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3 years ago

8

Alicia has a gold bracelet and a silver bracelet. She has a black ring, a blue ring, a brown ring, and a white ring. She also ha

s a gold necklace and a silver necklace. How many different combinations of bracelets, rings, and necklaces can Alicia make?

1 answer:

Artist 52 [7]3 years ago

8 0

This may not be the right answer but I do believe it is 16 different combinations

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3 years ago

Solve for w.<br>9- w = 224

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3 years ago

The hypotenuse of a right triangle is 25 feet long The height of the right triangle is shrinking at a rate of 1 ft/week. What is

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9514 1404 393

Answer:

increasing 7/24 ft per week

Step-by-step explanation:

An expression for the length of the base can be written from the Pythagorean theorem relation between the sides of the triangle.

If the height is 7-x, where x is the number of weeks after the height is 7 feet, then the base length is ...

b = √(25^2 -(7-x)^2) = √(625 -(49 -14x +x^2)) = √(-x^2 +14x +576)

Then the rate of change of b with respect to x is ...

b' = (-2x +14)/(2√(-x^2 +14x +576))

When x=0, the rate of change of the base is ...

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The base is increasing 7/24 ft per week when the height is 7 ft.

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3 years ago

Paul wants to buy a car. He needs to take out a loan for $7000. The car salesman offers him a loan with an interest rate of 8%,

Alisiya [41]

Answer:

a. It will take approximately 40 months

b. The total amount Paul has to pay is approximately $8,000

c. The amount Paul pays each month is approximately $316.59

d. The amount Paul has to pay is approximately $7,598.16

e. Lower monthly payment

f. Lower total payment amount (amount to be paid)

Step-by-step explanation:

a. The loan amount, PV = $7,000

The annual interest rate, r = 8%

Option 1; The amount of equal monthly payment to repay the loan = $200

Option 2; The number of equal monthly payment to repay the loan = 24

The formula for the present value of an annuity is given as follows;

$PMT = \dfrac{\dfrac{r}{12} \times PV}{1 - \left (1 + \dfrac{r}{12} \right)^{-n}}$

Where;

PMT = The monthly payment

n = The number of months

Where PMT = $200, we have;

$200 = \dfrac{\dfrac{0.08}{12} \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-n}}$

$1 - \dfrac{\dfrac{0.08}{12} \times 7,000}{200} = \left (1 + \dfrac{0.08}{12} \right)^{-n}$

$1 - \dfrac{7}{30} = \dfrac{23}{30} = \left ( \dfrac{151}{150} \right)^{-n}$

$-n = \dfrac{ ln \left(\dfrac{23}{30} \right)}{ln\left(\dfrac{151}{150} \right) } \approx -39.988$

∴ The number of months it will take for Paul to repay the loan, n ≈ 39.988 ≈ 40 months

b. The total amount Paul has to pay, A = PMT × n

Therefore, b plugging in the values of PMT, and 'n', we get;

A ≈ $200 × 40 = $8,000

c. Using option 2, we have;

n = 24

Therefore;

$PMT = \dfrac{\dfrac{0.08}{12} \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-24}} \approx 316.59$

The monthly payment, PMT ≈ $316.59

d. The total amount Paul has to pay using option 2, A ≈ 316.59 × 24 = 7,598.16

The total amount Paul has to pay using option 2, A ≈ $7,598.16

e. A reason why Paul might choose option 1 is that option 1 offers lower monthly payment

f. A reason why Paul may choose option 2 is that option 2 offers a lower total amount that he has to pay.

5 0

3 years ago