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Zanzabum
3 years ago
10

beth has a total of $6000 to invest, part at 6% simple interest and part at 8% simple interest. Her return for one year is $410.

How much did she invest at each rate?
Mathematics
1 answer:
natita [175]3 years ago
6 0
Since interest=investment*interest rate*time in years for simple interest, we know that there are 2 separate investments. If the amount invested at 6% simple interest is x dollars and the amount invested at 8% is y dollars, then we know that x+y=6000 since she spent all 6000 dollars on only 2 separate investments. Subtracting y from both sides, we get that 6000-y=x. In addition, we know that her interest for the 6% interest rate is x*0.06*1 as well as y*0.08*1 for the 8% simple interest. Since the total interest is 410$, we know that x*0.06*1+y*0.08*1=410. Since y=6000-x, we plug that in to get x*0.06+(6000-x)*0.08=410. Using the distributive property to expand, we get x*0.06+480-0.08x=410=-0.02*x+480. Subtracting 480 from both sides, we get -0.02*x=-70. After that, we can multiply both sides by -50 (since -0.02 times -50 is 1) to get x=3500=amount invested at 6%. Since the amount invested at 8% is 6000-x, that equals 6000-3500=2500
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OverLord2011 [107]

Answer:

Volume = 16 unit^3

Step-by-step explanation:

Given:

- Solid lies between planes x = 0 and x = 4.

- The diagonals rum from curves y = sqrt(x)  to  y = -sqrt(x)

Find:

Determine the Volume bounded.

Solution:

- First we will find the projected area of the solid on the x = 0 plane.

                              A(x) = 0.5*(diagonal)^2

- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,

                              A(x) = 0.5*(sqrt(x) + sqrt(x) )^2

                              A(x) = 0.5*(4x) = 2x

- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:

                              V = integral(A(x)).dx

                              V = integral(2*x).dx

                               V = x^2

- Evaluate limits 0 < x < 4:

                               V= 16 - 0 = 16 unit^3

3 0
3 years ago
At the local farmers market, it costs $10 to rent a stand and $7 for every hour you stay. If you pay a total of $38, how many ho
zhenek [66]
4 hours

Step by step:
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7 0
2 years ago
Read 2 more answers
Write two different rational functions whose graphs have the same end behaviour as the graph of y=3x^2
baherus [9]

Answer:

               y=x^2+5x+20\\ \\ y=8x^2+35

Explanation:

The <em>end behavior</em> of a <em>rational function</em> is the limit of the function as x approaches negative infinity and infinity.

Note that the the values of even functions are the same for ± x. That implies that their limits for ± ∞ are equal.

The limits of the quadratic function of general form y=ax^2+bx+c as x approaches negative infinity or infinity, when a  is positive, are infinity.

That is because as the absolute value of x gets bigger y becomes bigger too.

In mathematical symbols, that is:

\lim_{x \to -\infty}3x^2=\infty\\ \\ \lim_{x \to \infty}3x^2=\infty

Hence, the graphs of any quadratic function with positive coefficient of the quadratic term will have the same end behavior as the graph of y = 3x².

Two examples are:

         y=x^2+5x+20\\ \\ y=8x^2+35

5 0
3 years ago
chole is baking cookies to sell in boxes of 12 cookies.if she bakes 122 cookies,calculate the number she can fill and the number
Alborosie

Answer:

she can fill 10 boxes of 12 cookies and the the left over will be 2 cookies.

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8 0
3 years ago
Please Help, 35 Points.
Andrei [34K]

To answer this question, we have the start-up costs of $ 52,000

A monthly inflation of $ 0 is assumed

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The daily gain  is $960

For the Part A.

The inequality that this situation represents

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So:

d(960-680)>52000

Where d represents the number of days.

For the Part B.

To start earning, you must replace all the initial investment and cover the expenses per day. The time that must pass for this to happen is obtained by clearing "d" from the inequality.


 d>\frac{52000}{960-680}

d> 185.71 days

Then, the sum of the net profits will be greater than the initial investment after 186 days of starting the business.

4 0
2 years ago
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