D is the correct option since it represents a combination where neither p nor a equals zero.
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.
There is clear favoritism present. However, it is crucial to examine not just how many women were promoted in comparison to men but also the rate of promotion within each group. In the case of men, 21 out of 24 received promotions, indicating a substantial rate of 87.5%. In contrast, for women, only 14 out of 24 were promoted, which is 58.3%, just over half. Therefore, we can conclude that there is a distinct bias favoring male employees.
Answer: All real numbers except for x ≠ 7 and those x for which f(x)≠-3
Step-by-step explanation:
The domain of function f is defined as R - {7}
In other words, if x belongs to the domain of f,
then, x cannot equal 7
(gof)(x) = g(f(x))
Considering that g has a domain of R - {-3}
Therefore, if f(x) fits within the domain of g,
it follows that f(x)≠ -3
Consequently, the fourth option is the right choice.
a) The area of a rectangle is calculated by multiplying the length by the width:
A = l·w
This formula allows us to express the width in terms of area and length. By dividing A by l, we find
A/l = w
We also recognize that the perimeter of a rectangle is the total length around it.
P = l + w + l + w
P = 2(l + w)
We aim to rewrite the perimeter formula to isolate l on one side, using the expression for w derived earlier.
P = 2(l + A/l)
By substituting the known value for A, we can express p(l) as
p(l) = 2(l + 25/l)
p(l) = 2l + 50/l
b) For lengths exceeding widths, we have
l > w
l > A/l
l² > A
l > √A
l > √25
This indicates that the domain of p(l) is
l ∈ (5, ∞)..... meters
