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question 16:Valentina bought a yoyo from a company that claims that with each retraction, the string rolls up by 30% of the original length. She set up a tape measure and threw the yoyo three times. Her data are shown in the table.

question 16Valentina bought a yoyo from a company that claims that with each retraction the string rolls up by 30 of the original length She set up a tape measu class=

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Answer:

The length after the first throw is

[tex]L_1=3[/tex]

The strings rolls up by 30% of the original length

Hence,

The length after the second throw will be

[tex]L_2=\frac{30}{100}\times3=0.9[/tex]

The length after the third throw will be

[tex]L_3=\frac{30}{100}\times0.9=0.27[/tex]

The length after the fourth throw will be

[tex]L_4=\frac{30}{100}\times0.27=0.081[/tex]

The length after the fifth throw will be

[tex]L_5=\frac{30}{100}\times0.081=0.0243[/tex]

Hence,

To calculate the sum of the length after 5 throws, we will use the formula below

[tex]L=L_1+L_2+L_3+L_4+L_5[/tex]

By substituting the values, we will have

[tex]\begin{gathered} L=L_{1}+L_{2}+L_{3}+L_{4}+L_{5} \\ L=3+0.9+0.27+0.081+0.0243 \\ L=4.2753 \\ L\approx4.28(nearest\text{ hundredth\rparen} \end{gathered}[/tex]

Hence,

The final answer is = 4.28 feet

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