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AnnZ [28]
3 years ago
7

Least common denominator of 2/5 and 3/10

Mathematics
1 answer:
irga5000 [103]3 years ago
7 0
Least common denominator is 10
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If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle
stira [4]

Answer:

<em>The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²</em>

<em>   or </em>

<em>The equation of the circle    x² + 2 x + y² - 4 y  = 15</em>

<u>Step-by-step explanation:</u>

Given points end  Points are p(-3,-2) and q( 1,6)

<em>The distance of two points formula</em>

P Q = \sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2}   }

P Q = \sqrt{1 - (-3)^{2} + ((6 -(-2))^{2}   }

P Q = \sqrt{16+64} = \sqrt{80}

<em>The diameter 'd' = 2 r</em>

                       2 r = √80

                            = \sqrt{16 X 5}

                           = 4 \sqrt{5}

                     <em> r =  2√5</em>

<em>Mid-point of two end points </em>

<em>                        </em>(\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )<em></em>

<em>                                               = (-1 ,2)</em>

<em>Mid-point of two end points = center of the circle</em>

<em>                                     (h,k) = (-1 , 2)</em>

                 

The equation of the circle

           (x -h )² +(y-k)² = r²

<em>          (x -(-1) )² +(y-(2))² = (2(√5))²</em>

<em>         x² + 2 x + 1 + y² - 4 y + 4 = 20</em>

<em>          x² + 2 x + y² - 4 y  = 20 -5</em>

<em>           x² + 2 x + y² - 4 y  = 15</em>

<u><em>Final answer</em></u><em>:-</em>

<em>The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²</em>

<em>   or </em>

<em>The equation of the circle    x² + 2 x + y² - 4 y  = 15</em>

<em>                  </em>

6 0
3 years ago
Determine the critical value or values for a one-mean z-test at the 1% significance level if the hypothesis test is right-tailed
kifflom [539]

Answer:

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:      

Null hypothesis:\mu \leq \mu_o      

Alternative hypothesis:\mu > \mu_o      

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

z_{crit}= 2.326

Step-by-step explanation:

Notation

\bar X represent the sample mean

\sigma represent the standard deviation for the population      

n= sample size      

\mu_o represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

z would represent the statistic (variable of interest)      

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean is greater than specified value, the system of hypothesis would be:      

Null hypothesis:\mu \leq \mu_o      

Alternative hypothesis:\mu > \mu_o      

For this case the significance is 1%. So we need to find a critical value in the normal standard distribution who accumulates 0.99 of the area in the left and 0.01 in the right and for this case this critical value is:

z_{crit}= 2.326

3 0
2 years ago
What is the number of ways to arrange 5 objects from a set of 9 different objects
luda_lava [24]
\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad &#10;\begin{cases}&#10;n=9\\&#10;r=5&#10;\end{cases}\implies _9P_5=\cfrac{9!}{(9-5)!}
7 0
3 years ago
A function is shown in the table below. what equation represents this function?
Molodets [167]

Answer:

y=-3x+6

Step-by-step explanation:

8 0
3 years ago
James is building a deck for a client and has several pieces of wood he wants to use. The sizes of the pieces of wood are 1.5m,
TiliK225 [7]

Answer:

Total = 9.65m

Step-by-step explanation:

Given

Pieces: 1.5m, 2500mm, 850mm, 4.8m

 

Required

The total length in metres (this completes the question)

The total length is:

Total = 1.5m + 2500mm + 850mm + 4.8m

Convert mm to m

Total = 1.5m + 2500*0.001m + 850*0.001m + 4.8m

Total = 1.5m + 2.5m + 0.85m + 4.8m

Total = 9.65m

<em>The total length of the wood is 9.65 metres</em>

4 0
2 years ago
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