What percent of 16 is 10

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) Without doing an

stepladder [879]

Answer:

Step-by-step explanation:

Given are 3 data sets with values as:

(i) 8 9 10 11 12 ... Mean =10

(ii) 7 9 10 11 13 ... Mean =10

(iii) 7 8 10 12 13 ... Mean =10

We see that data set shows mean deviations as

(i) -2 -1 0 1 2

(ii) -3 -1 0 1 3

(iii) -3 -2 0 2 3

Since variance is the square of std deviation, we find that std deviation is larger when variance is larger.

Variance is the sum of squares of (x-mean). Whenever x-mean increases variance increases and also std deviation.

Hence we find that without calculations also (i) has least std dev followed by (ii) and then (iii)

(i) (ii) (iii) is the order.

b) Between (i) and (ii) we find that 3 entries are the same and 2 entries differ thus increasing square by 9-4 twice. But between (ii) and (iii) we find that

increase in square value would be 4-1 twice. Obviously the latter is less.

6 0

2 years ago

Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

gladu [14]

Answer:

Vertical asymptote: $x=3$

Horizontal asymptote: $f(x) =2$

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

$f (x) = -\dfrac{1 }{ x-3} +2$

One root, $x = 3.5$

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

$0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5$

One root, $x = 3.5$

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) $\rightarrow \infty$

For all, other values of $x$ , $f(x)$ is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is $\frac{1}{x-3}$ .

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) $\rightarrow \infty$ .

$-\dfrac{1 }{ x-3} +2 \rightarrow \infty$

It is possible only when

$x-3=0\\\Rightarrow x=3$

$\therefore$ vertical asymptote: $x=3$

Horizontal Asymptote is the value of f(x) , where value of x $\rightarrow \infty$ .

$x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2$

$\therefore$ Horizontal asymptote: $f(x) =2$

Please refer to the graph of given function as shown in the attached image.

5 0

2 years ago

Simplify by combining like terms 4s + 1/6s + 2 3/5s

HACTEHA [7]

<h3>The solution by combining like terms is 6.7667</h3>

Solution:

Given expression is:

$4s + \frac{1}{6}s + 2\frac{3}{5}s$

We have to simplify by combining the like terms

From given,

$4s + \frac{1}{6}s + 2\frac{3}{5}s$

Convert the mixed fraction to improper fraction

$4s + \frac{1}{6}s + \frac{13}{5}s$

Make the denominator same

$\frac{4s \times 30 }{30} + \frac{1s \times 5}{6 \times 5} + \frac{13s \times 6}{5 \times 6}\\\\\frac{120s}{30} + \frac{5s}{30} + \frac{78s}{30}\\\\\frac{203}{30} = 6.7667$

Thus the solution is 6.7667

7 0

2 years ago

Jina must choose a number between 49 and 95 that is a multiple of 3, 9. and 12.

emmainna [20.7K]

The answer should be 72 because all the multiples go into that number
72/3=24, 72/9=8, and 72/12= 6
And the number is between 49 and 95
Can u make me brainiest answer after please

4 0

2 years ago

The temperature last Monday was 32˚F at 8:00 am. During the next hour it dropped to 24˚F. What was the percent decrease?

jek_recluse [69]

Answer:

The percentage decrease in the temperature is 25%.

Step-by-step explanation:

The temperature last monday was =32°F

The dropped temperature during the next hour=24°F

The Percentage decrease in the temperature will be= $\frac{32^{{\circ}}-24^{{\circ}}}{32}{\times}100$