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3 years ago

Solve linear system using substitution y=6-2x 7x-y=3

1 answer:

5 0

$\left \{ {{y=6-2x} \atop {7x-y=3}} \right. \\\\substitute\ first\ equation\ into\ the\ second\\\\
7x-(6-2x)=3\\\\
7x-6+2x=3\\\\
9x-6=3\ \ \ | add\ 6\\\\
9x=9\ \ \ | divide\ by\ 9\\\\
x=1\\\\
y=6-2*1=6-2=4$

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What is the result when the number 64 is decreased by 4.1%? Round your answer to the nearest tenth.

Strike441 [17]

Answer:

61.4

Step-by-step explanation:

64 minus 4.1 percent is 61.376. Rounded to the nearest tenth would be 61.4.

3 0

2 years ago

Read 2 more answers

Find an equation in slope-intercept form of the line that has slope –9 and passes through point A(-9, - 1).

mojhsa [17]

Answer:

Step-by-step explanation:

y + 1 = -9(x + 9)

y + 1 = -9x - 81

y = -9x - 82

answer is A

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3 years ago

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

$X=1$ number of citrus trees that are infected with the citrus red mite.

$n=5$ random sample taken

$\hat p=\frac{1}{5}=0.2$ estimated proportion of citrus trees that are infected with the citrus red mite.

$p$ true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56$

And rounded up we have that n=6147

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3 years ago

Is 28.42 > 28. 404 true

Sav [38]

Answer:

28.42 > 28.404

it is true

3 0

3 years ago

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Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, –5).

posledela

So hmm check the picture below, that's about the circle and the endpoints, but notice, the endpoints make up a segment, namely the diameter of the circle, well.... let's see how long that is, because, the radius is half the diameter

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 7}}\quad ,&{{ 3}})\quad 
% (c,d)
&({{ 7}}\quad ,&{{ -5}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{(7-7)^2+(-5-3)^2}\implies d=\sqrt{0+(-8)^2}\implies d=8
\\\\\\
\textit{the radius is half that, so is }\boxed{r=4}$

now.. hmmm notice, the midpoint of the diameter, is the center of the circle, let's check that one out

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 7}}\quad ,&{{ 3}})\quad 
% (c,d)
&({{ 7}}\quad ,&{{ -5}})
\end{array}\qquad 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left(\cfrac{{{ 7+7}}}{2}\quad ,\quad \cfrac{{{ -5}} + {{ 3}}}{2} \right)\implies \left( \cfrac{14}{2}\ ,\ \cfrac{-2}{2} \right)\implies \boxed{(7,-1)}$

now.. that we know what the center is, and what the radius is, well

$\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k\quad }})\qquad 
radius=&{{ r}}\\
&7&-1&4
\end{array}$

5 0

3 years ago