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3 years ago

Number 3

Mathematics

1 answer:

sdas [7]3 years ago

3 0

Answer: Choice A) 1990 to 1991

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Explanation:

Let's go through the answer choices one by one.

For choice A, we go from the year 1990 to 1991 which is a change of 1 year. The wage goes from 3.80 to 4.25 over this timespan, which is an increase of 4.25-3.80 = 0.45 dollars. Divide the change in wage (0.45 dollars) over the change in change in time (1 year) to get 0.45/1 = 0.45; this indicates that the wage increased by 0.45 dollars per year over the timespan 1990 to 1991

Now onto choice B. We have a wage increase of 3.80-3.35 = 0.45 over a course of 9 years (since 1990-1981 = 9) so 0.45/9 = 0.05 is the rate of wage growth, meaning that the wage bumps up by a nickel each year. So far choice A is the winner.

Moving onto choice C, we have a wage increase of 0.25 dollars (3.35-3.10 = 0.25) over an 1 year period (1981-1980 = 1) so the rate of change for this slice of time is 0.25/1 = 0.25 dollars per year. Choice A is still the winner.

Finally, for choice D, this is over a year as well (1980-1979 = 1) and the wage increases by 0.20 dollars (3.10-2.90 = 0.20) leading to a rate of change to be 0.20/1 = 0.20

So choice A has the largest rate of change which is the same as saying it has the largest rate of wage increase. This shows why choice A is the answer.

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trapecia [35]

Answer:

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Step-by-step explanation:

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3 years ago

How many solutions are possible for a system of equations containing exactly one linear and one quadratic equation? (Select all

galina1969 [7]

Remember that a quadratic equation is a parabola. The equation is of the type y = Ax^2 + Bx + C

A linear equation is a straight line. The equation is of the type y = MX + N

The soluction of that system is Ax^2 + Bx + C = MX + N

=> Ax^2 + (B-M)x + (C-N) = 0

That is a quadratic equation.

A quadratic equation may have 0, 1 or 2 real solutions. Those are all the possibilitis.

So you must select 0, 1 and 2.

You can also get to that conclusion if you draw a parabola and figure out now many point of it you can intersect with a straight line.

You will realize that depending of the straight line position it can intersect the parabola in none point, or one point or two points.

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3 years ago

Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes. How long does it take for both Wilma and Rocky to

UNO [17]

<h3>Answer: 24 minutes</h3>

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Explanation:

Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.

Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.

Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.

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Another approach

Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is

1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute

x = number of minutes

(combined rate)*(time) = number of jobs done

(1/24)*x = 1

x = 1*24

x = 24 is the time it takes if they worked together without getting in each other's way.

Effectively, we are solving the equation

1/A + 1/B = 1/C

with

A = time it takes Wilma to do the job on her own

B = time it takes Rocky to do the job on his own

C = time it takes the two working together to get the job done

The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.

So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.

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