Rounding the answer to the nearest dollar, the monthly payment would be $475. Therefore, the correct answer is $475.
To calculate the monthly payments for a car loan, we can use the formula for the monthly payment on an amortizing loan:
P = (r * PV) / (1 - [tex](1 + r)^-^n[/tex])
Where:
P is the monthly payment
r is the monthly interest rate
PV is the loan principal (the amount borrowed)
n is the total number of payments
In this case, the loan principal (PV) is $20,000, the interest rate (r) is 14% per year, compounded monthly (monthly interest rate is 14%/12), and the total number of payments (n) is 4 years * 12 months/year = 48 months.
Let's calculate the monthly payment:
r = 14% / 12 = 0.14 / 12 = 0.01167 (monthly interest rate)
PV = $20,000
n = 48
P = (0.01167 * 20000) / (1 - [tex](1 + 0.01167)^-^4^8[/tex])
P ≈ $475.24
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Consider f(x)=−2x^2+4x+6 Evaluate the difference quotient f(2)-f(1)/2-1 . Use the equation editor to illustrate the process. What does f(2)-f(1)/2-1mean in terms of its relationship to f(x)=−2x^2+4x+6? Type
This code will print the value of the difference quotient, which is -2.
The difference quotient is a way of approximating the derivative of a function at a point. In this case, we are approximating the derivative of f(x) = -2x^2 + 4x + 6 at x = 1.
To evaluate the difference quotient, we first need to evaluate f(2) and f(1). f(2) = -2(2)^2 + 4(2) + 6 = 2 and f(1) = -2(1)^2 + 4(1) + 6 = 8.
Now, we can plug these values into the difference quotient formula to get:
```
f(2)-f(1)/(2-1) = (2)-(8)/(2-1) = -2
```
The difference quotient of a function at a point is equal to the slope of the secant line that intersects the graph of the function at that point. In this case, the secant line intersects the graph of f(x) = -2x^2 + 4x + 6 at x = 1 and x = 2. Therefore, the slope of the secant line is equal to the difference quotient, which is -2.
**Equation editor**
```python
def f(x):
return -2*x**2 + 4*x + 6
print(f(2)-f(1)/(2-1))
```
The difference quotient f(2)-f(1)/(2-1) = -2.
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Find the mean, variance, and standard deviation for the data set.
5,15,9,3,12,8,13,6,18,11
For the given data set, the mean is 10, the variance is 19.8, and the standard deviation is approximately 4.45.
We have,
The given data set is: 5, 15, 9, 3, 12, 8, 13, 6, 18, 11.
To find the mean, variance, and standard deviation, we can follow these steps:
Step 1: Calculate the mean:
Mean (μ) = (Sum of all values) / (Number of values)
Mean = (5 + 15 + 9 + 3 + 12 + 8 + 13 + 6 + 18 + 11) / 10
Mean = 100 / 10
Mean = 10
Step 2: Calculate the variance:
Variance (σ²) = (Sum of squared differences from the mean) / (Number of values)
To calculate the variance, we need to find the squared differences from the mean for each value:
(5 - 10)² + (15 - 10)² + (9 - 10)² + (3 - 10)² + (12 - 10)² + (8 - 10)² + (13 - 10)² + (6 - 10)² + (18 - 10)² + (11 - 10)²
Calculating the squared differences:
25 + 25 + 1 + 49 + 4 + 4 + 9 + 16 + 64 + 1 = 198
Variance = 198 / 10
Variance = 19.8
Step 3: Calculate the standard deviation:
Standard Deviation (σ) = Square root of the variance
Standard Deviation = √(19.8)
Standard Deviation ≈ 4.45 (rounded to two decimal places)
Therefore,
For the given data set, the mean is 10, the variance is 19.8, and the standard deviation is approximately 4.45.
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The open area south of the White House is known as the Ellipse, or President's Park South. It is 902ft wide and 1058 ft long. Assume the origin is at the center of the President's Park South. What is the equation of the ellipse in standard form?
c. How can you write the equation of the ellipse in standard form?
The equation of the ellipse in standard form, with the origin at the center, is: x²/203401 + y²/279841 = 1
To write the equation of an ellipse in standard form, we need to use the following information:
The width of the ellipse (2a): 902 ft
The length of the ellipse (2b): 1058 ft
In addition, since the origin is at the center of President's Park South, the coordinates of the center are (0,0).
The standard form equation of an ellipse centered at the origin is:
x²/a² + y²/b² = 1
To find the values of a and b, we divide the width and length by 2:
a = 902 ft / 2 = 451 ft
b = 1058 ft / 2 = 529 ft
Now we can substitute these values into the equation:
x²/451² + y²/529² = 1
Simplifying further, we have:
x²/203401 + y²/279841 = 1
Therefore, the equation of the ellipse in standard form, with the origin at the center, is:
x²/203401 + y²/279841 = 1
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On Monday, the temperature was –5°F. On Tuesday it rose 12 degrees. What was the temperature on Tuesday?
Answer:
7° F
Step-by-step explanation:
Originally the temperature was -5°.
It rose 12 degrees after that.
This means we have to add 12 degrees to the original temperature.
-5 + 12 = 7
So, on Tuesday, the temperature was 7° F.
Hope this helps! :)