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3 years ago

Show the original equation, then solve for x

Mathematics

1 answer:

Lina20 [59]3 years ago

6 0

Answer: 24.7

cos 54° = x/42

⇔ x = 42. cos 54°

⇔ x ≈ 24.7

Step-by-step explanation:

You might be interested in

Let X ~ N(0, 1) and Y = eX. Y is called a log-normal random variable.

Cloud [144]

If $F_Y(y)$ is the cumulative distribution function for $Y$ , then

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

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 $n$ th 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 $y^n=e^{nu}$ :

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

Complete the square in the exponent:

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

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

But $\frac1{\sqrt{2\pi}}e^{-\frac12(u-n)^2}$ is exactly the PDF of a normal distribution with mean $n$ and variance 1; in other words, the 0th moment of a random variable $U\sim N(n,1)$ :

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

so we end up with

$E[Y^n]=e^{\frac12n^2}$

3 0

3 years ago

Write 7 x 10^-3<br> in standard notation.

VashaNatasha [74]

Answer:

0.007

Step-by-step explanation:

A negative notation starts with 0's from the left.

count 3 places before the 7, that is where my point is.

I am pretty sure of my explanation but the answer is correct.

5 0

3 years ago

Angi has 32 nickels and dimes. Their total value is $1.90. How many of each coin does she have?

Radda [10]

Answer:

6 dimes, 26 nickels

Step-by-step explanation:

The number of nickels is N, and the number of dimes is D.

N + D = 32

5N + 10D = 190

N + 2D = 38

D = 6

N = 26

5 0

3 years ago

HELP pls!!

Rudiy27

<h3>Answer: Choice B) x = 65, y = 10</h3>

====================================================

Work Shown:

The upper pair of angles 60 degrees and (2x-y) degrees are supplementary angles. This is because of the parallel lines. Note how they are same side interior angles. Therefore, (2x-y) and 60 combine to 180 degrees like so

(2x-y)+60 = 180

2x-y = 180-60 ... subtract 60 from both sides

2x-y = 120 ... call this equation 1

-------

Similarly, (2x+y) and 40 also combine to 180

(2x+y) + 40 = 180

2x+y = 180-40 ... subtract 40 from both sides

2x+y = 140 ... call this equation 2

------

Line up equation 1 and equation 2. Then add straight down

$\ \ \ 2x-y = 120\\+ 2x+y = 140\\\hrule\\\\\\ \ \ \ 4x+0y = 260\\\\$

That becomes 4x = 260 which solves to x = 65 when you divide both sides by 4.

------

If x = 65, then,

2x-y = 120

2(65)-y = 120

130 - y = 120

-y = 120-130

-y = -10

y = 10

2x+y = 140

2(65)+y = 140

130+y = 140

y = 140-130

y = 10

----------

Either way end up with x = 65 and y = 10

4 0

3 years ago

Four friends played a game. At the end of the game, their scores were -8, -2, 1, and -3. What is the lowest score?

kiruha [24]

Answer:

the lowest scoreis -3

Step-by-step explanation:

the lowest score is -3

4 0

3 years ago