So area is 168 sq ft
That means that length * width = 168 sq ft
Since length = 10 + 2 w
we get (10+2w)(w) = 168
Multiply it out and you get 2w^2 + 10w - 168 = 0
This is a quadratic equation. You can use the formula here, but i'll just tell you the answer
w = -12, or 7
since it can't equal -12 (ever heard of a barn with a length of -12?), you figure out the answer is 7.
If the width is 7, then the length is 10+2(7) = 24.
Have a nice day!
Answer:
The value of x is 108°
Step-by-step explanation:
Given interior angles of parallelogram are:

<u>The sum of interior angles of a parallelogram is 360°.</u>
We will use this information to find the value of x.
So adding up all the angles and putting the sum equal to 360 we get,


Taking LCM on left side of the equation, as it involves fraction

Multiplying both sides by 3

Dividing both sides by 10

Hence,
The value of x is 108°
Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is 
Step-by-step explanation:
From the question we are told that
The margin of error is
The confidence level is
%
Given that the confidence level is 95% the level of significance is mathematically represented as

%

Next we obtain the critical value of
from the normal distribution table , the values is 
The reason we are obtaining critical values 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 sample size
Now the sample size is mathematically represented as
![n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}](https://tex.z-dn.net/?f=n%20%20%3D%20%20%5Cfrac%7B%5BZ_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%5D%20%5E2%20%2A%20%20%5Csigma%20%5E2%7D%7BMOE%5E2%7D)
substituting values


Answer:
27 cm
Step-by-step explanation:
So the ratio you have is
width(x) : length (36)= 3:4
Divide 36 (length) by the ratio length. 36÷4=9
They are multiples of nine, so multiply the width by 9 to get the 3.
3×9=27
You have 27:36
If you want to check it, divide both by 9 and you get 3:4