Both triangles that are given (with right angles) lie in plane m, proving that AC is perpendicular to plane m. As angle acd is from a triangle that shares the common perpendicular, it too is a right angle

4 0

2 years ago

The distance between each base on a field is 90 ft. How far does a catcher have to throw the ball from home plate to second base

Gnoma [55]

Step-by-step explanation:

A baseball field is in the shape of a square (or diamond). Home plate and second base are opposite corners of each other. So the distance is equal to the diagonal of the square.

Use Pythagorean theorem to find the diagonal, or use properties of a 45-45-90 triangle.

Using Pythagorean theorem:

c² = a² + b²

c² = (90 ft)² + (90 ft)²

c = 90√2 ft

c ≈ 127 ft

7 0

3 years ago

This season, the probability that the Yankees will win a game is 0.49 and the probability that the Yankees will score 5 or more

yanalaym [24]

Answer:

0.226 = 22.6% probability that the Yankees will lose when they score 5 or more runs

Step-by-step explanation:

Conditional probability:

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

If the Yankees score 5 or more runs, either they win, or they lose. The sum of these probabilities is 1.

Probability that the Yankees win:

Event A: Scoring 5 or more runs.

Event B: Winning

The probability that the Yankees will score 5 or more runs in a game is 0.53.

This means that

The probability that the Yankees win and score 5 or more runs is 0.41.

This means that

0.774 probability that the Yankees will win when they score 5 or more runs

What is the probability that the Yankees will lose when they score 5 or more runs?

p + 0.774 = 1

p = 1 - 0.774

p = 0.226

0.226 = 22.6% probability that the Yankees will lose when they score 5 or more runs

4 0

3 years ago

Jordan's pet grooming business has a monthly cost function of C = $12p + $2100. His Revenue is given by the function R = $62p, w

mash [69]

Answer:

Step-by-step explanation:

5 0

2 years ago