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Eddi Din [679]
2 years ago
8

In the figure below, the segments WX and W Y are tangent to the circle centered at 0. Given that OX= 4 and OW = 8.5, find WY.

Mathematics
1 answer:
zheka24 [161]2 years ago
6 0

Answer:

7.5

Step-by-step explanation:

because OY is a radius like OX they will have equal length of 4 so OY = 4

Because of the circle theorem that says that tangents meet the the radius of a circle at 90 degrees, angle OYW is 90 degrees so the triangle OYW is a right angle triangle and we can use pythagoras theorem to get WY as:

8.5^{2} - 4^{2} = WY^{2}   \\\sqrt{WY^{2}}=WY=7.5

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Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units ass
FrozenT [24]

Answer:

H0 is rejected.There difference in the means for the three assembly methods.

Step-by-step explanation:

Calculating gives the following results.

ANOVA Table

Source        DF                  Sum                Mean            F Statistic      

                                       of Square         Square

Treatments       2               4560               2280             9.865

(between groups)

 

<u>Error            27                  6240                231.111                                   </u>

Total         29                   10,800  

Error SS= SST -SSTR = -10,800-4560=6240    

d.f for SSTr = r-1= 3-1

D.f for SST= n-r= 30-3= 27

Total D.f= d.f for SSTr+D.f for SST= 27+29

MSTR= SSTR/d.f= 4560/2= 2280

MSError= Error SS/ d.f= 6240/27=231.111

F test= MSTR/ MsError= 2280/231.11= 9.865

The P- value < 0.01 which  is less than 0.05 therefore H0 is rejected.

There is sufficient evidence to reject H0.

3 0
3 years ago
How many gallons of pure water should be evaporated from 160 gallons of a solution containing 12% salt so that the remaining sol
bazaltina [42]
X= # gallons of pure water that should be evaporated

The total amount of salt must be equal before and after evaporation.
STEP 1
BEFORE EVAPORATION: multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% * 160 gallonsconvert 12% to decimal form (12% ÷ 100)
= 0.12 * 60

STEP 2
AFTER EVAPORATION: subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation

= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)

STEP 3
Set the before & after evaporation equations equal to one another to solve for x.
0.12 * 160= 0.20(160 - x)multiply 0.20 by each term in parentheses
19.2= (0.20 * 160) + (0.20 * -x)multiply in parentheses
19.2 = 32 - 0.20xsubtract 32 from both sides
-12.8= -0.20xdivide both sides by -0.20
64 gallons= x

CHECK:substitute x= 64 into the step 3 equation
0.12 * 160= 0.20(160 - x)19.2= 0.20(160 - 64)subtract in parentheses19.2= 0.20(96)19.2= 19.2

ANSWER: 64 gallons of pure water should be evaporated.
Hope this helps!  :)
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3 years ago
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Answer:

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The figure below shows a trapezoid, ABCD, having side AB parallel to side DC. The diagonals AC and BD intersect at point O.
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Answer:

<em>Length of BO is </em><em>three times the length of DO.</em>

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In trapezoid ABCD, CD\ ||\ AB

In ΔCDO and ΔABO,

  1. m\angle CDO=m\angle ABO (Alternate interior angles)
  2. m\angle DCO=m\angle BAO (Alternate interior angles)

So, \Delta CDO\sim \Delta ABO according to Angle-Angle similarity.

Therefore, the ratio of corresponding sides will be same.

\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{OA}

\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{3\cdot OC}

\Rightarrow \dfrac{OD}{OB}=\dfrac{1}{3}

\Rightarrow OB=3\cdot OD


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