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Genrish500 [490]

3 years ago

8

Kareem is participating in a 5-day cross-country biking challenge. He biked for 67, 62, 59, and 47 miles on the first four days.

How many miles does he need to bike on the last day so that his average (mean) is 60 miles per day? miles

1 answer:

BabaBlast [244]3 years ago

6 0

Answer:65miles

Step-by-step explanation:

Let the needed miles be x

(67+62+59+47+x)/5=60

235+x=60×5

235+x=300

x=300-235

x=65miles

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A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight ident

Fudgin [204]

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that $p = 0.9$

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when $n = 4$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486$

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that $n = 8$

It will operate if at least 4 components are working correctly, so we want:

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0$

$P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex][tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0$

$P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004$

Then

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996$

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

5 0

3 years ago

Use slopes to determine if the lines y=−4 and x=−1 are perpendicular.

Juli2301 [7.4K]

Answer:

they are perpindicular because they intersect at a right angle

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

-3x=x-(6-2x) explain how asap, please!!

OLEGan [10]

Answer: x=1
-3x=x-6+2x
-6x=-6
x=1

7 0

2 years ago

emmainna [20.7K]

Yes so he shows this by also doing what is called the flow. After this it is complete

8 0

3 years ago

Find difference 7 7/8-3 1/4

umka2103 [35]

So first convert to improper fractions
7 and 7/8=7+7/8=56/8+7/8=63/8

3 and 1/4=3+1/4=12/4+1/4=13/4

so nowe we have
63/8+13/4
convert bottom number to same
which is 8
13/4 times 2/2=26/8
now we have
63/8-26/8=37/8=4 and 5/8
answer is 4 and 5/8

8 0

3 years ago