To find the maximum number of identical packs we see we have 72 pencils and 24 calculators.
This involves discovering the largest number that divides both 72 and 24 evenly,
which is known as the GCM or greatest common multiplier.
To determine the GCM, factor 72 into primes and group them:
72=2 times 2 times 2 times 3 times 3
24=2 times 2 times 2 times 3
Thus, the common grouping is 2 times 2 times 2 times 3, equating to 24.
Therefore, the maximum number of packs is 24.
For pencils:
72 divided by 24=3
Resulting in 3 pencils per pack.
For calculators:
24 divided by 24=1
So, 1 calculator per pack.
The outcome is 3 pencils and 1 calculator in each pack.
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:
a) 0.32
b) 0.68
c) Office or den
Step-by-step explanation:
a) The likelihood that a personal computer is located in a bedroom can be calculated by adding the probabilities of it being in an adult bedroom, child bedroom, or another bedroom:
b) The probability of a PC not being located in a bedroom is found by calculating 100% minus the probability of it being in a bedroom:
c) The expected location for finding a personal computer in a randomly selected household is derived from the room most likely to contain a PC according to Consumer Digest. The Office or den ranks as the most likely place with a probability of 0.40.
A PC would most likely be found in the Office or den.
Answer:
According to my cupcake recipe, it yields $12$ cupcakes and calls for $1\frac{1}{2}$ sticks of butter. I can only purchase whole sticks of butter.
Consequently, a single whole stick of butter will suffice to prepare $100$ cupcakes.
3 distinct arrangements - 1 x 9 (or 9 x 1) and 3 x 3
Thus, the total number of arrangements = 2 x 2 = 4 = an even count
Initially, we identify pairs of different factors of 9.
The pairs of factors for 9 are:
(1, 9) and (3, 3)
For each of these pairs, Mr. Deets can create 2 arrangements.
This means the total arrangements Mr. Deets can construct = 2 x 2 = 4, confirming that the overall number is even.
