Given the three integers are 
, we arrive at
We can merge the fractions on the left side:
Honestly, I find Mrs. Garcia's method easier to perform mentally. It hinges on how familiar you are with your multiples of 5. (5*15 = 75 is a multiplication I often use)
Melissa's approach involves calculating 5*20 = 100 and 5*9 = 45, then combines the 3-digit result 100 with the 2-digit result 45, yielding 145. Adding 45 to 00 is simple and doesn’t require carrying digits, thus the arithmetic is fairly straightforward.
Mrs. Garcia's technique involves computing 5*14 = 70 and 5*15 = 75, then summing these two-digit results. Many people may not readily recall that 5*15=75, which complicates forming that product. The addition of 70 and 75 requires a carrying operation, making the math somewhat more complex. The resulting total is 145.
(The rationale behind my preference for Mrs. Garcia's method is that I can achieve the final sum by simply doubling 7 tens, followed by adding 5. The only 3-digit number to remember mentally is the ultimate total.)
_____Subtraction introduces a slight complication, yet reshaping it as $5(30 -1) = $150 - 5 = $145 is possible.
Or, you may reframe it as $5(28 +1) = $140 +5 = $145.
Dividing an even number by 2 to find the product of 5 is straightforward when you append a zero.
5*14 = 10*7 = 70
5*28 = 10*14 = 140.
Answer: D) 
Step-by-step explanation:
Based on the provided information, we have
Sample size: n= 15
sample mean: 
Sample standard deviation: s= $20
Since the population standard deviation is not known, we utilize a t-test.
For a significance level of 95% confidence: 
Critical t-value : 
[Using the Student's t-value table]
The required 95% confidence interval yields:-
Thus, the sought-after 95% confidence interval for the mean amount spent by credit card customers during their initial visit to the new store in the mall, assuming normal distribution of the spending amounts, is:
A(w) = -w² + 100w
Step-by-step explanation: Initially, we need to express the length (l) of the rectangular area in terms of the width (w). Given that the total perimeter of the rectangle is 200 feet implies that 2(w + l) = 200, leading to l = 100 - w. Hence, the area A can be given as width multiplied by length: A = w * l = w * (100 - w) = -w² + 100w. Consequently, A(w) = -w² + 100w.
y2 = C1xe^(4x) Step-by-step explanation: Knowing that y1 = e^(4x) satisfies the differential equation y'' - 8y' + 16y = 0, we need to derive the second solution y2 using the reduction of order technique. Let y2 = uy1. Since y2 is a solution to the differential equation, it holds that y2'' - 8y2' + 16y2 = 0. By substituting for y2, its derivatives become y2 = ue^(4x), y2' = u'e^(4x) + 4ue^(4x), and y2'' = u''e^(4x) + 8u'e^(4x) + 16ue^(4x). Plugging these into the differential equation gives us u''e^(4x) = 0. Let w = u', so w' = u''. This results in w' e^(4x) = 0, leading to w' = 0. Integrating gives w = C1. Since w = u', this implies u' = C1, and integrating once more results in u = C1x. Therefore, y2 = ue^(4x) becomes y2 = C1xe^(4x), which is the second solution.
