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Use the normalize function defined in Section 25.1.4 to create a [0,1] normalized version of the range of values of the years since Ph.D. variable.

Use the normalize function defined in Section 25.1.4 to create a [0,1] normalized version of the range of values of the years since Ph.D. variable. Then use the appropriate palette from (a) along with rgb to convert these to the required hex codes.

Modify the vector of colors you just created in (c), adjusting opacity. Colors in the vector that correspond to females should be reduced to 90 percent opacity; colors that correspond to males should be reduced to 30 percent opacity.

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