Eddie took out a 14-year loan for $72,000 at an APR of 4.7%, compounded monthly, while Lee took out a 14-year loan for $92,000 a
2 answers:
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Answer:
$12.18
Step-by-step explanation:
Given:
Cost of 0.8 liter bottle of Mexican wine = 101 pesos
or
cost of 1 liter bottle of Mexican wine = pesos
Now,
1 Mexican pesos = 0.051 dollars
thus,
cost of 1 liter bottle of Mexican wine = dollars
also,
1 gallon = 3.78541 Liter
Thus,
half gallon = = 1.892705 Liters
therefore,
cost of half gallon jug = dollars
or
cost of half gallon jug of wine = $12.18
Answer:
Option A. 0.6 is the right answer.
Step-by-step explanation:
Given information is:
Mean = $240
SD = $60
The probability of Dan making less than $255 has to be found.
Let x = 255
First of all, we will find the z-score of the given value
Now the z-score table will be used to see the probability of less than 0.25
Using the z-score table, we get:
P(x<0.25) = 0.5987
As the answer choices are rounded off to one decimal place, we will round off our answer to one digit after the decimal point
0.5987 => 0.6
Hence,
Option A. 0.6 is the right answer.
Refer to the diagram shown below.
The exit for Freestone is built midway between Roseville and Edgewood,
therefore the distance from O to the new exit is
(1/2)*(33+55) = 44 mi.
Let x = distance from Midtown to the new exit.
Because the distance from O to the new exit is equal to (x + 17), therefore
x + 17 = 44
x = 44 - 17 = 27 mi.
Answer:
When the new exit is built, the distance from the exit for Midtown to the exit for Freestone will be 27 miles.
The exit for Freestone is built midway between Roseville and Edgewood,
therefore the distance from O to the new exit is
(1/2)*(33+55) = 44 mi.
Let x = distance from Midtown to the new exit.
Because the distance from O to the new exit is equal to (x + 17), therefore
x + 17 = 44
x = 44 - 17 = 27 mi.
Answer:
When the new exit is built, the distance from the exit for Midtown to the exit for Freestone will be 27 miles.
Answer:
Maximum: ((1,-2,5) ; 30)
Minimum: ((-1,2,-5) ; -30)
Step-by-step explanation:
We have the function f(x,y,z) = x - 2y + 5z, with the constraint g(x,y,z) = 30, with g(x,y,z) = x²+y²+z². The Lagrange multipliers Theorem states that, the points (xo,yo,zo) of the sphere where the function takes its extreme values should satisfy this equation:
grad(f) (xo,yo,zo) = λ * grad(g) (xo,yo,zo)
for a certain real number λ. The gradient of f evaluated on a point (x,y,z) has in its coordinates the values of the partial derivates of f evaluated on (x,y,z). The partial derivates can be calculated by taking the derivate of the function by the respective variable, treating the other variables as if they were constants.
Thus, for example, fx (x,y,z) = d/dx x-2y+5z = 1, because we treat -2y and 5z as constant expressions, and the partial derivate on those terms is therefore 0. We calculate the partial derivates of both f and g
- fx(x,y,z) = 1
- fy(x,y,z) = -2
- fz(x,y,z) = 5
- gx(x,y,z) = 2x (remember that y² and z² are treated as constants)
- gy(x,y,z) = 2y
- gz(x,y,z) = 2z
Thus, for a critical point (x,y,z) we have this restrictions:
- 1 = λ 2x
- -2 = λ 2y
- 5 = λ 2z
- x²+y²+z² = 30
The last equation is just the constraint given by g, that (x,y,z) should verify.
We can put every variable in function of λ, and we obtain the following equations.
- x = 1/2λ
- y = -2/2λ = -1/λ
- z = 5/2λ
Now, we replace those values with the constraint, obtaining
(1/2λ)² + (-1/λ)²+(5/2λ)² = 30
Developing the squares and taking 1/λ² as common factor, we obtain
(1/λ²) * (1/4 + 1 + 25/4) = (1/λ²) * 30/4 = 30
Hence, λ² = 1/4, or, equivalently,
If then 1/λ is 2, and therefore
- x = 1
- y = -2
- z = 5
and f(x,y,z) = f(1,-2,5) = 1 -2 * (-2) + 5*5 = 30
If then 1/λ is -2, and we have
- x = -1
- y = 2
- z = -5
and f(x,y,z) = f(-1,2,-5) = -1 -2*2 + 5*(-5) = -30.
Since the extreme values can be reached only within those two points, we conclude that the maximun value of f in the sphere takes place on ((1,-2,5) ; 30), and the minimun value takes place on ((-1,2,-5) ; -30).