OK, so for this equation, your goal is to get the d, and ONLY the d, on one side of the equation. So, to start out, you need to multiply the entire equation, meaning both sides, by 8 because we are trying to get rid of those pesky fractions.
8(1/8(3d-2)=1/4(d+5))
The equation then turns into this because the 8 and 4 cancelled out with the 8.
1(3d-2)=2(d+5)
Now, we need to distribute the left over numbers into the parenthesis.
3d-2=2d+10
And finally, we need to get the d's on one side, and the numbers on the other, so we subtract 2d from both sides and add the 2 to both sides. They then cancel out to make
d=12
Hope it helps! :)
Answer:
a) Hyper-geometric distribution
b1) P(X=2) = 0.424
b2) P(X>2) = 0.152
C1) Mean of X = 1.67
C2) Standard Deviation of X = 0.65
Step-by-step explanation:
b1) P(X = 2) = (5C2 * 7C2)/(12C4) = (10 * 21)/(495) = 210/495
P(X=2) = 0.424
b2) P(X>2) = 1 - P(X≤2) = 1 - [P(X=0) + P(X=1) + P(X=2)]
P(X=0) = (7C4)/(12C4) = 35/495 = 0.071
P(X=1) = (5C1 * 7C3)/(12C4) = (5 * 35)/(495) = 175/495 = 0.354
P(X=2) = 0.424
P(X>2) = 1 - P(X≤2) = 1 - [0.424 + 0.071 + 0.354]
P(X>2) = 0.152
C1) Mean of X = nk/N
k = number of 3-megapixel cameras = 5
n = number of selected cameras = 4
N = Total number of cameras = 12
Mean of X = 5*4/12
Mean of X = 1.67
C2) Standard Deviation of X
Standard deviation of X=(nk/N*(1-k/N)*(N-n)/(N-1))1/2
Standard Deviation of X=(4*(5/20)*(1-5/12)*((12-4)/(12-1))^1/2 =0.65
Standard Deviation of X = 0.65
The Mean would increase to 82.17 or a total increase of .17
You have 99 students and the avg is 82, therefore we can multiply 99*82 to get our total points
99*82=8118
We add a single score of 99 to our total points 8118+99= 8217
Then we add the student to the total number of students bringing it to 100 and divide our new total by the our new number of students.
8217/100 = 82.17
TRUE
To visualize this property, you can draw two parallel lines and cross them by a third line.
Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines. You can see that those (corresponding) angles are equal if and only if the lines are parallel.
