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anygoal [31]
2 years ago
11

On a map, the distance between two towns is 12 centimeters. If 3 centimeters represents 90 miles, what is the actual distance be

tween the cities in miles?
Mathematics
1 answer:
dolphi86 [110]2 years ago
6 0
360 miles, I’m pretty sure
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A paint company mixes it's paint with water to create more paint per gallon. They currently have ten gallon jugs which contain 1
Karo-lina-s [1.5K]
<h3>Answer:  1.25 gallons</h3>

==================================

Explanation:

They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.

The ratio of paint to water is 90:10 which reduces to 9:1

Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%

--------------

Let x be the amount of water we add. This amount is in gallons.

We start off with 1 gallon of water and it bumps up to 1+x gallons of water.

The overall amount of 10 gallons also bumps up to 10+x gallons.

We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water

Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.

--------------

(1+x)/(10+x) = 20/100

100(1+x) = 20(10+x) ... cross multiply

100+100x = 200+20x ... distribute

100x-20x = 200-100

80x = 100

x = 100/80 ... divide both sides by 80

x = 1.25

You need to add 1.25 gallons of water

--------------

If you add 1.25 gallons of water, then,

amount of water = 1+x = 1+1.25 = 2.25

amount of paint&water = 10+x = 10+1.25 = 11.25

So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix

2.25/11.25 = 0.2 = 20% water

This confirms our answer.

--------------

Extra info:

1.25 gallons = 1 gallon + 1/4 gallon

1.25 gallons = 1 gallon + 1 quart

This is because 1 gallon = 4 quarts, so 1 quart = 1/4 gallon.

5 0
3 years ago
John translated parallelogram ABCD using the rule (x,y)→(x+3, y−2). If angle A is 110° and angle B is 70°, what is the degree me
bearhunter [10]
Answer: 110 degrees

Angle measurements are preserved when translations happen. Shifting a figure will not change the angle. So because angle A = 110 degrees, this means angle A' = 110 degrees as well. 
8 0
3 years ago
Read 2 more answers
A figure is made up of a triangle and a rectangle. The triangle has a height of 8.5 inches and a base of 10 inches. The rectangl
Brilliant_brown [7]

\sf  are a \  of \   triangle : \frac{1}{2}*base *height

\sf  are a \  of \   rectangle : Length * Width

total area :

\sf  are a \  of \   rectangle  + area \ of \  triangle

\rightarrow  \sf 9 * 10 + \frac{1}{2} *8.5*10

\rightarrow  \sf 132.5 \ in^2

5 0
2 years ago
Peopl3 what is x÷2=6.5​
zloy xaker [14]

Answer:

X=13

Step-by-step explanation:

4 0
2 years ago
Here is an expression: 2 + 3ⁱ ( Remember what you do when you replace i with a number) Evaluate the expression when i is 1.
Kamila [148]

Answer:

The value of the expression when i is 1 is equals to 5.

Step-by-step explanation:

We are given the following expression:

2 + 3^{i}

Evaluate the expression when i is 1.

We replace i by 1. When we elevate a number to the 1, the result is the number we elevate. So

2 + 3^{i} = 2 + 3^{1} = 2 + 3 = 5

The value of the expression when i is 1 is equals to 5.

3 0
3 years ago
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