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Home » Area of the square is \( 12^2 = 144 \) cm². - Get link 4share

Area of the square is \( 12^2 = 144 \) cm². - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 pH = -log(1 × 10⁻⁵) = -(-5) = <<-(-5)=5>>5

📌 #### 5A research scientist is testing the concentration of a protein solution. She dilutes 50 mL of a 0.8 M solution with 150 mL of buffer. What is the final concentration of the protein in moles per liter?

📌 The total volume after dilution is 50 mL + 150 mL = <<50+150=200>>200 mL = 0.2 L.

📌 The moles of protein remain constant: 0.8 mol/L × 0.050 L = <<0.8*0.050=0.04>>0.04 moles.

📌 Final concentration = 0.04 moles / 0.2 L = <<0.04/0.2=0.2>>0.2 M.

📌 A herpetologist tracks the population of a rare frog species in a Bornean rainforest. The population doubled in the first year due to conservation efforts but declined by 20% in the second year due to habitat loss. What was the overall percentage change in population over the two years?

📌 Let the initial population be 100. After doubling: 100 × 2 = <<100*2=200>>200.

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Set this equal to 150:
\frac{n}{2} (4n + 10) = 150 \implies n(4n + 10) = 300 \implies 4n^2 +...
Divide by 2: \( 2n^2 + 5n - 150 = 0 \). Use the quadratic formula:
n = \frac{-5 \pm \sqrt{5^2 - 4(2)(-150)}}{2(2)} = \frac{-5 \pm \sqrt{2...
Take the positive root: \( n = \frac{30}{4} = 7.5 \). Since \( n \) mu...
S_7 = \frac{7}{2} (4(7) + 10) = \frac{7}{2} (38) = 7 \cdot 19 = 133 \l...
\( S_8 = \frac{8}{2} (4(8) + 10) = 4 \cdot 42 = 168 > 150 \), so maxim...
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Question: An ichthyologist observes that the population of a rare fish...
Solution: The population grows as \( 324 \times 2^{t/3} \), where \( t...

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