Answer:
6 * 3/4 = 4.5 = 9/2 = 412
Step-by-step
6 * 3/4 = 6/1 3*4 = 18/4 = 9/2
2 · 2 = 9/2
Both the numerators and denominators are to be multiplied. Retain the resulting fraction with the lowest possible denominator; GCD(18, 4) = 2. In this intermediate calculation, cancelling by the common factor of 2 results in 9
2
.
In summary - six times three quarters equals nine halves.
Step-by-step explanation:
a) 7!
In absence of any restrictions, the answer is 7! as it represents the permutations of all animals.
b) 4! x 3!
Considering there are 6 cats and 5 dogs, the first and last slots must be occupied by cats to ensure alternate arrangements. The only options available then are based on the arrangement of the cats among themselves and the dogs among themselves, yielding 4! permutations for the cats and 3! for the dogs, thus leading to a total of 4! x 3! arrangements.
c) 3! x 5!
Here, the arrangement of the dogs among themselves can occur in 3! ways. Considering the dogs as a singular “object,” we can arrange this unit with the 4 cats, providing 5! total arrangements possible, leading to 3! · 5! arrangement possibilities.
d) 2 x 4! x 3!
In this scenario, both cats and dogs must be grouped together, allowing positions where all cats come before the dogs or vice versa. As there are two configurations, the resultant count is 2 multiplied by both arrangements, resulting in 2 x 4! x 3!
Answer:
Review the explanation
Step-by-step explanation:
The triangles ΔABC and ΔBAD are congruent, establishing:
- AB ≅ BA;
- AC ≅ BD;
- BC ≅ AD;
- ∠ABC ≅ ∠BAD;
- ∠BCA ≅ ∠ADB;
- ∠CAB ≅ ∠DBA.
Now, consider triangles AEC and BED. In these triangles, we have:
- AC ≅ BD;
- ∠EAC ≅ ∠EBD (due to ∠CBA ≅ ∠BAD);
- ∠AEC ≅ ∠BED (being vertical angles).
Therefore, ΔAEC ≅ ΔBED, which leads to the conclusion that:
AE ≅ EB.
This indicates that line segment CD bisects segment AD.
To identify the most sensible savings goal for Kirk and his family, follow these calculations:
a. $225 per month over 2 years equals $5400 (calculated as 225 * 2 * 12)
b. $200 per month for 3 years totals $7200 (calculated as 200 * 3 * 12)
c. $100 per month across 4 years will give $4800 (calculated as 100 * 4 * 12)
d. $75 saved monthly for 5 years amounts to $4500 (calculated as 75 * 5 * 12)
The optimal savings target would be option b, since $7200 exceeds <span>$6845.</span>
Answer: 7.50x should be greater than or equal to 200
Step-by-step explanation:
She aims to earn a minimum of $200.
