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3 years ago

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There are six wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attac

hed in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested. (Hint: There are six choices for the first wire, five for the second wire, four for the third wire, etc.)

1 answer:

lesya692 [45]3 years ago

5 0

Answer:

$S=720$

Step-by-step explanation:

From the question we are told that

Six wire are attached to a circuit board

Generally using multiplication rule

Let number of possible sequence be given as S

Mathematically

$S=6! =6*5*4*3*2*1=720$

Therefore

Number of possible sequence $S=720$

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Suppose that each time Giannis Antetokounmpo shoots a free throw, he has a 3/4 probability of success. If Giannis shoots three f

GREYUIT [131]

Answer:

84.38% probability that he succeeds on at least two of them

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either Giannis makes it, or he does not. The free throws are independent. So we use the binomial probability distribution 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.

He has a 3/4 probability of success.

This means that $p = \frac{3}{4} = 0.75$

Giannis shoots three free throws

This means that $n = 3$

What is the probability that he succeeds on at least two of them

$P(X \geq 2) = P(X = 2) + P(X = 3)$

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

$P(X = 2) = C_{3,2}.(0.75)^{2}.(0.25)^{1} = 0.4219$

$P(X = 3) = C_{3,3}.(0.75)^{3}.(0.25)^{0} = 0.4219$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4219 + 0.4219 = 0.8438$

84.38% probability that he succeeds on at least two of them

6 0

3 years ago

Without using a calculator, what is 30% of 546? (You can round up to avoid decimal points)

madreJ [45]

Answer:

Hey there!

We can solve this by multiplying 0.3 by 546, which is about 164.

Hope this helps :)

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3 years ago

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The product of 5 and a number x is 1/4. what is the value of x?

solniwko [45]

The mathematical expression is
5x = 1/4
Divide:
x = (1/4)/5 = (1/4)*5 = 5/4 (ANSWER)

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3 years ago

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What is the solution to the inequality?

nika2105 [10]

7x + 18 > -3

Subtract 18 from both sides,
7x > -21

Divide from 7,
x > -3

In short, Your Answer would be Option D

Hope this helps!

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3 years ago

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Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

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3 years ago