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3 years ago

The value of U.S exports to China increased from $1480 million in 2011 to $2768 million

Mathematics

1 answer:

aliya0001 [1]3 years ago

7 0

The percentage of increase was 87.027... %

<em><u>Explanation</u></em>

The value of U.S exports to China increased from $1480 million to $2768 million.

Suppose, the percentage of increase is $x\%$

So, <u>the amount of increase</u> = $x\%$ of 1480 $=1480*\frac{x}{100}=14.8x$

Thus, the equation will be......

$14.8x= 2768-1480\\ \\ 14.8x=1288\\ \\ x= \frac{1288}{14.8}=87.027....$

So, the percentage of increase was 87.027... %

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Are -2x + 9 = 7 and 2x = 2 equivalent?

DochEvi [55]

Answer:

Yes because the answer to both of them is 1

Step-by-step explanation:

Let's solve your equation step-by-step.

−2x+9=7

Step 1: Subtract 9 from both sides.

−2x+9−9=7−9

−2x=−2

Step 2: Divide both sides by -2.

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Answer:

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Let's solve your equation step-by-step.

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2 years ago

The high school leadership team is having a car wash. They charge $5.50 for large cars and $4.00 for small cars . They had a suc

11Alexandr11 [23.1K]

Answer: 56 large cars and 86 small cars.

Step-by-step explanation:

Let's call:

$l$ : the number of large cars.

$s$ : the number of small cars.

Then, you can set up the following system of equations:

$\left \{ {{l+s=142} \atop {5.50l+4.0s=652.50}} \right.$

You can use the Elimination Method:

- Multiply the first equation by -4.0

- Add both equations.

- Solve for l.

$\left \{ {{-4.0l-4.0s=-568} \atop {5.50l+4.0s=652.50}} \right.\\--------\\1.5l=84.5$

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Substitute $l=56$ into one of the original equations and solve for <em>s:</em>

<em> </em> $56+s=142\\s=142-56\\s=86$

3 0

2 years ago

Help meeeeeeeeeeeeeee!!!!!!

koban [17]

Answer:

2x+3=9

2x=6

x=3

3w-1=14

3w=15

w=5

7y+2=30

7y=28

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5x+20=35

5x=15

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6c-12=48

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8m-4=20

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12p-18=30

12p=48

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your welcome

8 0

3 years ago

Read 2 more answers

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :