Solve for Y= 1680 + 0.72

Find the savings plan balance after 2 years with an APR of 4% and monthly payments of $250. The balance is $ (Do not round until

alexdok [17]

Answer:

$6,506.51

Step-by-step explanation:

Recall that increasing an amount C in x% is equivalent to multiply it by (1+x/100)

As we have 4% APR, the monthly interest would be (4/12)% = 0.04/12

Month 0 (first payment)

$250

Month 1

$250 + 250 \frac{0.04}{12}= 250(\frac{12.04}{12})$

Month 2

$250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2)$

Month 3

$250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3)$

Month 24 (2 years)

$250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24})$

The sum

$1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24}$

is the sum of the first 24 terms of a geometric sequence with common ratio $\frac{12.04}{12}$ which is

$\frac{1-(12.04/12)^{25}}{1-(12.04/12)}=26.02603071$

so, after 2 years the saving balance is

250*26.02603071 = 6,506.50767= $6,506.51 rounded to the nearest cent.

6 0

3 years ago

The measures of the angles of a triangle are shown in the figure below. Solve for x.

tino4ka555 [31]

Answer:

The vale of x=4

Step-by-step explanation:

We know that the sum of angles of a triangle = 180°

Given

(3x+13)

(8x+14)

109°

Thus, the equation becomes

(3x+13) + (8x+14) + 109° = 180°

11x + 27 + 109° = 180°

11x = 180°- 109° - 27

11x = 44

x = 4

Thus, the vale of x=4

6 0

3 years ago

How much does the CEO earns?

melomori [17]

p = number of items sold (note: this is not the profit)

1 item sells for $855, so p items sell for 855p dollars

Subtract off the cost of 6780 and we have the expression 855p-6780 which is the profit for that given month.

Now plug in p = 250 because 250 items were sold in that given month

855*p - 6780 = 855*250 - 6780 = 206,970

The company earns $206,970 in profit for that month. Apply 15% to this value

15% of 206,970 = (15/100)*206,970 = 0.15*206,970 = 31,045.50

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Answer: $31,045.50 which is choice C

8 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=2x%5E2%2B5x%2B3%3D0" id="TexFormula1" title="2x^2+5x+3=0" alt="2x^2+5x+3=0" align="absmiddle"

melamori03 [73]

Answer:

$x=-\frac{3}{2},-1$

Step-by-step explanation:

$2x^2+5x+3=0$

Split the second term (5x) into two terms. Multiply the coefficient of the first term (2) by the constant term (3):

$2*3=6$

Find which two numbers add up to 5 and multiply into 6:

$3+2=5\\3*2=6\\3,2$

Split 5x as the sum of 3x and 2x:

$2x^2+3x+2x+3$

Now factor out a common term for the first 2 terms:

$2x^2+3x\\x(2x+3)$

And do the same for the last 2 terms:

$2x+3\\1(2x+3)$

Re-insert:

$x(2x+3)+1(2x+3)=0$

Factor out the common term 2x+3 and insert the values in front of the parentheses (x and 1):

$(2x+3)(x+1)=0$

Separate the parentheses and equal them to 0. Solve for x:

$2x+3=0\\2x+3-3=0-3\\2x=-3\\\\\frac{2x}{2}=\frac{-3}{2}\\\\ x=-\frac{3}{2}$

and

$x+1=0\\x+1-1=0-1\\x=-1$

5 0

3 years ago

Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.

lakkis [162]

$\sf 5x+2y=21$
$\sf -2x+6y=-34$

We could solve for 'x' in the 2nd equation and then plug that into the first equation for 'x' and solve for 'y':

$\sf -2x+6y=-34$

Subtract 6y to both sides:

$\sf -2x=-6y-34$

Divide -2 to both sides:

$\sf x=3y+17$

Plug in 3y + 17 for 'x' in the first equation:

$\sf 5x+2y=21$

$\sf 5(3y+17)+2y=21$

Distribute 5:

$\sf 15y+85+2y=21$

Combine like terms:

$\sf 17y+85=21$

Subtract 85 to both sides:

$\sf 17y=-64$

Divide 17 to both sides:

$\boxed{\sf y\approx -3.8}$

This is the y-coordinate of the solution.

5 0

3 years ago

Read 3 more answers