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mr Goodwill [35]

2 years ago

6

A lorry is travelling at 13.5 m/s along a stretch of road where the speed limit is 50 km/h. 1 kilometre = 1000metres 1 hour = 36

00 seconds show that the lorry is travelling below the speed limit.

1 answer:

BabaBlast [244]2 years ago

4 0

3600x13.5÷1000=48.6km/h

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The caller times at a customer service center has an exponential distribution with an average of 22 seconds. Find the probabilit

jenyasd209 [6]

Answer:

The probability that a randomly selected call time will be less than 30 seconds is 0.7443.

Step-by-step explanation:

We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.

Let X = caller times at a customer service center

The probability distribution (pdf) of the exponential distribution is given by;

$f(x) = \lambda e^{-\lambda x} ; x > 0$

Here, $\lambda$ = exponential parameter

Now, the mean of the exponential distribution is given by;

Mean = $\frac{1}{\lambda}$

So, $22=\frac{1}{\lambda}$ ⇒ $\lambda=\frac{1}{22}$

SO, X ~ Exp( $\lambda=\frac{1}{22}$ )

To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;

$P(X\leq x) = 1 - e^{-\lambda x}$ ; x > 0

Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)

P(X < 30) = $1 - e^{-\frac{1}{22} \times 30}$

= 1 - 0.2557

= 0.7443

7 0

2 years ago

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested i

lidiya [134]

Answer:

Step-by-step explanation:

We are given that 30% of California residents have adequate earthquake supplies.

a) Ramon variable X denotes the number of the california residents that have adequate earthquake insurance

B) x can take value 1 ,2 ,3 ......

C)The distribution of random variable is geometric distribution with parameter p=0.3

The pmf of geometric distribution is

$P(X=x)=0.3(1-0.3)^{x-1} , x=1,2,3...$

D)P(X=1) or P(X=2)=P(X=1)+P(X=2)

P(X=1) or P(X=2)= $0.3(1-0.3)^{1-1}+0.3(1-0.3)^{2-1}=0.51$

E)

$P(X \geq 3)=1-P(X$

F)

$E(X)=\frac{1}{p}$

p is the resident who does not have adequate earthquake supplies.

p = 1-0.3 = 0.7

$E(X)=\frac{1}{0.7}=1.42$

G) $E(X)=\frac{1}{q}=\frac{1}{0.3}=3.33$

8 0

2 years ago

It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long doe

lina2011 [118]

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u $\frac{km}{hr}$

Speed of current = v $\frac{km}{hr}$

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

$32 = \frac{100}{u +v}$

$u + v = \frac{100}{32}$

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

$48 = \frac{100}{u -v}$

$u -v = \frac{100}{48}$

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045 $\frac{km}{hr}$

v = 0.5205 $\frac{km}{hr}$

Now the time taken by the un powered raft to cover this distance

$T = \frac{100}{v}$

Because un powered raft travel with the speed of the current.

$T = \frac{100}{0.5205}$

T = 192.12 hr

Therefore the time taken by the un powered raft to cover this distance is

T = 192.12 hr

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Which expression is equivalent to 6x2 – 19x – 55?

seraphim [82]

Answer, (6x + 11) (x - 5)

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On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4).

Evgesh-ka [11]

Answer:

y ≤ One-thirdx – 4

Step-by-step explanation:

The key hint to know this answer is to understand that the line cuts the y-axis at -4. And, we can know that y is less than or equal to (≤) 1/3x-4 for the shaded area to the RIGHT of the line, telling us that y exists for all values from -4 and under.

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