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bulgar [2K]
3 years ago
15

In a trolley ride around an amusement park, a child traveled from one signpost to a second signpost at a constant speed of 125 m

eters per minute. Was the distance that the child traveled from the first signpost to the second signpost greater than 0.8 kilometer? (1 kilometer = 1,000 meters) (1) It took less than 450 seconds for the child to travel from the first signpost to the second signpost. (2) It took more than 400 seconds for the child to travel from the first signpost to the second signpost.
Mathematics
1 answer:
Inessa05 [86]3 years ago
4 0

Answer:

Given speed of trolley = 125 meters per minute

Speed= 125 meters/minute\\\\Speed =\frac{125}{60}meters/second\\\\Speed=2.083m/s

Now we know that

Distance= Speed x time

Thus for the first case since the time of travel is less than 450 seconds thus the distance traveled is less than

Distance < 2.083 x 450 =937.5 meters

hence depending on the given information we cannot come to any conclusion weather the distance travelled is less than 800 m or greater than 800 m.

For the second case

since the time of travel is greater than 400 seconds

Thus the distance traveled is

Distance>2.083\times 400=833.2meters

which is greater than 800 meters.

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F_Y(y)=P(Y\le y)=P(e^X\le y)=P(X\le\ln y)=F_X(\ln y)

Then the probability density function for Y is f_Y(y)={F_Y}'(y):

f_Y(y)=\dfrac{\mathrm d}{\mathrm dy}F_X(\ln y)=\dfrac1yf_X(\ln y)=\begin{cases}\frac1{y\sqrt{2\pi}}e^{-\frac12(\ln y)^2}&\text{for }y>0\\0&\text{otherwise}\end{cases}

The nth moment of Y is

E[Y^n]=\displaystyle\int_{-\infty}^\infty y^nf_Y(y)\,\mathrm dy=\frac1{\sqrt{2\pi}}\int_0^\infty y^{n-1}e^{-\frac12(\ln y)^2}\,\mathrm dy

Let u=\ln y, so that \mathrm du=\frac{\mathrm dy}y and y^n=e^{nu}:

E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu}e^{-\frac12u^2}\,\mathrm du=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu-\frac12u^2}\,\mathrm du

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nu-\dfrac12u^2=-\dfrac12(u^2-2nu+n^2-n^2)=\dfrac12n^2-\dfrac12(u-n)^2

E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{\frac12(n^2-(u-n)^2)}\,\mathrm du=\frac{e^{\frac12n^2}}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du

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E[U^0]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du=1

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3 0
2 years ago
The value of x for which 3 (x-2) = 2 (x+1)​
netineya [11]

Answer:

x = 8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

3(x - 2) = 2(x + 1)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                     3x - 6 = 2x + 2
  2. Subtract 2x on both sides:          x - 6 = 2
  3. Add 6 to both sides:                    x = 8

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    3(8 - 2) = 2(8 + 1)
  2. Subtract/Add:                      3(6) = 2(9)
  3. Multiply:                               18 = 18

Here we see that 18 does indeed equal 18.

∴ x = 8 is a solution to the equation.

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Answer:

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You are finding the perimeter. Your answer should include yd (yd² is for area, yd³ is for 3d images).

Note that the two lines segments (? & 9) is parallel to the other line segment (16). Find the ?:

? + 9 = 16

? + 9 (-9) = 16 (-9)

? = 16 - 9

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Gennadij [26K]

Answer:

(0,5)

Step-by-step explanation:

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gladu [14]

Answer:

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  5. Division
  6. Addition
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Step-by-step explanation:

<u>Step 1: Define</u>

n² - m

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<u>Step 2: Evaluate</u>

  1. Substitute:                    8² - 7
  2. Exponents:                   64 - 7
  3. Subtract:                       57
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2 years ago
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