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liq [111]
2 years ago
11

Kito makes on online purchase of a guitar case for $39.99, a tuner for $24.99 and picks for $26.99. Taxes are 6% of the total pu

rchase price. Shipping charges are based on the following table:
Amount of Purchase
Standard Shipping
Express Shipping
up to $50
$5.10
$7.00
$50 up to $100
$6.35
$8.20
$100 up to $200
$7.80
$11.60
$200 and over
$10.50
$16.45
Kito selects express shipping and the company bills his credit card $105.69 for the total of the online purchase. Determine if Kito has been billed correctly for his purchase.
a.
Kito has been billed correctly.
b.
Kito has not been charged enough for his purchase.
c.
Kito has been over charged by $1.85 for his purchase.
d.
Kito has been over charged by $3.40 for his purchase.
Mathematics
1 answer:
maria [59]2 years ago
4 0

Answer:

a. Kito has been billed correctly

Step-by-step explanation:

We simply need to check Kito's work to see if his price is accurate.

First, we can add the prices together to find the price before the sales tax is applied:  39.99 + 24.99 + 26.99 = $91.97

We can use this formula to figure out the total cost, C, after the sales tax, t is added:

C = l + (l * (t / 100)), where l = the price before applying the sales tax

C = 91.97 + (91.97 * (6 / 100)) = 97.4882 = $97.49

We know that the total cost lies between the 50 and 100 and that Kito chose the express shipping.  Thus we add:  97.49 + 8.20 = $105.69.

If we did not round before, we would still get the same answer when rounding:  97.4882 + 8.20 = 105.6882 = $105.69

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3 years ago
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The profit per acre from a grove of orange trees is given by x(190 − x) dollars, where x is the number of orange trees per acre.
nasty-shy [4]

Answer:

P(x) = 190 x -x^2

In order to maximize the last equation we can derivate the function in term of x and we got:

\frac{dP}{dx} = 190 -2x

And setting this derivate equal to 0 we got:

\frac{dP}{dx} = 190 -2x=0

And solving for x we got:

x = 95

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

P(x=95)= 95(190-95)= 95*95 = 9025

Step-by-step explanation:

For this case we have the following function for the profit:

P(x) = x(190-x)

And we can rewrite this expression like this:

P(x) = 190 x -x^2

In order to maximize the last equation we can derivate the function in term of x and we got:

\frac{dP}{dx} = 190 -2x

And setting this derivate equal to 0 we got:

\frac{dP}{dx} = 190 -2x=0

And solving for x we got:

x = 95

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

P(x=95)= 95(190-95)= 95*95 = 9025

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3 years ago
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9514 1404 393

Answer:

  78.71 mph

Step-by-step explanation:

You're looking for the solution to ...

  d = 88

  0.0015r^2 +r = 88

  0.0015r^2 +r -88 = 0

Using the quadratic formula*, we find ...

  r = (-1 +√(1² -4(0.0015)(-88)))/(2×0.0015)

  r = (-1 +√1.528)/0.003 = 0.236123/0.003 = 78.7077

The speed of the car was about 78.71 mph.

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* The quadratic formula will also give a negative answer of about -745 mph, which is not relevant to the situation.

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