Answer:
The estimate is
Step-by-step explanation:
From the question we are told that
The sample mean is 
The sample size is n = 24
The standard deviation is 
Given that the confidence level is 90% the level of significance is mathematically represented as
Next we obtain the critical value of 
from the normal distribution table.The value is
The reason we are obtaining critical value of instead of 
is because
represents the area under the normal curve where the confidence level interval ( 
) did not cover which include both the left and right tail while
is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
substituting values
The estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as
substituting values
<h3>
Answer: 51 square inches</h3>
=======================================================
Explanation:
There are a few ways to do this. One way is to divide the figure as shown in the diagram below. I divided it into a rectangle and a triangle. Find the area of the rectangle and triangle, then add up those areas to get the final answer.
A = area of rectangle
A = length*width
A = 7*6
A = 42
B = area of triangle
B = 0.5*base*height
B = 0.5*(6-3)*(13-7)
B = 0.5*3*6
B = 1.5*6
B = 9
C = total area
C = A+B
C = 42+9
C = 51 square inches
![\bf \begin{array}{clclll} -6&+&6\sqrt{3}\ i\\ \uparrow &&\uparrow \\ a&&b \end{array}\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bclclll%7D%0A-6%26%2B%266%5Csqrt%7B3%7D%5C%20i%5C%5C%0A%5Cuparrow%20%26%26%5Cuparrow%20%5C%5C%0Aa%26%26b%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ar%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%0A%5Ctheta%20%3Dtan%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7Bb%7D%7Ba%7D%20%5Cright%29%0A%5Cend%7Bcases%7D%5Cqquad%20r%5Bcos%28%5Ctheta%20%29%2Bi%5C%20sin%28%5Ctheta%20%29%5D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.
thus
![\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]](https://tex.z-dn.net/?f=%5Cbf%2012%5Cleft%5Bcos%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%2Bi%5C%20sin%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%5Cright%5D)
Answer:
number 1. is C and number 2. is A
Answer:
7 gallons per minute
Step-by-step explanation:
315/45 = 7
