Let the area of the original rectangle be A₁.
A₁ = (12 ft)(8 feet) = 96 ft²
To determine the area of the reduced triangle, let's compute the new dimensions first.
Length = 12 ft * 3/4 - 9 ft
Width = 8 ft *3/4 = 6 ft
Thus, the area of the new rectangle denoted as A₂ is
A₂ = (9 ft)(6 ft) = 54 ft
The ratio of the areas are:
A₂/A₁ = 54/96 = 9/16
The ratio of the sides are given to be 3/4.
Finally the ratios of the area to side would be:
Ratio = 9/16 ÷ 3/4 = 3/4
Therefore, the ratio of the areas is 3/4 of the ratio of the corresponding sides.
Answer:
The standard deviation for the income of super shoppers is 76.12.
Step-by-step explanation:
The formula to compute the standard deviation for the grouped data probability distribution is:
![\sigma=\sqrt{\sum [(x-\mu)^{2}\cdot P(x)]}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Csum%20%5B%28x-%5Cmu%29%5E%7B2%7D%5Ccdot%20P%28x%29%5D%7D)
Here,
<em>x</em> = midpoints
Consider the Excel table attached below.
The mean is:
Compute the standard deviation as follows:
Thus, the standard deviation for the income of super shoppers is 76.12.
Answer:
To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2.
The picture below shows a dilation with a scale factor of 2. This means that the image, A', is twice as large as the pre-image A. Like other transformations, prime notation is used to distinguish the image fromthe pre-image.
Step-by-step explanation:
ur welcome
Answer:
Step-by-step explanation:
5x+20 = 0
5X= -20
X= -20/5 = -4
8(4n+3) = 32n+24 =0
32n = -24
n = -24/32 = -3/4
12n-6=0
12n =6
n = 6/12 = 1/2
9(2x+9)
18x+81 =0
18x= -81
x= -81/18 = -9/2= -4.5
36+9y=0
36=-9y
36/-9 = y = -4
7(n-3) = 0
7n-21=0
7n = 21
n = 21/7
n=3
21+15a = 0
21= -15a
a= 21/-15 = 7/-5 = -1.4
32x-12x=0
20x=0
x=0/20 = 0
n-4-9=0
n-13=0
n=13
-3x-9+15x=0
-3x+15x-9 =0
12x-9=0
12x=9
x=9/12 = 3/4 = 0.75
-16N-14N=0
-30n=0
n=0/-30 =0
-10-90x-6x-10x²-2
-10-2-96x-10x²
-12-96x-10x²
10x²+96x+12
x= -b±√b²-4(a)(c)/2a
{-96±√96²-4(10)(12)}/2(10)
{-96±√(9216-480)}/20
-96±√8736/20
-96±(93.4665715644)/20
-96+93.4665715644/20 -96-93.4665715644/20
-2.5334284356/20 -189.466571564/20
-0.12667142178≅ -0.13 -9.4733285782≅ -9.47
-0.13 -9.47
-5(9n+9) =0
-45n-45 =0
-45n = 45
n = 45/-45 =-1
-5n+3(6+7n)
-5n+18+21n=0
-5n+21n+18 =0
16n+18 =0
16n = -18
n = -18/16 = -9/8 = -1.125
-4+7(1-3n)=0
-4+7-21n=0
3-21n=0
3=21n
3/21=n = 1/7
3n-(2n-8)
3n-2n+8=0
n+8=0
n=-8
