Answer:
x = 9
Step-by-step explanation:
50+80+(6x-4)=180 (ANGLE SUM PROPERTY)
130 +(6x-4)=180
6x-4=180-130
6x-4=50
6x=50+4
x=54/6
x = 9
Step-by-step explanation:
Divide 180 by 3 = 60
Divide 150 by 2 = 75
The faster vehicle is truck and its speed is 75 mph
Answer:
a. [ 0.454,0.51]
b. 599.472 ~ 600
Step-by-step explanation:
a)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=410
Sample Size(n)=850
Sample proportion = x/n =0.482
Confidence Interval = [ 0.482 ±Z a/2 ( Sqrt ( 0.482*0.518) /850)]
= [ 0.482 - 1.645* Sqrt(0) , 0.482 + 1.65* Sqrt(0) ]
= [ 0.454,0.51]
b)
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Samle Proportion = 0.482
ME = 0.04
n = ( 1.96 / 0.04 )^2 * 0.482*0.518
= 599.472 ~ 600
now, for a rational expression, the domain, or "values that x can safely take", applies to the denominator NOT becoming 0, because if the denominator is 0, then the rational turns to
undefined.
now, what value of "x" makes this denominator turn to 0, let's check by setting it to 0 then.
![\bf 2-x^{12}=0\implies 2=x^{12}\implies \pm\sqrt[12]{2}=x\\\\ -------------------------------\\\\ \cfrac{x^2-9}{2-x^{12}}\qquad \boxed{x=\pm \sqrt[12]{2}}\qquad \cfrac{x^2-9}{2-(\pm\sqrt[12]{2})^{12}}\implies \cfrac{x^2-9}{2-\boxed{2}}\implies \stackrel{und efined}{\cfrac{x^2-9}{0}}](https://tex.z-dn.net/?f=%5Cbf%202-x%5E%7B12%7D%3D0%5Cimplies%202%3Dx%5E%7B12%7D%5Cimplies%20%5Cpm%5Csqrt%5B12%5D%7B2%7D%3Dx%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bx%5E2-9%7D%7B2-x%5E%7B12%7D%7D%5Cqquad%20%5Cboxed%7Bx%3D%5Cpm%20%5Csqrt%5B12%5D%7B2%7D%7D%5Cqquad%20%5Ccfrac%7Bx%5E2-9%7D%7B2-%28%5Cpm%5Csqrt%5B12%5D%7B2%7D%29%5E%7B12%7D%7D%5Cimplies%20%5Ccfrac%7Bx%5E2-9%7D%7B2-%5Cboxed%7B2%7D%7D%5Cimplies%20%5Cstackrel%7Bund%20efined%7D%7B%5Ccfrac%7Bx%5E2-9%7D%7B0%7D%7D)
so, the domain is all real numbers EXCEPT that one.
Answer:
D.
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals. That means that their product is -1.
In option D, since the slopes are 1 and -1, their product is -1, and the lines are perpendicular.
Answer: D.
