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ikadub [295]
3 years ago
15

A classic counting problem is to determine the number of different ways that the letters of millennium can be arranged. Find tha

t number. The number of different ways that the letters of millennium can be arranged is
Mathematics
1 answer:
Eddi Din [679]3 years ago
7 0

Answer:

<u>The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of letters of the word "millennium" = 10

Letters repeated:

m = 2 times

i = 2 times

l = 2 times

n = 2 times

2. The number of different ways that the letters of millennium can be arranged is:

We will use the n! or factorial formula, this way:

10!/2! * 2! * 2! * 2!

(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) * (2 * 1) * (2 * 1) * (2 *1)

3'628,800/2*2*2*2 = 3'628,800/16 = 226,800

<u>The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800</u>

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If Joseph buys a T.V. At 35% off and it’s original costs $599.99 how much did he pay for the tv?
Monica [59]

Answer: He paid \$389.9935 for the T.V.

Step-by-step explanation:

We need to analize the information provided:

- The original cost of the T.V. was $599.99

- Joseph buys it at 35% off the original cost.

Let be "x" the amount Joseph paid for the T.V.

We can calculate "x" with the following expression:

x=\$599.99-(\$599.99)(0.35)\\\\x=\$389.9935

Therefore, he paid \$389.9935 for the T.V.

7 0
3 years ago
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.

5 0
3 years ago
The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).
pashok25 [27]
<span>Slope of JK=((-1)-2)/(4-(-3)=-3/7 Slope of KL=((-5)-(-1)/(2-4=2 Slope of LM=((-2)-(-5))/(-5-2)=-3/7 Slope of MJ=(2-(-2))/((-3)-(-5))= 2 JK is parallel to LM and KL is parallel to MJ. Therefore JKLM is a parallelogram.</span>
5 0
3 years ago
You received a 27 out of 30 on your test. What is your percent correct?
Oksana_A [137]

Answer:

90%

Step-by-step explanation:

divide - 27/30

6 0
3 years ago
Read 2 more answers
The population of deer in a state park in 1985 was 46,000. The population in 1990 was 72,000. What is the rate of change of the
Vesnalui [34]

Answer:

5200 deer/year

Step-by-step explanation:

  • rateofchange=changeinpopulation \div changeinyears
  • we will call the rate of change, the slope of the function
  • slope=(72000-46000)deer\div (1990-1985)years\\=26000deer\div 5years\\=(\frac{26000}{5}) deer/year\\==5200deer/year
3 0
3 years ago
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