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9 months ago

An item $4 before tax and 4.32 after sales tax what is the sales tax rate

Mathematics

1 answer:

Rzqust [24]9 months ago

4 0

Answer:

8 %

Step-by-step explanation:

To find the tax rate, we first have to find the tax

4.32 - 4 = .32

The tax rate is found by the tax / total

.32 /4 =.08

To change this to a percent multiply by 100

.08 * 100% = 8 %

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Anne runs 6 laps on a track. She runs a total of 1 mile or 5,280 feet. Write and solve an equation to find the distance, in feet

attashe74 [19]

You could use the equation: 5,280/6= 880

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3 years ago

Find the Laplace transform

Tom [10]

In mathematics, the Laplace transform is an integral transform named after its inventor Pierre-Simon Laplace. It transforms a function of a real variable t to a function of a complex variable s.

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2 years ago

How many nonzero terms of the Maclaurin series for ln(1 x) do you need to use to estimate ln(1.4) to within 0.001?

Vilka [71]

Answer:

The estimate of In(1.4) is the first five non-zero terms.

Step-by-step explanation:

From the given information:

We are to find the estimate of In(1 . 4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)

So, by the application of Maclurin Series which can be expressed as:

$f(x) = f(0) + \dfrac{xf'(0)}{1!}+ \dfrac{x^2 f"(0)}{2!}+ \dfrac{x^3f'(0)}{3!}+... \ \ \ \ \ --- (1)$

Let examine f(x) = In(1+x), then find its derivatives;

f(x) = In(1+x)

$f'(x) = \dfrac{1}{1+x}$

f'(0) $= \dfrac{1}{1+0}=1$

f ' ' (x) $= \dfrac{1}{(1+x)^2}$

f ' ' (x) $= \dfrac{1}{(1+0)^2}=-1$

f ' ' '(x) $= \dfrac{2}{(1+x)^3}$

f ' ' '(x) $= \dfrac{2}{(1+0)^3} = 2$

f ' ' ' '(x) $= \dfrac{6}{(1+x)^4}$

f ' ' ' '(x) $= \dfrac{6}{(1+0)^4}=-6$

f ' ' ' ' ' (x) $= \dfrac{24}{(1+x)^5} = 24$

f ' ' ' ' ' (x) $= \dfrac{24}{(1+0)^5} = 24$

Now, the next process is to substitute the above values back into equation (1)

$f(x) = f(0) + \dfrac{xf'(0)}{1!}+ \dfrac{x^2f' \ '(0)}{2!}+\dfrac{x^3f \ '\ '\ '(0)}{3!}+\dfrac{x^4f '\ '\ ' \ ' \(0)}{4!}+\dfrac{x^5f' \ ' \ ' \ ' \ '0)}{5!}+ ...$

$In(1+x) = o + \dfrac{x(1)}{1!}+ \dfrac{x^2(-1)}{2!}+ \dfrac{x^3(2)}{3!}+ \dfrac{x^4(-6)}{4!}+ \dfrac{x^5(24)}{5!}+ ...$

$In (1+x) = x - \dfrac{x^2}{2}+\dfrac{x^3}{3}-\dfrac{x^4}{4}+\dfrac{x^5}{5}- \dfrac{x^6}{6}+...$

To estimate the value of In(1.4), let's replace x with 0.4

$In (1+x) = x - \dfrac{x^2}{2}+\dfrac{x^3}{3}-\dfrac{x^4}{4}+\dfrac{x^5}{5}- \dfrac{x^6}{6}+...$

$In (1+0.4) = 0.4 - \dfrac{0.4^2}{2}+\dfrac{0.4^3}{3}-\dfrac{0.4^4}{4}+\dfrac{0.4^5}{5}- \dfrac{0.4^6}{6}+...$

Therefore, from the above calculations, we will realize that the value of $\dfrac{0.4^5}{5}= 0.002048$ as well as $\dfrac{0.4^6}{6}= 0.00068267$ which are less than 0.001

Hence, the estimate of In(1.4) to the term is $\dfrac{0.4^5}{5}$ is said to be enough to justify our claim.

∴

The estimate of In(1.4) is the first five non-zero terms.

8 0

2 years ago

X + 20 is greater than 4x -1

Paul [167]

Answer:

False; they are equal.

Step-by-step explanation:

The equation is x + 20 > 4x - 1.

First, do the opposite of -1 and add one to the other side while -1+1 cancels out. Now it's x+21 > 4x. Now subtract x from both sides. Positive x minus negative x cancels out and 4x minus x or 1x is 3x. Now you're left with 21> 3x. Now do the inverse operation of multiplication and divide both sides by 3. Now the 3x over 3 cancels out and 21 divided by 3 is 7. So x is 7. If you substitute it in. It will be 7+20 which is 27 which is great than 4(7)-1 which is 28-1. 28-1 is 27. So, the equation is false. They are equal.

7 0

2 years ago

11 + 5 + 22 × 12 − 10

Masteriza [31]

Follow PEMDAS

22 x 12 = 264

11 + 5 = 16

264 + 16 = 280

280 - 10 = 270

270 is your answer

hope this helps

6 0

3 years ago

Read 2 more answers