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3 years ago

Dwain is out shopping and finds a $110.00 scooter that is

Mathematics

1 answer:

Vsevolod [243]3 years ago

8 0

Answer:

$55

Step-by-step explanation:

1) since we are taking 50% of the price of lets find 50% of 110

so 0.50*110=55

50% of 110 is 55 hence we can subtract 55 from 110(since its getting marked down)

110-55=55

$55 is the new price

Hope this helps!

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Y=x.arctan(x)^1/2. find dy/dx. pls show steps

Whitepunk [10]

$y=x(\arctan x)^{1/2}$

Use the product rule first:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dx}{\mathrm dx}(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

Use the chain rule to compute the derivative of $(\arctan x)^{1/2}$ . Let $z=(\arctan x)^{1/2}$ and take $u=\arctan x$ , so that by the chain rule

$\dfrac{\mathrm dz}{\mathrm dx}=\dfrac{\mathrm dz}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm dz}{\mathrm du}=\dfrac{\mathrm du^{1/2}}{\mathrm du}=\dfrac12u^{-1/2}$

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\mathrm d\arctan x}{\mathrm dx}=\dfrac1{1+x^2}$

$\implies\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}(1+x^2)}$

So we have

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+\dfrac x{2(\arctan x)^{1/2}(1+x^2)}$

You can rewrite this a bit by factoring $(\arctan x)^{-1/2}$ , just to make it look neater:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}}\left(2\arctan x+\dfrac x{1+x^2}\right)$

3 0

3 years ago

A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the

Lubov Fominskaja [6]

Answer:

The required sample size for the new study is 801.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

25% of all adults had used the Internet for such a purpose

This means that $\pi = 0.25$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What is the required sample size for the new study?

This is n for which M = 0.03. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.25*0.75)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2$

$n = 800.3$

Rounding up:

The required sample size for the new study is 801.

4 0

3 years ago

Ron wants to build a ramp with a length of 14 ft and an angle of 26 degrees. The height of the ramp is about

Olin [163]

y = 6.14 ft

The height of the ramp is about 6.14 ft.

3 0

3 years ago

Read 2 more answers

ANSWER ASAP PLEASE! WILL GIVE BRAINLIEST, RATING, AND THANKS!

vladimir2022 [97]

she is incorrect the numbers listed above is neither arithmetic or geometric its quadratic sequence . its addition being shown

2+1=3

3+2=5

5+3=8

8+4=12

hope i broke it down enough for you're understanding

8 0

4 years ago

Read 2 more answers

Which expression is equivalent to -3x(x-4)-2x(x+3)?

Ymorist [56]

Answer:

x(x^2 + 6)

Step-by-step explanation:

We are to simplify -3x(x-4)-2x(x+3). Begin by performing the indicated multiplication. We get -3x^2 + 12x - 2x^2 - 6x.

Combining like terms, we get -5x^2 + 6x, which is equivalent to

x(x^2 + 6)

4 0

3 years ago

Read 2 more answers