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mixas84 [53]
3 years ago
11

Ms. Etienne deposited $450 into an account that paid 5% interest compounded annually. She did not make any

Mathematics
1 answer:
Alexus [3.1K]3 years ago
6 0

Answer:

$603.04

Step-by-step explanation:

The Compound Amout formula is A = P(1 + r)^t, where:

P is the principal (initial deposit), r is the annual interest rate as a decimal fraction, and t is the time period in years.

In this particular case, the Compound Amount is:

A  = ($450)(1 + 0. 05)^6 = ($450)(1.34) = $603.04

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The height in feet above the water of a diver can be modeled by ℎ() = −16*2 − 16 + 192, where t is the time in seconds after the
Maurinko [17]

h(t) is the height of the diver in feet above the water

Now it asks about the time at which diver reaches the water

When diver reaches the water , the height of diver from water should be zero

So we plug h(t) =0

So

-16t^2 -16 t +192 =0

divide whole equation by -16

t^2 +t -12 =0

we can now factor the quadratic equation

So we get

(t+4)(t-3) =0

plug each factor equal to zero and solve for t

t+4 =0 and t-3 =0

So t=-4 and t=3

Now time cannot be negative , So t=3

So time = 3 seconds

It takes 3 seconds for the diver to reach the water

3 0
4 years ago
Ben wants to try a new honey-glazed salmon recipe. He starts with 1 2/3 cups of honey. He uses 1/5 of it to make the glaze. How
GalinKa [24]

Answer:

1 1/3

Step-by-step explanation:

Firstly, 1 2/3 is converted into an improper fraction being 5/3. Next, 1/5 of 5/3 is one portion of 5 equal portions. You can split 5/3 into five equal portions of 1/3. Therefore, 1/3 cup of honey was used to make the honey glaze. Lastly, that is subtracted from the 1 2/3 to end up with 1 1/3.

8 0
3 years ago
A candy company makes boxes of chocolates. Each box has 32 chocolates total. Of those 32 chocolates 14 of them have nuts. If the
Agata [3.3K]

Answer: 266

Step-by-step explanation: This is a ratio problem. If there are 14 chocolates with nuts out of every 32 chocolates, you can use this as a ratio and set it up as a proportion.

(1) 14 chocolates w/ nuts / 32 chocolates = n chocolates / 608 chocolates

(2) Solve for n: 8,512 = 32n; n = 266

7 0
4 years ago
Which statement about the dilation of these triangles is true?
Gwar [14]

Given:

The figure of two triangles.

To find:

The scale factor.

Solution:

We know that,

\text{Scale factor}=\dfrac{\text{Side of Image}}{\text{Corresponding side of original figure}}

In the given figure,

\text{Scale factor}=\dfrac{5(2)}{5}

\text{Scale factor}=2

The scale factor is 2. Therefore, the correct option is B.

7 0
3 years ago
Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt
Paladinen [302]

Answer:

y(x)=4a\sqrt{3}* sin(x)-3a

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}

But:

\frac{1}{tan(x)} =cot(x)

So:

\frac{dy(x)}{dx} =cot(x)*(3a+y)

Multiplying both sides by dx and dividing both sides by 3a+y:

\frac{dy}{3a+y} =cot(x)dx

Integrating both sides:

\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx

Evaluating the integrals:

log(3a+y)=log(sin(x))+C_1

Where C1 is an arbitrary constant.

Solving for y:

y(x)=-3a+e^{C_1} sin(x)

e^{C_1} =constant

So:

y(x)=C_1*sin(x)-3a

Finally, let's evaluate the initial condition in order to find C1:

y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a

Solving for C1:

C_1=4a\sqrt{3}

Therefore:

y(x)=4a\sqrt{3}* sin(x)-3a

3 0
4 years ago
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