You surveyed 350 students, out of which 182 were unsure.
The calculation gives: 182/350 = 0.52, indicating that 52% of the students were uncertain.
Now, apply this percentage to the national survey total:
50,000 x 0.52 = 26,000
The final result is 26,000 students who wouldn't know.
The estimated height would be around 3 feet, which would correspond to a level that is approximately at waist height.
Answer:
The angles m∠Q and m∠S together equal 90°
Step-by-step explanation:
A right angle measures 90°.
The total measure of angles in a triangle sums to 180°.
This gives us:
m∠Q + m∠S + ∠R = 180°
m∠Q + m∠S + 90° = 180°
Rearranging yields:
m∠Q + m∠S = 180° - 90°
m∠Q + m∠S = 90°
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!
The total number of bills and coins is 14.
Step-by-step explanation:
To minimize the count of bills and coins, start with the largest denominations that fit within the amount.
The change due is $39.49.
Start with:
-$20 bill (largest under $39.49)
Remaining: $19.49
-$10 bill (largest under $19.49)
Remaining: $9.49
-$5 bill (largest under $9.49)
Remaining: $4.49
Then:
4 × $1 bills (to cover $4.49)
Remaining: $0.49
-$0.25 coin (quarter)
Remaining: $0.24
2 × $0.10 coins (dimes)
Remaining: $0.04
4 × $0.01 coins (pennies)
The final composition includes:
1 twenty-dollar bill
1 ten-dollar bill
1 five-dollar bill
4 one-dollar bills
1 quarter
2 dimes
4 pennies
Totaling 14 pieces.
