Apolitical interest group wants to determine what fraction p ∈ (0, 1) of the population intends to vote for candidate a in the next election. 1000 randomly chosen individuals are polled. 457 of these indicate that they intend to vote for candidate a. find the 95% confidence interval for the true fraction p.

95% confidence interval for the true fraction p is (0.426, 0.488)

Step-by-step explanation:

Confidence Interval can be calculated using p±ME where

and margin of error (ME) around the mean can be found using the formula

ME= where

then ME= ≈ 0.031

Then 95% confidence interval would be 0.457±0.031 or (0.426, 0.488)

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.