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3 years ago

The rate of change in y = 24x

Mathematics

1 answer:

Artyom0805 [142]3 years ago

5 0

Answer:

Step-by-step explanation:

Using the formula y = mx + b we can find the slope or rate of change. First we must convert it into the formula or equation we currently have which is y = 24x + 0.

24 = m

x = x

0 = b

m is always the rate of change or slope so by finding m we find the slope or rate of change.

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Solve for . Round to the nearest tenth, if necessary.

Len [333]

Answer:

x ≈ 8.7

Step-by-step explanation:

Using the sine ratio in the right triangle

sin75° = $\frac{opposite}{hypotenuse}$ = $\frac{RS}{QS}$ = $\frac{x}{9}$ ( multiply both sides by 9 )

9 × sin75° = x , then

x ≈ 8.7 ( to the nearest tenth )

7 0

3 years ago

According to the United States Census Bureau, on September 11, 2014, the population of the United States was increasing by 11 pe

Papessa [141]

Answer:

317,988,000

Step-by-step explanation:

We have been given that according to the United States Census Bureau, on September 11, 2014, the population of the United States was increasing by 11 people every 12 seconds.

Let us find number of people increased in 1 minute as:

$11\times \frac{60}{12}=11\times 5 =55$

Now, we will convert 11 years into minutes and multiply by 55 to find increase in population in 11 years.

$\text{11 years}=11\text{ years}\times \frac{365\text{ days}}{\text{year}}\times \frac{24\text{ hours}}{\text{days}}\times \frac{60\text{ min}}{\text{hour}}$

$\text{11 years}=11\times 365\times 24\times 60\text{ min}$

$\text{11 years}=5,781,600\text{ min}$

Upon multiplying 5,781,600 by 55, we will get:

$\text{Population increase in 11 years}=5,781,600\text{ min}\times \frac{55 \text{ people}}{\text{min}}$

$\text{Population increase in 11 years}=5,781,600\times 55 \text{ people}$

$\text{Population increase in 11 years}=317,988,000 \text{ people}$

Therefore, the population of United States would increase 317,988,000 in 11 years.

4 0

3 years ago

Space is a way of joining together points, lines, and

erastovalidia [21]

Space is a way of joining together points, lines and...

Shapes

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4 years ago

I don't know how to write a proportional line with a slope of 3?

kirill115 [55]

Me either :(
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5 0

3 years ago

The nine squares of a 3-by-3 chessboard are to be colored red and blue. The chessboard is free to rotate but cannot be flipped o

nignag [31]

Answer:

$a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}$

For n = 3, there are 134 possibilities

Step-by-step explanation:

First, lets calculate the generating function.

For each square we have 2 possibilities: red and blue. The Possibilities between n² squares multiply one with each other, giving you a total of 2^n² possibilities to fill the chessboard with the colors blue or red.

However, rotations are to be considered, then we should divide the result by 4, because there are 4 ways to flip the chessboard (including not moving it), that means that each configuration is equivalent to three other ones, so we are counting each configuration 4 times, with the exception of configurations that doesnt change with rotations.

A chessboard that doesnt change with rotations should have, in each position different from the center, the same colors than the other three positions it could be rotated into. As a result, we can define a <em>symmetric by rotations chessboard</em> with only (n²-1)/4 + 1 squares (the quarter part of the total of squares excluding the center plus the center).

We cocnlude that the total of configurations of symmetrical boards is $2^{\frac{n^2-1}{4} + 1}$

Since we have to divide by 4 the rest of configurations (because we are counted 4 times each one considering rotations), then the total number of configutations is

$a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}$

If n = 3, then the total amount of possibilities are

$a_3 = 2^{\frac{3^2-1}{4} + 1} + \frac{2^{3^2} - \, 2^{\frac{3^2-1}{4} + 1}}{4} = 134$

3 0

3 years ago