Using Bayes' theorem, P(Disease | Positive) = (Sensitivity × Prevalence) / ((Sensitivity × Prevalence) + (1 - Specificity) × (1 - Prevalence)) = (0.9 × 0.01) / ((0.9 × 0.01) + (0.05 × 0.99)) = 0.018.

True positive rate = Sensitivity × Prevalence = 0.9 × 0.01 = 0.009.

Speed = Distance / Time = 120 km / 1.5 hours = 80 km/h.

Speed = Distance / Time = 300 km / 4 hours = 75 km/h.

Distance = speed × time = 60 km/h × 3 h = 180 km.

Distance = speed * time = 60 km/h * 2.5 h = 150 km.

Time = distance / speed = 320 km / 80 km/h = 4 hours.

The cross Aa x aa will produce offspring in a 1:1 phenotypic ratio (A:a).

The son will inherit the X chromosome from his mother. If she is a carrier (X^HX^h), there is a 50% chance he will inherit the X^h and express the trait.

A transversal intersecting two parallel lines forms 4 pairs of corresponding angles.

When a transversal intersects two parallel lines, the same-side interior angles are supplementary, meaning they add up to 180 degrees.

Probability that treatment is not effective for one patient = 1 - 0.8 = 0.2. For three patients, the probability that it is not effective for all = 0.2^3 = 0.008. Therefore, the probability that it is effective for at least one = 1 - 0.008 = 0.992.

Using the binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Here, n=5, k=3, p=0.8. Thus, P(3 out of 5) = C(5,3) * (0.8)^3 * (0.2)^2 = 10 * 0.512 * 0.04 = 0.2048.

The area of a triangle is given by (1/2) × base × height. Therefore, the area is (1/2) × 8 cm × 5 cm = 20 cm².

Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 30 / 5 = 6 units.

Area = 1/2 * base * height. Therefore, 30 = 1/2 * 10 * height, height = 6 units.

The sum of angles in a triangle is 180°. Therefore, the third angle is 180° - 30° - 60° = 90°.

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Area = 1/2 × base × height = 1/2 × 3 cm × 4 cm = 6 cm².

A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right-angled triangle.

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus it is a right triangle.

The maximum length of the third side is less than the sum of the other two sides, so it can be at most 6 + 8 - 1 = 13, but must also be greater than the difference, so it can be at most 10.

The maximum length of the third side is less than the sum of the other two sides, which is 7 + 24 = 31.

The new probability of infection after vaccination = Initial probability × (1 - reduction) = 0.1 × (1 - 0.75) = 0.1 × 0.25 = 0.025.

The probability of infection after vaccination = Initial probability × (1 - reduction) = 0.2 × (1 - 0.75) = 0.2 × 0.25 = 0.05.

Total distance = 100 km + 50 km = 150 km; Total time = 2 h + 1 h = 3 h. Average speed = Total distance / Total time = 150 km / 3 h = 50 km/h.

Speed = Distance / Time = 90 km / 1.5 hours = 60 km/h.

The leading zeros are not significant. Therefore, 0.050 kg has 2 significant figures.

Power is given by P = I^2 * R. Here, P = (3 A)^2 * 2 Ω = 9 * 2 = 18 W.