Answer:
<4 and <12
Step-by-step explanation:
When looking at Corresponding Angles, they need to be on opposite sides of a transversal. In this case, the answer is <4 and <12
Question:
Find the constant of proportionality k. Then write an equation for the relationship between x and y
Answer:
(a) 
(b) 
Step-by-step explanation:
Given
Solving (a): The constant of proportionality:
Pick any two corresponding x and y values
The constant of proportionality k is:
Solving (b): The equation
In (a), we have:
k can also be expressed as:
Substitute values for x1, y1 and k
Cross multiply:
Open bracket
Add 10 to both sides
Answer:. This would be 0.81^20 for none of the 19=0.0148
Step-by-step explanation:With a tree diagram, there are two possibilities, one is ND from 1 D from 2, with probability (5/8)(2/5)=(1/4) and the other is (3/8)(3/5)=9/40 That would be 19/40 for the answer.
3. Poisson parameter lambda=5
for P(0), it is e^(-5)(5^0)/0! or e^(-5)=0.0067
for P(1), it is e^(-5)(5^1)/1! or 5e(-5)
The total probability is 6e^-5 or 0.0404
4. the mean is 1000 hours, so lambda is the reciprocal or 1/1000
the probability it will last <800 hours is 1-e^(-800*1/1000) or 1-e^(-.8)=0.5507
5. assume p=0.4 since it ca't be 4
sd is sqrt (np*(1-p))=sqrt (6*0.6=sqrt(3.6)=1.90
The length of the rectangle is based on its width, so let's call width w and put the length in terms of the width. We are told that the width is 45 less than 4 times the width, so the length is 4w - 45. Area is found by multiplying length times width and we are given the area as 3325. So we will set up length times width and solve for w, which we will then use to solve for l. 3325 = (4w - 45)(w). Multiplying out we have 
. Move the constant over by subtraction and then we will have a quadratic that can be factored to solve for w. 
. We would put that through the quadratic formula to solve for w. When we do that we get that w = 35 and w = -23.75. The 2 things in math that will never EVER be negative is time and distance/length, so -23.75 is out. That means that the width is 35. The length is 4(35) - 45 which is 95. The dimensions of your rectangle are length is 95 and width is 35. There you go!
