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sveticcg [70]
2 years ago
6

I need help with it pls

Mathematics
1 answer:
Basile [38]2 years ago
4 0

Answer:

Step-by-step explanation:

Step 1: What are the couch's original coordinates?

  • A: (-4, 2)
  • N: (-4, 3)
  • G: (-1, 3)
  • L: (-1, 4)
  • E: (-5, 4)
  • S: (-5, 2)

Step 2: Rotate the couch 90° counterclockwise.

Rule: (x, y) → (-y, x)

  • A': (-4, 2) → (-2, -4)
  • N': (-4, 3) → (-3, -4)
  • G': (-1, 3) → (-3, -1)
  • L': (-1, 4) → (-4, -1)
  • E': (-5, 4) → (-4, -5)
  • S': (-5, 2) → (-2, -5)

Step 3: Now reflect the "new" couch over the y-axis.

Rule: (x, y) → (-x, y)

  • A'': (-2, -4) → (2, -4)
  • N'': (-3, -4) → (3, -4)
  • G'': (-3, -1) → (3, -1)
  • L'': (-4, -1) → (4, -1)
  • E'': (-4, -5) → (4, -5)
  • S'': (-2, -5) → (2, -5)

Step 4: Finally translate the new new" couch right 1 unit and up 5 units.

Rule: (x + 1, y + 5)

  • A''': (2, -4) → (2 + 1, -4 + 5) → (3, 1)
  • N''': (3, -4) → (3 + 1, -4 + 5) → (4, 1)
  • G''': (3, -1) → (3 + 1, -1 + 5) → (4, 4)
  • L''': (4, -1) → (4 + 1, -1 + 5) → (5, 4)
  • E''': (4, -5) → (4 + 1, -5 + 5) → (5, 0)
  • S''': (2, -5) → (2 + 1, -5 + 5) → (3, 0)

Step 5: Use the distance formula to show that the length of EG is the same as the length of E'''G'''.

  • EG: (-5, 4)(-1, 3)
  • E'''G''': (5, 0)(4, 4)

Distance between E(-5, 4) and G(-1, 3)

  • x₁ = -5
  • x₂ = -1
  • y₁ = 4
  • y₂ = 3

\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(-1-(-5))^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{(-1+5)^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{4^2+(-1)^2}$}\\\\\ \large \textsf {d = $\sqrt{16+1}$}\\\\\large \textsf {d = $\sqrt{17}$}\\\\\large \textsf {d = ${4.12}$}

Distance between E'''(5, 0) and G'''(4, 4)

  • x₁ = 5
  • x₂ = 4
  • y₁ = 0
  • y₂ = 4

\large \textsf  {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(4-5)^2+(4-0)^2}$}\\\\\large \textsf {d = $\sqrt{(-1)^2+4^2}$}\\\\\large \textsf {d = $\sqrt{1+16}$}\\\\\ \large \textsf {d = $\sqrt{17}$}\\\\ \large \textsf {d = ${4.12}$}

This means that the length of EG is the same as the length of E'''G'''.

Hope this helps!

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Answer: 0.383 and 0.6671

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Take 22%, that is 0.22 to be probability of success.

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n is the total number of sample =10

r is the varying outcome of number of success.

For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)

Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.

By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes

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=1 *1 * 0.0834= 0.0834

Hence, Probability of Choosing 0 adult that will Pay more is 0.0834

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This gives 1-0.617 = 0.383

Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.

To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.

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For probability of choosing 3 adults, it becomes

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For the probability of choosign 4 adults, it becomes

10C4 * 0.22^4 * 0.78^6

= 210 * 0.0023 * 0.2252 = 0.1088

For the probability of choosing 5 adults, it becomes

10C5 * 0.22^5 * 0.78^5

= 252 * 0.0005 * 0.2887 = 0.0364

Hence, the probability of choosing between 2 and 5 adults becomes

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