A number is multiplied by 4 then 7 is added to the product after subtracting 3 the result is 8. what is the number
2 answers:
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Answer:
The x-intercept of CD is B(18/5,0). The point C(32,-71) lies on the line CD.
Step-by-step explanation:
the x-intercept of CD is[ A(3,0) B(18/5,0) C(9,0) D(45/2,0) ] . Point [ A(-52,117) B(-20,57) C(32,-71) D(-54,-128) ] lies on CD.
Given :
CD is perpendicular bisector of AB.
The coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6).
C is the midpoint of AB.
The coordinates of C are (2,4).
Line AB has a slope of:
The product of slopes of two perpendicular lines is -1. Since the line CD is perpendicular to AB, therefore the slope of CD :
The point slope form of a line is given by:
The slope of line CD is and the line passing through the point (2,4), the equation of line CD can be written as:
The equation of CD is
In order to find the x-intercept, put y=0.
Therefore the x-intercept of CD is B(18/5,0).
Put x=-52 in eq(1).
Put x=-20 in eq(1).
Put x=32 in eq(1)
Put x=-54 in eq1).
Thus, only point (32,-71) satisfies the equation of CD. Therefore the point C(32,-71) lies on the line CD.
Answer:
Part 1: The statistic
(1)
And the degrees of freedom are given by
Replacing we got
Part 2: P value
Since is a right tailed test the p value would be:
Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense
Step-by-step explanation:
Data given
represent the mean for four year college
represent the mean for two year college
represent the sample standard deviation for four year college
represent the sample standard deviation two year college
sample size for the group four year college
sample size for the group two year college
Significance level provided
t would represent the statistic (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the mean enrollment at four-year colleges is higher than at two-year colleges in the United States , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We can assume that the normal distribution is assumed since we have a large sample size for each case n>30. So then the sample mean can be assumed as normally distributed.
Part 1: The statistic
(1)
And the degrees of freedom are given by
Replacing we got
Part 2: P value
Since is a right tailed test the p value would be:
Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense
