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2 years ago

Paolo paid $ 28 $ 28 for a hat that was originally priced at $ 35 $ 35 . By what percent was the hat discounted?

Mathematics

1 answer:

devlian [24]2 years ago

5 0

The original price of the hat is $35. Paolo paid $28 for the hat.

So discount for the hat is $(35-28) = $7

$7 is discounted from $35. We have to find the percentage of the discount.

To find the percentage we have to divide the discount amount by the original price and then have to multiply it by 100.

So the discount percentage =

((7/35)×100) %

We can simplify 7/35 by dividing 7 and 35 both by 7. So we will get 1/5 after simplifying.

((1/5) ×100) %

(100/5)% = 20%

So the hat was discounted by 20%.

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Maya bought a dozen specialty donuts at the bakery for $18. She purchased a mixture of frosted donuts for $2 each, glazed donuts

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Answer:

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1

Step-by-step explanation:

Let the quantity of frosted donuts = $x$

Let the quantity of glazed donuts = $y$

Let the quantity of custard filled donuts = $z$

As per question statements, following equations can be made:

$x+y+z=12......(1)\\2x+y+5z=18.....(2)\\x=2z ...... (3)$

Putting $x=2x$ in (1) and (2):

$y+3z=12 .... (4)\\y+9z=18 .... (5)$

Subtracting (4) from (5):

$6z=6\\\Rightarrow z =\bold{1}$

By equation (3):

$x=\bold{2}$

By equation (1):

$y=\bold{9}$

Therefore, the answers are:

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1

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2 years ago

An angle t is drawn from the center of the unit circle. Find a formula in terms of t for the straight line distance d between th

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Answer:

$d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}$

Step-by-step explanation:

Let suppose that one of the radii meets the circle at the point (1,0). The straight line distance formula is:

$d = \sqrt{(\cos t - 1)^{2}+(\sin t - 1)^{2}}$

$d = \sqrt{(\cos^{2}t - 2\cdot \cos t + 1)+(\sin^{2}t - 2\cdot \sin t + 1)}$

$d = \sqrt{2-2\cdot (\cos t + \sin t )}$

$d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}$

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Jinni opened a bank account. She deposited $87.60 into her account every month for 10 months. She used $25.60 every month to pay

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2 years ago

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2 years ago

Read 2 more answers

A small business makes cookies and sells them at the farmer's market. The fixed monthly cost for use of a Health Department–appr

DENIUS [597]

Answer:

Cost function:

$C(x)=790+2.88x$

Revenue function

$R(x)=6x$

Profit function

$P(x)=3.12x-790$

Dozens needed for a specific profit P

$x=\dfrac{P-790}{3.12}$

If 150 dozen cookies are sold the profit is negative, so the business is loosing $322.

Step-by-step explanation:

We can list the costs as:

- Fixed monthly cost, $790/month.

- Variable costs, $0.24/cookie, which are (12*0.24) = $2.88 a dozen.

Then, we can write the cost function C(x) as:

$C(x)=790+2.88x$

being C(x): the monthly cost and x: the number of dozens produced per month.

The revenue can be calculated as the price ($6 a dozen) multiplied by the number of dozens x:

$R(x)=6x$

The profit can be calculated substracting the total cost C(x) from the revenue R(x).

$P(x)=R(x)-C(x)\\\\P(x)=(6x)-(790+2.88x)=(6-2.88)x-790\\\\P(x)=3.12x-790$

The number of cookies (in dozens) that must be produced and sold for a monthly profit can be calculated from the previous equation for P(x).

For a monthly profit P, the number of dozens that need to be sold are:

$P=3.12x-790\\\\P+790=3.12x\\\\\\x=\dfrac{P-790}{3.12}$

If 150 dozen cookies are sold, the profit made is:

$P(150)=3.12(150)-790=468-790=-322$

The profit is negative, so the business is loosing $322.

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2 years ago