Ask question

Ask question

All categories

valentinak56 [21]

3 years ago

13

A stoplight has the following cycle: green for 40 seconds, yellow for 3 seconds , and red for 75 seconds. What is the probabilit

y that the light will be yellow when you arrive to the nearest hundredth?

1 answer:

frutty [35]3 years ago

8 0

Answer:

3/118=0.02 rounded to the nearest hundredth.

Step-by-step explanation:

In total, all the lights flash fro 118 seconds.

Because the yellow light takes up 3 of those 118 seconds, the probability that you come to a yellow light is 3/118 = 0.02542372881 round to the nearest hundredth

= 0.02

P.S. Could you mark this as brainliest it it is okay plz?

You might be interested in

Lana cuts 2 pieces for every 5 inches from a dowel for a craft project, for a total of 6 pieces.

Nesterboy [21]

She would end up with:
1) A total of 15 inches of dowel (or 1' 3" - A foot and 3 inches)
2) Pieces that are 2 1/2" (inches) long.

5 0

4 years ago

Whats is the distance between the ferris wheel and the merry-go-round? Ferris wheel on the coordinate plane is (-9,6) and the lo

Bezzdna [24]

Answer:

19 units

Step-by-step explanation:

use distance formula: d = $\sqrt{(x_2-x_1)^{2}+(y_2+y_1)^{2}}$

x₂ = 10

x₁ = -1

y₂ = 6

y₁ = 6

now plug in

$\sqrt{(10-(-9))^{2}+(6-6)^{2}}\\= \sqrt{19^{2}+0^{2}\\}\\= \sqrt{361}\\= 19$

8 0

3 years ago

Evaluate the following integral (Calculus 2) Please show step by step explanation!

Nuetrik [128]

Answer:

$4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}$

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x$

Rewrite 9 as 3²:

$\implies \displaystyle \int \dfrac{4}{x\sqrt{3^2+(\ln(x))^2}}\:\:\text{d}x$

<u>Integration by substitution</u>

$\boxed{\textsf{For }\sqrt{a^2+x^2} \textsf{ use the substitution }x=a \tan\theta}$

$\textsf{Let } \ln x=3 \tan \theta$

$\begin{aligned}\implies \sqrt{3^2+(\ln x)^2} & =\sqrt{3^2+(3 \tan\theta)^2}\\ & = \sqrt{9+9\tan^2 \theta}\\ & = \sqrt{9(1+\tan^2 \theta)}\\ & = \sqrt{9\sec^2 \theta}\\ & = 3 \sec\theta\end{aligned}$

Find the derivative of ln x and rewrite it so that dx is on its own:

$\implies \ln x=3 \tan \theta$

$\implies \dfrac{1}{x}\dfrac{\text{d}x}{\text{d}\theta}=3 \sec^2\theta$

$\implies \text{d}x=3x \sec^2\theta\:\:\text{d}\theta$

<u>Substitute</u> everything into the original integral:

$\begin{aligned} \implies \displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x & = \int \dfrac{4}{3x \sec \theta} \cdot 3x \sec^2\theta\:\:\text{d}\theta\\\\ & = \int 4 \sec \theta \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle 4 \int \sec \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{7 cm}\underline{Integrating $\sec kx$}\\\\$\displaystyle \int \sec kx\:\text{d}x=\dfrac{1}{k} \ln \left| \sec kx + \tan kx \right|\:\:(+\text{C})$\end{minipage}}$

$\implies 4\ln \left| \sec \theta + \tan \theta \right|+\text{C}$

$\textsf{Substitute back in } \tan\theta=\dfrac{1}{3}\ln x :$

$\implies 4\ln \left| \sec \theta + \dfrac{1}{3}\ln x \right|+\text{C}$

$\textsf{Substitute back in } \sec\theta=\dfrac{1}{3}\sqrt{9+(\ln x)^2}:$

$\implies 4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}$

Learn more about integration by trigonometric substitution here:

brainly.com/question/28157322

brainly.com/question/28156093

8 0

2 years ago

When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10

LiRa [457]

Answer:

Step-by-step explanation:

Alright, lets get started.

The given equation is :

$-2(x+3)=-10$

If we divide the equation with -2 in both sides

$\frac{-2(x+3)}{-2}=\frac{-10}{-2}$

$(x+3)=5$

$x+3=5$

Subtract 3 in both sides

$x+3-3=5-3$

$x=2$

So, the first step of simplifying equation is divide equation with -2. : Answer

Hope it will help :)

3 0

3 years ago

Read 2 more answers

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr^2. Find the instantaneous rate of change of the surface area

8090 [49]

Instantaneous rate of change = S'(r) = 8πr
S'(8) = 8π(8) = 64π

Therefore, the instantaneoud rate of change of the <span>surface area with respect to the radius r at r = 8</span> is 64π

7 0

3 years ago