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3 years ago

Twice the sum of a number and 7 is equal to three times the difference of the number and 8.

1 answer:

4 0

First, set up what you know. Twice the sum of a number and seven means: 2x+7. Three times the difference of the number and 8 is 3(x-8).

Set both of them equal to each other and you'll get this:
2x+7 = 3(x-8)
Afterwards just follow through with algebra.
2x+7 = 3x - 24

2x + 31 = 3x

31 = 3x - 2x

31 = x

Afterwards check your work to see if it is correct.
2(31) + 7 = 3( 31 - 8 )

62 + 7 = 3(23)

69 = 69

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Various problems with data collection can cause some observations to be missing. Suppose a data set has 20 cases. Here are the v

mr Goodwill [35]

Answer:

a) Mean= 15, standard deviation= 5.1575

b) Mean= 15, standard deviation= 3.6469

c) See below

Step-by-step explanation:

(a) Compute the mean and standard deviation for the 10 cases for which x is not missing.

The mean using the ten known values is

$\bar x=\frac{17+6+12+14+20+23+9+12+16+21}{10}=15$

The standard deviation is

$\small s=\sqrt{\frac{(17-15)^2+(6-15)^2+(12-15)^2+(14-15)^2+(20-15)^2+(23-15)^2+(9-15)^2+(12-15)^2+(16-15)^2+(21-15)^2}{10}}=5.1575$

(b) Create a new data set with 20 cases by using imputation where you set the values for the 10 missing cases equal to the mean that you computed in the previous part. Compute the mean and standard deviation for this new data set with 20 cases.

The new data set would be

17, 6, 12, 14, 20, 23, 9, 12, 16, 21, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15

The new mean for this set of values would be then

$\bar x=\frac{\displaystyle\sum_{i=1}^{20}x_i}{20}=15$

The new standard deviation is now

$s=\sqrt{\frac{\displaystyle\sum_{i=1}^{20}(x_i-\bar x)^2}{20}}=3.6469$

(c) Summarize what you have learned about the possible effects of this type of imputation on the mean and the standard deviation.

Obviously, this way of imputation is somewhat arbitrary and will produce a set of data undoubtedly skewed.

It could possibly be a sensible way of imputing data if the amount of missing data is very little compared to the whole set, for example one or two data in a set of 100, but in this case we have 50% of missing data and it makes no sense this procedure.

4 0

3 years ago

Which expression is equivalent to 4 (2p+4q)?

ch4aika [34]

Answer:

None of the above.........

6 0

3 years ago

Jayne is driving 440 miles and wants to make the trip in 8 hours. write an equation and solve to determine the average speed jay

Nuetrik [128]

Distance÷time
440÷8= 55
Therefore he needs to drive at the speed of 55 miles/hour

7 0

3 years ago

What is 3627×673:(876)?

Delicious77 [7]

3627 x 673:(876)= 2138290596 I got that by taking 3627x876(876) and got that

7 0

3 years ago

Read 2 more answers

PLEASE HELP ME AS SOON AS POSSIBLE

tatyana61 [14]

a) The linear function that models the population in t years after 2004 is: P(t) = -200t + 29600.

b) Using the function, the estimate for the population in 2020 is of 26,400.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The initial population in 2004, of 29600, is the y-intercept. In 12 years, the population decayed 2400, hence the slope is:

m = -2400/12 = -200.

Hence the equation is:

P(t) = -200t + 29600.

2020 is 16 years after 2004, hence the estimate is:

P(16) = -200(16) + 29600 = 26,400.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

3 0

2 years ago