Answer:
(x + 1) (x^2 + 5)
Step-by-step explanation:
Simplify the following:
x^3 + x^2 + 5 x + 5
Factor terms by grouping. x^3 + x^2 + 5 x + 5 = (x^3 + x^2) + (5 x + 5) = x^2 (x + 1) + 5 (x + 1):
x^2 (x + 1) + 5 (x + 1)
Factor x + 1 from x^2 (x + 1) + 5 (x + 1):
Answer: (x + 1) (x^2 + 5)
Answer
a) 0.035
b) 0.14
Step-by-step explanation:
Let J be the event that Joe has the disease.
Let The be the event that Joe's test is positive.
Pr(J) = 1/2%
= 0.5/100 = 0.005
Pr(J') = 99.5%
= 0.995
Pr(T|J) = 98%
= 0.98 since 2% if the time if a person having the disease is omitted ("false negative ")
Pr(T|J') = 3% = 0.03 since there are 3 false positives
a( Pr(T) = us the probability that Joe tests positive
Pr(T) = Pr(T|J)* P(J) + Pr(T|J')*Pr(J')
= (0.98*0.005) + (0.03*0.995)
= 0.00049 + 0.02985
= 0.03475
= 0.035
b) Pr( J|T) = Pr(JnT) / Pr(T)
= (Pr(T|J)*Pr(J)) / Pr(T)
= (0.005*0.98) / 0.035
= 0.0049/0.035
= 0.14
1. =4/16 which in simplified terms = 1/4
2. = 37/99 (find the lowest common denominator which is 99 then multiply them, then combine fractions then subtract them)
3. 2/25
4. 12/18 which simplified is 2/3
5. 5/15 which simplified = 1/3
Hope you understand that:)
Using factorization method;
x²+13x+40=0
x²+13+40
Find two numbers that you can add together to give the co-efficient of variable x. (I.e 13 for this question). Also, you'll find two numbers that you can multiply with each other to give you the whole number as an answer. (I.e 40 in this question). The two numbers must be the same (i.e the two numbers that will be added to give the co-efficient of x and the two numbers that will be multiplied to give the whole number must be the same two).
The two numbers are +5 and +8
The equation will therefore be = x²+5x+8x+40
You'll then factorize (I.e use a common factor of both values to bracket them)
x(x+5)+8(x+5)
(x+8)(x+5)
x is therefore (x+8=0) or (x+5=0)
x=(x=0-8) or (x=0-5)
x= -8 or x= -5
Answer:
Instantaneous Velocity at t = 1 is 20 feet per second
Step-by-step explanation:
We are given he following information in the question:
![y(t)=43t-23t^{2}](https://tex.z-dn.net/?f=y%28t%29%3D43t-23t%5E%7B2%7D)
B) Instantaneous Velocity at t = 1
![y(1) = 43(1)-23(1)^2 = 20](https://tex.z-dn.net/?f=y%281%29%20%3D%2043%281%29-23%281%29%5E2%20%3D%2020)
A) Formula:
Average velocity =
![\displaystyle\frac{\text{Displacement}}{\text{Time}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B%5Ctext%7BDisplacement%7D%7D%7B%5Ctext%7BTime%7D%7D)
1) 0.01
![y(1 + 0.01)=y(1.01) = 43(1.01)-23(1.01)^{2} = 19.9677\\\\\text{Average Velocity} = \dfrac{y(1.01)-y(1)}{1.01-1} =\dfrac{19.9677-20}{1.01-1}= \dfrac{-0.0323}{0.01} = -3.230000 \text{feet per second}](https://tex.z-dn.net/?f=y%281%20%2B%200.01%29%3Dy%281.01%29%20%3D%2043%281.01%29-23%281.01%29%5E%7B2%7D%20%3D%2019.9677%5C%5C%5C%5C%5Ctext%7BAverage%20Velocity%7D%20%3D%20%5Cdfrac%7By%281.01%29-y%281%29%7D%7B1.01-1%7D%20%3D%5Cdfrac%7B19.9677-20%7D%7B1.01-1%7D%3D%20%5Cdfrac%7B-0.0323%7D%7B0.01%7D%20%3D%20-3.230000%20%5Ctext%7Bfeet%20per%20second%7D)
2) 0.005 s
![y(1 + 0.005)=y(1.005) = 43(1.005)-23(1.005)^{2} = 19.984425\\\\\text{Average Velocity} = \dfrac{y(1.005)-y(1)}{1.005-1} =\dfrac{19.984425-20}{1.005-1} = -3.1150000 \text{feet per second}](https://tex.z-dn.net/?f=y%281%20%2B%200.005%29%3Dy%281.005%29%20%3D%2043%281.005%29-23%281.005%29%5E%7B2%7D%20%3D%2019.984425%5C%5C%5C%5C%5Ctext%7BAverage%20Velocity%7D%20%3D%20%5Cdfrac%7By%281.005%29-y%281%29%7D%7B1.005-1%7D%20%3D%5Cdfrac%7B19.984425-20%7D%7B1.005-1%7D%20%3D%20-3.1150000%20%5Ctext%7Bfeet%20per%20second%7D)
3) 0.002 s
![y(1 + 0.002)=y(1.002) = 43(1.002)-23(1.002)^{2} = 19.993908\\\\\text{Average Velocity} = \dfrac{y(1.002)-y(1)}{1.002-1} =\dfrac{19.993908-20}{1.002-1} = -3.0460000 \text{feet per second}](https://tex.z-dn.net/?f=y%281%20%2B%200.002%29%3Dy%281.002%29%20%3D%2043%281.002%29-23%281.002%29%5E%7B2%7D%20%3D%2019.993908%5C%5C%5C%5C%5Ctext%7BAverage%20Velocity%7D%20%3D%20%5Cdfrac%7By%281.002%29-y%281%29%7D%7B1.002-1%7D%20%3D%5Cdfrac%7B19.993908-20%7D%7B1.002-1%7D%20%3D%20-3.0460000%20%5Ctext%7Bfeet%20per%20second%7D)
4) 0.001 s
![y(1 + 0.001)=y(1.001) = 43(1.001)-23(1.001)^{2} = 19.996977\\\\\text{Average Velocity} = \dfrac{y(1.001)-y(1)}{1.001-1} =\frac{19.996977-20}{1.001-1} = -3.0230000 \text{feet per second}](https://tex.z-dn.net/?f=y%281%20%2B%200.001%29%3Dy%281.001%29%20%3D%2043%281.001%29-23%281.001%29%5E%7B2%7D%20%3D%2019.996977%5C%5C%5C%5C%5Ctext%7BAverage%20Velocity%7D%20%3D%20%5Cdfrac%7By%281.001%29-y%281%29%7D%7B1.001-1%7D%20%3D%5Cfrac%7B19.996977-20%7D%7B1.001-1%7D%20%3D%20-3.0230000%20%5Ctext%7Bfeet%20per%20second%7D)