The angle is 75.52 degrees
If there is a vector with the form a i + b j, the cosine of the angle between the given vector and the positive direction of the x - axis is calculated as:
cos θ =
So, given the vector i+, the cosine of the angle between the vector and the x-axis is:
cos θ = 0.25
Therefore, the angle θ between the given vector and the positive direction of the x-axis is:
θ = cos-1(0.25) = 75.52
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The height of the cone is 4 cm (approx).
Step-by-step explanation:
Given,
The radius (r) of the cone = 4.96 cm
Volume (V) = 102 cm³
To find the height (h) of the cone.
Formula
The volume of a cone V = πr²h
Now,
According to the problem,
πr²h = 102
or, ×
×(4.96)²h= 102
or, h =
or, h = 3.95 = 4 (approx)
so,
Height = 4 cm (approx)
Answer:
Step-by-step explanation:
to find the surface area we need to find the followng areas:
And once we have those areas, we add them to find the surface area.
Area of the square:
the formula to find the area of a square is:
where is the length of the side:
thus the area of the square is:
Area of the triangles:
the are of 1 triangle is given by
where is the base of the triangle:
(the base of the triangle is the side of the square)
and is the height of the triangle:
thus, the area of 1 triangle is:
the area of the 4 triangles is (we multiply by 4):
finally we add the area of the square and the area of the 4 triangles to find the total surface area:
Answer:
a. As college debt increases current investment decreases.
b. Y= 68778.2406 - 1.9112X
Every time the college debt increases one dollar, the estimated mean of the current investments decreases 1.9112 dollars.
c. There is a significant linear relationship between college debt and current investment because the P-value is less than 0.1.
d. Y= $59222.2406
e. R²= 0.9818
Step-by-step explanation:
Hello!
You have the information on a random sample of 20 individuals who graduated from college five years ago. The variables of interest are:
Y: Current investment of an individual that graduated from college 5 years ago.
X: Total debt of an individual when he graduated from college 5 years ago.
a)
To see the relationship between the information about the debt and the investment is it best to make a scatterplot with the sample information.
As you can see in the scatterplot (attachment) there is a negative relationship between the current investment and the debt after college, this means that the greater the debt these individuals had, the less they are currently investing.
The statement that best describes it is: As college debt increases current investment decreases.
b)
The population regression equation is Y= α + βX +Ei
To develope the regression equation you have to estimate alpha and beta:
a= Y[bar] -bX[bar]
a= 44248.55 - (-1.91)*12829.70
a= 68778.2406
b=
b=
b= -1.9112
∑X= 256594
∑X²= 4515520748
∑Y= 884971
∑Y²= 43710429303
∑XY= 9014653088
n= 20
Means:
Y[bar]= ∑Y/n= 884971/20= 44248.55
X[bar]= ∑X/n= 256594/20= 12829.70
The estimated regression equation is:
Y= 68778.2406 - 1.9112X
Every time the college debt increases one dollar, the estimated mean of the current investments decreases 1.9112 dollars.
c)
The hypotheses to test if there is a linear regression between the two variables are two tailed:
H₀: β = 0
H₁: β ≠ 0
α: 0.01
To make this test you can use either a Student t or the Snedecor's F (ANOVA)
Using t=<u> b - β </u>=<u> -1.91 - 0 </u>= -31.83
Sb 0.06
The critical region and the p-value for this test are two tailed.
The p-value is: 0.0001
The p-value is less than the level of signification, the decision is to reject the null hypothesis.
Using the
The rejection region using the ANOVA is one-tailed to the right, and so is the p-value.
The p-value is: 0.0001
Using this approach, the decision is also to reject the null hypothesis.
The conclusion is that at a 1% significance level, there is a linear regression between the current investment and the college debt.
The correct statement is:
There is a significant linear relationship between college debt and current investment because the P-value is less than 0.1.
d)
To predict what value will take Y to a given value of X you have to replace it in the estimated regression equation.
Y/X=$5000
Y= 68778.2406 - 1.9112*5000
Y= $59222.2406
The current investment of an individual that had a $5000 college debt is $59222.2406.
e)
To estimate the proportion of variation of the dependent variable that is explained/ given by the independent variable you have to calculate the coefficient of determination R².
R²= 0.9818
This means that 98.18% of the variability of the current investments are explained by the college debt at graduation under the estimated regression model: Y= 68778.2406 - 1.9112X
I hope it helps!
