Most musicians have different popularities among various age groupings. In a random sample of 200 high school students, 163 said they liked Beyoncé or her work. In a random sampling of 200 adults aged 30 to 40, 128 of them said they liked Beyoncé or her work.

Check the conditions needed before creating a 95% confidence interval:

You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule.    set the derivative to equal -1 and solve for x.      take log base 10 of both sides. also recall that  .    so the x-coord of the point of tangency is .the y-coordinate of this point of tangency can be calculated using the original function:     using point-slope form, the equation of the tangent line is      the x-intercept of this tangent line is when the graph is at y=0.    this rounds off to  .choice c.

Find  the  area  of the  region bounded  by the  curves y equals  the  inverse sine  of  x divided  by 4,  y  =  0, andx  = 4  obtained  by  integrating  with  respect  to  y.  your work must include  the  definite integral  and theantiderivative.

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