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RUDIKE [14]
3 years ago
10

Simplify.

id="TexFormula1" title="3^{ \frac{1}{2} } * 3^\frac{1}{2}" alt="3^{ \frac{1}{2} } * 3^\frac{1}{2}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Lapatulllka [165]3 years ago
3 0
3^{1/2}\times3^{1/2}=3^{1/2+1/2}=3^1=3
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Solve for x: |2x + 12| = 18
Mashcka [7]
2x + 12 = 18
18 - 12 = 6
2x = 6
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Jalen traded $4100 for Mexican pesos, immediately changed his mind, and then promptly traded his Mexican pesos back into dollars
Tcecarenko [31]
The answer is the option <span>A.) More than $0 but less than $4100
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3 years ago
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In a random sample of 500 handwritten zip code digits, 464 were read correctly by an optical character recognition (OCR) system
In-s [12.5K]

Answer:

z= 2.38

P = 0.008656

Step-by-step explanation:

Here n= 500 and p~= 464/500= 0.928 and q`= 1- 0.928 = 0.072

We formulate our null and alternate hypothesis as

H0 =  0.9 ;       H0 > 0.9

The degree of confidence = 90%

z₀.₀₅ = 1.645 for  α= 0.05

We use the test statistic

z=  x- np/√npq

z= 466-500 *0.9/ √500 * 0.9(1-0.9)

z= 466- 450/ √45

z= 16/6.7082

z= 2.38

As the calculated value of z= 2.38  is greater than α =1.645 so we reject H0.

If H0 is true the P value is calculated as

P = 1- Ф( 2.38)

P = 1-0.991344=0.008656

7 0
3 years ago
Find the equation for the plane that contains the line x=−1+3t , y=1+2t, z=2+4t and is perpendicular to the plane containing the
Ivan

Let L be the line given by the vector equation

(-1,1,2) + \lambda(3,2,4) \ , \lambda \in \mathbb{R}.

First, we use the director vectors of the lines L1 and L2 to get the

vector equation of the plane containing them, which we denote by \Pi_1. This is,

\\\\\Pi_1  : (1,-1,5) + \alpha (2,-1,6) + \beta (1,1,-3) \ , \alpha, \beta \in \mathbb{R}\\\\\\

We observe that \vec{N} = (2,-1,6)\times(1,1,-3) = (-3,12,3) \ne (0,0,0). Therefore, the vector equation of \Pi_1 defines a plane and \vec{N} is a normal vector to \Pi_1.

 

Finally, the vector equation for the wanted plane, which we denote by \Pi, is

\Pi : (-1,1,2) + r(3,2,4) + s(-3,12,3), r,s \in \mathbb{R} \ .

Thus, if s = 0, then L \subset \Pi and since \vec{N} is parallel to \Pi, then it is perpendicular to \Pi_1.

8 0
3 years ago
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