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AleksAgata [21]
3 years ago
15

in 2011, an Action Comics no. 1, featuring first appearance of superman, was sold at auction for $2,161,000. The comic book was

originally sold in 1938 for $.10. What was the annual increase in the value of this comic book?
Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
3 0

Price of book in 1938 = $ 0.10

Price of book in 2011 = $ 2,161,000

Number of years over 1938-2011 = 2011 - 1938 = 73

Annual increase in the price = ((\frac{\text{Price of book in 2011}}{\text{Price of book in 1938}}) ^ \frac{1}{\text{Number of years}} - 1 ) * 100

⇒ Annual increase in the price = ((\frac{2,161,000}{0.1}) ^ \frac{1}{73} - 1 ) * 100

⇒ Annual increase in the price = (1.260302283  - 1 ) × 100

⇒ Annual increase in the price = 0.260302283 × 100

⇒ Annual increase in the price = 26.0302283 %

⇒ Annual increase in the price = 26%

Hence, the comic book price increased by 26% annually

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A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter
Anastasy [175]

Answer:

56.7°

Step-by-step explanation:

A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?

We solve this question using the Trigonometric function of Sine

From the question, we are told that:

A rectangle is 5.1 cm wide

and each diagonal is 9.3 cm long.

Since we have a diagonal, this means the shape is transformed to a triangle.

The width of the rectangle = Adjacent side of a triangle = 5.1cm

The diagonal of the rectangle = Hypotenuse = 9.3cm

Hence,

cosθ = Adjacent/Hypotenuse

cosθ = 5.1/9.3

cosθ = 0.5483870968

θ = arccos(0.5483870968)

θ = 56.743568714°

Approximately = 56.7°

The measure of the angle is 56.7°

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3 years ago
A vial contains 80 mg of drug in 2 mL of injection. How many milliliters of the injection should be administered to obtain 0.02
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Answer:

0.5mL of the injection should be administered to obtain 0.02 g of the drug.

Step-by-step explanation:

First step: The first step of this problem is the conversion of 0.02g to mg.

Each gram has 1000 miligrams. So:

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x = 20mg

Final step:

A vial contains 80 mg of drug in 2 mL of injection. How many mL should be administered to obtain 0.02 g = 20mg of the drug.

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

In this step, as the dose of the injection increases, so the quantity of the drug. So the relationship between the measures is direct. So:

80 mg - 2mL

20 mg - xmL

80x = 40

x = \frac{40}{80}

x = 0.5mL

0.5mL of the injection should be administered to obtain 0.02 g of the drug.

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