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jekas [21]
3 years ago
13

Help please!! Step by step!!

Mathematics
1 answer:
GarryVolchara [31]3 years ago
5 0

Answer:

P(Ice Cream|Frogtown) = 67.4\%

Step-by-step explanation:

Given

The attached plot

Required

P(Ice Cream|Frogtown)

This is calculated as:

P(Ice Cream|Frogtown) = \frac{P(Ice\ Cream\ n\ Frogtown)}{P(Frogtown)}

From the attachment;

P(Ice\ Cream\ n\ Frogtown) = 0.31

P(Frogtown) = 0.31 + 0.15 = 0.46

So, we have:

P(Ice Cream|Frogtown) = \frac{P(Ice\ Cream\ n\ Frogtown)}{P(Frogtown)}

P(Ice Cream|Frogtown) = \frac{0.31}{0.46}

P(Ice Cream|Frogtown) = 0.6739

Express as percentage

P(Ice Cream|Frogtown) = 0.6739 * 100\%

P(Ice Cream|Frogtown) = 67.39\%

P(Ice Cream|Frogtown) = 67.4\% -- approximated

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Answer:

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Discussion:

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Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

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Step-by-step explanation:

~Refer to the attachment for the solution.

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