Answer:
x = - 1, x = 1, x = 2
Step-by-step explanation:
The coefficients of the polynomial sum to zero, that is
- 1 + 2 + 1 - 2 = 0
This indicates that x = 1 is a zero
let x = - 1, then
- (- 1)³ + 2(- 1)² + (- 1) - 2 = 1 + 2 - 1 - 2 = 0
Thus x = - 1 is a zero
let x = 2
- (2)³ + 2(2)² + 2 - 2 = - 8 + 8 + 2 - 2 = 0
Thus x = 2 is a zero
The 3 zeros are x = - 1, x = 1, x = 2
Let events
A=Nathan has allergy
~A=Nathan does not have allergy
T=Nathan tests positive
~T=Nathan does not test positive
We are given
P(A)=0.75 [ probability that Nathan is allergic ]
P(T|A)=0.98 [probability of testing positive given Nathan is allergic to Penicillin]
We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)
From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
P(T n A) = 0.75*0.98 = 0.735
Hope this helps!!
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
Answer:
42 feet
Step-by-step explanation:
if each inch equals 6 feet, and if her drawing is 7 inches long, then 7×6 would equal the auctual length of the boat, which is 42 feet.
C) They solve the same number of problems per minute
172.5 Divided by 2
115 divided by 2
= 57.5
