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3 years ago

Shirley Smith's total insurance premium is $1,050. His employer pays 50% of the total premium. How much does Shirley pay?

Mathematics

1 answer:

allsm [11]3 years ago

8 0

Answer:

$525

Step-by-step explanation:

Shirley pays the other 50%, so pays ...

0.50 · $1050 = $525

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A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

Nat2105 [25]

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

$\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}$

We know, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

According to the question,

$\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}$

Taking LCM and 6 common

$6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}$

Take 6 to another side,

$\frac{9}{9x-x^2}=\frac{8}{3\times 6}$

Cross multiply,

$9\times 18=8\times(9x-x^2)$

$162=72x-8x^2$

Taking 4 common and cancel out

$4x^2-36x+81=0$

Solve quadratic equation by middle term split,

$4x^2-18x-18x+81=0$

$2x(2x-9)-9(2x-9)=0$

$(2x-9)(2x-9)=0$

$\Rightarrow 2x-9=0$

$\Rightarrow x=\frac{9}{2}=4.5$

Therefore, The speed of the river's current is 4.5 km/hr.

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Answer:

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The length of a rectangle is 3 inches longer than half of its width. The area of the rectangle is 416 square inches. How many in

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Answer:

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Step-by-step explanation:

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