Math Answers

A random sample of 50 perceived age estimates for a model in a cigarette advertisement showed that Picture = 26.72 years and that s = 3.7323 years.

(a)
Use this sample to calculate a 95 percent confidence interval for the population mean age estimate for all viewers of the ad. (Round your answers to 3 decimal places.)

The 95 percent confidence interval is [
,
].

(b)
Remembering that the cigarette industry requires that models must appear at least 25 years old, does the confidence interval make us 95 percent confident that the population mean perceived age estimate is at least 25? Is the mean perceived age estimate much more than 25?

, than 25.

the differential equation y"'-y''=8x^2. I know after solving the homogeneous part of the equation you get that 1 and 0 are roots of the equation. I know for the 8x^2 you're supposed to substitute the constant for a variable then that would be Ax^2 and that i have to derive three times, My question is, after i derive three times what would i do with the second and the first derivative? there isn't any y'' or y' where to replace that in the original equation. Thanks you very much!

Find range of f(x) = 4/(6sinx+5cosx+7)

if theta=sin^-1(x)+cos^-1(x)-tan^-1(x) and x>0 or x=0 then
optins-1)45<theta<90
2)0<theta<180

INTEGERS AND DIVISIBILITY CONCEPTS

1.Show that if d ≠ 0, then d | (-a) and -d | a.
2.Show that it is false that a>b implies a|b.
3.Is 980637 divisible by 7? Show.
4.Determine whether of the following are divisible by 3, 5, 7, 9, or 11 using the methods described int he text:
A. 1969
B. 28350
C. 1421
D. 17303
E. 116424
F. 1089
5.Classify each of the following as true or false:
A. 6 is a divisor of 24.
B. 40 is a multiple of 8.
C. 0 divides 10.
D. 13 is a factor of 33.
E. 12 divides 6.
6.Show that 23n -1 is divisible by 7.
7.Show that 5n - 1 is divisible by 4.

GREATEST COMMON FACTOR (GCF) AND THE LEAST COMMON MULTIPLE (LCM)

1.Calculate (3141 , 1592).
2.Find x and y such that, 3141x + 1592y =1.
3.Find the solution of 803x + 154y = 33.
4.Find the GCD and LCM of the numbers 63,24, 99.

2.Find the focus, vertex, directrix, and axis of the parabola. Sketch the curve.
A.Y = x2- 2x + 3
B. X = y2 + 2x - 4
C.Y = -2x2 +4x + 5

3.Find the equations of the parabolas from the definition
A.Directrix X = 0, focus at (6,0)
B.Vertex (0,4), focus (0,2)
C.Vertex (-2,0), directrix X= 1
D.Focus (-1,-2) directrix: X - 2y + 3 = 0

ELLIPESE
1.Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, the eccentricity, the coordinates of the foci and vertices. Sketch the ellipse.
2.Find the equation of the ellipse with eccentricity 3/4. Foci in the y-axis, center at origin, and passing through (6,4).

CIRCLES
1.Find the equation of the circle with center at (2,3), tangent to the line 3x +4y + 2 = 0. Answer x2 + y2 -4y -6y - 3 = 0.
2.Find the equation of the circle tangent to both axes, radius 6, in the second quadrant. Answer x2 + y2 + 12x - 12y +36 = 0.
3.Find the equation of the line tangent to the circle x2 + y2 + 2x -4y = 0 at P(1,3) on the circle.

PARABOLA
1.Find the equation of the parabola with vertex at the origin which satisfies the given additional condition:

A.Focus(-3,0)
B.Directrix: y-2
C.Passing through (2,3) and axis along the x-axis
D.Passing through (2,3) and axis along the y-axis

DIVISION OF LINE SEGMENT
1.The segment joining (1,3), and (4,6) is extended a distance equal to one-sixth of its own length. Find the terminal points.
2.The vertices of a triangle are (-3,-7), (3,1), and (-8,2). Find the intersection of its medians.
3.A circle has its center at (3,-2) and one end of a diameter at (7,2). Find the other end of the diameter.

DISTANCE FROM A POINT TO A LINE
1.Find the distance from the line 3x + 7y + 12 = 0 to (6,-7)
2.Find the distance from the line 2x - y + 4 = 0 to (2,8)
3.Find the distance of the line x + 4y - 7 = 0 to (-5,4)
4.Find the bisectors of the interior angles of the triangle whose sides are the lines 7x + y - 7 = 0; x + y + 1 = 0; and x + 7y -4 = 0.
5.Find the distance of the point (6,-3) from the line 2x - y + 4 = 0.
6.Find the bisector of the obtuse angle between the lines 11x + 2y - 7 = 0 and x + 2y = 0.

DISTANCE BETWEEN TWO POINTS
1.Show that the points (2,-3), (5,0), (2,3) and (-1,0), are the vertices of a square.
2.The distance (x,1) is 2√5 units from (2,3). Find x.
3.What are the coordinates of the point 3 units from the y-axis and at distance √5 from (5,3)?

EQUATIONS OF LINES
1.What is the equation of a line through (7,-3) and perpendicular to the line whose inclination is Arctan 2.
2.Show that lines 2x + 3y - 2 = 0, 3x - 2y + 23 = 0 and x - 5y + 12 = 0 are the sides of an isosceles triangle.
3.What is the equation of the line passing through (4, -7) and perpendicular to the line through (0, 1) and (3, -3).
4.Find the equations of the altitudes of the triangle with vertices at (1, -1), (5,2) and (-2,4). Where do they intersect?

Find the equations of the straight lines which pass through the intersection of 3x-4y+1=0 and 5x+y=1 and which cut off equal intercepts from the axes