Answer:
1. 14 cm
2. 20.4 cm
3. 24 - w
Step-by-step explanation:
Let's start with the last question, as it'll make answering the previous two a lot easier. In the 3rd question, we are asked to create a formula to find the length of a given rectangle, using its given perimeter of 48 centimeters and width of 
centimeters.
Therefore, let the length of the rectangle be 
, we can construct the following equation:
Now we have a formula that defines our length, if given the width of the rectangle. The only thing from here on out is to substitute the given widths to the formula we just found.
1. 
, therefore, 
.
2. 
, therefore, 
.
Answer:
v<3
Step-by-step explanation:
From the equation we see that the center of the circle is at (-2,3) and the radius is 9.
So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...
d^2=(8--2)^2+(4-3)^2 and d^2=r^2=81 so
81=10^2+1^2
81=101 which is not true...
So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.
Thus the point lies outside or on the exterior of the circle...
Answer:
The probability that a family spends less than $410 per month
P( X < 410) = 0.1151
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given mean of the population = 500 </em>
<em>Given standard deviation of the Population = 75</em>
Let 'X' be the variable in normal distribution
<em>Given X = $410</em>
<em></em>
<em></em>
<u><em>Step(ii):-</em></u>
The probability that a family spends less than $410 per month
P( X < 410) = P( Z < - 1.2 )
= 0.5 - A( -1.2)
= 0.5 - A(1.2)
= 0.5 - 0.3849 ( ∵from normal table)
= 0.1151
<u>Final answer:-</u>
The probability that a family spends less than $410 per month
P( X < 410) = 0.1151
