Answer:
0.11
Step-by-step explanation:
Probability that house sale will increase = P(A) = 0.25
Probability that interest rate on house loans will go up = P(B) = 0.74
Probability that either house sales will go up or interest rates will go up = P(A or B ) = 0.89
We have to find the probability that neither house sales nor interest rates will increase. This event is the compliment of the event that either house sales will go up or interest rates will go up.
i.e.
Probability that neither house sales nor interest rates will increase = ![P(A \cup B)^{c}](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%5E%7Bc%7D)
![P(A\cup B)^{c} = 1 - P(A \cup B)](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%29%5E%7Bc%7D%20%3D%201%20-%20P%28A%20%5Ccup%20B%29)
Using the value of P(A U B), we get:
![P(A\cup B)^{c} = 1 - 0.89\\\\ P(A\cup B)^{c} = 0.11](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%29%5E%7Bc%7D%20%3D%201%20-%200.89%5C%5C%5C%5C%20P%28A%5Ccup%20B%29%5E%7Bc%7D%20%3D%200.11)
The probability that neither house sales nor interest rates will increase during the next 6 months is 0.11
Ok so
parabola standard form is
y=ax^2+bx+c
if you have the points
(-2,18)
(0,4)
(4,24)
sub points to find a,b and c
(-2,18)
sub -2 for x and sub 18 for y
18=a(-2)^2+b(-2)+c
18=4a-2b+c
(0,4)
sub 0 for x, nice a, an b cancel
4=a(0)^2+b(0)+c
4=0+0+c
4=c
we can sub that back later
(4,24)
24=a(4)^2+b(4)+c
24=16a+4b+c
we have
18=4a-2b+c
c=4
24=16a+4b+c
sub 4 for c
18=4a-2b+4
24=16a+4b+4
minus 4 from both sides
14=4a-2b
20=16a+4b
simlify all equations
7=2a-b
5=4a+b
add to solve for 6a
12=6a+0b
12=6a
divide both sides by 6
2=a
sub back
7=2a-b
7=2(2)-b
7=4-b
-3=b
equation is
y=2x^2-3x+4
Diameter of cone = d = 4mm
So,
Radius of cone = r = 2mm
Slant Height = l = 6mm
Surface Area = A = ?
The formula for the surface area of cone is:
![A= \pi r(r+l)](https://tex.z-dn.net/?f=A%3D%20%5Cpi%20r%28r%2Bl%29)
Using the values, we get:
![A= \pi (2)(2+6)=16 \pi](https://tex.z-dn.net/?f=A%3D%20%5Cpi%20%282%29%282%2B6%29%3D16%20%5Cpi%20)
mm²
Therefore, the surface area of the cone with diameter 4mm and slant height of 6mm will be 16π mm²
For this case we must resolve the following inequality:
![2 (4 + 2x)> 5x + 5](https://tex.z-dn.net/?f=2%20%284%20%2B%202x%29%3E%205x%20%2B%205)
Applying distributive property on the left side of inequality we have:
![8 + 4x> 5x + 5](https://tex.z-dn.net/?f=8%20%2B%204x%3E%205x%20%2B%205)
Subtracting 5 from both sides of the inequality:
![8-5 + 4x> 5x\\3 + 4x> 5x](https://tex.z-dn.net/?f=8-5%20%2B%204x%3E%205x%5C%5C3%20%2B%204x%3E%205x)
Subtracting 4x from both sides of the inequality:
![3> 5x-4x\\3> x](https://tex.z-dn.net/?f=3%3E%205x-4x%5C%5C3%3E%20x)
Thus, the result is ![x](https://tex.z-dn.net/?f=x%20%3C3.)
Answer:
![x](https://tex.z-dn.net/?f=x%20%3C3)