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3 years ago

Compare investing $1500 at 9% compounded monthly for 11 years with investing $1500 at 14% compounded monthly for 11 years.

Mathematics

1 answer:

kogti [31]3 years ago

4 0

Answer:

Final amount after 11 years = $4021.97

Step-by-step explanation:

We will use the formula to get the final amount after t years,

Final amount = $a(1+\frac{r}{n})^{nt}$

here a = Initial amount

r = Rate of interest

n = Number of compounding in a year

For Initial amount 'a' = $1500

r = 9%

t = 11 years

n = 12 [Compounded monthly]

F = $1500(1+\frac{9}{12})^{12\times 11}$

= $4021.97

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Wish someone can do this for me.

Makovka662 [10]

Given : Two inequality is given to us . The inequality is v + 8 ≤ -4 and v - 6 ≥ 10 .

To Find : To write those two inequality as a compound inequality with integers .

Solution: First inequality given to us is v + 8 ≤ -4 . So let's simplify it ;

⇒ v + 8 ≤ -4 .

⇒ v ≤ -4 - 8.

⇒ v ≤ -12 .

Now , on simplifying the second inequality ,

⇒ v - 6 ≥ 10 .

⇒ v ≥ 10 + 6.

⇒ v ≥ 16 .

Hence the required answer will be :

$\Large{\boxed{\red{\bf \blue{\dag} v\leqslant -12 \:\:or\:\:v\geqslant 16}}}$

First one implies that v is less than or equal to -12 whereas the second one implies that v is greater than or equal to 16 .

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3 years ago

What is the constant of proportionality for the relationship between the length of the arc intercepted by a 80 degree angle and

Over [174]

So the length of the arc is given by: l = r*theta, here theta is the intercepted angle in unit radian

So, 80 degrees = 80/360 * 2pi = 4/9 * pi

So l = r * (4/9 * pi), the constant ratio is 4/9 * pi

3 0

3 years ago

How do you do number 2? Help please and thank you.

Dmitrij [34]

Answer:

{3,-1}

Step-by-step explanation:

m^2 -2m -3=0

What 2 numbers multiply to -3 and add to negative 2

-3* 1 = -3

-3 +1 =-2

(m-3) (m+1) =0

Using the zero product property

m-3 = 0 m+1 =0

m=3 m=-1

{3,-1}

6 0

4 years ago

370 is 125% of what number?

bonufazy [111]

Answer:

125/100 x N = 370

x 100 x 100

125n = 37,000 (since your multiplying what you got to the variable)

Divide by 125

N = 296

7 0

3 years ago

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

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