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Answer:
Step-by-step explanation:
Given is a table showing the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving.
Weight Fuel eff. x^2 xy y^2
X Y
28 20 784 560 400
3 22 9 66 484
35 19 1225 665 361
32 22 1024 704 484
30 23 900 690 529
29 21 841 609 441
Mean 26.16666667 21.16666667 797.1666667 549 449.8333333
Variance 112.4722222 1.805555556
Covariance -553.8611111
r -0.341120235
Correlaton coefficient =cov (xy)/S_x S_y
Covariance (x,y) = E(xy)-E(x)E(y)
The correlation coefficient between the weight of a car and the fuel efficiency is -0.341
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0
As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81
Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2
So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2
A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.
3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.
So 2k^2 = 9 + 3k have two rational solutions (Option B).
Hope this Helps! :)
The green arrow thing is a ray. So, question b. is a ray. So the dot would be B and the arrow would be C.
The volume of this right rectangular prism is 263.52 and it is to the nearest hundredths as a decimal, hope it helps!
