Manuel has opted to construct a fence to define a play area for his dogs, which will be a rectangular shape. Since only three sides require fencing because his house acts as one side of the rectangle, we conclude that the optimal area configuration will consist of two shorter sides each measuring 20 feet and a longer side measuring 40 feet.
Part A
To identify the values of x that make 2x−1 positive
⇒ 2x - 1 > 0
⇒ 2x > 1
⇒ x > 
As a result, for any x greater than
, the expression 2x-1 is positive
Part B
To find values of y making 21−37 negative
⇒ 21-3y < 0
⇒ 21 < 3y
⇒ 7 < y
Thus, for all y values exceeding 7, the expression 21-3y is negative
Part C
To identify values of c that digit 5−3c greater than 80
⇒ 5-3c > 80
⇒ -3c > 75
⇒ -c > 25
⇒ c < -25
Therefore, for values of c less than -25, the expression 5-3c surpasses 80
To tackle this issue, we need to clarify what each variable stands for. Here, n indicates the number of pencil packages purchased by Yolanda, while m represents the number of paper pads she buys. We calculate the total cost by multiplying these variables by their individual prices, which helps us determine the expense for both pencil packages and pads of paper.
The expression "1.4n" indicates the overall cost for n pencil packages.
On the other hand, "1.2m" signifies the complete expense for m pads of paper.
As we sum these two expressions, the resulting total reflects the overall expenditure for both items.
The equation "1.4n + 1.2m" summarizes this calculation.
I hope this provides clarity!
a) The specified probability distribution is b) 0.5, representing a 50% chance that X assumes a value between 21 and 25. c) 0.25 denotes a 25% likelihood that X takes on a value of at least 26. A uniform probability distribution encompasses two limits, a and b. The probability of obtaining a value lower than x is calculated accordingly. Also, the likelihood of finding a value between c and d is defined in correlation with the observed uniform distribution ranging from 20 to 28.
<span>The distribution of a data set is indicated by the standard deviation, and the range can serve as an estimate for this characteristic. Consequently, Set b (100, 140, 150, 160, 200, 10, 50, 60, 70, 110) exhibits the greatest standard deviation due to its 190 range (i.e., 200 - 10).</span>
