Answer:
Perpendicular = Y = 34.64 ft (Approx)
Base = X = 20 ft
Step-by-step explanation:
Given:
θ = 60°
Hypotenuse = 40 ft
Perpendicular = Y
Base = X
Find:
X and Y
Computation:
Sinθ = Perpendicular / Hypotenuse
Sin 60 = Y / 40
Perpendicular = Y = 34.64 ft (Approx)
Cosθ = base / Hypotenuse
cos 60 = X / 40
Base = X = 20 ft
Answer:
The vertex is y=-4
Step-by-step explanation:
The vertex is the minimum point of the graph of the quadratic equation.
Let's first find the like of symmetry.
dy/dx=2x+12
2x+12=0
2x=-12
x=-6
Now plug -6 into the quadratic equation
y=(-6)²+12(-6)+32
y=-4
I think its 10
Correct me if im wrong
But all u have to do is multiply 2.5 x 4=10
Answer: 0.8461
Step-by-step explanation:
Let p be the proportion of residents are against the increase of taxes to fund alternatives to drug addiction treatment.
As per given , we have p=0.40
A random sample is taken with size : n= 400
Expecting sample proportion : 
Now , the probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed will be :

![=P(z>\dfrac{0.375-0.40}{\sqrt{\dfrac{0.40(0.60)}{400}}})\ \ [\because\ z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]](https://tex.z-dn.net/?f=%3DP%28z%3E%5Cdfrac%7B0.375-0.40%7D%7B%5Csqrt%7B%5Cdfrac%7B0.40%280.60%29%7D%7B400%7D%7D%7D%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D)

[By z-table]
Hence, the approximate probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed is 0.8461 .
Make it 49800/50000 and 50200/50000 and then compare.