Answer:
XZ ≈ 14.4 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos29° =  =
 =  =
 = 
Multiply both sides by XZ
XZ × cos29° = 12.6 ( divide both sides by cos29° )
XZ =  ≈ 14. 4 ( to 3 sig. figs )
 ≈ 14. 4 ( to 3 sig. figs )
 
        
             
        
        
        
Answer:
x = -3
Step-by-step explanation:
 
        
             
        
        
        
Differentiate the given solution:

Substitute  and
 and  into the ODE:
 into the ODE:

and it's easy to see the left side indeed reduces to 0.
 
        
             
        
        
        
As stated in (i), the equation of the line is: ln y = -0.015x + .26
(By the way, I checked your answers for parts (i) and (ii) and they are both correct)
(iii)
Plug in (1.1) for y and solve:
ln (1.1) = -0.015x + .26
0.095 = -0.015x + .26
-0.165 = - 0.015x
 10.979 = x
Answer: x = 10.979 
        
             
        
        
        
Answer:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.