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3 years ago

What is the equation of the plane that contains the triangle shown in the diagram?

Mathematics

2 answers:

Anastaziya [24]3 years ago

6 0

The first equation

2x + 3y + 6z = 12

kolezko [41]3 years ago

3 0

Answer:

Option A is correct.

$2x + 3y +z = 6$

Step-by-step explanation:

The intercept form of the equation of plane is given by:

$\frac{x}{l}+\frac{y}{m} +\frac{z}{n} =1$ .....[1]

where

l is the intercept of x-axes

m is the intercept of y-axes and

n is the intercept of z-axes respectively;

From the given figure;

we have;

The intercepts of coordinates axes are;

$l = 3$

$m = 2$

$n = 6$

Substitute these values in the equation [1]; we have;

$\frac{x}{3}+\frac{y}{2} +\frac{z}{6} =1$

Taking LCM of 3, 2 and 6 is 6

$2x + 3y +z = 6$

therefore, the equation of plane that contains the triangle as shown in the diagram is, $2x + 3y +z = 6$

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<h2>Answer with explanation:</h2>

Given : The proportion of New Zealanders consume five or more servings of soft drinks per week : $\hat{p}= 0.16$

a) The number of survey respondents reported that they consume five or more servings of soft drinks per week = 2006

b) Confidence interval for population proportion (p) :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

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For n= 2006 , $\hat{p}= 0.16$ and critical value for 95% confidence interval : z* = 1.96

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$0.16\pm (1.96)\sqrt{\dfrac{ 0.16(1- 0.16)}{2006}}$

$0.16\pm (1.96)\sqrt{ 0.000066999002991}$

$0.16\pm (1.96)(0.00818529186963)$

$0.16\pm 0.0160431720645$

$(0.16-0.0160431720645,\ 0.16+0.0160431720645)$

$(0.143956827935,\ 0.176043172064)\approx(0.144,\ 0.176)$

i.e. A 95% confidence interval for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week. = $(0.144,\ 0.176)$