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cluponka [151]
3 years ago
15

George has a triangle-shaped garden in his backyard. He drew a model of this garden on a coordinate grid with vertices A(4, 2),

B(2, 4), and C(6, 4). He wants to create another, similar-shaped garden, A′B′C′, by dilating triangle ABC by a scale factor of 0.5. What are the coordinates of triangle A′B′C′?
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
6 0
Given:

Vertices of a triangular garden:

A(4,2)
B(2,4)
C(6,4)
Scale factor = 0.5

Find the distance between points:

d = √(x2-x1)^2 + (y2-y1)^2

dAB = 2√2
dBC = 4
dCA = 2√2

A similarly shaped garden is to be created using the scale factor, 0.5:

A' = 2√2 / 0.5 = 4√2
B' = 4 / 0.5 = 8
C' = 2√2 / 0.5 = 4√2 
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Ivahew [28]

the metal bar/random line is almost the same size as the other two sides of the triangle. if one side is 32ft, then the opposite side is 32ft also. the bottom is 100ft, so we could eliminate C. because it couldnt be that number. now the bottom triangle, one side is 40ft so the other side has to be 40ft as well. its asking about the metal bar.

its either:

A. 53.2ft     or

B. 44.4

because the line is almost the same size as 32ft. its almost a equallateral triangle. i would go with A. though because if you imagine the line at the bottom of the line (100ft.) the line would go over half of it (and 53.2 is over half of 100) so i would say

A.53.2

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7 0
3 years ago
Element X is a radioactive isotope such that every 3 years, its mass decreases by half. Given that the initial mass of a sample
Volgvan

Answer:Y=41

Step-by-step explanation:

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3 years ago
There are a total of 96 children in Years 4, 5 and 6
BaLLatris [955]

Answer: 20 children

Step-by-step explanation:

<u>Given</u>

Year 4: 11 cannot swim

Year 5: 21 can swim

Year 6: 18 of 30 can swim

Total 96 children

Total 37 cannot swim

<u>First Step: find the number of people from year 5 who cannot swim</u>

  • There are 30-18=12 people who cannot swim in year 6
  • There are 11 who cannot swim in year 4
  • Thus, we use the total number [37]-[year 4+year 6]=37-23=14 people who cannot swim in the year 5

<u>Second Step: find the number of children in year 5</u>

  • There are 21 children who can swim
  • There are 14 children who cannot swim
  • 21+14=35 children

<u>Third Step: find the number of children in year 4 who can swim</u>

  • There are 30 children in year 6
  • There are 35 children in year 5
  • There are 11 children in year 4 who cannot swim
  • There are in total 96 children
  • 96-30-35-11=20 children in year 4 who can swim

Hope this helps!! :)

Please let me know if you have any questions

7 0
3 years ago
Mr. Good Wrench advertises that a customer will have to wait no more than 30 minutes for an oil change. A sample of 26 oil chang
Andru [333]

Answer:

The 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population standard deviation is:

CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}

The information provided is:

<em>n</em> = 26

<em>s</em> = 4.8 minutes

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Compute the critical values of Chi-square as follows:

\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.10/2, (26-1)}=\chi^{2}_{0.05, 25}=37.652

\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.10/2, (26-1)}=\chi^{2}_{0.95, 25}=14.611

*Use a Chi-square table.

Compute the 90% confidence interval for the population standard deviation waiting time for an oil change as follows:

CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}

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Thus, the 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).

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Rom4ik [11]

Answer:

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5 0
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