What is the distance between the two points (-2, 6) and (-2, -1)?

In a Gallup poll, 26.6% of 5000 people reported a Body Mass Index (BMI) greater than 30, which is classified as obese. The 5000

PSYCHO15rus [73]

Answer:

The 99% confidence interval for the proportion of the population who are obese is (0.25, 0.282)

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:

$n = 5000, \pi = 0.266$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 - 2.575\sqrt{\frac{0.266*0.734}{5000}} = 0.25$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 + 2.575\sqrt{\frac{0.266*0.734}{5000}} = 0.282$

The 99% confidence interval for the proportion of the population who are obese is (0.25, 0.282)

6 0

3 years ago

9/11=?/22 A.12 B.4 C.9 D.18

Yanka [14]

9/11 is equal to 18/22, so then D.

8 0

4 years ago

What are the coordinates of the vertex for the function shown below ?

Anuta_ua [19.1K]

Answer:

Step-by-step explanation:

We can answer this in two ways: Differentiation and Graphing.

Differentitate:

The first derivative of a function yields a function that provides the slope for any point on the line of the original function. The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.

f(x) = 3(x-1)^2 + 4

f(x) = 3(x-1)(x-1) + 4

f(x) = 3(x^2 - 2x + 1) + 4

f(x) = 3x^2 - 6x + 7

f'(x) = 6x -6

Set this = 0 and find x:

0 = 6x -6

x = 1

The value of y when x=1 in the original equation is:

f(1) = 3(1-1)^2 + 4

y = 4

The vertex is (1,4)

Graph:

You can use DESMOS to plot the function. The result is attached. Look for the vertex and read the coordinates. (1,4) seems to work.

6 0

3 years ago

In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz

BabaBlast [244]

Answer:

C (2, -1)

Step-by-step explanation:

C has the same x coordinate as A = 2

that eliminates A and B.

and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).

so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.

but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.

so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.

the y difference A to B is 2 - -6 = 8

the 5/3 split of 8 units is actually 5 and 3.

so, the y coordinate of D is -6 + 5 = -1

and C must have the same y coordinate.

therefore, it is proven that answer C (2, -1) is the right answer.

4 0

3 years ago

An experiment is given together with an event. find the (modeled) probability of each event, assuming that the coins are disting

tamaranim1 [39]

Saying that the result is "at most" one tail means that there can be zero or one tail.

Consider the sample space S, which is the set of all possible outcomes: S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}. Therefore: S = 8.

Now, consider the event space E, which is the set of successful outcomes: E = {TTT, TTH, THT, HTT}. Therefore: E = 4.

The probability will be:
p = E / S = 4 / 8 = 0.5

Hence, when three coins are tossed the probability that the result is at most one tail is 50%.

7 0

3 years ago