6 times the forth root of 405

9. An article was sold at a profit of 12%. Had it been sold for Nu 80 more, there would be a profit of

Kamila [148]

Answer:

The cost price of the article was Nu 1,000

The original selling price was Nu 1,120

The second selling price was Nu 1,200

Step-by-step explanation:

System of Equations

Let's call:

x = Original selling price of the article

y = Cost of the article

The first condition implies that the difference between the selling price and the cost price (the profit) is 12%. Recall the profit % is always calculated with respect to the cost, that is, the profit at the first condition is:

0.12y = Original profit

Setting up the equation, we have:

$x-y=0.12y$

The second condition states the selling price is 80 Nu more than before, that is:

x+80= Second selling price of the article

y = Cost of the article (it doesn't change)

The profit of this condition is 20%, thus:

0.2y = Second profit

This produces a second equation:

$x+80-y=0.2y$

Let's put both equations together to form a system of equations:

$x-y=0.12y$

$x+80-y=0.2y$

Operating on both equations:

$x=1.12y$

$x=1.2y-80$

Equating both equations, we have an equation with only y's:

$1.12y=1.2y-80$

Subtracting 1.2y on each side:

$1.12y-1.2y=-80$

Operating:

$-0.08y=-80$

Solving:

$\displaystyle y=\frac{-80}{-0.08}=1,000$

a)

The cost price of the article was Nu 1,000

b) The selling price of the article will be calculated in both cases:

Original selling price: x=1.12y= 1.12*1000=1,120

The original selling price was Nu 1,120

The second selling price was x+80=1,200

The second selling price was Nu 1,200

8 0

4 years ago

The diameter of a circle has endpoints whosever coordinates are R(-2,2) and S(4,2). find the center of the circle

lisov135 [29]

Hello!

As you can see this line is horizontal. It is 6 units long. Therefore the center is three units in. Therefore the center of this circle is at (1,2).

I hope this helps!

3 0

3 years ago

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

attashe74 [19]

Answer:

$0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286$

$0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562$

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

$X= 36$ represent the families owned at least one DVD player

$n= 85$ represent the total number of families

$\hat p=\frac{36}{85}= 0.424$ represent the estimated proportion of families owned at least one DVD player

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.05$ . And the critical value would be given by: