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1 year ago

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An auto dealership is advertising that a new car with a sticker price of $35,208 is on sale for $25,995 if payment is made in fu

ll, or it can be financed at 0% interest for 72 months with a monthly payment of $489. Note that 72 payments × $489 per payment = $35,208, which is the sticker price of the car. By allowing you to pay for the car in a series of payments (starting one month from now) rather than $25,995 now, the dealer is effectively loaning you $25,995. If you choose the 0% financing option, what is the effective interest rate that the auto dealership is earning on your loan?

1 answer:

frutty [35]1 year ago

6 0

The answer is: APR = 10.56%

Explanation: Using an excel spreadsheet and the RATE function, we can calculate the monthly interest rate of buying the car:

=RATE(72,-489,25995)

= 0.8803% monthly interest rate

Then we multiply the monthly interest rate by twelve to get the APR:

APR = 0.8803% x 12 = 10.56%

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Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

Masja [62]

Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

(c) What is the maximum height of the quarter?

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112

= -144 + 288 + 112

= 256

The maximum height is therefore 256 feet, and time needed to reach the height will be 3 seconds.

c. The maximum height has been calculated and it is 256 feet.

d. The time it take for the quarter to hit the water will be:

= 3 seconds × 2 = 6 seconds

Since the maximum height took 3 seconds, it would take another 3 seconds to hit the water. This makes it 6 seconds

4 0

2 years ago

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 –

SVETLANKA909090 [29]

We have to identify the function which has the same set of potential rational roots as the function $g(x)= 3x^5-2x^4+9x^3-x^2+12$ .

Firstly, we will find the rational roots of the given function.

Let 'p' be the factors of 12

So, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' be the factors of 3

So, q= $\pm 1, \pm 3$

So, the rational roots are given by $\frac{p}{q}$ which are as:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Consider the first function given in part A.

f(x) = $3x^5-2x^4-9x^3+x^2-12$

Here also, Let 'p' be the factors of 12

So, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' be the factors of 3

So, q= $\pm 1, \pm 3$

So, the rational roots are given by $\frac{p}{q}$ which are as:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Therefore, this equation has same rational roots of the given function.

Option A is the correct answer.

4 0

2 years ago

Read 2 more answers

Sylvia invested $500 in an account compounded annually with an interest rate of 8%. Manuel invested $600 in an account with a co

Sav [38]

Syliva
T=72÷8=9 years

Manul
T=72÷7.25=9.9=10 years

Option A

8 0

2 years ago

Read 2 more answers

Report Error Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\

motikmotik

Answer:

We want a polynomial of smallest degree with rational coefficients with zeros in $\sqrt{7}$ , $1 - \sqrt{6}$ and -3. The last root gives us the factor (x+3). Hence, our polynomial is

$P(x) =(x+3)q(x)$

where $q$ is a polynomial with rational coefficients and roots $\sqrt{7}$ and $1 - \sqrt{6}$ . The root $\sqrt{7}$ gives us a factor $x-\sqrt{7}$ , but in order to obtain rational coefficients we must consider the factor $x^2-7$ .

An analogue idea works with $1 - \sqrt{6}$ . For convenience write $x - 1 + \sqrt{6} = ( x - 1) + \sqrt{6}$ . This gives the factor $(x-1)^2-6$ . Hence,

$P(x) = (x+3)(x^2-7)((x-1)^2-6)=x^5+x^4-18x^3-22x^2+77x+105$

Notice that $P(-1)=24$ . So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

$P(x) =(1/3)x^5+(1/3)x^4-6x^3-(22/3)x^2+(77/3)x+35$

Step-by-step explanation:

We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type $x-\sqrt7$ will introduce in the expression, we need to multiply by its conjugate $x+\sqrt7$ . Hence, we will obtain $x^2-7$ that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.

4 0

2 years ago

A golf-course architect has fivefive linden trees, fourfour white birch trees, and threethree bald cypress trees to plant in

adell [148]

Answer:

27,720 ways

Step-by-step explanation:

The number of permutations of non-distinct items is determined by the following expression:

$P = \frac{(N_1+N_2+N_3)!}{N_1!N_2!N_3!}$

If there are five linden trees, four white birch trees, and three bald cypress trees:

$P = \frac{(5+4+3)!}{5!4!3!}\\P=27,720\ ways$

The landscaper can plant the trees is 27,720 distinct ways.

7 0

2 years ago