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mestny [16]
3 years ago
8

A government agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted

messages. In standard English​ text, a particular letter is used at a rate of 6.8​%.
a. Find the mean and standard deviation for the number of times this letter will be found on a typical page of 3000 characters.
Mathematics
1 answer:
mylen [45]3 years ago
4 0

let n be the number of times letter be found (1800), p be the success rate (0.068), and q be the failure rate (1 - 0.068 = 0.932)  

mean = np = 1800 x 0.068 = 122.4  

standard deviation = √(npq) = √(1800 x 0.068 x 0.932) = 10.6807414

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hammer [34]
Simple interest = Cost Price + (Interest Percentage of Cost Price × number of years or months we are paying off)

a) SI = £20 000 + (5% of £20 000 × 4)
SI = £20 000 + (£1000 × 4)
SI = £20 000 + £4000 = £24 000

b) SI = £20 000 + (5% of £20 000 × 3)
SI = £20 000 + (£1000 × 3)
SI = £20 000 + £3000 = £23 000

£24 000 - £23 000 = £1000 that you saved!
3 0
3 years ago
Maggie needs to spend at least six hours each week practicing the piano. She has already practiced three and one fourth hours th
vfiekz [6]

Answer:

three and one fourth + 2x ≥ 6

Step-by-step explanation:

Let

x -----> the minimum number of hours he needs to practice on each of the two days

we know that

needs to spend at least seven hours each week practicing the drums

so

3\frac{1}{4}+2x\geq 6\ hours

Convert mixed number to an improper fraction

3\frac{1}{4}\ hours=\frac{3*4+1}{4}=\frac{13}{4}\ hours

substitute

\frac{13}{4}+2x\geq 6\ hours

Subtract 13/4 both sides

2x\geq 6-\frac{13}{4}

2x\geq \frac{11}{4}

Divide by 2 both sides

x\geq \frac{11}{8}

therefore

The minimum number of hours he needs to practice on each of the two days is \frac{11}{8}\ hours

5 0
3 years ago
The U.S. Department of Housing and Urban Development publishes data on the fair market monthly rent for existing one-bedroom hou
Aleksandr [31]

Answer:

n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247

So the answer for this case would be n=247 rounded up to the nearest integer

Step-by-step explanation:

We know that the standard deviation is :

\sigma = 80 represent the deviation

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution and the critical value would be z_{\alpha/2}=1.960, replacing into formula (b) we got:

n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247

So the answer for this case would be n=247 rounded up to the nearest integer

8 0
3 years ago
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Olegator [25]

Answer:

12 ÷ –6, –12 ÷ 6, 6 ÷ –3, –6 ÷ 3

Step-by-step explanation:

Ignore the negative signs. If their quotient is 2 and only 1 of the 2 numbers have a negative sign, they make -2.

5 0
3 years ago
Read 2 more answers
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cupoosta [38]

Answer: 11:23

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8 0
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