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just olya [345]

3 years ago

5

Rob goes to work each day by two different routes. As he leaves the apartment parking lot there is a traffic light. If he has a

green light but not a turn arrow, he goes straight and travels for 15-20 minutes, uniformly distributed. If he has a left turn arrow, he turns left, and travels 10-15 minutes, uniformly distributed. If he has a red light, he waits for a left turn arrow. He has timed the traffic light and the light is red for 2 minutes, followed by a left turn arrow for 1 minute, and a green light for 3 minutes. He arrives at the traffic light at uniformly random times each day. What is his expected travel time?

1 answer:

Effectus [21]3 years ago

8 0

Can i send a pic pls help me do it ????

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Which sequence of transformations performed on triangle J could result in similar triangle J'?

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Please help ASAP! Which answer choice is it???

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Solve for x.<br> 10x=2<br> Simplify your answer as much as possible.<br> x = 1

svetoff [14.1K]

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Step-by-step explanation:

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3 years ago

when the polynomial f(x) is divided by (x-2) the remainder is 4, and when it is divided by (x-3) the remainder is 7. Given that

natima [27]

$f(x)=(x-2)(x-3)Q(x)+ax+b$

Recall the polynomial remainder theorem: the remainder upon dividing a polynomial $p(x)$ by $x-c$ is equal to $p(c)$ . This means that $f(2)=4$ and $f(3)=7$ , which tell us

$4=2a+b$

$7=3a+b$

From here we can solve for $a,b$ :

$4=2a+b\implies b=4-2a$

$7=3a+b=3a+(4-2a)\implies a=3\implies b=-2$

so that

$f(x)=(x-2)(x-3)Q(x)+3x-2$

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$\dfrac{f(x)}{(x-2)(x-3)}=Q(x)+\dfrac{3x-2}{(x-2)(x-3)}$

so the remainder upon dividing $f(x)$ by $(x-2)(x-3)$ is $3x-2$ .

Next, if $f$ is a cubic function, then $Q(x)$ is a linear polynomial that can be written as $Q(x)=cx-d$ . The coefficient of $x^3$ in $f(x)$ is 1 (unity), so that expanding $f(x)$ gives us

$f(x)=(x-2)(x-3)(cx-d)+3x-2$

$f(x)=(cx^3-(5c+d)x^2+(6c+5d)x-6d)+3x-2$

$f(x)=cx^3-(5c+d)x^2+(6c+5d+3)x-(6d+2)$

$\implies c=1$

and we also have that $f(1)=1$ , so that

$1=1-(5+d)+(6+5d+3)-(6d+2)$

$\implies2d=2\implies d=1$

so that

$Q(x)=x-1$

4 0

3 years ago

Four couples at a dinner party play a board game after the meal. They decide to play as teams of two and to select the teams ran

Llana [10]

Answer:

0.29

Step-by-step explanation:

We are given that there are 4 couples i.e. 8 people

They decide to play as teams of two and to select the teams randomly

Now we are asked How likely is it that every person will be teamed with someone other than the person he or she came to the party with

For people 1 , there are 6 options for pairing Since he or she cannot pair with his /her own partner

So, Choices For people 1 will be 6 person

So, Probability that person 1 will be teamed with someone other than the person he or she came to the party with = $\frac{\text{No. of choices for Person 1}}{\text{Total no. of choices available}}=\frac{6}{7}$

So, Probability that every person (=8 person) will be teamed with someone other than the person he or she came to the party with = $(\frac{6}{7})^8=0.29$

Hence Probability that every person will be teamed with someone other than the person he or she came to the party with is 0.29

4 0

3 years ago