Answer:
We conclude that the bowler's score is equal to 150 points.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 150
Sample mean,
= 2 157
Sample size, n = 22
Alpha, α = 0.05
Population standard deviation, σ = 18
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
z-statistic lies within the range of acceptance region that is from -1.96 to 1.96, we fail to reject the null hypothesis and accept the null hypothesis.
Thus, bowler claims that her bowling score is not equal to 150 points is not true and we conclude that the bowler's score is equal to 150 points.
4y^2 - 8y + 25x^2 +150x - 171 = 0
4y^2 - 8y + 25x^2 +150x - 171 = 0 Rearrange and regroup.
(25x^2 + 150x) + (4y^2 - 8y) = 0+171. Group the xs together and the ys together.
25(X^2 + 6x) + 4(y^2-2y) = 171. Factorising.
We are going to use completing the square method.
Coefficient of x in the first expression = 6.
Half of it = 1/2 * 6 = 3. (Note this value)
Square it = 3^2 = 9. (Note this value)
Coefficient of y in the second expression = -2.
Half of it = 1/2 * -2 = -1. (Note this value)
Square it = (-1)^2 = 1. (Note this value)
We are going to carry out a manipulation of completing the square with the values
9 and 1. By adding and substracting it.
25(X^2 + 6x) + 4(y^2-2y) = 171.
25(X^2 + 6x + 9 -9) + 4(y^2-2y + 1 -1) = 171
Note that +9 - 9 = 0. +1 -1 = 0. So the equation is not altered.
25(X^2 + 6x + 9) -25(9) + 4(y^2-2y + 1) -4(1) = 171
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1) Transferring the terms -25(9) and -4(1)
to other side of equation.
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1)
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 400
We now complete the square by using the value when coefficient was halved.
25(x+3)^2 + 4(y-1)^2 = 400
Divide both sides of the equation by 400
(25(x+3)^2)/400 + (4(y-1)^2)/400 = 400/400 Note also that, 16*25 = 400.
((x+3)^2)/16 + ((y-1)^2)/100 = 1
((x+3)^2)/(5^2) + ((y-1)^2)/(10^2) = 1
Comparing to the general format of an ellipse.
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
Coordinates of the center = (h,k).
Comparing with above (x+3) = (x - h) , h = -3.
Comparing with above (y-1) = (y - k) , k = 1.
Therefore center = (h,k) = (-3, 1).
You can easily draw the ellipse...Cheers.
The actual is 60 feet long, the drawing is only 1 foot long. So the scale factor must be 1/60. You know that the scale factor has to be less than one in this case because you're going from a bigger measurement to a smaller measurement(60 to 1).
Answer:
A. v(t) = sin (2πft + π/2) = A cos (2πft)
Step-by-step explanation:
According to trigonometry friction, the following relationship are true;
Sin(A+B) = sinAcosB + cosAsinB
We will be using this relationship to check which option is true.
Wave equation is represented as shown;
y(t) = Asin(2πft±theta)
For positive displacement,
y(t) = Asin(2πft+theta)
If theta = π/2
y(t) = Asin(2πft+π/2)
y(t) = A[ sin 2πftcosπ/2 + cos2πft sin π/2]
Since sinπ/2 = 1 and cos (π/2) = 0
y(t) = A[ sin 2πft (0)+ cos2πft (1)]
y(t) = A[0+ cos2πft]
y(t) = Acos2πft
Hence the expression that is true is expressed as;
v(t) = Asin(2πft+π/2) = Acos2πft