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Klio2033 [76]
3 years ago
14

How many three-digit phone prefixes that are used to represent a particular geographic area are possible that have no 0 or 1 in

the first or second digits?
Mathematics
1 answer:
Sonbull [250]3 years ago
4 0

Answer:

The number of possible three-digit phone prefixes that are used to represent a particular geographic area is 640.

Step-by-step explanation:

The phone prefixes used to represent a particular geographic area are a 3 digit code consisting of numbers from 0 to 9.

The prefix code are of the form: <u>x</u> <u>x</u> <u>x</u>

Condition: The first or the second place cannot take values 0 or 1.

Then the first place can be occupied by the remaining 8 digits.

Similarly the second place can also be occupied by the remaining 8 digits.

And the third place can be occupied by any of the 10 digits.

So the number of ways to construct a phone prefix for any area is:

Possible\ number\ of\ phone\ prefixes=8\times8\times10=640

Thus, the number of phone prefixes possible for any area is 640.

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Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sa
xxMikexx [17]

Answer:

\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221

Now we can calculate the degrees of freedom for the statistic given by:

df=(rows-1)(cols-1)=(3-1)(2-1)=2

And we can calculate the p value given by:

p_v = P(\chi^2_{2} >19.221)=0.000067

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example \alpha=0.05, we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

Size Company/ Heal. Ins.   Yes   No  Total

Small                                      32   18    50

Medium                                 68     7    75

Large                                     89    11    100

_____________________________________

Total                                     189    36   225

We need to conduct a chi square test in order to check the following hypothesis:

H0: independence between heath insurance coverage and size of the company

H1:  NO independence between heath insurance coverage and size of the company

The statistic to check the hypothesis is given by:

\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

The table given represent the observed values, we just need to calculate the expected values with the following formula E_i = \frac{total col * total row}{grand total}

And the calculations are given by:

E_{1} =\frac{50*189}{225}=42

E_{2} =\frac{50*36}{225}=8

E_{3} =\frac{75*189}{225}=63

E_{4} =\frac{75*36}{225}=12

E_{5} =\frac{100*189}{225}=84

E_{6} =\frac{100*36}{225}=16

And the expected values are given by:

Size Company/ Heal. Ins.   Yes   No  Total

Small                                      42    8    50

Medium                                 63     12    75

Large                                     84    16    100

_____________________________________

Total                                     189    36   225

And now we can calculate the statistic:

\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221

Now we can calculate the degrees of freedom for the statistic given by:

df=(rows-1)(cols-1)=(3-1)(2-1)=2

And we can calculate the p value given by:

p_v = P(\chi^2_{2} >19.221)=0.000067

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example \alpha=0.05, we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

3 0
3 years ago
Which of these describes the equation –18x + 9y = –416?
Minchanka [31]

Answer:

We conclude the equation is linear because it can be rewritten in the form y = mx + b.

Hence, option D is correct.

Step-by-step explanation:

The slope-intercept form of the line or linear equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

<u>Important Tip:</u>

The graph of a linear equation is always a straight line.

Convert the given equation in the slope-intercept form

18x + 9y = -416

subtract 18x from both sides

18x+9y-18x = - 18x-416

simplify

9y = -18x - 416

divide both sides by 9

y=-2x-\frac{416}{9}

Now, comparing the equation y=-2x-\frac{416}{9} with a slop-intercept form of linear equation

  • The slope m = -2
  • The y-intercept b = -416/9

Therefore, we conclude the equation is linear because it can be rewritten in the form y = mx + b.

From the attached graph, is also clear that the graph of the equation y=-2x-\frac{416}{9} is a straight line.

Hence, option D is correct.

3 0
2 years ago
Read 2 more answers
Help plz:))) I’ll mark you BRAINLIEST
inessss [21]

Answer:

not idea sorry but 4 no is idea it can be solve the 10 std

6 0
2 years ago
A hummer gets 300 miles on 20 gallons of gas how many on 50 gallons of gas
bija089 [108]

。☆✼★ ━━━━━━━━━━━━━━  ☾  

300/2 = 150

150 x 5 = 750

It would be 750 gallons.  

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

。☆✼★ ━━━━━━━━━━━━━━  ☾

5 0
3 years ago
PLEASE HELP MATH
Novosadov [1.4K]
I believe C is your answer. 
I hope this helps!
7 0
2 years ago
Read 2 more answers
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