Answer: 6x
Work Shown:
For each step, the logs are all base b. This is to save time and hassle of writing tricky notation of having to write the smaller subscript 'b' multiple times. The first rule to use is that log(x^y) = y*log(x) for any base of a logarithm. The second rule is that meaning that the log base of itself is 1
log(b^(6x)) = 6x*log(b) .... pull down exponent using the first rule above
log(b^(6x)) = 6x*1 .... use the second rule mentioned
log(b^(6x)) = 6x
Answer:
the variance of the refund payment to the couple = 9463.394
Step-by-step explanation:
Given that :
A couple book a cruise to Alaska that promises to refund 100 per day of rain on the seven day cruise up to a maximum of 300.
It is possible that the couple won't be able to refund up 100 per day or more than 100 per day.
SO; let assume that the refund payment happens to be 0, 100,200, 300
Let X be the total refund payment on the seven day cruise.
We can say X = 0, if there is no rain on all 7 days.
If it rains on any one day; then X = 100
if it rains on any two day ; then X = 200
if it rains on any three day or more than that ; then X = 300
Now; we have our probability distribution function as:
P(X = 0) = 0.2097152
P(X = 100) = 0.3670016
P(X = 200) = 0.2752512
P(X = 300) = 0.148032
In order to determine the variance of the refund payment to the couple; we use the formula:
variance of the refund payment to the couple
where;
NOW;
the variance of the refund payment to the couple = 28002.944 - 18539.55
the variance of the refund payment to the couple = 9463.394
Answer: The dimension of the lawn = 85 × 40
Area of the lawn = 3250 square feet
Step-by-step explanation:
Let x represents the width of the rectangle,
Then According to the question,
The length of the rectangle = 2 x + 5
Also it is given that the perimeter of the rectangle = 250 feet.
But we know that the perimeter of the rectangle = 2 × ( length + width)
Thus, the perimeter of the rectangle = 2( 2x+5+x) = 2(3x+5) = 6x+10
If x = 30, the perimeter of the rectangle = 6 × 30 + 10 = 190 < 250
Thus, x ≠ 10.
If x = 50, the perimeter of the rectangle = 6 × 50 + 10 = 310 > 250
Thus, x ≠ 50
If x = 40, the the perimeter of the rectangle = 6 × 40 + 10 = 250 = 250
Thus, x = 40
Therefore, the width of the rectangle, x = 40 feet.
And, the length of the rectangle, 2 x + 5 = 2 × 40 + 5 = 85 feet.
1) The dimension of the rectangle = 85 × 40
2)The area of the rectangle = length × width = 85 × 40 = 3250 square feet.
