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polet [3.4K]
2 years ago
4

Find the total purchase price to the nearest cent if a $65.00 dress is on sale for 20% off, and the sales tax is 7%. (When findi

ng the total purchase price, make sure you calculate the amount of sales tax on the original price.)
Mathematics
2 answers:
Leno4ka [110]2 years ago
5 0
_Award brainliest if helped!
$ 65 Dress Final Price : 
65 + (7% of 65) - (20% Of 65)
= 65 + 0.07*65 - 0.2*65
= $56.55

Lina20 [59]2 years ago
4 0

Answer:

$56.55

Step-by-step explanation:

Given : A $65.00 dress is on sale for 20% off, and the sales tax is 7%.

To Find : Find the total purchase price to the nearest cent

Solution:

Normal Price of dress = $65

Sale is of 20 %

So, price of dress on sale = 65-20\% \times 65

                                           = 52

Sales tax = 7%

So, Final price including sales tax = 52+7\% \times 65

                                                        = 56.55

Hence the total purchase price is $56.55

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Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to
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Answer:

Part 1)

See Below.

Part 2)

\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)

Step-by-step explanation:

Part 1)

The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

\displaystyle L \approx f'(a)(x-a) + f(a)

We want to verify that the expression:

1-36x

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\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36

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Part B)

We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.

In other words:

\displaystyle \left| f(x) - L(x) \right | \leq 0.1

By definition:

\displaystyle -0.1\leq f(x) - L(x) \leq 0.1

Therefore:

\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)

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If a ramp is 17 feet long rises 8 feet above the floor and covers a horizontal distance of 15 feet what is the ratio of _____ to
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