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3 years ago

12

Colton opened a savings account and deposited $1,000.00 as principal. The account earns 11% interest, compounded annually. What

is the balance after 8 years? Round your answer to the nearest cent.

1 answer:

jeka943 years ago

5 0

Answer:

$2304.5

Step-by-step explanation:

The balance after 8years=P(1+R/100)^t

=1000(1+11/100)^8

=$2304.5

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If a job can be completed in 4 hours, then the rate of work is ____ of the job per hour

Nataly_w [17]

It would be equal to 1/4.

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3 years ago

Can someone step by step explain the answer to me please and thank u

True [87]

First

angle in front of c is 30°, so hypotenuse is equal to 2c

it's right triangle, so let's use Pythagorean theorem\

$(2c)^2=c^2+4^2\\4c^2=c^2+16\\3c^2=16\\\\c^2=\dfrac{16}{3} \\\\c=\dfrac{4}{\sqrt{3} } =\dfrac{4\sqrt{3} }{3 }$

Second

b - the base of the triangle, angles at the base are equal ⇒ cathets are equal

it's right triangle, so let's use Pythagorean theorem

$b^2=7^2+7^2\\b^2=49+49\\b=\sqrt{2\times49} =7\sqrt{2}$

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2 years ago

Scott bought a 50-pound (b) bag of corn He sprinkle 125 Ihs of the common the ground and

gulaghasi [49]

Answer:

C. 37.8 lb

Step-by-step explanation:

3 0

3 years ago

Find the roots of:

Elena-2011 [213]

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

| 2 -7 8 -3

<u>1 | 2 -5 3</u>

| 2 -5 3 0

<u> 1 | 2 -3 </u>

2 -3 0

So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

| 1 -1 0 -4

<u>2 | 2 2 </u>

1 2 2 0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

$\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

| 6 7 9 2

<u>-2 | -12 10 -2</u>

6 -5 1 0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

$\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}$

$\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}$

6 0

2 years ago

Find the area under the curve y = 13/x3 from x = 1 to x = t. Evaluate the area under the curve for t = 10, t = 100, and t = 1000

zvonat [6]

Answer:

t = 10

$A = 32496.75$

t = 100

$A = 324999996.8$

t = 1000

$A=3.25\times 10^{12}$

Step-by-step explanation:

The area under the curve is calculated by using the following definite integral:

$A = \int\limits^t_ {1} \,{13\cdot x^{3}} dx$

$A = 13 \int\limits^t_1 {x^{3}} \, dx$

$A = \frac{13}{4}\cdot (t^{4}-1)$

Evaluated areas are presented below:

t = 10

$A = 32496.75$

t = 100

$A = 324999996.8$

t = 1000

$A=3.25\times 10^{12}$

8 0

3 years ago