Answer:
Step-by-step explanation:
For question 1, the result is calculated by dividing the percentage of students in the sports club by the SAT average, while for question 2, the answer is no since the definitions yield contrary outcomes.
(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now we will express 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
This reduces to
1 ≡ -1082 * 1234 (mod 4321)
Thus, the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.
Let
s--------> denote the cube's side length
We know that
the volume of a cube is calculated as
if the side length s measures 
then
and thus, the volume is defined as
This leads us to conclude
the correct option is
D. A cube with side lengths of 2 feet has a volume of 8 cubic feet.
Answer:
With the addition of a child, both the family's income and expenses increase. Although the initial expenses might be higher, the financial benefits will manifest over time.
