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Ivan
3 years ago
12

Let p = log10 x, q = log10 y, and r = log10 z. (The 10s are base numbers.)

Mathematics
1 answer:
KatRina [158]3 years ago
4 0

Answer:

(p / q^2 √r)

Just make x, y, z into p, q, r.

Very simple!

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Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

6 0
3 years ago
Lisa is seven times as old as her brother. She will be four times as old as her brother in three years. Represent the above situ
dlinn [17]

Answer:

3

Step-by-step explanation:

3 0
2 years ago
James estimated the total cost of groceries to be $50. The actual cost of the groceries is $65. What is the percent error? Round
Alex777 [14]

To get percent error you take actual-predicted and divide by the actual then multiply by 100 to get the percent.

65-50=15

15/60=0.25

0.25 times 100 =25%

7 0
3 years ago
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Please help ASAP!! Will mark brainliest!!
Sergio [31]

The answer is 10 because all the angles are equal making it a equilateral triangle.

Therefore, the sides are all equal to one another, 3x - 8 = 5x - 20.

You just solve for x and get 6. You then plug in 6 for x and evauluate the equation, getting 10.

3 0
3 years ago
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Which of the following is an angle shown in the drawing?
DanielleElmas [232]

Answer: All of them besides <AEB

Step-by-step explanation:

Everyone of those can be measured but the <AEB therefore all the answers besides <AEB is correct

5 0
3 years ago
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