Use the drop-downs to choose the value for the

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

4 0

Answer:

a=-18

b=7

c=27

Step-by-step explanation:

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Write the general equation for the circle that passes through the points (-5,0), (0.4), and (2,4).

Advocard [28]

Answer:

(x-1)^2+(y+19/8)^2=2665/64

Step-by-step explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2

Substituting the values of the 3 given points:

(-5 - h)^2 + (0 - k)^2 = r^2

(0 - h)^2 + (4 - k)^2 = r^2

(2 - h)^2 + (4 -k)^2 = r^2

Subtracting the second equation from the first:

(-5-h)^2 - h^2 + k^2 - (4 - k)^2 = 0

25 + 10h + h^2 - h^2 + k^2 - 16 + 8k - k^2 = 0

10h + 8k = -9 ------------ (A).

Subtract the third equation for the second:

h^2 - (2 - h)^2 + 0 = 0

h^2 - 4 + 4h - h^2 = 0

4h = 4

h = 1.

Substituting for h in equation A:

10 + 8k = -9

8k = -19

k = -19/8

So r^2 = (-5-1)^2 + (0 + 19/8)^2 =

36 + 361/ 64

= 2665/64

7 0

3 years ago

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of peopl

Sholpan [36]

Answer:

1.) .399

2.) {.369, .429}

Step-by-step explanation:

The proportion of criminals in this sample that were caught was $\frac{286}{716}$ =.39944, .399 rounded to three decimal places.

To construct the confidence interval, you need three pieces of information: the statistic, the critical value, and the standard error.

The statistic is given in the first part of the problem with the proportion of criminals in the sample that were caught was .399.

The critical value, we are told, is the z equivalent of 90%, or 1.645. You can find this value using a z table or with the inverse normal function on a calculator.

Finally, we need the standard error. The formula for standard error for a proportion with a single population is $\sqrt{\frac{(proportion)(1-proportion)}{sample size} }$ so in this situation it would be $\sqrt{\frac{(.399)(.601)}{716} }$ =.0183.