A right triangle has side lengths 7, 24, and 25 as shown below.
1 answer:
Answer: Tan B = 0.2917 (16.26 degrees)
Sin B = 0.2800 (16.26 degrees)
Cos B = 0.9600 (16.26 degrees)
Step-by-step explanation: Please refer to the picture attached for details.
The right angled triangle LNB has been drawn with the sides labeled as 7, 24 and 25 as indicated. With angle B as the reference angle, we can now identify each side as follows;
Side 7 (opposite, facing the reference angle)
Side 24 (adjacent, between the reference angle and the right angle)
Side 25 (hypotenuse, facing the right angle).
Hence, using the trigonometric ratios,
Tan B = opposite/adjacent
Tan B = 7/24
Tan B = 0.2917 (16.26 degrees)
Sin B = opposite/hypotenuse
Sin B = 7/25
Sin B = 0.2800 (16.26 degrees)
Cos B = adjacent/hypotenuse
Cos B = 24/25
Cos B = 0.9600 (16.26 degrees)
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Answer:
a)
Price=150.414-16.626 Age
b)
$34.032
c)
We can't estimate the price of 18 year old car using the above regression equation because the price of 18 year old car falls outside the scope of the model
Step-by-step explanation:
Age(X) Price(Y)
8 18
3 94
6 50
9 21
2 145
5 42
6 36
3 99
a)
The regression equation can be written as
y=a+bx
a=ybar-bxbar
xbar=sumx/n
xbar=(8+3+6+9+2+5+6+3)/8=5.25
ybar=sumy/n
ybar=(18+94+50+21+145+42+36+99)/8=63.125
x y x-xbar y-ybar (x-xbar)^2 (x-xbar)(y-ybar)
8 18 2.75 -45.125 7.5625 -124.09375
3 94 -2.25 30.875 5.0625 -69.46875
6 50 0.75 -13.125 0.5625 -9.84375
9 21 3.75 -42.125 14.0625 -157.96875
2 145 -3.25 81.875 10.5625 -266.09375
5 42 -0.25 -21.125 0.0625 5.28125
6 36 0.75 -27.125 0.5625 -20.34375
3 99 -2.25 35.875 5.0625 -80.71875
Total 43.5 -723.25
b=-723.25/43.5
b=-16.626
a=ybar-bxbar
a=63.125-(16.626)*5.25
a=150.414
Thus, the required regression equation is
y=150.414-16.626 x
Price=150.414-16.626 Age
b)
For predicting price of 7 years old car we put x=7 in the estimated regression equation
y=150.414-16.626 x
y=150.414-16.626(7)
y=150.414-116.382
y=34.032
The predicted price of a 7 year old car is $34.032.
c)
We can't estimate the price of 18 year old car using the above regression equation because the price of 18 year old car falls outside the scope of the model. The estimate of price is only valid for 2 to 9 year old car.