Write the equation of the line in fully simplified slope-intercept form

What is the value of x? Enter your answer, as a decimal, in the box. cm

kirza4 [7]

Answer:

50.6 cm

Step-by-step explanation:

We can use similar triangles and proportions to solve. Put the smaller triangle side over the larger triangle side.

x 46.2-14 (This is the length of the short side of the triangle)

--------- = -------------

72.6 46.2

Using cross products

46.2 *x = (46.2-14) *72.6

46.2 *x = (32.2) *72.6

46.2x =2337.72

Divide each side by 46.2

46.2/46.2 *x = 2337.72/46.2

x = 50.6

5 0

2 years ago

Suppose customers in a certain queue are served one at a time sequentially, that the time for each individual customer is Expone

alexandr402 [8]

Answer:

The shape and rate parameters are $\frac{1}{12}$ and $3$ .

Step-by-step explanation:

Let X = service time for each individual.

The average service time is, β = 12 minutes.

The random variable follows an Exponential distribution with parameter, $\lambda=\frac{1}{\beta}=\frac{1}{12}$ .

The service time for the next 3 customers is,

Z = X₁ + X₂ + X₃

All the X $_{i}$ 's are independent Exponential random variable.

The sum of independent Exponential random variables is known as a Gamma or Erlang random variable.

The random variable Z follows a Gamma distribution with parameters (α, n).

The parameters are:

$\alpha =\lambda=\frac{1}{12}\\n=3$

Thus, the shape and rate parameters are $\frac{1}{12}$ and $3$ .

5 0

2 years ago

Calculator

Sedaia [141]

Check the picture below.

so let's find the lengths of those two sides in red, since are the length and width of the rectangle.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[-3-(-6)]^2+[6-3]^2}\implies d=\sqrt{(-3+6)^2+(6-3)^2} \\\\\\ d=\sqrt{9+9}\implies \boxed{d=\sqrt{18}} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})~\hfill d=\sqrt{[-2-(-6)]^2+[-1-3]^2} \\\\\\ d=\sqrt{(-2+6)^2+(-1-3)^2}\implies d=\sqrt{16+16}\implies \boxed{d=\sqrt{32}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{(\sqrt{18})(\sqrt{32})}\implies \sqrt{18\cdot 32}\implies \sqrt{576}\implies 24$