Answer:
Step 1 t = - 2.552
Step 2 t = 1.356
Step 3 two values t = - 2.12 on the left and t = 2.12 on the right
Step-by-step explanation:
Normal Distribution
size sample < 30
Table to use t-student table
a) left-tailed test α = 0,01 n = 19 gl = 19 -1 gl = 18
Directly from t table
t = - 2.552
b) Right-tailed test α = 0,1 n = 13 gl = 13 - 1 gl =12
Directly from t table
t = 1.356
c) Two-tailed test α = 0,05 but two tails means we use α/2
α/2 = 0,025 n = 17 gl = n - 1 gl = 17 -1 gl = 16
From table:
t = - 2.12 on the left tail and t = 2.12 on the right tail
Determine the quadrant adding or subtracting periods -10pi/3+2pi=-4pi/3+2pi=2pi/3
which is the second quadrant because
first quadrant is between 0 and pi/2
second quadrant is between pi/2 and pi
third quadrant is between pi and 3pi/2
fourth is between 3pi/2 and 2pi
now we find the terminal angle since it is the second quadrant we use theta'=pi-theta=pi-2pi/3=pi/3
sin(pi/3)=sqrt(3)/2 sin is positive in the second quadrant
cos(pi/3)=-0.5 cos is negative in the second quadrant
tan(pi/3)=sin(pi/3)/cos(pi/3)=-sqrt(3) tan is negative in the second quadrant
Answer:
The three zeros of the original function f(x) are {-1/2, -3, -5}.
Step-by-step explanation:
"Synthetic division" is the perfect tool for approaching this problem. Long div. would also "work."
Use -5 as the first divisor in synthetic division:
------------------------
-5 2 17 38 15
-10 -35 -15
--------------------------
2 7 3 0
Note that there's no remainder here. That tells us that -5 is indeed a zero of the given function. We can apply synthetic div. again to the remaining three coefficients, as follows:
-------------
-3 2 7 3
-6 -3
-----------------
2 1 0
Note that the '3' in 2 7 3 tells me that -3, 3, -1 or 1 may be an additional zero. As luck would have it, using -3 as a divisor (see above) results in no remainder, confirming that -3 is the second zero of the original function.
That leaves the coefficients 2 1. This corresponds to 2x + 1 = 0, which is easily solved for x:
If 2x + 1 = 0, then 2x = -1, and x = -1/2.
Thus, the three zeros of the original function f(x) are {-1/2, -3, -5}.
X equals 15 because 90-30 equals 60 divide by 4 equals 15
