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3 years ago

andrea drove 200 miles using 9 gallons of gas. At this rate, how many gallons of gas would she need to drive 420 miles?

Mathematics

1 answer:

Anika [276]3 years ago

7 0

Given : Andre drove 200 Miles using 9 Gallons of Gas

⇒ Andre drives 1 Mile using $[\frac{9}{200}]\;Gallons\;of\;Gas$

⇒ Andre drives (420 × 1 Mile) using $[\frac{420\times9}{200}]\;Gallons\;of\;Gas$

⇒ Andre drives 420 Miles using 18.9 Gallons of Gas

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the scale on the map is 1 cm : 80 km . if two cities are 4 cm apart on the map, what is the actual distance between the cities?

jarptica [38.1K]

Hello there! Your answer would be '<em>the actual distance between the cities is 320 kilometers</em>'.

Okay, so to solve this, we can use unit rates. We know that for every one centimeter we have eighty kilometers. So, whatever we multiply the centimeter value by, we can multiply the kilometer value by the same number and get our answer.

So if the centimeter value is 4, multiply the kilometer value by 4.

80 x 4 = 320

This means that the cities are 320 kilometers apart, and you have your answer!

Hope this helps, and have a great day!

8 0

3 years ago

14 Type the correct answer in each box. Use numerals instead of words. a Ava, Lucas, and Maria are playing a game where they pas

jeka94

Answer:

Maria–Ava: 15.7 feet
Lucas–Maria: 10.1 feet
angle at Maria: 50°

Step-by-step explanation:

The cosine and tangent functions are useful here. The relevant relations are ...

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...

cos(40°) = 12/ma

ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet

The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...

tan(40°) = ml/12

ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet

The angle formed at Maria's position is the complement of the other acute angle in the right triangle:

M = 90° -40° = 50°

In summary, ...

Maria–Ava: 15.7 feet
Lucas–Maria: 10.1 feet
angle at Maria: 50°

5 0

2 years ago

The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .