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2 years ago

7

You have $5,000 to invest for ten years. Crown of The Sun bank pays compound interest at an annual rate of 4.5%. Calculate your

balance after 10 years. Round to the nearest hundreth

2 answers:

Simora [160]2 years ago

5 0

Answer:

$7764.85

Step-by-step explanation:

Assume the compounding is annual.

F = P(1 + r/n)^(nt)

F = 5000(1 + 0.045/1)^10

F = 7764.85

Answer: $7764.85

Dmitry_Shevchenko [17]2 years ago

3 0

Answer: $7,764.85

Step-by-step explanation:

Use the formula for Compound Interest: CI = P(1 + r/n)^nt

CI = 5000(1 + 0.045/1)^10

CI = 5000(1.045)^10

CI ≅ $7,764.85

After 10 years, the balance should be $7,764.85

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A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides, one is burned on only one side, and th

Semmy [17]

Answer:

50%

Step-by-step explanation:

Given that one side of the pancake is burned. The pancake you were served cannot be the one that is not burned on either side. Therefore, you were either served the pancake burned on both sides, or the pancake that was only burned in one side. Thus, there is a 50% percent chance that the other side is also burned.

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3 years ago

What am I doing wrong? I've tried every conceivable answer, I thought I knew this type of math well, but this program keeps tell

Pachacha [2.7K]

Answer:

15.0 units

Step-by-step explanation:

Here, we want to get the distance between the two points as follows;

CD = √(x2-x1)^2 + (y2-y1)^2

So we have;

CD = √(7+8)^2 + (-5+4)^2

CD = √225+ 1 =

CD = √(226

CD = 15.0 units

8 0

3 years ago

The side lengths of a triangle are 9, 12, and 15. Is this a right triangle?

andriy [413]

Answer:

<h2>Yes, this is a right triangle.</h2>

Step-by-step explanation:

Hypotenuse always have the highest number than base and perpendicular.

Hypotenuse ( h ) = 15

Base ( b ) = 9

Perpendicular ( p ) = 12

Let's see whether the given triangle is a right triangle or not

Using Pythagoras theorem:

${h}^{2} = {p}^{2} + {b}^{2}$

Plugging the values,

${15}^{2} = {12}^{2} + {9}^{2}$

Evaluate the power

$225 = 144 + 81$

Calculate the sum

$225 = 225$

Hypotenuse is equal to the sum of perpendicular and base.

So , we can say that the given lengths of the triangle makes a right triangle.

Hope this helps..

Best regards!!

4 0

3 years ago

Read 2 more answers

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

aliya0001 [1]

The Lagrangian

$L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(x^4+y^4+z^4-13)$

has critical points where the first derivatives vanish:

$L_x=2x+4\lambda x^3=2x(1+2\lambda x^2)=0\implies x=0\text{ or }x^2=-\dfrac1{2\lambda}$

$L_y=2y+4\lambda y^3=2y(1+2\lambda y^2)=0\implies y=0\text{ or }y^2=-\dfrac1{2\lambda}$

$L_z=2z+4\lambda z^3=2z(1+2\lambda z^2)=0\implies z=0\text{ or }z^2=-\dfrac1{2\lambda}$

$L_\lambda=x^4+y^4+z^4-13=0$

We can't have $x=y=z=0$ , since that contradicts the last condition.

(0 critical points)

If two of them are zero, then the remaining variable has two possible values of $\pm\sqrt[4]{13}$ . For example, if $y=z=0$ , then $x^4=13\implies x=\pm\sqrt[4]{13}$ .

(6 critical points; 2 for each non-zero variable)

If only one of them is zero, then the squares of the remaining variables are equal and we would find $\lambda=-\frac1{\sqrt{26}}$ (taking the negative root because $x^2,y^2,z^2$ must be non-negative), and we can immediately find the critical points from there. For example, if $z=0$ , then $x^4+y^4=13$ . If both $x,y$ are non-zero, then $x^2=y^2=-\frac1{2\lambda}$ , and

$xL_x+yL_y=2(x^2+y^2)+52\lambda=-\dfrac2\lambda+52\lambda=0\implies\lambda=\pm\dfrac1{\sqrt{26}}$

$\implies x^2=\sqrt{\dfrac{13}2}\implies x=\pm\sqrt[4]{\dfrac{13}2}$

and for either choice of $x$ , we can independently choose from $y=\pm\sqrt[4]{\frac{13}2}$ .

