In summary. The graph of each equation is a straight line, m is the gradient of the line and c is the y-intercept. Conversely, if a straight line has gradient m and y-intercept c it has equation y = mx + c.
Answer:
The scientist can use only the angle x and the distance y to calculate the distance between the Earth and the Sun using the cosine function.Step-by-step explanation:
The cosine of an angle is equal to the ratio of the length of the adjacent side and the length of the hypotenuse. In equation form:
cos x = BC / y
Solving for BC
BC = y cos x
BC is the distance between the Earth and the sun
A. To answer this question, we must consider two inequalities. The first inequality we will construct is regarding the number of tickets sold with respect to capacity. The theater cannot exceed the allotted 200 seats, so this would indicate we would use a less than or equal to inequality. The inequality we would construct to illustrate this using adult and child tickets is x + y <= 200.
The second inequality we will construct is based upon the ticket prices set and the theater’s goal. The problem indicates the theater wants to sell “at least $1,500 worth of tickets...” To create the inequality here, we will create it as follows: 12.5x + 6.25y >= 1,500.
To find the intersection point, we must isolate y. In order to do this, move x to the other side of both inequalities. Inequality 2 can be simplified to y >= -12.5x / 6.25 + 1,500 / 6.25. Graph and identify the solution from there.
Answer:
(a)z=-1
(b)48.5 pounds
(c)61.5 pounds
Step-by-step explanation:

Given:
Mean, μ = 55 pounds
Standard deviation,σ = 6 pounds.
(a)For a dog that weighs 49 pounds.
x=49 pounds
The z-score

(b)When a dog has a z-score of -1.09

The weight of a dog with a z-score of -1.09 is 48.5 pounds.
(c)When a dog has a z-score of 1.09

The weight of a dog with a z-score of 1.09 is 61.5 pounds.