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3 years ago

-25 Points-

Mathematics

1 answer:

Furkat [3]3 years ago

6 0

$\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \cfrac{s}{s}=\cfrac{\sqrt{64}}{\sqrt{81}}\implies \cfrac{s}{s}=\cfrac{8}{9}\qquad \leftarrow \textit{ratio of the sides or scale factor}$

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3 mL of hot sauce mixed with 2 ounces of barbecue sauce

45 mL of hot sauce mixed with 30 ounces of barbecue sauce

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Step-by-step explanation:

we know that

A restaurant makes a dipping sauce with

$\frac{9}{6}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

Simplify

$1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

<u><em>Verify each case</em></u>

case A) we have

6 mL of hot sauce mixed with 10 ounces of barbecue sauce

$\frac{6}{10}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

simplify

$0.6\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

Compare

$0.6 \neq 1.5$

therefore

This mixture is not the same that as Flaming BBQ's dipping sauce

case B) we have

3 mL of hot sauce mixed with 2 ounces of barbecue sauce

$\frac{3}{2}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

simplify

$1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

Compare

$1.5 =1.5$

therefore

This mixture is the same that as Flaming BBQ's dipping sauce

case C) we have

45 mL of hot sauce mixed with 30 ounces of barbecue sauce

$\frac{45}{30}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

simplify

$1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

Compare

$1.5=1.5$

therefore

This mixture is the same that as Flaming BBQ's dipping sauce

case D) we have

24 mL of hot sauce mixed with 18 ounces of barbecue sauce

$\frac{24}{18}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

simplify

$1.33\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

Compare

$1.33 \neq 1.5$

therefore

This mixture is not the same that as Flaming BBQ's dipping sauce

case E) we have

12 mL of hot sauce mixed with 8 ounces of barbecue sauce

$\frac{12}{8}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

simplify

$1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}$

Compare

$1.5=1.5$

therefore

This mixture is the same that as Flaming BBQ's dipping sauce

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