(12 critical points; 3 ways of picking one variable to be zero, and 4 choices of sign for the remaining two variables)

If none of the variables are zero, then $x^2=y^2=z^2=-\frac1{2\lambda}$ . We have

$xL_x+yL_y+zL_z=2(x^2+y^2+z^2)+52\lambda=-\dfrac3\lambda+52\lambda=0\implies\lambda=\pm\dfrac{\sqrt{39}}{26}$

$\implies x^2=\sqrt{\dfrac{13}3}\implies x=\pm\sqrt[4]{\dfrac{13}3}$

and similary $y,z$ have the same solutions whose signs can be picked independently of one another.

(8 critical points)

Now evaluate $f$ at each critical point; you should end up with a maximum value of $\sqrt{39}$ and a minimum value of $\sqrt{13}$ (both occurring at various critical points).

Here's a comprehensive list of all the critical points we found:

$(\sqrt[4]{13},0,0)$

$(-\sqrt[4]{13},0,0)$

$(0,\sqrt[4]{13},0)$

$(0,-\sqrt[4]{13},0)$

$(0,0,\sqrt[4]{13})$

$(0,0,-\sqrt[4]{13})$

$\left(\sqrt[4]{\dfrac{13}2},\sqrt[4]{\dfrac{13}2},0\right)$

$\left(\sqrt[4]{\dfrac{13}2},-\sqrt[4]{\dfrac{13}2},0\right)$

$\left(-\sqrt[4]{\dfrac{13}2},\sqrt[4]{\dfrac{13}2},0\right)$

$\left(-\sqrt[4]{\dfrac{13}2},-\sqrt[4]{\dfrac{13}2},0\right)$

$\left(\sqrt[4]{\dfrac{13}2},0,\sqrt[4]{\dfrac{13}2}\right)$

$\left(\sqrt[4]{\dfrac{13}2},0,-\sqrt[4]{\dfrac{13}2}\right)$

$\left(-\sqrt[4]{\dfrac{13}2},0,\sqrt[4]{\dfrac{13}2}\right)$

$\left(-\sqrt[4]{\dfrac{13}2},0,-\sqrt[4]{\dfrac{13}2}\right)$

$\left(0,\sqrt[4]{\dfrac{13}2},\sqrt[4]{\dfrac{13}2}\right)$

$\left(0,\sqrt[4]{\dfrac{13}2},-\sqrt[4]{\dfrac{13}2}\right)$

$\left(0,-\sqrt[4]{\dfrac{13}2},\sqrt[4]{\dfrac{13}2}\right)$

$\left(0,-\sqrt[4]{\dfrac{13}2},-\sqrt[4]{\dfrac{13}2}\right)$

$\left(\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3}\right)$

$\left(\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3}\right)$

$\left(\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3}\right)$

$\left(-\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3}\right)$

$\left(\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3}\right)$

$\left(-\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3}\right)$

$\left(-\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3},\sqrt[4]{\dfrac{13}3}\right)$

$\left(-\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3},-\sqrt[4]{\dfrac{13}3}\right)$

5 0

3 years ago

Solve linear equations <br><br> Solve for x <br><br> -2(4x + 3) = 3(x + 1)

inna [77]

Answer:

x = - $\frac{9}{11}$

Step-by-step explanation:

Given

- 2(4x + 3) = 3(x + 1) ← distribute parenthesis on both sides

- 8x - 6 = 3x + 3 ( subtract 3x from both sides )

- 11x - 6 = 3 ( add 6 to both sides )

- 11x = 9 ( divide both sides by - 11 )

x = - $\frac{9}{11}$

7 0

3 years ago

Read 2 more answers