MATHEMATICS HIGH SCHOOL

On the basis of data from 1990 to 2006, the median income y in year x for men and women is approximated by the equations given below, where xequals0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, in what year will the median income of men and women be the same?Men: -255x+2y=56,937Women: - 842x+3y=42,751

Answers

Answer 1

Answer:

Answer:

In 2083

Step-by-step explanation:

Given,

The median income y in year x since 1990 for men,

-255x+2y=56,937 .......(1),

For women,

-842x+3y=42,751 ........(2),

From equation (1),

2y = 56937 + 255x

$\implies y = (1)/(2)( 56937 + 255x)$

From equation (2),

842x+3y=42,751,

$3y = 42751 + 842x$

$\implies y =(1)/(3)(42751 + 842x)$

When the median income of men and women are same,

$(1)/(2)( 56937 + 255x)=(1)/(3)(42751 + 842x)$

$3( 56937 + 255x)=2(42751 + 842x)$

$170811 + 765x = 85502 + 1684x$

$765x = 85502 + 1684x-170811$

$765x - 1684x = 85502 -170811$

$-919x = -85309$

$\implies x = (85309)/(919)=92.828\approx 93$

∵ 1990 + 93 = 2083,

Hence, in 2083, the median income of men and women would be the same

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B. 1 12⁄7
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Answers

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will bought 3 college textbooks. one cost $32, one cost $45, and one cost $39. what is the average price of his books? choose the statement that correctly calculates the average. a. ($32 $45 $39) ÷ 3 b. $32 ÷ 3 $45 ÷ 3 $39 c. $32 $45 $39 ÷ 3 d. 3 × $32 $45 $39

Answers

The correct answer is a. ($32 + $45 + $39) ÷ 3

For a scavenger hunt, Chessa put one coin in each of10 small boxes. Four coins are quarters, 4 are dimes, and 2 are nickels.How could you simulate choosing one box at random? Would you use thesame simulation if you planned to put these coins in your pocket andchoose one? Explain your reasoning.

Answers

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now in the pockets different, and depending if the coins are the same.

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What is the value of...?

Answers

Answer:

Step-by-step explanation:

I'm not sure I know exactly what that [1] means.

But here's how you get the answer

g(x) = 3x + 12

The symbolism means that wherever you see an x on the right side of g(x) you put f(x)

So it looks like this

g(f(x) ) = 3(f(x)) + 12 Now you put f(x) = 2x + 7 in for f(x) on the right.

g(f(x)) = 3(2x + 7) + 12 Remove the brackets

g(f(x)) = 6x + 21 + 12

g(f(x)) = 6x + 33

Now you deal with the x on the left. It becomes - 6

g(f(-6)) = 6(-6) + 33

g(f(-6)) = -36 + 33

g(f(-6)) = - 3

Rule 1

(g · f)(x)

has the meaning of whatever the function on the left is (in this case g) then the function of f is put in the xs place.

Which ordered pair is the best estimate for the solution of the system of equations? y=3/2x+6y=1/4x−2

(−7,−3.5)

(−6,−3)

(−7,−4)

(−6.5,−3.5)

Answers

The answer is (-6.5,-3.5)

The sum of two odd numbers is 198. Both of the numbers are multiples of 3. One of the numbers is 5 times the other. Which equation could you use to find the two numbers?

Answers

Answer:

The equation used to find the two numbers is:

x+5x=198

and numbers are:

33 and 165

Step-by-step explanation:

The sum of two odd numbers is 198.

One of the numbers is 5 times the other.

Let one number be x

other number=5x

⇒ x+5x=198

⇒ 6x=198

Dividing both sides by 6,we get

x=33

Other number=5x=5×33=165

The equation used to find the two numbers is:

x+5x=198

and numbers are:

33 and 165

You could use m= the lesser number and n as the greater number. Since one is 5 times the other you will start with m+5m=198. Then you will combine like terms so it will become 6m=198. Then you will solve it as a regular equation. m=33 and n=165.

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