Answer:
Correct option: A. Weight.
Step-by-step explanation:
In regression analysis there are two kinds of variables: Explanatory and Response variable.
The explanatory variable are used to predict the changes in the response variable. They are also known as independent or predictor variable.
The response variable are observed for any changes caused by the explanatory variable. They are also known as the dependent or experimental variable.
In this case it is provided that heavier cars have lower fuel efficiencies.
It implies that there is linear inverse relationship between the variables weight of the car and fuel efficiency.
The response variable is the fuel efficiency and the explanatory variable is the weight of the car. Since the weight of the car is used to determine the fuel efficiency.
Thus, the explanatory variable is the weight of the car.
From the scatter plot, the equation that could represent the relationship shown is y = 1/2x + 7.
Answer:
p v q = x < -3 or x > 3
Step-by-step explanation:
We are given
p: x < -3
q: x > 3
and we need to find p v q
v symbols represents disjunction and in simple terms it is called "or"
So, p v q represents either p holds or q holds
So, p v q = x < -3 or x > 3
Answer:
Step-by-step explanation:
To prove sin(a+b)*sin(a-b)=cos^2b-cos^2a
we simplify the left side sin(a+b)*sin(a-b) first
sin(a+b) = sin a cos b + cos a sin b
sin(a-b) = sin a cos b - cos a sin b
sin(a+b)*sin(a-b) = (sin a cos b + cos a sin b) x (sin a cos b -cos a sin b)
sin a cos b((sin a cos b + cos a sin b) - cos a sin b (sin a cos b + cos a sin b)
open the bracket
sin a cos b(sin a cos b) + sin a cos b(cos a sin b) -cos a sin b (sin a cos b)+ cos a sin b ( cos a sin b)
sin²a cos²b + sin a cos b cos a sin b - cos a sin b sin a cos b + cos²a sin²b
sin²a cos²b + 0 + cos²a sin²b
sin²a cos²b + cos²a sin²b
- sin²a = 1-cos² a
- sin²b = 1-cos² b
(1-cos² a)cos² b - cos² a(1-cos² b)
= cos² b - cos² a cos² b - cos² a +cos² a cos² b
cos² b - cos² a - cos² a cos² b + cos² a cos² b = cos² b - cos² a + 0
cos² b - cos² a
left hand side equals right hand side
Answer:
x = 7.5
Step-by-step explanation:
5/6 = 10/2x-3
Solve using cross products
5 ( 2x-3) = 6*10
Divide each side by 5
2x-3 = 6*10/5
2x-3 =12
Add 3 to each side
2x-3+3 = 12+3
2x =15
Divide each side by 2
2x/2 = 15/2
x = 7.5
