is '11-2x'.
The breadth of the box is '7-2x'.
The volume of the box is 
Derivate w.r.t x,
The critical point when V'(x)=0
Solve by quadratic formula,
Derivate again w.r.t x,
Now, 
(+ve)
(-ve)
So, there is maximum at x=1.392.
The length of the box is 
The breadth of the box is 
The height of the box is h=1.392.
The dimension of the open rectangular box is .
The volume of the box is
The volume of the box is 8.217 cubic inches.
Answer:
23
Step-by-step explanation:
Answer:
<h2>x = -11</h2>
Step-by-step explanation:
In algebra, the goal is always to isolate the variable, so that its value can be determined.
<h3>Step 1: Add x</h3>
6 + x = -5
<h3>Step 2: Subtract 6</h3>
x = -11
<h3>Step 3: Check</h3>
6 = -5 - -11
6 = -5 + 11
6 = 6 ✔
<h3>Step 4: Answer</h3>
x = -11
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Solution :
Sampling may be defined as the technique of selecting the individual members or the subset of the population to make a statistical inferences and estimates the characteristics of the entire population.
There are several sampling methods. This includes : Systematic sampling, clustered sampling, stratified sampling, quota sampling, judgement sampling, random sampling, convenience sampling and many more.
In the context, the sampling methods for each of the descriptions are :
a). The researcher use computer program to randomly choose a sample of 30 mice of the 1000 mice for using her study
--- Simple Random
b). The researcher chose the 1st 30 mice as she can reach the door to the mouse room
--- Convenience sampling
c). The mice those whose are kept in the cages on 10 various shelves in mouse room. The researcher or the experimenter chose the three mice from each shelve.
---- Stratified sampling
d). Each of the cage have 5 mice and the researcher randomly chooses 6 cages for her study
----- Cluster sampling
e). The researcher generates the list of the identification numbers which has been sorted from the smallest to the largest. The researcher randomly picks 1 mouse form the list and selects every 4 mouse until the researcher has 30 mice.
---- Systematic sampling
Answer: Original expression: 2x - 11 + 4x + 7 + 3(x-4)
Simplified: 9x - 16
Step-by-step explanation:
2x - 11 + 4x + 7 + 3(x-4) becomes 2x - 11 + 4x + 7 + 3x -12
Group like terms, then combine to simplify:
2x + 4x + 3x -11 + 7 - 12
2x + 4x + 3x = 9x
-11 -12 + 7 = =23+7= -16
Simplified expression: 9x - 16
