Answer:
a) y = 0.74x + 18.99; b) 80; c) r = 0.92, r² = 0.85; r² tells us that 85% of the variance in the dependent variable, the final average, is predictable from the independent variable, the first test score.
Step-by-step explanation:
For part a,
We first plot the data using a graphing calculator. We then run a linear regression on the data.
In the form y = ax + b, we get an a value that rounds to 0.74 and a b value that rounds to 18.99. This gives us the equation
y = 0.74x + 18.99.
For part b,
To find the final average of a student who made an 83 on the first test, we substitute 83 in place of x in our regression equation:
y = 0.74(83) + 18.99
y = 61.42 + 18.99 = 80.41
Rounded to the nearest percent, this is 80.
For part c,
The value of r is 0.92. This tells us that the line is a 92% fit for the data.
The value of r² is 0.85. This is the coefficient of determination; it tells us how much of the dependent variable can be predicted from the independent variable.
Answer:
C. Integer
Step-by-step explanation: Since the square root of 144 could either be -12 or 12, so it is an integer.
So, how far is the car from where it was at t = 0 is 40 m
<h3>Velocity of the car</h3>
Since the location x of the car in meters is given by the function x = 30t - 5t² where t is in seconds, we need to find the time at which its velocity is 10 m/s in the negative direction by differentiating x with respect to t to find its velocity, v.
So, v = dx/dt
= d(30t - 5t²)/dt
= d30t/dt - d5t²/dt
= 30 - 10t
When v is 10 m/s in the negative direction, v = -10 m/s.
So, v = 30 - 10t
-10 = 30 - 10t
-10 - 30 = -10t
-40 = -10t
t = -40/-10
t = 4 s
<h3>The distance at 4 s when its velocity is -10 m/s</h3>
Since at t = 4 s, its velocity is -10 m/s and x = 30t - 5t² is the car's location. The car's distance from t = 0 after its velocity is -10 m/s is
x(4) - x(0) = 30(4) - 5(4)² - [30(0) - 5(0)²]
= 120 - 5(16) - [0 - 0]
= 120 - 80 - 0
= 40 m
So, how far is the car from where it was at t = 0 is 40 m
Learn more about distance of car here:
brainly.com/question/17097458
5x/2 = 10/11
55x = 20
x = 4/11
**Not sure if I did this right I think I did
Answer:
289feet²
Step-by-step explanation:
Area of a rectangle = length x breadth
area of a square = length²
area of the yard that is not covered by the hot tub and fire pit =
Area of the yard - (area of the hot tub + area of the fire pit)
Area of the yard = 20 feet² = 400 feet²
area of the hot tub = 6 feet² x 8 feet² = 48 feet²
area of the fire pit = 7 feet² x 9 feet² = 63 feet²
400 - (48 + 63) = 289 feet²
