3. You invested $11,000 in stocks and bonds paying 5% and 8% annual interest. If the total interest for the year was $730, how much was invested in each account? 4. A California company needs to blend a wine that is 6% alcohol, with a French wine which has a 9% content to obtain 200 gallons with a 7% alcohol content. How much of each kind should he use?

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  3. $6000 at 8%; $5000 at 5%

  4. 66 2/3 gallons of 9%; 133 1/3 gallons of 6%

Step-by-step explanation:

For many mixture problems, it works well to let a variable represent the amount of the largest contributor used in the mix.

3. Let x represent the amount invested at 8%. Then the total interest is ...

  8%x +5%(11000-x) = 730

  3%x = 730 -550

  x = 180/0.03 = 6000

$6000 was invested at 8%; $5000 was invested at 5%.

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4. Let x represent the number of gallons of 9% content. Then the alcohol content of the mix is ...

  9%x +6%(200 -x) = 7%(200)

  3%x = 1%(200) . . . . . subtract 6%(200)

  x = 200/3 = 66 2/3 . . . . . divide by 3%

  200 -x = 133 1/3

66 2/3 gallons of 9% wine and 133 1/3 gallons of 6% wine should be used.

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step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).