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3 years ago

Suppose you invest $400 at an annual interest rate of 7.6% compounded continuously. How much will you have in the account after

1.5 years? Round the solution to the nearest dollar.

Mathematics

1 answer:

likoan [24]3 years ago

6 0

$\bf ~~~~~~ \textit{Compounding Continuosly Interest Earned Amount}\\\\
A=Pe^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$400\\
r=rate\to 7.6\%\to \frac{7.6}{100}\to &0.076\\
t=years\to &1.5
\end{cases}
\\\\\\
A=400e^{0.076\cdot 1.5}\implies A=400e^{0.114}$

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Igoryamba

Answer:

1. x= -56.25

Expand

19.5-6.5x+36=201-4.5x-33

Simplify

-6.5x+55.5=201-4.5x-33

Simplify again

6.5x+55.5=-4.5x+168

Add 6.5 to both sides

55.5=-4.5x+168+6.5x

Simplify

55.5=2x+168

Subtract

55.5-168=2x

Simplify

112.5=2x

Divide both sides by 2

−112.5÷2 = x

Simplfy

x = -56.25

2. x > -7 ÷ 4

Decimal Form: -1.75

Remove parentheses

12x>4x+5−19

Simplify

12x>4x-14

Subtract

12x-4x>-14

Simplify

8x>-14

Divide both sides by 8

x > -14 ÷ 8

Simplify

x > -7 ÷ 4

Decimal Form: -1.75

3. Answer: Step 2 has an error

Step-by-step explanation:

Given equation,

2(10 - 13x) = -34x + 60

By distributive property,

20 - 26x = -34x + 60

Now, we need to isolate x on the left side of the equation,

For this we need to eliminate constant term from the left side,

20 will be eliminated by subtracting 20 from both sides ( subtraction property of equality )

I.e. Step 2 has an error,

We need to use subtraction property of equality instead of using addition property of Equality,

Note : The correct steps would be,

Step 2 : 20 - 26x = -34x + 60 ( Subtraction property of equality )

Step 3 : 8x = 40 ( addition property of Equality )

Step 4 : x = 5 ( Division Property of Equality )

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Step-by-step explanation:

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3 years ago

Y=4x-6 and passes through point 8,12

umka2103 [35]

Answer:

Slope of required line if both lines are parallel: y=4x-20

Slope of required line if both lines are perpendicular: y=-1/4x+14

Step-by-step explanation:

We need to find equation of line while we are given another line having equation y=4x-6 and passes through point (8,12)

Note: Since it is not given if the required line is parallel or perpendicular to the given line. I will solve for both cases.

If Both lines are parallel the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are parallel there slopes are same

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=4

Now finding y-intercept

Using slope m=4 and point (8,12) we can find y-intercept

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y-intercept of new line is: b=-20

Equation of required line having slope m=4 and y-intercept b=-20 is

$y=mx+b\\y=4x-20$

If Both lines are perpendicular the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are perpendicular there slopes are opposite of each other

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=-1/4

Now finding y-intercept

Using slope m=-1/4 and point (8,12) we can find y-intercept

$y=mx+b\\12=-\frac{1}{4} (8)+b\\12=-2+b\\b=12+2\\b=14$

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$y=mx+b\\y=-\frac{1}{4} x+14$

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