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aleksandr82 [10.1K]
3 years ago
12

Debbie invests $100 in an account that pays 3% annual interest, compounded monthly. Rachel invests $80 in an account that pays 2

.5% annual interest compounded weekly. Whose balance is greater after 1 year?
Mathematics
1 answer:
Viefleur [7K]3 years ago
6 0

Answer:

Greetings!

The formula for compound interest is A = P(1+r)^t, where A = total amount, P = principal (initial amount), r = interest rate (in decimal form), and t = time in years. The rate is 5%. 5% is 0.05 in decimal form. 1 + 0.05 is 1.05. 1 is added, because the 1 represents the whole amount and the amount of money in the account grows. t = 10. Using a calculator, raise 1.05^10. You should get the long decimal 1.62889462678. Do not delete it from the calculator. Multiply it by 1,000 to find the new amount. You get 1,628.89462678 or 1,628.89 when rounded to the nearest hundredth. There. Rachel will have $1,628.89 in her bank account after 10 years.

Step-by-step explanation:

can i get brianist

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At the local video game store, a popular game went from $120 to $85 in a weeks time. What is the percent decrease of the item? R
Svetllana [295]

Answer: 29%

Step-by-step explanation:

The game went from the price of $120 to $85.

In calculating percentage decrease, use the following formula:

= (New Price - Old price) / Old price

= (85 - 120) / 120

= -35 / 120

= -29%

<em>Price therefore decreased by 25%</em>

6 0
3 years ago
Which of the following is a perfect square trinomial?
yanalaym [24]
Your answer is D. 16x² - 56xy + 49y².

A perfect square trinomial is the result of a squared binomial, like (a + b)². Using this example, the perfect square trinomial would be a² + 2ab + b², as that is what you get when you expand the brackets.

Therefore, to determine which of these is a perfect square trinomial, we have to see if it can be factorised into the form (a + b)².

I did this by first square rooting the 16x² and 49y² to get 4x and 7y as our two terms in the brackets. We automatically know the answer isn't A or B as you cannot have a negative square number.

Now that we know the brackets are (4x + 7y)², we can expand to find out what the middle term is, so:

(4x + 7y)(4x + 7y)
= 16x² + (7y × 4x) + (7y × 4x) + 49y²
= 16x² + 28xy + 28xy + 49y²
= 16x² + 56xy + 49y².

So we know that the middle number is 56xy. Now we assumed that it was (4x + 7y)², but the same 16x² and 49y² can also be formed by (4x - 7y)², and expanding this bracket turns the +56xy into -56xy, forming option D, 16x² - 56xy + 49y².

I hope this helps!
6 0
3 years ago
Read 2 more answers
Allison can jog 3 blocks in the same amount of time it takes her brother, Blake, to jog 2 blocks. If they keep jogging at the sa
Nitella [24]

Answer:

Blake will jog 12 blocks

Step-by-step explanation:

Allison : Blake = 3 : 2

If they keep jogging at the same rate, how many blocks will Blake jog if Allison jogs 18 blocks?

Allison : Blake = 18 : x

Equate the ratios

3 : 2 = 18 : x

3/2 = 18/x

Cross multiply

3 * x = 2 * 18

3x = 36

Divide both sides by 3

x = 36 / 3

= 12

x = 12

Blake will jog 12 blocks

6 0
3 years ago
Read 2 more answers
A ladder is leaning against a tall wall with the foot of the ladder placed at 7 feet from the base of the wall and the angle of
djverab [1.8K]

Complete question is;

A 21 ft ladder is leaning against a tall wall with the foot of the ladder placed at 7 feet from the base of the wall and the angle of elevation is?

Answer:

θ = 70.5°

Step-by-step explanation:

The angle of elevation simply means the angle that the ladder makes with the ground. Let's call this angle θ.

I've attached a diagram showing the triangle made by this ladder and the wall.

From the attached diagram, we can see the triangle formed by the ladder and the wall.

We can find the angle of elevation θ from trigonometric ratios.

Thus;

7/21 = cos θ

cos θ = 0.3333

θ = cos^(-1) 0.3333

θ = 70.5°

7 0
3 years ago
A. What is the circumference of the
erik [133]

Answer:

a) 94.2 cm

b) 78.5%

Step-by-step explanation:

a) since the square side = 30 cm

it means the diameter = 30 cm

then circumference of the largest circle that can be cut = 3.14×30 = 94.2 cm

b) the perimeter of the square = 30×4 = 120

94.2 for 120

x% for 100%

x = (100×94.2)/120 = 9420/120 = 942/12 = 78.5%

6 0
3 years ago
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