Hippalectryon
1 answer:
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Answer:
Area of Δ ABC = 21.86 units square
Perimeter of Δ ABC = 24.59 units
Step-by-step explanation:
Given:
In Δ ABC
∠A=45°
∠C=30°
Height of triangle = 4 units.
To find area and perimeter of triangle we need to find the sides of the triangle.
Naming the end point of altitude as 'D'
Given
For Δ ABD
Since its a right triangle with one angle 45°, it means it is a special 45-45-90 triangle.
The sides of 45-45-90 triangle is given as:
Leg1
Leg2
Hypotenuse
where is any positive number
We are given BD(Leg 1)=4
∴ AD(Leg2)=4
∴ AB (hypotenuse)
For Δ CBD
Since its a right triangle with one angle 30°, it means it is a special 30-60-90 triangle.
The sides of 30-60-90 triangle is given as:
Leg1(side opposite 30° angle)
Leg2(side opposite 60° angle)
Hypotenuse
where is any positive number
We are given BD(Leg 1)=4
∴ CD(Leg2)
∴ BC (hypotenuse)
Length of side AC is given as sum of segments AD and CD
Perimeter of Δ ABC= Sum of sides of triangle
⇒ AB+BC+AC
⇒
⇒ units
Area of Δ ABC =
⇒
⇒ units square
Answer:
The inspector's claim has strong statistical evidence.
Step-by-step explanation:
To answer this we have to perform a hypothesis test.
The inspector claimed that the actual proportion of code violations is greater than 0.07, so the null and alternative hypothesis are:
We assume a significance level of 0.05.
The sample size is 200 and the proportion of the sample is:
The standard deviation is
The z-value can be calculated as
The P-value for this z-value is P=0.00914.
This P-value is smaller than the significance level, so the effect is significant and the null hypothesis is rejected.
The inspector's claim has strong statistical evidence.