Answer:
Point (1,8)
Step-by-step explanation:
We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.
When a point divides any segment internally in the ratio m:n, the formula is:
![[x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2Cy%3D%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5D)
Let us substitute coordinates of point P and Q as:
,
![[x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B%283%2A4%29%2B%281%2A-8%29%7D%7B3%2B1%7D%2Cy%3D%5Cfrac%7B%283%2A12%29%2B%281%2A-4%29%7D%7B3%2B1%7D%5D)
![[x=\frac{12-8}{4},y=\frac{36-4}{4}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B12-8%7D%7B4%7D%2Cy%3D%5Cfrac%7B36-4%7D%7B4%7D%5D)
![[x=\frac{4}{4},y=\frac{32}{4}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B4%7D%7B4%7D%2Cy%3D%5Cfrac%7B32%7D%7B4%7D%5D)
![[x=1,y=8]](https://tex.z-dn.net/?f=%5Bx%3D1%2Cy%3D8%5D)
Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.
Answer:
<u>The probability that both companies become profitable is 0.03 or 3%.</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Probability of biotechnology start-up company of becoming profitable = 0.2
Probability of information technology start-up company of becoming profitable = 0.15
2. Assume the companies function independently What is the probability that both companies become profitable?
We will answer this question, assuming these are independent events, this way:
Probability that both companies become profitable = Probability of biotechnology start-up company of becoming profitable * Probability of information technology start-up company of becoming profitable
Replacing with the values given, we have:
Probability that both companies become profitable = 0.2 * 0.15 = 0.03
<u>The probability that both companies become profitable is 0.03 or 3%.</u>
Answer:
x = 4/9 + sqrt(2)/3 or x = 4/9 - sqrt(2)/3
Step-by-step explanation:
Solve for x over the real numbers:
(9 x - 4)^2 = 18
Take the square root of both sides:
9 x - 4 = 3 sqrt(2) or 9 x - 4 = -3 sqrt(2)
Add 4 to both sides:
9 x = 4 + 3 sqrt(2) or 9 x - 4 = -3 sqrt(2)
Divide both sides by 9:
x = 4/9 + sqrt(2)/3 or 9 x - 4 = -3 sqrt(2)
Add 4 to both sides:
x = 4/9 + sqrt(2)/3 or 9 x = 4 - 3 sqrt(2)
Divide both sides by 9:
Answer: x = 4/9 + sqrt(2)/3 or x = 4/9 - sqrt(2)/3
It would be C - You round up when the second number is past 4 :)
And tenth is talking about decimals.
