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3 years ago

8

The price of a train ticket from Orlando to New York is normally $171.00. However, children under the age of 16 receive a 25% di

scount. Find the sale price for someone under the age of 16.

2 answers:

lys-0071 [83]3 years ago

7 0

The sale price I believe would be 128.24

Pachacha [2.7K]3 years ago

3 0

I have no idea but i really tried hard

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If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.

vitfil [10]

Answer:

a = 2

Step-by-step explanation:

given x = - 1 is a zero then f(- 1) = 0 , that is

a(- 1)³ - (- 1)² - 1 + 4 = 0

- a - 1 - 1 + 4 = 0

- a + 2 = 0 ( subtract 2 from both sides )

- a = - 2 ( multiply both sides by - 1 )

a = 2

8 0

2 years ago

Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

$\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

5 0

3 years ago

Find the t-value such that the area in the right tail is 0.005 with 28 degrees of freedom.

klasskru [66]

Answer:

$t = 3.673900$

Step-by-step explanation:

Given

$df = 28$ -- degree of freedom

$Area = 0.005$

Required

Determine the t-value

The given parameters can be illustrated as follows:

$P(T > t) = \alpha$

Where

$\alpha = 0.005$

So, we have:

$P(T>t) = 0.005$

To solve further, we make use of the attached the student's t distribution table.

From the attached table,

The t-value is given at the row with df = 28 and $\alpha = 0.005$ is 3.673900

Hence, $t = 3.673900$

4 0

2 years ago

Christian's bill at a restaurant is $840.If Christian's wants to leave a 17% tip, how much tip should he leave?

Ilya [14]

Hey there!

840 = 100%

x = 17%

840/x = 100%/17%

(840/x) * x = (100/17) * x 840 = <span>5.8823529411765
</span>
<span>= 840/5.8823529411765 = 142.80

The correct answer to your question is option C.

The tip Christian should leave is $142.80.

Hope this helps you.
Have a great day!
</span>

5 0

3 years ago

If it takes 4 people 20<br>hours to decorate 200<br>biscuits, how long would<br>it take 5 people?

DIA [1.3K]

it would take 5 people 16 hours do decorate 200 biscuits

7 0

2 years ago

Read 2 more answers