Use Graphs A-D for Exercises 9-11. During the winter, the amount of water that flows

A national survey of companies included a question that asked whether the customers like the new flavor of a cola from company A

mote1985 [20]

Answer:

The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1000, \pi = \frac{850}{1000} = 0.85$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 - 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8237$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 + 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8763$

The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).

3 0

4 years ago

A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minute

SSSSS [86.1K]

Answer:

A) 290 km
B) 4 hours
C) 72.5 km/h

Step-by-step explanation:

Let distance be d and time t

At 75 km/h speed the distance is

d = 75(t - 48 min) = 75(t - 48/60 hours)

At 50 km/h speed the distance is

d = 50t + 40

Since the distance is same, we get the equation:

75(t - 48/60) = 50t + 40
75t - 75*4/5 = 50t + 40
75t - 60 = 50t + 40
75t - 50t = 40 + 60
25t = 100
t = 4 hours

A) The distance between A and B

d = 50*5 + 40 = 290 km

B) Time is

4 hours as found above

C) The speed = d/t

Speed = 290/4 = 72.5 km/h

6 0

3 years ago

6. Square RSTU with vertices R(0, 3), S(5, 4),

Olenka [21]

The reflection of a point across a line also known as the mirror line, forms an image that is equal distance from the as the preimage

The coordinates of the image following a reflection across the line x = -1 are;

R'(-2, 3), S'(-7, 4), T'(-8, -1), and U'(-3, -2)

Reason:

Question; Square RSTU with vertices R(0, 3), S(5, 4), T(6, -1), and U(1, -2), reflected about the line x = -1

Required:

To find the coordinate of the image

The line x = -1 is parallel to the y-axis, therefore, the distances of the x-coordinates of the preimage and the image from the line x = -1 are equal,

The y-coordinates of the image ang preimage are equal

The differences of distances are;

Δx, of point R (0 - (-1)) = 1, coordinates of image = R'(-1 - 1, 3) = R'(-2, 3)

Δx of point S = (5 - (-1)) = 6, coordinates of image = S'(-1 - 6, 4) = S'(-7, 4)

Δx of point T = (6 - (-1)) = 7, coordinates of image = T'(-1 - 7, -1) = T'(-8, -1)

Δx of point U = (1 - (-1)) = 2, coordinates of image = U'(-1 - 2, -2) = U'(-3, -2)

The coordinates of the vertex of image of the square RSTU following a reflection across the line x = -1 which is the square R'S'T'U' are;

R'(-2, 3), S'(-7, 4), T'(-8, -1), and U'(-3, -2)

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