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scoray [572]
3 years ago
5

Clara is growing her hair out and wants it to be no longer than 15 cm but more than 11 cm. Her hair is 7 cm right now and grows

at a rate of 0.25 cm per week. Let t be the time in weeks. Which compound inequality models the scenario? 0.25 + 7t > 11 or 0.25 + 7t ≤ 15 7 + 0.25t ≥ 11 or 7 + 0.25t < 15 11 ≤ 0.25 + 7t < 15 11 < 7 + 0.25t ≤ 15
Mathematics
1 answer:
Agata [3.3K]3 years ago
8 0

Answer:

Last option

Step-by-step explanation:

After t weeks, Clara's hair will be 7 + 0.25t cm long. "No longer than" means that we use the symbol ≤ and "more than" means that we use the symbol >, hence, the answer is 11 < 7 + 0.25t ≤ 15.

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The coffee Lily likes is composed of 97.3% water and 2.7% cocoa. The coffee John likes is composed of 96% water and 4% cocoa. Ho
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30 ounces of the coffee John likes consists of

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  • 0.04\cdot30=1.2 ounces of cocoa

To this mixture we're adding x ounces of water, so that the new mix has a total volume of 30+x ounces and matches the composition of the coffee Lily likes. This means it would consist of

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Solve for x:

0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x

\implies0.39=0.027x

\implies x\approx14.4

###

Just to confirm: the new mixture consists of

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  • 1.2+0=1.2 ounces of cocoa

giving a total volume of 43.2+1.2=44.4 ounces of coffee, and \dfrac{43.2}{44.4}\approx0.973, as required.

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