Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions, the mean is 
and the standard deviation is 
In this problem, we have that:
.
So
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Answer:
Volume of box is 
Step-by-step explanation:
Let x be the side of square corner
Length of box after cutting corners =22-2x
Breadth of box after cutting corners =15-2x
Height =x
Volume of box = (22-2x)(15-2x)x
Volume of box =
Differentiate w.r.t x
Substitute derivative =0
at 
hence maximum
at 
hence minimum
So,Volume of box =
Hence Volume of box is
Answer:
a) Empty set
b) 
Step-by-step explanation:
Roster form is a comma separated list form of set.
a) The set of natural numbers x that satisfy x + 4 = 1.
Thus, x is an empty set.
b) set-builder notation for the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
We use x to represent this set. Now x belongs to natural number and is less than equal to 12.
Thus, it can be written as:
The value of x is 5
Explanation
Given <ACD=2x+4
<ACB=5x-11
Given that ABCD is a rhombus. So the opposite angles will be same and all the sides will be equal.
diagonal AC divides the rhombus into two triangles ACD and ACB
according to angle sum property, the sum of all angles of a triangle is 180.
consider triangle ACD
Answer:
The break even point is 8400.
Step-by-step explanation:
Tom's Trashbins Inc. has fixed costs of $226,800.
The firm's sales are expected to be $427,500 this year if the firm sells 9500 units.
The unit sales price is = 
dollars
Variable costs amount to 40% of sales.
So, the contribution margin per unit cost is 
dollars
So, the break even point in units for Tom's Trashbins is =
fixed cost/contribution margin per unit cost
= 
= 8400
