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dsp73
3 years ago
8

Three numbers are in an arithmetic progression with a common difference of 6. if 4 is subtracted from the first number, 1 is sub

tracted from the second number, and the third number is first decreased by 3 and then multiplied by 3, then the resulting three numbers form a geometric progression. find the original three numbers.
Mathematics
1 answer:
UkoKoshka [18]3 years ago
8 0

Answer:

  either of {-9.5, -3.5, 2.5} or {7, 13, 19}

Step-by-step explanation:

Let x represent the first number of the arithmetic sequence. Then the second number is x+6, and the third number is x+12. The geometric sequence is then ...

  (x -4), (x +5), 3(x+9)

The common ratio is then ...

  (x +5)/(x -4) = 3(x +9)/(x +5)

Cross-multiplying gives ...

  (x +5)² = 3(x -4)(x +9)

  x² +10x +25 = 3x² +15x -108 . . . . eliminate parentheses

  0 = 2x² +5x -133 . . . . . . . . . . . . . . subtract the left side

  0 = (2x +19)(x -7) . . . . . . . . . . . . . . factor

  x = -9.5 . . or . . 7

The possible original three numbers are ...

  {-9.5, -3.5, 2.5} . .  or . . {7, 13, 19}

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Among 500 freshmen pursuing a business degree at a university, 311 are enrolled in an economics course, 243 are enrolled in a ma
Allushta [10]

Solution :

Let A = Economics, B = Mathematics

n(A) = 311, n(B) = 243, $n(A \cap B) = 135$

a). So, $n(A \cup B) = n(A) +n(B) - n(A \cap B)$

                     = 311 + 243 - 135

                     = 419

b). n(A only) = 311 - 135

                   = 176

     n(B only) = 243 - 135

                   = 108

Exactly one of these two courses

  $=\frac{176+108}{500}$

  = 0.568

c). Neither economics nor mathematics

    $=\frac{500-419}{500} $

  $=\frac{81}{500}$

 = 0.162

7 0
3 years ago
What is a decimal in standard form: <br>12 and six hundredths <br><br>forty-six ten-thousandths
aev [14]
The decimal in standard form for 12 and six hundredths is 12.06
4 0
3 years ago
What is the answer to 3/4 +1/3
Elis [28]
Well, to add fractions, you need to find a common denominator. In this case, the smallest common denominator would be 12. So you must multiply each fraction so that both denominators are 12.
3/4*3/3=9/12
1/3*4/4=4/12
Add those two fractions together, reduce if possible, and you have your answer!
9/12+4/12=13/12
You can't reduce, so 13/12 is your answer.
Hope it helps!
-Lacy
3 0
4 years ago
Find the number that makes the ratio equivalent to 1:4.
amid [387]
8:2 hope this helps
7 0
3 years ago
Read 2 more answers
This is not Math its SCIENCE if you can answer all u get to be brailiest
ss7ja [257]

Answer:

1a) A chemical compound is a chemical substance composed of many identical molecules composed of atoms from more than one element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound.

1b)An ionic compound formed by acid-base reactions and without those ions is called a salt. Water is definitely one of the most important inorganic compounds to all living things. It is a compound comprised of two hydrogen atoms and one oxygen atom.

The four major classes of biological macromolecules are carbohydrates, lipids, proteins, and nucleic acids.

2a)Regulates body temperature. Moistens tissues in the eyes, nose and mouth. Protects body organs and tissues. Carries nutrients and oxygen to cells.

2b)If a cell is seriously deprived of water,

this lack of water would most likely affect

the cell's enzymes because:

• The cytoplasm and plasma

membrane would not function

properly

Both the plant and animal cell needs

water in order to perform their basic

functions which include transport of

materials, waste distribution, production

of genetic information, and many more.

As a result of this, we can see that there

would be a serious problem if any

of these cells are deprived of water

which would lead to the cytoplasm and

plasma membrane to partially shut

down because they would not be able to

engage in protein synthesis and other

important functions.

3a)Carbohydrates provides energy rich for organic compounds made of elements carbon, hydrogen and oxygen. The lipids contain the element nitrogen. The carbohydrates contain the only elements carbon, hydrogen, and oxygen.

3b)Organic nitrogen occurs in many forms, including amino acids, proteins, nucleic acids, nucleotides, and urea.

3c)A carbohydrate has only Carbon, Hydrogen and Oxygen, with the hydrogen and oxygen in the ratio 2:1. A protein is made of amino acids. ... So without nitrogen atoms the compound can not be a protein.

3 0
3 years ago
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