Answer:
The 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).
Step-by-step explanation:
In a random sample of 300 boards the number of boards that fall outside the specification is 12.
Compute the sample proportion of boards that fall outside the specification in this sample as follows:
The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:
The critical value of <em>z</em> for 95% confidence level is,
*Use a <em>z</em>-table.
Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:
Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).
Given:
The figure of a rhombus QRST.
To find:
A. The value of x.
B. The measure of angle RQP.
Solution:
A. We need to find the value of x.
We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.
[Right angle]
Divide both sides by 5.
Therefore, the value of x is 15.
B. We need to find the measure of angle RQP.
From the given figure, it is clear that
Putting , we get
Therefore, the measure of angle RQP is 33 degrees.
Answer:
So minute hand will rotate 
in half an hour
Step-by-step explanation:
In one hour minute hand of clock rotate about 360°
So in half an hour minute hand clock rotate 
We have to find how many minute hand rotate in radian
For conversion of degree to radian we have to multiply with 
So 
So minute hand will rotate in half an hour
Answer:
-19
Step-by-step explanation:
It is a non repeating decimal
Answer:
Product (multiplication) of 2a+3b-c and 2a+3b-c is −2ac+2a+6b−c.
Explanation:
2a+3b−c(2)a+3b−c
= 2a+3b+−2ac+3b+−c
Combine Like Terms:
= 2a+3b+−2ac+3b+−c
= (−2ac)+(2a)+(3b+3b)+(−c)
= −2ac+2a+6b+−c
