Let
. Then
, and differentiating both sides with respect to
gives
Now, when
, you get
You have
, so
and
. So
Answer:
- 8 3/4
- 2, 3
- 4 1/2, 11 1/4
- 9 3/4, 16 1/4
- Y/B = 2/3
Step-by-step explanation:
<h3>a)</h3>
The first line is simply the sum of the two given numbers.
3 1/2 +5 1/4 = (3+5) +(2/4+1/4) = 8 3/4
__
To find values on the remaining lines, it is convenient to find the ratios of the numbers involved. The ratio of yellow to blue is ...
Y/B = (3 1/2)/(5 1/4) = (7/2)/(21/4) = (7/2)(4/21) = 2/3
Then ...
Y : B : total = 2 : 3 : 5
This tells you the numbers on the second line are ...
Y = 2; B = 3
__
The value for B on the third line is the basic ratio number multiplied by (6 3/4)/3 = 2 1/4. Then the other two numbers are ...
Y = 2(2 1/4) = 4 1/2
total = 5(2 1/4) = 11 1/4
__
The value for Y on the fourth line is the basic ratio number multiplied by (6 1/2)/2 = 3 1/4. Then the other two numbers are ...
B = 3(3 1/4) = 9 3/4
total = 5(3 1/4) = 16 1/4
_____
<h3>b)</h3>
The equation is the one we used to find the values on the second line:
Y/B = 2/3
Answer:
The data is skewed to the bottom and contains an outlier.
Step-by-step explanation:
1. Test for outlier
An outlier is a point that is more than 1.5IQR below Q1 or above Q3.
IQR = Q3 - Q1 = 74 - 51 = 23
1.5 IQR = 1.5 × 23 = 34.5
51 - 15 = 36 > 1.5IQR
The point at 15 is an outlier.
2. Test for normal distribution
The median is not in the middle of the box.
Rather, it cuts the box into two unequal parts, so the data does not have a normal distribution.
3. Test for skewness
The longer part is to the left of the median, so the data is skewed left.
The lengths of the rectangles are 7 and 12 respectively. Form the ratio 7/12. The widths of the rects. are x and 5 respectively. Form the ratio x/5. Now equate these two ratios:
7 x
--- = ---
12 5
Solve this for x. One way to do this would be to cross-multiply, obtaining 12x = 35, and solving this result for x. x will be a fraction. Write the numerator and denominator in the boxes given.
Answer:
19.64
the permieter is 5 so 5/2=2.5 2.5x2.5=6.25 6.25x3.14=19.64
