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Natasha2012 [34]
3 years ago
13

3. (a) Are triangles PQR and STU congruent?

Mathematics
1 answer:
yawa3891 [41]3 years ago
8 0

We already know that PQ and ST are congruent because they both equal 4 and QR and TU are congruent because they both equal 6. Also I'm not sure if it is marking the two angles congruent but it looks like that to me so if that is the case then both of the triangles are congruent by SAS, PQ=ST, WR=TU, angle PQR = angle STU.

Now that we need to set up a system of equations to find y. Since we already proved the triangles congruent SU must be = to PR because of CPCTC "corresponding parts of congruent triangles are congruent" So the equation would be:

3y-2=y+4 (move y variable to one side) subtract y from right, add 2 to right

2y=6 (divide)

y=3

Then plug 3 into where y is (and since we need PQR perimeter plug it into 3(3)-2) and PR should equal 7 so add up all the sides (4+6+7) and your perimeter is 17ft.

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A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What pe
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Answer:

(a) 5.48%

(b) 17.82 years

(c) 21.19%

(d) 15.21 years

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

µ=12 years and σ=2.5 years.

(a) What percent of the radios will function for more than 16 years?

For x = 16

z = 16 - 12/2.5

z = 1.6

Probability value from Z-Table:

P(x<16) = 0.9452

P(x>16) = 1 - P(x<16)

1 - 0.9452

= 0.054799

Converting to percentage = 0.054799 × 100

= 5.4799%

Approximately = 5.48%

(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.

find the z score of the 99th percentile = 2.326

Hence:z = (x-μ)/σ

2.326 = x - 12/2.5

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x = 12 + 5.815

x = 17.815

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(c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years?

When x < 10

Hence,

z = 10 - 12/2.5

z = -0.8

Probability value from Z-Table:

P(x<10) = 0.21186

Converting to percentage

0.21186 × 100

= 21.186%

Approximately = 21.19%

(d) If 10% of the radios will function for more than X years, find X.

The z score would be : 100 - 10%

= 90th percentile z score

We find the z score of the 90th percentile = 1.282

Hence:z = (x-μ)/σ

1.282 = x - 12/2.5

Cross Multiply

1.282 × 2.5 = x - 12

3.205 = x - 12

x = 12 + 3.205

x = 15.205

Approximately = 15.21 years

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