Answer:
0.451751 is the proportion of variability of Gini Coefficient explained by our least squares lines
Step-by-step explanation:
Given
To predict: Gini by year
Required
Interpret the R squared
In statistics, r squared measures the extent to which the variance of one variable explains the variance of the other variable.
In this question, the variable to predict is Gini:
From the list of options, (c) is correct
The answer is
w = 6 in
l = 16 in
h = 12 in
The volume of a rectangular prism with length l, width w, and height h is:
V = l * w * h
V = 1152 in³
After some internet research, I found out that:
l = 2w + 4
h = 18 - w
So,
V = l * w * h
1152 = (2w + 4) * w * (18 - w)
Multiply the first two factors:
1152 = (2w² + 4w) * (18 - w)
Multiply two remaining factors:
1152 = 36w² + 72w - 2 w³ - 4w²
Rearrange:
-2w³ + 36w² - 4w² + 72w = 1152
-2w³ + 32w² + 72w = 1152
-2w³ + 32w² + 72w - 1152 = 0
Divide all by 2:
-w³ + 16w² + 36w - 576 = 0
Multiply by (-1):
w³ - 16w² - 36w + 576 = 0
Rearrange:
(w³ - 36w) - (16w² - 576) = 0
Factor:
w * w² - w * 36 - (16 * w² - 16 * 36) = 0
w(w² - 36) - 16(w² - 36) = 0
(w - 16)(w² - 36) = 0
(w - 16)(w² - 6²) = 0
(w - 16)(w - 6)(w + 6) = 0
So, w - 16 = 0, or w - 6 = 0, or w + 6 = 0.
In other words: w = 16, or w = 6, or w = -6.
Width cannot be negative, so w ≠ -6.
If w = 16, then l = 2 * 16 + 4 = 32 + 4 = 36 and h = 18 - 16 = 2
But, since the height must be greater than the width (h > w), w ≠ 16
If w = 6, then l = 2 * 6 + 4 = 12 + 4 = 16 and h = 18 - 6 = 12.
Thus:
w = 6 in
l = 16 in
h = 12 in
Answer:
Step-by-step explanation:
Let's solve the given system of linear equations:
a+b = 13
0.750 + 1.15b = 12.55
Let's eliminate b. To do this, solve the first equation for b, obtaining b = 13 - a, and then substitute 13 - a for b in the second equation:
0.750 + 1.15(13 - a) = 12.55.
Next, subtract 0.750 from both sides, obtaining: 1.15(13 - a) = 11.8
Dividing both sides by 1.15 yields 13 - a = 10.26
Then a = 13 - 10.26, or a = 2.74.
Since a + b = 13, b = 13 - 2.74, or 10.26
This person bought 2.74 pounds of apples and 10.26 pounds of bananas.
