Write an equation for the line that passes through (4,10) and is perpendicular to the line 6x-3y=5
2 answers:
Answer:
y = x + 12
Step-by-step explanation:
Given expressions:
Coordinates = (4,10)
Equation of the line; 6x - 3y = 5
Unknown:
Equation of the line perpendicular = ?
Solution:
A line perpendicular to the given one will have a negative inverse slope.
Equation of any given line is expressed as:
y = mx + c
y and x are the coordinates
m is the slope
c is the intercept
Now; re-write 6x-3y = 5 in the form y= mx + c and find the slope;
6x - 3y = 5
-3y = 5- 6x
y = + 2x
The slope of a perpendicular line will be
Also, let us find the y-intercept, c;
y = mx + c
10 = x 4 + c
10 = -2 + c
c = 12
The equation of the new line is ;
y = x + 12
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<h2>Answer with explanation:</h2>
Given : In a restaurant, the proportion of people who order coffee with their dinner is p.
Sample size : n= 144
x= 120
The null and the alternative hypotheses if you want to test if p is greater than or equal to 0.85 will be :-
Null hypothesis : [ it takes equality (=, ≤, ≥) ]
Alternative hypothesis : [its exactly opposite of null hypothesis]
∵Alternative hypothesis is left tailed, so the test is a left tailed test.
Test statistic :
Using z-vale table ,
Critical value for 0.05 significance ( left-tailed test)=-1.645
Since the calculated value of test statistic is greater than the critical value , so we failed to reject the null hypothesis.
Conclusion : We have enough evidence to support the claim that p is greater than or equal to 0.85.