Answer:
Radius = 5
center is (19,-1)

Step-by-step explanation:
Two points in the plane, (19,4) and (19,−6), represent the endpoints of the diameter of a circle.
Distance between the points is calculated using formula


diameter = 10
radius = diameter divide by 2
Radius = 5
midpoint is the center of the circle


(19,-1)
Equation of the circle

h,k is the center and r is the radius
h=19 and k=-1 , r=5

Equal sets have the exact same elements, so they must have the same number of elements. Therefore, equal sets must also be equivalent. No, not all equivalent sets are also equal sets
Answer:
a) 
b) 
Step-by-step explanation:
Given that:
population mean
= 30,000
sample size n = 800
population proportion p = 0.6
a)
The mean of the the sampling distribution is equal to the population proportion.


b)
The standard deviation of the sampling distribution can be estimated by using the formula:






We are given radius = 6 yards
area of circle = pi * r * r = 3.14 * 6*6 = 113.04 yard square
cost of carpet is $14 per square yard
cost of 113.04 square yard = 14*113.04= 1582.56 dollars
Answer: cost to carpet the planetarium is $1582.56
Answer:
- t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground.
Explanation:
<u>1) Explanation of the model:</u>
- Given: h(t) = -16t² + 48t
- This is a quadratic function, so the height is modeled by a patabola.
- This means that it has a vertex which is the minimum or maximu, height. Since the coefficient of the leading (quadratic) term is negative, the parabola opens downward and the vertex is the maximum height of the soccer ball.
<u>2) Axis of symmetry:</u>
- The axis of symmetry of a parabola is the vertical line that passes through the vertex.
- In the general form of the parabola, ax² + bx + c, the axis of symmetry is given by x = -b/(2a)
- In our model a = - 16, and b = 48, so you get: t = - ( 48) / ( 2 × (-16) ) = 1.5
<u>Conclusion</u>: since t = 1.5 is the axys of symmetry, it means that at t = 1.5 the ball reachs its maximum height and that it will take the same additional time to fall back to the ground, whic is a tolal of 1. 5 s + 1.5 s = 3.0 s.
Answer: t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground.