11) Adam can mop a warehouse in ten hours. Wilbur can mop the same warehouse in nine

Answer:

53

Step-by-step explanation:

When I entered 53 into PLATO, it appears to be the correct answer.

(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.

Answer:

The equation 0 = 3x² + 17x - 160 might be useful in determining the length.

Step-by-step explanation:

The area of the vegetable garden is specified as 170 ft².

Now, regarding the provided equations;

1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:

x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)

x = [-2 ± √(-2151)]/6

The square root value is negative, indicating no real solution for x.

Thus, this equation does not help find the length.

2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.

3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.

4) For 0 = 3x² - 160, simplifying gives;

3x² = 160

x² = 160/3

x = ±√(160/3)

x = ±7.303

Since the area is a whole number but this length isn't, this equation may not accurately determine the length.

Answer:

Step-by-step explanation:

To establish independence between two events, we must understand the concept of independence:

Events are deemed independent if , which means that the occurrence of one does not influence the probability of the other event.

In this situation, the only selection that aligns with the independence criterion is . Other options do not comply with the independent events definition.

The answer is C. Explanation: The shirt originally priced at $35 has a discount of 15%. Therefore, the savings amount will be calculated accordingly.