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2 years ago

How did the gulf of Tonkin resolutions affect US involvement in the Vietnam war?

Mathematics

1 answer:

klio [65]2 years ago

7 0

Answer:

I don't know how this is math but...

The Gulf of Tonkin Resolution authorized President Lyndon Johnson to “take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression” by the communist government of North Vietnam. Hope I helped! ☺

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PLEASE HELP!!

miskamm [114]

Answer: Choice A. 4 times

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

Explanation:

We'll be using this formula

$m = \frac{f(b)-f(a)}{b-a}$

to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).

To start things off, we'll compute the AROC from x = 1 to x = 2.

$m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\$

Do the same for the AROC from x = 3 to x = 4.

$m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\$

The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.

7 0

2 years ago

You are having a discussion about sequences with your classmate. She insists the the sequence 2,3,5,8,12 must be either arithmat

IgorC [24]

The sequence is, in fact, quadratic. It is described by the equation
.. a[n] = (n*(n -1))/2 +2

First differences are increasing, so the sequence will not be arithmetic. An arithmetic sequence has constant first differences.

Second differences are constant, so the sequence will not be geometric. A geometric sequence will have first-, second-, third-differences, and those to any level, that have the same constant ratio as the terms of the original sequence.

4 0

2 years ago

Is this sequence arithmetic, geometric or neither? 3.5. -4, -7.5...

kvasek [131]

Answer:

Neither

Step-by-step explanation:

If the sequence was geometric, each term would be multiplied by the same multiplier to get to the next one. We can check if the multiplier is the same by taking a term and dividing it by the term before it. For example,

-4/3.5=-1.14285714

-7.5/-4=1.87500

The multiplier between the terms aren't the same so it's not geometric.

For arithmetic, the distances between each term would be the same, and we can take the same idea from the geometric sequence, but use subtraction instead of division

-4-3,5=-7.5

-7.5-(-4)=-3.5

Again, the distances aren't the same, so it's not arithmetic.

8 0

2 years ago

The following table shows the percent increase of donations made on behalf of a non-profit organization for the period of 1984 t

pashok25 [27]

Giving the table below which shows the percent increase of donations made on behalf of a non-profit organization for the period of 1984 to 2003.

Year: 1984 1989 1993 1997 2001 2003

Percent: 7.8 16.3 26.2 38.9 49.2 62.1

The scatter plot of the data is attached with the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.

To find the equation for the line of regression where the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.
$\begin{center}
\begin{tabular}{ c| c| c| c| }
 x & y & x^2 & xy \\ [1ex] 
 4 & 7.8 & 16 & 31.2 \\ 
 9 & 16.3 & 81 & 146.7 \\ 
13 & 26.2 & 169 & 340.6 \\ 
17 & 38.9 & 289 & 661.3 \\ 
21 & 49.2 & 441 & 1,033.2 \\ 
23 & 62.1 & 529 & 1,428.3 \\ [1ex]
\Sigma x=87 & \Sigma y=200.5 & \Sigma x^2=1,525 & \Sigma xy=3,641.3 
\end{tabular}
\end{center}$

Recall that the equation of the regression line is given by
$y=a+bx$
where
$a= \frac{(\Sigma y)(\Sigma x^2)-(\Sigma x)(\Sigma xy)}{n(\Sigma x^2)-(\Sigma x)^2} = \frac{200.5(1,525)-87(3,641.3)}{6(1,525)-(87)^2} \\ \\ = \frac{305,762.5-316793.1}{9,150-7,569} = \frac{-11,030.6}{1,581} =-6.977$
and
$b= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{n(\Sigma x^2)-(\Sigma x)^2} = \frac{6(3,641.3)-(87)(200.5)}{6(1,525)-(87)^2} \\ \\ = \frac{21,847.8-17,443.5}{9,150-7,569} = \frac{4,404.3}{1,581} =2.7858$

Thus, the equation of the regresson line is given by
$y=-6.977+2.7858x$

The graph of the regression line is attached.

Using the equation, we can predict the percent donated in the year 2015. Recall that 2015 is 35 years after 1980. Thus x = 35.

The percent donated in the year 2015 is given by
$-6.977+2.7858(35)=-6.977+97.503=90.526$

Therefore, the percent donated in the year 2015 is predicted to be 90.5